Daily Papers

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

We study Einstein-Maxwell-dilaton gravity models in four-dimensional anti-de Sitter (AdS) spacetime which admit the Reissner-Nordstrom (RN) black hole solution. We show that below a critical temperature the AdS-RN solution becomes unstable against scalar perturbations and the gravitational system undergoes a phase transition. We show using numerical calculations that the new phase is a charged dilatonic black hole. Using the AdS/CFT correspondence we discuss the phase transition in the dual field theory both for non-vanishing temperatures and in the extremal limit. The extremal solution has a Lifshitz scaling symmetry. We discuss the optical conductivity in the new dual phase and find interesting behavior at low frequencies where it shows a "Drude peak". The resistivity varies with temperature in a non-monotonic way and displays a minimum at low temperatures which is reminiscent of the celebrated Kondo effect.

Symbolic logical reasoning is a critical yet underexplored capability of large language models (LLMs), providing reliable and verifiable decision-making in high-stakes domains such as mathematical reasoning and legal judgment. In this study, we present a systematic analysis of logical reasoning under controlled increases in logical complexity, and reveal a previously unrecognized phenomenon, which we term Logical Phase Transitions: rather than degrading smoothly, logical reasoning performance remains stable within a regime but collapses abruptly beyond a critical logical depth, mirroring physical phase transitions such as water freezing beyond a critical temperature threshold. Building on this insight, we propose Neuro-Symbolic Curriculum Tuning, a principled framework that adaptively aligns natural language with logical symbols to establish a shared representation, and reshapes training dynamics around phase-transition boundaries to progressively strengthen reasoning at increasing logical depths. Experiments on five benchmarks show that our approach effectively mitigates logical reasoning collapse at high complexity, yielding average accuracy gains of +1.26 in naive prompting and +3.95 in CoT, while improving generalization to unseen logical compositions. Code and data are available at https://github.com/AI4SS/Logical-Phase-Transitions.

The use of machine learning algorithms to investigate phase transitions in physical systems is a valuable way to better understand the characteristics of these systems. Neural networks have been used to extract information of phases and phase transitions directly from many-body configurations. However, one limitation of neural networks is that they require the definition of the model architecture and parameters previous to their application, and such determination is itself a difficult problem. In this paper, we investigate for the first time the relationship between the accuracy of neural networks for information of phases and the network configuration (that comprises the architecture and hyperparameters). We formulate the phase analysis as a regression task, address the question of generating data that reflects the different states of the physical system, and evaluate the performance of neural architecture search for this task. After obtaining the optimized architectures, we further implement smart data processing and analytics by means of neuron coverage metrics, assessing the capability of these metrics to estimate phase transitions. Our results identify the neuron coverage metric as promising for detecting phase transitions in physical systems.

Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows exponentially as the argument expands. When a mathematician encounters a proof, how does she come to believe it? Here we show that, under a cognitively-plausible belief formation mechanism combining deductive and abductive reasoning, belief in mathematical arguments can undergo what we call an epistemic phase transition: a dramatic and rapidly-propagating jump from uncertainty to near-complete confidence at reasonable levels of claim-to-claim error rates. To show this, we analyze an unusual dataset of forty-eight machine-aided proofs from the formalized reasoning system Coq, including major theorems ranging from ancient to 21st Century mathematics, along with five hand-constructed cases including Euclid, Apollonius, Hernstein's Topics in Algebra, and Andrew Wiles's proof of Fermat's Last Theorem. Our results bear both on recent work in the history and philosophy of mathematics on how we understand proofs, and on a question, basic to cognitive science, of how we justify complex beliefs.

We discuss two solvable grokking (generalisation beyond overfitting) models in a rule learning scenario. We show that grokking is a phase transition and find exact analytic expressions for the critical exponents, grokking probability, and grokking time distribution. Further, we introduce a tensor-network map that connects the proposed grokking setup with the standard (perceptron) statistical learning theory and show that grokking is a consequence of the locality of the teacher model. As an example, we analyse the cellular automata learning task, numerically determine the critical exponent and the grokking time distributions and compare them with the prediction of the proposed grokking model. Finally, we numerically analyse the connection between structure formation and grokking.

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

We study the emergence of multi-step reasoning in deep Transformer language models through a geometric and statistical-physics lens. Treating the hidden-state trajectory as a flow on an implicit Riemannian manifold, we analyze the layerwise covariance spectrum of activations, where C^{(ell)}=E[h^{(ell)}h^{(ell)top}], and track deviations from a random-matrix bulk. Across model scales (1.5B--30B), we observe a sharp reduction in effective dimensionality consistent with a phase transition: an order parameter based on sparsity/localization, Ω(h)=1-|h|_1/(d|h|_2), exhibits a discontinuity near a critical normalized depth γ_capprox 0.42 in sufficiently large models. We formalize the forward pass as a discrete coarse-graining map and relate the appearance of stable "concept basins" to fixed points of this renormalization-like dynamics. The resulting low-entropy regime is characterized by a spectral tail collapse and by the formation of transient, reusable object-like structures in representation space, which we call Transient Class Objects (TCOs). We provide theoretical conditions connecting logical separability to spectral decay and validate the predicted signatures with layerwise probes on multiple open-weight model families.

Foundation models are often used as fixed black-box predictors for downstream tasks with limited labeled data, but their predictions may be biased and unsafe to trust blindly. We study this setting through black-box assisted nonparametric regression: a learner observes labeled samples and can query a fixed predictor f_0, while the target f^* is close to f_0 in L_2(P_X) up to an unknown radius δ. We give a finite-sample minimax characterization showing a phase transition at δ_c(n) asymp n^{-β/(2β+d)}, with leading risk min{δ^2, n^{-2β/(2β+d)}}. We then analyze a Safe Residual Estimator: it learns a correction around f_0, initializes the residual head at zero so the initial predictor equals f_0, and uses holdout selection to revert to f_0 when the learned correction is not supported by validation data. Here, "safe" means avoiding negative transfer, i.e., performing worse than the black-box predictor alone. The estimator matches the leading minimax term up to an additive validation-selection cost. Synthetic regression experiments verify the predicted phase transition, while CIFAR-100 with CLIP and AG News with Qwen3-8B provide practice-facing evidence that the same residual-correction tradeoff is useful beyond the formal squared-loss regression setting.

Large Language Models (LLMs) are typically trained on data mixtures: most data come from web scrapes, while a small portion is curated from high-quality sources with dense domain-specific knowledge. In this paper, we show that when training LLMs on such data mixtures, knowledge acquisition from knowledge-dense datasets, unlike training exclusively on knowledge-dense data (arXiv:2404.05405), does not always follow a smooth scaling law but can exhibit phase transitions with respect to the mixing ratio and model size. Through controlled experiments on a synthetic biography dataset mixed with web-scraped data, we demonstrate that: (1) as we increase the model size to a critical value, the model suddenly transitions from memorizing very few to most of the biographies; (2) below a critical mixing ratio, the model memorizes almost nothing even with extensive training, but beyond this threshold, it rapidly memorizes more biographies. We attribute these phase transitions to a capacity allocation phenomenon: a model with bounded capacity must act like a knapsack problem solver to minimize the overall test loss, and the optimal allocation across datasets can change discontinuously as the model size or mixing ratio varies. We formalize this intuition in an information-theoretic framework and reveal that these phase transitions are predictable, with the critical mixing ratio following a power-law relationship with the model size. Our findings highlight a concrete case where a good mixing recipe for large models may not be optimal for small models, and vice versa.

Cosmological first-order phase transitions can generate curvature perturbations through inhomogeneous quantum tunneling, as studied previously on superhorizon scales. In this work, we for the first time conduct three-dimensional lattice simulations that incorporate scalar metric perturbations and radiation perturbations, covering a range from bubble wall scales to super-horizon scales. We obtain the precise scalar perturbation power spectrum and the probability density function of energy density perturbations. Furthermore, we simulate the gravitational-wave energy spectra generated by each source during the first-order phase transition, including the scalar field itself, scalar metric perturbations, and the energy density and velocity perturbations of radiation. For gravitational waves, the contribution from other sources can exceed 1/3 of that from the scalar field at superhorizon scales. Additionally, we compare the effects of different values of the transition strength and rate on the results. This paper provides more accurate numerical results for research aimed at detecting or constraining first-order phase transitions via gravitational waves and curvature perturbations.

We study flat space cosmologies in two dimensions by taking the flat space limit of the Achucarro-Ortiz model. We unravel a phase transition between hot flat space and flat space cosmologies, and derive a new dilaton-dependent counterterm required for the consistency of the Euclidean partition function. Our results generalize to asymptotically mass-dominated 2-dimensional dilaton gravity models, whose thermodynamical properties we discuss. The novel case of asymptotic mass-domination is neither covered by the comprehensive discussion of hep-th/0703230 nor by the more recent generalization to dilaton gravity with confining U(1) charges in 1406.7007.

Neural quantum states (NQS) have emerged as a powerful tool for approximating quantum wavefunctions using deep learning. While these models achieve remarkable accuracy, understanding how they encode physical information remains an open challenge. In this work, we introduce adiabatic fine-tuning, a scheme that trains NQS across a phase diagram, leading to strongly correlated weight representations across different models. This correlation in weight space enables the detection of phase transitions in quantum systems by analyzing the trained network weights alone. We validate our approach on the transverse field Ising model and the J1-J2 Heisenberg model, demonstrating that phase transitions manifest as distinct structures in weight space. Our results establish a connection between physical phase transitions and the geometry of neural network parameters, opening new directions for the interpretability of machine learning models in physics.

Deep Neural Networks are highly susceptible to shortcut learning, frequently memorizing low-dimensional spurious correlations instead of underlying causal mechanisms. This phenomenon not only degrades out-of-distribution robustness but also induces severe demographic biases in sensitive applications. In this paper, we propose a geometric a priori methodology to mitigate shortcut learning. By deploying a zero-hidden-layer (N=1) Topological Auditor, we mathematically isolate features that monopolize the gradient without human intervention. We empirically demonstrate a Capacity Phase Transition: once linear shortcuts are pruned, networks are forced to utilize higher geometric capacity (N geq 16) to curve the decision boundary and learn ethical representations. Our approach outperforms L1 Regularization -- which collapses into demographic bias -- and operates at a fraction of the computational cost of post-hoc methods like Just Train Twice (JTT), successfully reducing counterfactual gender vulnerability from 21.18\% to 7.66\%.

We discover that large language models exhibit spectral phase transitions in their hidden activation spaces when engaging in reasoning versus factual recall. Through systematic spectral analysis across 11 models spanning 5 architecture families (Qwen, Pythia, Phi, Llama, DeepSeek-R1), we identify seven core phenomena: (1)~Reasoning Spectral Compression -- 9/11 models show significantly lower α for reasoning (p < 0.05), with larger effects in stronger models; (2)~Instruction Tuning Spectral Reversal -- base models show reasoning α< factual α, while instruction-tuned models reverse this relationship; (3)~Architecture-Dependent Generation Taxonomy -- prompt-to-response shifts partition into expansion, compression, and equilibrium regimes; (4)~Spectral Scaling Law -- α_reasoning propto -0.074 ln N across 4 Qwen base models (R^2 = 0.46); (5)~Token-Level Spectral Cascade -- per-token alpha tracking reveals local synchronization that decays exponentially with layer distance, and is weaker for reasoning than factual tasks; (6)~Reasoning Step Spectral Punctuation -- phase-transition signatures align with reasoning step boundaries; and (7)~Spectral Correctness Prediction -- spectral α alone achieves AUC = 1.000 (Qwen2.5-7B, late layers) and mean AUC = 0.893 across 6 models in predicting correctness before the final answer is generated. Together, these findings establish a comprehensive spectral theory of reasoning in transformers, revealing that the geometry of thought is universal in direction, architecture-specific in dynamics, and predictive of outcome.

We show how to construct perturbative effective field theories for strong phase transitions, where the standard tools of high-temperature dimensional reduction fail. By identifying the relevant power counting relations for the couplings, masses and background fields, we construct a controlled perturbative expansion adapted to this regime. We find that the order parameter field remains light at the transition, so that there is a controlled derivative expansion, even though large external fields need to be resummed. The resulting effective field theories for strong phase transitions live in three dimensions and have nonpolynomial field dependence. Applying our framework to a two-scalar model, we verify renormalisation scale cancellation through next-to-next-to-leading order and find decreasing corrections to the latent heat as the perturbative order is increased. Extending to include fermions and gauge fields, we identify a broad class of models in which strong-transition thermodynamics are systematically improvable.

We investigate the connection between the entanglement entropy in scattering processes and the dynamics of electroweak phase transitions. Recent work has shown that the scattering entanglement entropy can provide new insight into Standard Model parameters. In this study, we propose that the maximum of the entanglement entropy in scattering amplitudes may serve as a diagnostic for first-order electroweak phase transitions in the early universe. We analyze a simplified extension of the Standard Model consisting of the Higgs boson h coupled to O(N) real singlet scalars S via the Higgs portal coupling λ_{hS}. By explicitly calculating the maximum entanglement entropy, we demonstrate that it grows with increasing λ_{hS}, and that both first-order and strong first-order electroweak phase transitions are favored in regions of parameter space with large maximum entropy. Our results suggest that entanglement-based observables may encode meaningful information about the underlying dynamics of electroweak symmetry breaking and provide a novel perspective on phase transition phenomena.

The system-size scaling of bipartite entanglement can be used to detect phase transitions. We develop a related approach for strongly correlated electron models where large density matrices or large system size scaling are inaccessible. To this end, we demonstrate that phase transitions of various kinds are signaled by a sharp signature in the first- or second-order logarithmic derivatives of the negativity measuring entanglement between small clusters at varying distances. Crucially, we show how to mitigate the effect of quantum Monte Carlo noise at large distances when computing the negativity. Our focus is on the t'-π-flux Hubbard model using auxiliary-field quantum Monte Carlo simulations. It has the particular advantage of showing three distinct phase transitions in a single model: semimetal to band insulator, semimetal to antiferromagnetic Mott insulator, and a magnetic order-disorder transition belonging to the Gaussian, Gross-Neveu, and O(3) Wilson-Fisher universality classes, respectively.

Most interpretability research in NLP focuses on understanding the behavior and features of a fully trained model. However, certain insights into model behavior may only be accessible by observing the trajectory of the training process. We present a case study of syntax acquisition in masked language models (MLMs) that demonstrates how analyzing the evolution of interpretable artifacts throughout training deepens our understanding of emergent behavior. In particular, we study Syntactic Attention Structure (SAS), a naturally emerging property of MLMs wherein specific Transformer heads tend to focus on specific syntactic relations. We identify a brief window in pretraining when models abruptly acquire SAS, concurrent with a steep drop in loss. This breakthrough precipitates the subsequent acquisition of linguistic capabilities. We then examine the causal role of SAS by manipulating SAS during training, and demonstrate that SAS is necessary for the development of grammatical capabilities. We further find that SAS competes with other beneficial traits during training, and that briefly suppressing SAS improves model quality. These findings offer an interpretation of a real-world example of both simplicity bias and breakthrough training dynamics.

We study the formation of primordial black holes (PBHs) and stochastic gravitational waves background (SGWB) produced by the supercooled radion phase transition (PT) in warped extra-dimension models solving the gauge hierarchy problem. We first determine how the SGWB and the produced PBH mass and abundance depend on the warped model's infrared energy scale rho, and the number of holographic colors N. With this finding, we recast on the plane {rho, N} the current SGWB and PBH constraints, as well as the expected parameter reaches of GW detectors, as LISA and ET, and the gravitational lensing ones, such as NGRST. On the same plane, we also map the collider bounds on massive graviton production, and cosmological bounds on the radion phenomenology. We find that, for N sim 10-50, the considered PT predicts a PBH population mass in the range M_{rm PBH}sim(10^{-1} - 10^{-25}) M_{odot} for rho sim (10^{-4} - 10^{8}) TeV. In the range rho simeq (0.05 - 0.5) GeV, it can explain the recent SGWB hint at nHz frequencies and generate PBH binaries with mass M_{rm PBH}sim(0.1 - 1 ) M_odot detectable at LISA and ET. The experimentally allowed mass region where PBHs can account for the whole dark matter abundance, and are produced with a tuning lesssim 10^{-4}, corresponds to 10 TeV lesssim rholesssim 10^4 TeV. These PBHs can compensate the lack of natural candidates for dark matter in warped extra dimensional models. Such a region represents a great science case where forthcoming and future colliders like HE-LHC and FCC-hh, gravitational-wave observatories and other PBHs probes play a key complementary role.

We investigate BZT shocks and the QCD phase transition in the dense core of a cold quark star in beta equilibrium subject to the multicomponent van der Waals (MvdW) equation of state (EoS) as a model of internal structure. When this system is expressed in terms of multiple components, it can be used to explore the impact of a phase transition from a hadronic state to a quark plasma state with a complex clustering structure. The clustering can take the form of colored diquarks or triquarks and bound colorless meson, baryon, or hyperon states at the phase transition boundary. The resulting multicomponent EoS system is nonconvex, which can give rise to Bethe-Zel'dovich-Thompson (BZT) phase changing shock waves. Using the BZT shock wave condition we find constraints on the quark density and examine how this changes the tidal deformability of the compact core. These results are then combined with the TOV equations to find the resulting mass and radius relationship. These state are compared to recent astrophysical high-mass neutron star systems, which may provide evidence for a core that has undergone a quark gluon phase transition such as PSR 0943+10 or GW 190814.

Coupling together distinct correlated and topologically non-trivial electronic phases of matter can potentially induce novel electronic orders and phase transitions among them. Transition metal dichalcogenide compounds serve as a bedrock for exploration of such hybrid systems. They host a variety of exotic electronic phases and their Van der Waals nature enables to admix them, either by exfoliation and stacking or by stoichiometric growth, and thereby induce novel correlated complexes. Here we investigate the compound 4Hb-TaS_2 that interleaves the Mott-insulating state of 1T-TaS_2 and the putative spin liquid it hosts together with the metallic state of 2H-TaS_2 and the low temperature superconducting phase it harbors. We reveal a thermodynamic phase diagram that hosts a first order quantum phase transition between a correlated Kondo cluster state and a flat band state in which the Kondo cluster becomes depleted. We demonstrate that this intrinsic transition can be induced by an electric field and temperature as well as by manipulation of the interlayer coupling with the probe tip, hence allowing to reversibly toggle between the Kondo cluster and the flat band states. The phase transition is manifested by a discontinuous change of the complete electronic spectrum accompanied by hysteresis and low frequency noise. We find that the shape of the transition line in the phase diagram is determined by the local compressibility and the entropy of the two electronic states. Our findings set such heterogeneous structures as an exciting platform for systematic investigation and manipulation of Mott-metal transitions and strongly correlated phases and quantum phase transitions therein.

Intelligent robots need to interact with diverse objects across various environments. The appearance and state of objects frequently undergo complex transformations depending on the object properties, e.g., phase transitions. However, in the vision community, segmenting dynamic objects with phase transitions is overlooked. In light of this, we introduce the concept of phase in segmentation, which categorizes real-world objects based on their visual characteristics and potential morphological and appearance changes. Then, we present a new benchmark, Multi-Phase, Multi-Transition, and Multi-Scenery Video Object Segmentation (M^3-VOS), to verify the ability of models to understand object phases, which consists of 479 high-resolution videos spanning over 10 distinct everyday scenarios. It provides dense instance mask annotations that capture both object phases and their transitions. We evaluate state-of-the-art methods on M^3-VOS, yielding several key insights. Notably, current appearance-based approaches show significant room for improvement when handling objects with phase transitions. The inherent changes in disorder suggest that the predictive performance of the forward entropy-increasing process can be improved through a reverse entropy-reducing process. These findings lead us to propose ReVOS, a new plug-andplay model that improves its performance by reversal refinement. Our data and code will be publicly available at https://zixuan-chen.github.io/M-cube-VOS.github.io/.

Robotic-assisted minimally invasive esophagectomy (RAMIE) is a recognized treatment for esophageal cancer, offering better patient outcomes compared to open surgery and traditional minimally invasive surgery. RAMIE is highly complex, spanning multiple anatomical areas and involving repetitive phases and non-sequential phase transitions. Our goal is to leverage deep learning for surgical phase recognition in RAMIE to provide intraoperative support to surgeons. To achieve this, we have developed a new surgical phase recognition dataset comprising 27 videos. Using this dataset, we conducted a comparative analysis of state-of-the-art surgical phase recognition models. To more effectively capture the temporal dynamics of this complex procedure, we developed a novel deep learning model featuring an encoder-decoder structure with causal hierarchical attention, which demonstrates superior performance compared to existing models.

Endoscopic Submucosal Dissection (ESD) is a minimally invasive procedure initially developed for early gastric cancer treatment and has expanded to address diverse gastrointestinal lesions. While computer-assisted surgery (CAS) systems enhance ESD precision and safety, their efficacy hinges on accurate real-time surgical phase recognition, a task complicated by ESD's inherent complexity, including heterogeneous lesion characteristics and dynamic tissue interactions. Existing video-based phase recognition algorithms, constrained by inefficient temporal context modeling, exhibit limited performance in capturing fine-grained phase transitions and long-range dependencies. To overcome these limitations, we propose SPRMamba, a novel framework integrating a Mamba-based architecture with a Scaled Residual TranMamba (SRTM) block to synergize long-term temporal modeling and localized detail extraction. SPRMamba further introduces the Hierarchical Sampling Strategy to optimize computational efficiency, enabling real-time processing critical for clinical deployment. Evaluated on the ESD385 dataset and the cholecystectomy benchmark Cholec80, SPRMamba achieves state-of-the-art performance (87.64% accuracy on ESD385, +1.0% over prior methods), demonstrating robust generalizability across surgical workflows. This advancement bridges the gap between computational efficiency and temporal sensitivity, offering a transformative tool for intraoperative guidance and skill assessment in ESD surgery. The code is accessible at https://github.com/Zxnyyyyy/SPRMamba.

A key property of deep neural networks (DNNs) is their ability to learn new features during training. This intriguing aspect of deep learning stands out most clearly in recently reported Grokking phenomena. While mainly reflected as a sudden increase in test accuracy, Grokking is also believed to be a beyond lazy-learning/Gaussian Process (GP) phenomenon involving feature learning. Here we apply a recent development in the theory of feature learning, the adaptive kernel approach, to two teacher-student models with cubic-polynomial and modular addition teachers. We provide analytical predictions on feature learning and Grokking properties of these models and demonstrate a mapping between Grokking and the theory of phase transitions. We show that after Grokking, the state of the DNN is analogous to the mixed phase following a first-order phase transition. In this mixed phase, the DNN generates useful internal representations of the teacher that are sharply distinct from those before the transition.

An accurate description of the scalar potential at finite temperature is crucial for studying cosmological first-order phase transitions (FOPT) in the early Universe. At finite temperatures, a precise treatment of thermal resummations is essential, as bosonic fields encounter significant infrared issues that can compromise standard perturbative approaches. The Partial Dressing (or the tadpole resummation) method provides a self consistent resummation of higher order corrections, allowing the computation of thermal masses and the effective potential including the proper Boltzmann suppression factors and without relying on any high-temperature approximation. We systematically compare the Partial dressing resummation scheme results with the Parwani and Arnold Espinosa (AE) ones to investigate the thermal phase transition dynamics in the Two-Higgs-Doublet Model (2HDM). Our findings reveal that different resummation prescriptions can significantly alter the nature of the phase transition within the same region of parameter space, confirming the differences that have already been noticed between the Parwani and AE schemes. Notably, the more refined resummation prescription, the Partial Dressing scheme, does not support symmetry non-restoration in 2HDM at high temperatures observed using the AE prescription. Furthermore, we quantify the uncertainties in the stochastic gravitational wave (GW) spectrum from an FOPT due to variations in resummation methods, illustrating their role in shaping theoretical predictions for upcoming GW experiments. Finally, we discuss the capability of the High-Luminosity LHC and proposed GW experiments to probe the FOEWPT-favored region of the parameter space.

Online Surgical Phase Recognition (SPR) models can reach high frame-wise accuracy, yet their predictions often lack temporal stability, fragmenting workflow understanding and reducing the reliability of downstream assistance. We show that this instability is not random noise but arises from two mechanisms: early misclassifications corrupt temporal feature states and propagate forward to form error cascades, and phase transitions follow evidence-accumulation dynamics whereas most online SPR systems rely on memoryless frame-wise decisions, making them sensitive to transient confidence fluctuations. We propose a unified Train-Inference-Evaluation framework that explicitly stabilizes temporal inference dynamics using model-agnostic, plug-and-play components. For training, the Temporal Error-Cascade (TEC) loss suppresses error onset and mitigates forward error propagation by stabilizing temporal feature evolution. For inference, the Evidence-Gated Transition Predictor (EGTP) enforces evidence-driven state transitions, allowing phase changes only when accumulated evidence exceeds a confidence boundary. For evaluation, we introduce the Temporal Fragmentation Index (TFI), a reliability-aware metric that quantifies instability-induced temporal disagreement beyond conventional frame-wise and token-based measures. Experiments on Cholec80 and AutoLaparo across three representative backbones show that the proposed framework substantially improves temporal stability and reduces prediction fragmentation, while maintaining or modestly improving frame-wise performance.

Large language models like GPT-4 exhibit emergent capabilities across general-purpose tasks, such as basic arithmetic, when trained on extensive text data, even though these tasks are not explicitly encoded by the unsupervised, next-token prediction objective. This study investigates how small transformers, trained from random initialization, can efficiently learn arithmetic operations such as addition, multiplication, and elementary functions like square root, using the next-token prediction objective. We first demonstrate that conventional training data is not the most effective for arithmetic learning, and simple formatting changes can significantly improve accuracy. This leads to sharp phase transitions as a function of training data scale, which, in some cases, can be explained through connections to low-rank matrix completion. Building on prior work, we then train on chain-of-thought style data that includes intermediate step results. Even in the complete absence of pretraining, this approach significantly and simultaneously improves accuracy, sample complexity, and convergence speed. We also study the interplay between arithmetic and text data during training and examine the effects of few-shot prompting, pretraining, and model scale. Additionally, we discuss length generalization challenges. Our work highlights the importance of high-quality, instructive data that considers the particular characteristics of the next-word prediction objective for rapidly eliciting arithmetic capabilities.

We explore the critical data size in language models, a threshold that marks a fundamental shift from quick memorization to slow generalization. We formalize the phase transition under the grokking configuration into the Data Efficiency Hypothesis and identify data insufficiency, sufficiency, and surplus regimes in language models training dynamics. We develop a grokking configuration to reproduce grokking on simplistic language models stably by rescaling initialization and weight decay. We show that generalization occurs only when language models reach a critical size. We analyze grokking across sample-wise and model-wise, verifying the proposed data efficiency hypothesis. Our experiments reveal smoother phase transitions occurring at the critical dataset size for language datasets. As the model size increases, this critical point also becomes larger, indicating that larger models require more data. Our results deepen the understanding of language model training, offering a novel perspective on the role of data in the learning mechanism of language models.

The impact of randomness on model training is poorly understood. How do differences in data order and initialization actually manifest in the model, such that some training runs outperform others or converge faster? Furthermore, how can we interpret the resulting training dynamics and the phase transitions that characterize different trajectories? To understand the effect of randomness on the dynamics and outcomes of neural network training, we train models multiple times with different random seeds and compute a variety of metrics throughout training, such as the L_2 norm, mean, and variance of the neural network's weights. We then fit a hidden Markov model (HMM) over the resulting sequences of metrics. The HMM represents training as a stochastic process of transitions between latent states, providing an intuitive overview of significant changes during training. Using our method, we produce a low-dimensional, discrete representation of training dynamics on grokking tasks, image classification, and masked language modeling. We use the HMM representation to study phase transitions and identify latent "detour" states that slow down convergence.

We show that deep neural networks (DNNs) can efficiently learn any composition of functions with bounded F_{1}-norm, which allows DNNs to break the curse of dimensionality in ways that shallow networks cannot. More specifically, we derive a generalization bound that combines a covering number argument for compositionality, and the F_{1}-norm (or the related Barron norm) for large width adaptivity. We show that the global minimizer of the regularized loss of DNNs can fit for example the composition of two functions f^{*}=hcirc g from a small number of observations, assuming g is smooth/regular and reduces the dimensionality (e.g. g could be the modulo map of the symmetries of f^{*}), so that h can be learned in spite of its low regularity. The measures of regularity we consider is the Sobolev norm with different levels of differentiability, which is well adapted to the F_{1} norm. We compute scaling laws empirically and observe phase transitions depending on whether g or h is harder to learn, as predicted by our theory.

Polymers are a versatile class of materials with widespread industrial applications. Advanced computational tools could revolutionize their design, but their complex, multi-scale nature poses significant modeling challenges. Conventional force fields often lack the accuracy and transferability required to capture the intricate interactions governing polymer behavior. Conversely, quantum-chemical methods are computationally prohibitive for the large systems and long timescales required to simulate relevant polymer phenomena. Here, we overcome these limitations with a machine learning force field (MLFF) approach. We demonstrate that macroscopic properties for a broad range of polymers can be predicted ab initio, without fitting to experimental data. Specifically, we develop a fast and scalable MLFF to accurately predict polymer densities, outperforming established classical force fields. Our MLFF also captures second-order phase transitions, enabling the prediction of glass transition temperatures. To accelerate progress in this domain, we introduce a benchmark of experimental bulk properties for 130 polymers and an accompanying quantum-chemical dataset. This work lays the foundation for a fully in silico design pipeline for next-generation polymeric materials.

Reciprocity is a fundamental symmetry present in many natural phenomena and engineered systems. Distinct situations where this symmetry is broken are typically grouped under the umbrella term "nonreciprocity", colloquially defined by: the action of A on B neq the action of B on A. In this review, we elucidate what nonreciprocity is by providing an introduction to its most salient classes: nonvariational dynamics, violations of Newton's third law, broken detailed balance, nonreciprocal responses and nonreciprocity of arbitrary linear operators. Next, we point out where to find these manifestations of non-reciprocity, from ensembles of particles with field mediated interactions to synthetic neural networks and open quantum systems. Given this breadth of contexts and the lack of an all-encompassing definition, it makes it all the more intriguing that some general conclusions can be gathered, when distinct definitions of nonreciprocity overlap. We explore what these universal consequences are with a special emphasis on collective phenomena that arise in nonreciprocal many-body systems. The topics covered include nonreciprocal phase transitions and non-normal amplification of noise and perturbations. We conclude with some open questions.

Chemical reaction networks can undergo nonequilibrium phase transitions upon variation of external control parameters like the chemical potential of a species. We investigate the flux in the associated chemostats that is proportional to the entropy production and its critical fluctuations within the Schlögl model. Numerical simulations show that the corresponding diffusion coefficient diverges at the critical point as a function of system size. In the vicinity of the critical point, the diffusion coefficient follows a scaling form. We develop an analytical approach based on the chemical Langevin equation and van Kampen's system size expansion that yields the corresponding exponents in the monostable regime. In the bistable regime, we rely on a two-state approximation in order to analytically describe the critical behavior.

Stochastic bubble nucleation makes the local completion time of a first-order phase transition a random spatial field. We study its power spectrum and equilateral bispectrum in Minkowski and de Sitter backgrounds, with particular emphasis on the infrared consequences of a finite transition duration. In an eternally extended de Sitter history, rare bubbles nucleated in the remote past generate an ancient-bubble tail that produces a hierarchy of infrared-sensitive spatial moments. For the two-point function, the first finite-k correction becomes tail sensitive at H/β=1/5, while the leading moment becomes singular at H/β=1/3. The corresponding three-point thresholds are H/β=1/8 and 1/6, showing that the bispectrum is more infrared sensitive than the power spectrum. For any finite starting time, however, the ancient-bubble tail is cut off, all spatial moments remain finite, and the strict infrared spectra recover the analytic white-noise limits {cal P}_τpropto k^3 and {cal B}^{rm eq}_τpropto k^6. The eternal-background thresholds instead control the duration dependence of the moment coefficients and the crossover into an intermediate tail-sensitive regime, in agreement with our numerical calculations. We further show that temporal localization of the nucleation history provides a smooth regulator of the ancient-bubble tail and restores the same analytic infrared limits. These results establish a general first-arrival framework for completion-time fluctuations and clarify how de Sitter expansion can generate distinct power-spectrum and bispectrum infrared hierarchies relevant to curvature perturbations and non-Gaussianity.

We study the dynamics of Stochastic Gradient Descent (SGD), which is known to steer deep neural networks toward invariant sets that correspond to simpler subnetworks. How this steering unfolds over time remains poorly understood. We answer this by modeling the stochastic gradient flow (SGF) as a percolation process, in which architectural symmetries force subnetworks to merge in discrete simultaneous blocks rather than one at a time. These structural transitions register as variance spikes in a macroscopic order parameter, echoing physical phase transitions. We further show this trapping mechanism and its associated scaling cascade extend to Adam and AdamW under an explicit heavy-tailed noise model.

We propose a general correspondence between gravity and spin models, inspired by the well-known IR equivalence between lattice gauge theories and the spin models. This suggests a connection between continuous type Hawking-phase transitions in gravity and the continuous order-disorder transitions in ferromagnets. The black-hole phase corresponds to the ordered and the graviton gas corresponds to the disordered phases respectively. A simple set-up based on Einstein-dilaton gravity indicates that the vicinity of the phase transition is governed by a linear-dilaton CFT. Employing this CFT we calculate scaling of observables near T_c, and obtain mean-field scaling in a semi-classical approximation. In case of the XY model the Goldstone mode is identified with the zero mode of the NS-NS two-form. We show that the second speed of sound vanishes at the transition also with the mean field exponent.

The Lee-Yang circle theorem revolutionized our understanding of phase transitions in ferromagnetic systems by showing that the complex zeros of partition functions lie on the unit circle, with criticality arising as these zeros approach the real axis in the thermodynamic limit. However, in frustrated systems such as antiferromagnets and spin glasses, the zeros deviate from this structure, making it challenging to extend the Lee-Yang theory to disordered systems. In this work, we establish a new circle theorem for two-dimensional Ising spin glasses, proving that the square of the partition function exhibits zeros densely packed along the unit circle. Numerical simulations on the square lattice confirm our theoretical predictions, demonstrating the validity of the circle law for quenched disorder. Furthermore, our results uncover a finite-temperature crossover in pm J spin glasses, characterized by the emergence of a spectral gap in the angular distribution of zeros. This result extends the Lee-Yang framework to disordered systems, offering new insights into spin-glass criticality.

Generative Adversarial Networks (GANs) are a popular formulation to train generative models for complex high dimensional data. The standard method for training GANs involves a gradient descent-ascent (GDA) procedure on a minimax optimization problem. This procedure is hard to analyze in general due to the nonlinear nature of the dynamics. We study the local dynamics of GDA for training a GAN with a kernel-based discriminator. This convergence analysis is based on a linearization of a non-linear dynamical system that describes the GDA iterations, under an isolated points model assumption from [Becker et al. 2022]. Our analysis brings out the effect of the learning rates, regularization, and the bandwidth of the kernel discriminator, on the local convergence rate of GDA. Importantly, we show phase transitions that indicate when the system converges, oscillates, or diverges. We also provide numerical simulations that verify our claims.

Symmetries play a central role in both equilibrium and nonequilibrium phase transitions, yet their quantitative characterization in dynamical quantum phase transitions (DQPTs) remains an open challenge. In this work, we establish a direct connection between symmetry properties of a many-body model and measures of quantum asymmetry, showing that asymmetry monotones provide a robust and physically transparent indicator of dynamical quantum criticality. Focusing on the quenched Lipkin-Meshkov-Glick model, we demonstrate that asymmetry measures associated with collective spin generators faithfully capture the onset of DQPTs, reflecting the dynamical restoration or breaking of underlying symmetries. Remarkably, the time-averaged asymmetry exhibits clear signatures of the dynamical critical point, in close correspondence with both the dynamical order parameter and the behavior of entropy production. We further uncover a quantitative link between asymmetry generation and thermodynamic irreversibility, showing that peaks in asymmetry coincide with maximal entropy production across the transition. Our results position asymmetry as a unifying concept bridging symmetry, information-theoretic quantifiers, and nonequilibrium thermodynamics in dynamical quantum phase transitions, providing a powerful framework for understanding critical dynamics beyond traditional order parameters.

We evaluate electromagnetic-response observables in a half-filled Chern band, across a topological phase transition between a composite Fermi liquid (CFL) and a Fermi liquid (FL) phase. While a sharp gapped plasma mode exists deep in the CFL phase, we demonstrate that it is damped near the proposed continuous phase transition between CFL and FL. This plasmon-damping phenomenon originates from emergent gauge fields and a Dirac-fermion-like spectrum. Similar features also occur in other continuous deconfined topological phase transitions, such as the Laughlin to superfluid transition in a bosonic system. In particular, this damping behavior extends over a finite range across the phase boundary, and, hence, we expect it to persist even when the transition is weakly first-order. Furthermore, we analyze the behavior of the Drude weight, the wavevector-dependent conductivity, and the chiral mirror effect across these topological phase transitions.

Electron-phonon interaction is of central importance for the electrical and heat transport properties of metals, and is directly responsible for charge-density-waves or (conventional) superconducting instabilities. The direct observation of phonon dispersion anomalies across electronic phase transitions can provide insightful information regarding the mechanisms underlying their formation. Here, we review the current status of phonon dispersion studies in superconductors under hydrostatic and uniaxial pressure. Advances in the instrumentation of high resolution inelastic X-ray scattering beamlines and pressure generating devices allow these measurements to be performed routinely at synchrotron beamlines worldwide.

PURPOSE: Surgical workflow and skill analysis are key technologies for the next generation of cognitive surgical assistance systems. These systems could increase the safety of the operation through context-sensitive warnings and semi-autonomous robotic assistance or improve training of surgeons via data-driven feedback. In surgical workflow analysis up to 91% average precision has been reported for phase recognition on an open data single-center dataset. In this work we investigated the generalizability of phase recognition algorithms in a multi-center setting including more difficult recognition tasks such as surgical action and surgical skill. METHODS: To achieve this goal, a dataset with 33 laparoscopic cholecystectomy videos from three surgical centers with a total operation time of 22 hours was created. Labels included annotation of seven surgical phases with 250 phase transitions, 5514 occurences of four surgical actions, 6980 occurences of 21 surgical instruments from seven instrument categories and 495 skill classifications in five skill dimensions. The dataset was used in the 2019 Endoscopic Vision challenge, sub-challenge for surgical workflow and skill analysis. Here, 12 teams submitted their machine learning algorithms for recognition of phase, action, instrument and/or skill assessment. RESULTS: F1-scores were achieved for phase recognition between 23.9% and 67.7% (n=9 teams), for instrument presence detection between 38.5% and 63.8% (n=8 teams), but for action recognition only between 21.8% and 23.3% (n=5 teams). The average absolute error for skill assessment was 0.78 (n=1 team). CONCLUSION: Surgical workflow and skill analysis are promising technologies to support the surgical team, but are not solved yet, as shown by our comparison of algorithms. This novel benchmark can be used for comparable evaluation and validation of future work.

Monodisperse, purely repulsive, hard spheres (MPRHS) are an important model system for mechanistically exploring phase behavior in atomic systems and colloids. Since the 1940s, phase transitions in these systems have been obtained via simulation, theory, and experiments. But there is a gap in this literature: despite decades of reports of phase transition from one pure state to another, no computational studies report spontaneous phase separation into coexisting domains of liquid and crystal regions. This gap owes its origin to the underlying mechanism of entropically-driven phase separation in MPRHS - the competition between short-range entropy and long-range entropy. Frenkel proposed that spontaneous phase separation in simulations of up to 1,000,000 particles would require more than 317,000,000 years to sample enough microstates to converge to phase separated macrostate. Some brute-force simulations do show brief spontaneous coexistence but a metastable crystal or fluid subsequently overtakes the system. To bypass these difficulties, many studies use seeding, gravity, or direct construction of liquid and solid phases to study interfacial energy and nucleation rates of MPRHS systems. WCA potentials have also been used to bypass metastability, where softness provides free volume, lowers osmotic pressure and the energy barrier. It is argued that the transition path taken in bypassing metastability is mechanistically the same as without triggers. But as acknowledged by Alder & Wainwright, explicit observation of spontaneous coexistence is central to computational prediction of first-order transition. Such observation would provide satisfying demonstration of Frenkel's entropy exchange mechanism. We explore literature revealing these interesting behaviors and conclude that computational demonstration of Frenkel's mechanism for MPRHS awaits large systems with careful hardness perturbations.

Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data. rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange-correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principle PIMC and DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions.

Pressure, together with temperature and magnetic field, is an important thermodynamical parameter in physics. Investigating the response of a compound or of a material to pressure allows to elucidate ground states, investigate their interplay and interactions and determine microscopic parameters. Pressure tuning is used to establish phase diagrams, study phase transitions and identify critical points. Muon spin rotation/relaxation (muSR) is now a standard technique making increasing significant contribution in condensed matter physics, material science research and other fields. In this review, we will discuss specific requirements and challenges to perform muSR experiments under pressure, introduce the high-pressure muon facility at the Paul Scherrer Institute (PSI, Switzerland) and present selected results obtained by combining the sensitivity of the muSR technique with pressure.

When agents are acting together, they may need a simple mechanism to decide on joint actions. One possibility is to have the agents express their preferences in the form of a ballot and use a voting rule to decide the winning action(s). Unfortunately, agents may try to manipulate such an election by misreporting their preferences. Fortunately, it has been shown that it is NP-hard to compute how to manipulate a number of different voting rules. However, NP-hardness only bounds the worst-case complexity. Recent theoretical results suggest that manipulation may often be easy in practice. To address this issue, I suggest studying empirically if computational complexity is in practice a barrier to manipulation. The basic tool used in my investigations is the identification of computational "phase transitions". Such an approach has been fruitful in identifying hard instances of propositional satisfiability and other NP-hard problems. I show that phase transition behaviour gives insight into the hardness of manipulating voting rules, increasing concern that computational complexity is indeed any sort of barrier. Finally, I look at the problem of computing manipulation of other, related problems like stable marriage and tournament problems.

Safety alignment in large language models is typically evaluated under isolated queries, yet real-world use is inherently multi-turn. Although multi-turn jailbreaks are empirically effective, the structure of conversational safety failure remains insufficiently understood. In this work, we study safety failures from a state-space perspective and show that many multi-turn failures arise from structured contextual state evolution rather than isolated prompt vulnerabilities. We introduce STAR, a state-oriented diagnostic framework that treats dialogue history as a state transition operator and enables controlled analysis of safety behavior along interaction trajectories. Rather than optimizing attack strength, STAR provides a principled probe of how aligned models traverse the safety boundary under autoregressive conditioning. Across multiple frontier language models, we find that systems that appear robust under static evaluation can undergo rapid and reproducible safety collapse under structured multi-turn interaction. Mechanistic analysis reveals monotonic drift away from refusal-related representations and abrupt phase transitions induced by role-conditioned context. Together, these findings motivate viewing language model safety as a dynamic, state-dependent process defined over conversational trajectories.

We study the capacity of the self-attention key-query channel: for a fixed budget, how many distinct token-token relations can a single layer reliably encode? We introduce Relational Graph Recognition, where the key-query channel encodes a directed graph and, given a context (a subset of the vertices), must recover the neighbors of each vertex in the context. We measure resources by the total key dimension D_K = h,d_k. In a tractable multi-head model, we prove matching information-theoretic lower bounds and upper bounds via explicit constructions showing that recovering a graph with m' relations in d_{model}-dimensional embeddings requires D_K to grow essentially as m'/d_{model} up to logarithmic factors, and we obtain corresponding guarantees for scaled-softmax attention. This analysis yields a new, capacity-based rationale for multi-head attention: even in permutation graphs, where all queries attend to a single target, splitting a fixed D_K budget into multiple heads increases capacity by reducing interference from embedding superposition. Controlled experiments mirror the theory, revealing sharp phase transitions at the predicted capacity, and the multi-head advantage persists when adding softmax normalization, value routing, and a full Transformer block trained with frozen GPT-2 embeddings.

We show that PLDR-LLMs pretrained at self-organized criticality exhibit reasoning at inference time. The characteristics of PLDR-LLM deductive outputs at criticality is similar to second-order phase transitions. At criticality, the correlation length diverges, and the deductive outputs attain a metastable steady state. The steady state behaviour suggests that deductive outputs learn representations equivalent to scaling functions, universality classes and renormalization groups from the training dataset, leading to generalization and reasoning capabilities in the process. We can then define an order parameter from the global statistics of the model's deductive output parameters at inference. The reasoning capabilities of a PLDR-LLM is better when its order parameter is close to zero at criticality. This observation is supported by the benchmark scores of the models trained at near-criticality and sub-criticality. Our results provide a self-contained explanation on how reasoning manifests in large language models, and the ability to reason can be quantified solely from global model parameter values of the deductive outputs at steady state, without any need for evaluation of curated benchmark datasets through inductive output for reasoning and comprehension.

Correlated electron systems are among the centerpieces of modern condensed matter sciences, where many interesting physical phenomena, such as metal-insulator transition and high-Tc superconductivity appear. Recent efforts have been focused on electrostatic doping of such materials to probe the underlying physics without introducing disorder as well as to build field-effect transistors that may complement conventional semiconductor metal-oxide-semiconductor field effect transistor (MOSFET) technology. This review focuses on metal-insulator transition mechanisms in correlated electron materials and three-terminal field effect devices utilizing such correlated oxides as the channel layer. We first describe how electron-disorder interaction, electron-phonon interaction and/or electron correlation in solids could modify the electronic properties of materials and lead to metal-insulator transitions. Then we analyze experimental efforts toward utilizing these transitions in field effect transistors and their underlying principles. It is pointed out that correlated electron systems show promise among these various materials displaying phase transitions for logic technologies. Furthermore, novel phenomena emerging from electronic correlation could enable new functionalities in field effect devices. We then briefly review unconventional electrostatic gating techniques, such as ionic liquid gating and ferroelectric gating, which enables ultra large carrier accumulation density in the correlated materials which could in turn lead to phase transitions. The review concludes with a brief discussion on the prospects and suggestions for future research directions in correlated oxide electronics for information processing.

We present a neural flow wavefunction, Gauge-Fermion FlowNet, and use it to simulate 2+1D lattice compact quantum electrodynamics with finite density dynamical fermions. The gauge field is represented by a neural network which parameterizes a discretized flow-based transformation of the amplitude while the fermionic sign structure is represented by a neural net backflow. This approach directly represents the U(1) degree of freedom without any truncation, obeys Guass's law by construction, samples autoregressively avoiding any equilibration time, and variationally simulates Gauge-Fermion systems with sign problems accurately. In this model, we investigate confinement and string breaking phenomena in different fermion density and hopping regimes. We study the phase transition from the charge crystal phase to the vacuum phase at zero density, and observe the phase seperation and the net charge penetration blocking effect under magnetic interaction at finite density. In addition, we investigate a magnetic phase transition due to the competition effect between the kinetic energy of fermions and the magnetic energy of the gauge field. With our method, we further note potential differences on the order of the phase transitions between a continuous U(1) system and one with finite truncation. Our state-of-the-art neural network approach opens up new possibilities to study different gauge theories coupled to dynamical matter in higher dimensions.

Four lectures on holography and the AdS/CFT correspondence applied to condensed matter systems. The first lecture introduces the concept of a quantum phase transition. The second lecture discusses linear response theory and Ward identities. The third lecture presents transport coefficients derived from AdS/CFT that should be applicable in the quantum critical region associated to a quantum phase transition. The fourth lecture builds in the physics of a superconducting or superfluid phase transition to the simple holographic model of the third lecture.

We present dla-ideal-solver, a high-performance framework for simulating two-dimensional Diffusion-Limited Aggregation (DLA) using Numba-accelerated Python. By leveraging just-in-time (JIT) compilation, we achieve computational throughput comparable to legacy static implementations while retaining high-level flexibility. We investigate the Laplacian growth instability across varying injection geometries and walker concentrations. Our analysis confirms the robustness of the standard fractal dimension D_f approx 1.71 for dilute regimes, consistent with the Witten-Sander universality class. However, we report a distinct crossover to Eden-like compact growth (D_f approx 1.87) in high-density environments, attributed to the saturation of the screening length. Beyond standard mass-radius scaling, we employ generalized Rényi dimensions and lacunarity metrics to quantify the monofractal character and spatial heterogeneity of the aggregates. This work establishes a reproducible, open-source testbed for exploring phase transitions in non-equilibrium statistical mechanics.

This paper introduces a continuous-time stochastic dynamical framework for understanding how large language models (LLMs) may self-amplify latent biases or toxicity through their own chain-of-thought reasoning. The model posits an instantaneous "severity" variable x(t) in [0,1] evolving under a stochastic differential equation (SDE) with a drift term μ(x) and diffusion σ(x). Crucially, such a process can be consistently analyzed via the Fokker--Planck approach if each incremental step behaves nearly Markovian in severity space. The analysis investigates critical phenomena, showing that certain parameter regimes create phase transitions from subcritical (self-correcting) to supercritical (runaway severity). The paper derives stationary distributions, first-passage times to harmful thresholds, and scaling laws near critical points. Finally, it highlights implications for agents and extended LLM reasoning models: in principle, these equations might serve as a basis for formal verification of whether a model remains stable or propagates bias over repeated inferences.

Text-to-motion generation requires modeling both global action structure and fine-grained motion dynamics from natural language. Existing approaches typically rely on either continuous diffusion models or vector-quantized discrete representations. Diffusion models generate smooth motions but lack explicit compositional structure for temporal planning, while discrete token-based methods improve controllability but compress motion into finite codebooks, losing fine-grained dynamics. We argue that this limitation stems from a representation mismatch: action semantics such as intent, phase transitions, and temporal layout are inherently discrete and compositional, whereas joint trajectories and motion dynamics are continuous and locally correlated. To address this, we propose DC-Motion, a discrete-continuous factorized framework for human motion generation. DC-Motion decomposes motion into discrete structural tokens capturing global action layout and continuous residual latents modeling fine-grained dynamics. A text-conditioned structure generator predicts discrete tokens via iterative masked modeling, and a diffusion-based residual generator produces continuous motion conditioned on the structure. Experiments on HumanML3D and KIT-ML demonstrate that DC-Motion achieves strong performance in both FID and R-Precision, outperforming representative diffusion-based and discrete-token baselines.

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias. After suggesting algebraic topology as a measure for data complexity, we show that the power of a network to express the topological complexity of a dataset in its decision region is a strictly limiting factor in its ability to generalize. We then provide the first empirical characterization of the topological capacity of neural networks. Our empirical analysis shows that at every level of dataset complexity, neural networks exhibit topological phase transitions. This observation allowed us to connect existing theory to empirically driven conjectures on the choice of architectures for fully-connected neural networks.

Rydberg atom arrays have emerged as a powerful platform to simulate a number of exotic quantum ground states and phase transitions. To verify these capabilities numerically, we develop a versatile quantum Monte Carlo sampling technique which operates in the reduced Hilbert space generated by enforcing the constraint of a Rydberg blockade. We use the framework of stochastic series expansion and show that in the restricted space, the configuration space of operator strings can be understood as a hard rod gas in d+1 dimensions. We use this mapping to develop cluster algorithms which can be visualized as various non-local movements of rods. We study the efficiency of each of our updates individually and collectively. To elucidate the utility of the algorithm, we show that it can efficiently generate the phase diagram of a Rydberg atom array, to temperatures much smaller than all energy scales involved, on a Kagom\'e link lattice. This is of broad interest as the presence of a Z_2 spin liquid has been hypothesized recently.

We investigate Einstein-Gauss-Bonnet (EGB) 4D massive gravity coupled to nonlinear electrodynamics (NED) in an Anti-de-Sitter (AdS) background and find an exact magnetically charged black hole solution. The metric function was analyzed for different values of massive gravity parameters. We verified the first law of black hole thermodynamics and the generalized Smarr formula, treating the cosmological constant as thermodynamic pressure. Vacuum polarization is defined as the conjugate to the NED parameter. To analyze the local stability of the black hole, we compute specific heat. We investigated the Van der Waals-like/reentrant phase transition of the black holes and estimated the critical points. We observed small/large black hole (SBH/LBH) and small/intermediate/large black hole (SBH/IBH/LBH) phase transitions. The Joule-Thomson coefficient, inversion, and isenthalpic curves are discussed. Finally, the minimum inversion temperature and the corresponding event horizon radius are obtained using numerical techniques.

The performance of quantum annealing for combinatorial optimization is fundamentally limited by the minimum energy gap Δ encountered at quantum phase transitions. We investigate the scaling of Δ with system size N for two paradigmatic quantum spin-glass models: the two-dimensional Edwards-Anderson (2D-EA) and the all-to-all Sherrington-Kirkpatrick (SK) models. Utilizing a newly proposed unbiased energy-gap estimator for continuous-time projection quantum Monte Carlo simulations, complemented by high-performance sparse eigenvalue solvers, we characterize the gap distributions across disorder realizations. It is found that, in the 2D-EA case, the inverse-gap distribution develops a fat tail with infinite variance as N increases. This indicates that the unfavorable super-algebraic scaling of Δ, recently reported for binary couplings [Nature 631, 749 (2024)], persists for the Gaussian disorder considered here, pointing to a universal feature of 2D spin glasses. Conversely, the SK model retains a finite-variance distribution, with the disorder-averaged gap following a rather slow power law, close to Δpropto N^{-1/3}. This finding provides a promising outlook for the potential efficiency of quantum annealers for optimization problems with dense connectivity.

Motivated by recent observations of symmtry broken phases in lightly-doped multilayer graphene, we investigate magnetic phase transitions in a generalized electron gas model with four-component electron spin. This model simplifies the problem with a parabolic dispersion band, abstracting away the details of the graphene band structure to focus solely on the effects of the Coulomb interaction. We report four findings: 1) In the Hartree-Fock approximation, we observe that the paramagnetic state undergoes a sequence of density-driven, first-order phase transitions, progressively depopulating electrons from each spin component until achieving complete polarization within a very narrow density window where 1.2<r_s<2 (r_s being the electron gas parameter). 2) Further incorporating the correlation energy via the Bohm-Pines random-phase approximation shows that the cascade of transitions obtained within Hartree-Fock approximation is replaced by a single ferromagnetic phase transition at r_s = 6.12. 3) The disappearance of cascade is due to the correlation energy difference between the four-component paramagnetic state and symmetry-broken phases, which is nearly an order of magnitude more negative than the corresponding Hartree-Fock energy difference for 1.2 < r_s < 2. 4) The transition from the paramagnetic state to the fully polarized state at r_s=6.12 is governed by the balance between exchange and correlation energies, a competition that cannot be captured by mean-field approximations to models featuring effective (density-dependent) delta-function interactions, such as the Stoner model. We use the insights from our model to comment on the phase diagram of multilayer graphene electron gas.

We study the computational limits of Low-Rank Adaptation (LoRA) update for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient computation of LoRA adaptation leads to possible algorithmic speedup. This allows us to (i) identify a phase transition behavior and (ii) prove the existence of nearly linear algorithms by controlling the LoRA update computation term by term, assuming the Strong Exponential Time Hypothesis (SETH). For the former, we identify a sharp transition in the efficiency of all possible rank-r LoRA update algorithms for transformers, based on specific norms resulting from the multiplications of the input sequence X, pretrained weights W^star, and adapter matrices alpha B A / r. Specifically, we derive a shared upper bound threshold for such norms and show that efficient (sub-quadratic) approximation algorithms of LoRA exist only below this threshold. For the latter, we prove the existence of nearly linear approximation algorithms for LoRA adaptation by utilizing the hierarchical low-rank structures of LoRA gradients and approximating the gradients with a series of chained low-rank approximations. To showcase our theory, we consider two practical scenarios: partial (e.g., only W_V and W_Q) and full adaptations (e.g., W_Q, W_V, and W_K) of weights in attention heads.

Colloids play an important role in fundamental science as well as in nature and technology. They have had a strong impact on the fundamental understanding of statistical physics. For example, colloids have helped to obtain a better understanding of collective phenomena, ranging from phase transitions and glass formation to the swarming of active Brownian particles. Yet the success of colloidal systems hinges crucially on the specific physical and chemical properties of the colloidal particles, i.e. particles with the appropriate characteristics must be available. Here we present an idea to create particles with freely selectable properties. The properties might depend, for example, on the presence of other particles (hence mimicking specific pair or many-body interactions), previous configurations (hence introducing some memory or feedback), or a directional bias (hence changing the dynamics). Without directly interfering with the sample, each particle is fully controlled and can receive external commands through a predefined algorithm that can take into account any input parameters. This is realized with computer-controlled colloids, which we term cybloids - short for cybernetic colloids. The potential of cybloids is illustrated by programming a time-delayed external potential acting on a single colloid and interaction potentials for many colloids. Both an attractive harmonic potential and an annular potential are implemented. For a single particle, this programming can cause subdiffusive behavior or lend activity. For many colloids, the programmed interaction potential allows to select a crystal structure at wish. Beyond these examples, we discuss further opportunities which cybloids offer.

The recent detection of nanohertz stochastic gravitational-wave backgrounds (SGWBs) by pulsar timing arrays (PTAs) promises unique insights into astrophysical and cosmological origins. However, traditional Markov Chain Monte Carlo (MCMC) approaches become prohibitively expensive for large datasets. We employ a normalizing flow (NF)-based machine learning framework to accelerate Bayesian inference in PTA analyses. For the first time, we perform Bayesian model comparison across SGWB source models in the framework of machine learning by training NF architectures on the PTA dataset (NANOGrav 15-year) and enabling direct evidence estimation via learned harmonic mean estimators. Our examples include 10 conventional SGWB source models such as supermassive black hole binaries, power-law spectrum, cosmic strings, domain walls, scalar-induced GWs, first-order phase transitions, and dual scenario/inflationary gravitational wave. Our approach jointly infers 20 red noise parameters and 2 SGWB parameters per model in sim 20\,hours (including training), compared to sim 10\,days with MCMC. Critically, the NF method preserves rigorous model selection accuracy, with small Hellinger distances (lesssim 0.3) relative to MCMC posteriors, and reproduces MCMC-based Bayes factors across all tested scenarios. This scalable technique for SGWB source comparison will be essential for future PTA expansions and next-generation arrays such as the SKA, offering orders-of-magnitude efficiency gains without sacrificing physical interpretability.

In this paper, we study the role of feedback in online learning with switching costs. It has been shown that the minimax regret is Theta(T^{2/3}) under bandit feedback and improves to Theta(T) under full-information feedback, where T is the length of the time horizon. However, it remains largely unknown how the amount and type of feedback generally impact regret. To this end, we first consider the setting of bandit learning with extra observations; that is, in addition to the typical bandit feedback, the learner can freely make a total of B_{ex} extra observations. We fully characterize the minimax regret in this setting, which exhibits an interesting phase-transition phenomenon: when B_{ex} = O(T^{2/3}), the regret remains Theta(T^{2/3}), but when B_{ex} = Omega(T^{2/3}), it becomes Theta(T/B_{mathrm{ex}}), which improves as the budget B_{ex} increases. To design algorithms that can achieve the minimax regret, it is instructive to consider a more general setting where the learner has a budget of B total observations. We fully characterize the minimax regret in this setting as well and show that it is Theta(T/B), which scales smoothly with the total budget B. Furthermore, we propose a generic algorithmic framework, which enables us to design different learning algorithms that can achieve matching upper bounds for both settings based on the amount and type of feedback. One interesting finding is that while bandit feedback can still guarantee optimal regret when the budget is relatively limited, it no longer suffices to achieve optimal regret when the budget is relatively large.

We use the AdS/CFT correspondence to study the thermodynamics of massive N=2 supersymmetric hypermultiplets coupled to N=4 supersymmetric SU(Nc) Yang-Mills theory in the limits of large Nc and large 't Hooft coupling. In particular, we study the theory at finite baryon number density. At zero temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy, and in the supergravity description we clarify which D-brane configuration is appropriate for any given value of the chemical potential. We find a second-order phase transition when the chemical potential equals the mass. At finite temperature, we present an exact expression for the hypermultiplets' leading-order contribution to the free energy at zero mass.

Popular guidance for denoising diffusion probabilistic model (DDPM) linearly combines distinct conditional models together to provide enhanced control over samples. However, this approach overlooks nonlinear effects that become significant when guidance scale is large. To address this issue, we propose characteristic guidance, a guidance method that provides first-principle non-linear correction for classifier-free guidance. Such correction forces the guided DDPMs to respect the Fokker-Planck (FP) equation of diffusion process, in a way that is training-free and compatible with existing sampling methods. Experiments show that characteristic guidance enhances semantic characteristics of prompts and mitigate irregularities in image generation, proving effective in diverse applications ranging from simulating magnet phase transitions to latent space sampling.

Surgical future prediction, driven by real-time AI analysis of surgical video, is critical for operating room safety and efficiency. It provides actionable insights into upcoming events, their timing, and risks-enabling better resource allocation, timely instrument readiness, and early warnings for complications (e.g., bleeding, bile duct injury). Despite this need, current surgical AI research focuses on understanding what is happening rather than predicting future events. Existing methods target specific tasks in isolation, lacking unified approaches that span both short-term (action triplets, events) and long-term horizons (remaining surgery duration, phase transitions). These methods rely on coarse-grained supervision while fine-grained surgical action triplets and steps remain underexplored. Furthermore, methods based only on future feature prediction struggle to generalize across different surgical contexts and procedures. We address these limits by reframing surgical future prediction as state-change learning. Rather than forecasting raw observations, our approach classifies state transitions between current and future timesteps. We introduce SurgFUTR, implementing this through a teacher-student architecture. Video clips are compressed into state representations via Sinkhorn-Knopp clustering; the teacher network learns from both current and future clips, while the student network predicts future states from current videos alone, guided by our Action Dynamics (ActDyn) module. We establish SFPBench with five prediction tasks spanning short-term (triplets, events) and long-term (remaining surgery duration, phase and step transitions) horizons. Experiments across four datasets and three procedures show consistent improvements. Cross-procedure transfer validates generalizability.

Electron-electron (e-e) and electron-phonon (e-ph) interactions are challenging to describe in correlated materials, where their joint effects govern unconventional transport, phase transitions, and superconductivity. Here we combine first-principles e-ph calculations with dynamical mean field theory (DMFT) as a step toward a unified description of e-e and e-ph interactions in correlated materials. We compute the e-ph self-energy using the DMFT electron Green's function, and combine it with the e-e self-energy from DMFT to obtain a Green's function including both interactions. This approach captures the renormalization of quasiparticle dispersion and spectral weight on equal footing. Using our method, we study the e-ph and e-e contributions to the resistivity and spectral functions in the correlated metal Sr_2RuO_4. In this material, our results show that e-e interactions dominate transport and spectral broadening in the temperature range we study (50-310~K), while e-ph interactions are relatively weak and account for only sim10\% of the experimental resistivity. We also compute effective scattering rates, and find that the e-e interactions result in scattering several times greater than the Planckian value k_BT, whereas e-ph interactions are associated with scattering rates lower than k_BT. Our work demonstrates a first-principles approach to combine electron dynamical correlations from DMFT with e-ph interactions in a consistent way, advancing quantitative studies of correlated materials.

Motivated by the recent experimental observation of the topological Anderson insulator in disordered atomic wires based on the Su-Schrieffer-Heeger (SSH) model, we study disorder effects on a dimerized Kitaev superconductor chain which is regarded as the superconductor version of the SSH model. By computing the real-space winding number and the zero-bias differential conductance, we analyze the topological phase transitions occurring in a dimerized Kitaev superconductor chain with disorder. It is found that disorder can induce a topologically nontrivial superconductor phase hosting Majorana zero modes (MZMs). We can regulate the appearance of disorder-induced MZMs by adjusting the dimerization parameter. Finally, we use the self-consistent Born approximation method to verify the numerical results.

Large language models have emergent capabilities that come unexpectedly at scale, but we need a theoretical framework to explain why and how they emerge. We prove that language models are actually non-ergodic systems while providing a mathematical framework based on Stuart Kauffman's theory of the adjacent possible (TAP) to explain capability emergence. Our resource-constrained TAP equation demonstrates how architectural, training, and contextual constraints interact to shape model capabilities through phase transitions in semantic space. We prove through experiments with three different language models that capacities emerge through discrete transitions guided by constraint interactions and path-dependent exploration. This framework provides a theoretical basis for understanding emergence in language models and guides the development of architectures that can guide capability emergence.

Half a billion citation edges extracted from 100.7 million Ukrainian court decisions reveal that judicial citation structure encodes legal domain boundaries without supervision and predicts future legislative importance with near-perfect accuracy. We construct the first large-scale citation graph from the complete EDRSR registry (99.5 million full texts, 1.1 TB), extracting 502 million citation links across six types via regex on commodity hardware in approximately 5 hours, with precision of 1.00 on a 200-decision validation sample (95% Wilson CI: [0.982, 1.000]). Three principal findings emerge. (1) The degree distribution follows a power law (alpha = 1.57 +/- 0.008), placing the Ukrainian court network near the EU Court of Justice and below the US Supreme Court, with hub articles cited by millions of decisions. (2) Louvain community detection on the co-citation projection recovers legal domain boundaries (civil, criminal, administrative, commercial) with modularity Q = 0.44-0.55 and temporal stability (NMI = 0.83-0.86 across periods), constituting an automatically constructed legal ontology grounded in judicial practice. (3) Citation features predict top-1000 articles with AUC = 0.9984, substantially outperforming a naive frequency baseline (P@1000 = 0.655); temporal dynamics detect legislative regime changes as phase transitions and the 2022 invasion as a citation entropy spike (H: 11.02 -> 13.49) with emergent wartime legislation nodes. The citation-derived ontology is operationalized as the domain layer of a workflow memory system for LLM-assisted legal analysis, connecting to the ontology-controlled paradigm. The extraction pipeline, analysis code, and aggregated statistics are released as open data.

As context windows in LLMs scale to 100K+ tokens, the key-value (KV) cache becomes the dominant memory bottleneck, with recent methods claiming 80-90% savings and minimal benchmark degradation. We argue these evaluations miss a structural issue: attention is not just storage but routing, and retaining KV pairs does not guarantee semantic accessibility. We propose a physics-inspired view of KV compression as a controlled perturbation of token-level routing, distinguishing retention, accessibility, and utilization. Using synthetic tasks probing multi-entity tracking, disambiguation, coreference, and multi-hop reasoning, we find that moderate compression degrades internal representations with little accuracy loss, revealing redundancy; all models exhibit a sharp hallucination safety cliff near 90% compression, correlated with spikes in Global Eviction Ratio (GER), suggesting a phase transition in semantic reachability; and architectures differ in routing dynamics, with LLaMA showing early consensus and late diversification, and Qwen showing funnel-like late convergence, leading to distinct resilience profiles. Beyond erasure, we identify representational rigidity, where excessive head-level consensus collapses routing flexibility despite token survival. These results suggest sparse token-route structures govern compression tolerance, reframing KV compression as a structural probe of attention geometry and linking long-context scalability to sparsity and the lottery ticket hypothesis in self-attention.

Machine-learned interatomic potentials are revolutionising atomistic materials simulations by providing accurate and scalable predictions within the scope covered by the training data. However, generation of an accurate and robust training data set remains a challenge, often requiring thousands of first-principles calculations to achieve high accuracy. Foundation models have started to emerge with the ambition to create universally applicable potentials across a wide range of materials. While foundation models can be robust and transferable, they do not yet achieve the accuracy required to predict reaction barriers, phase transitions, and material stability. This work demonstrates that foundation model potentials can reach chemical accuracy when fine-tuned using transfer learning with partially frozen weights and biases. For two challenging datasets on reactive chemistry at surfaces and stability and elastic properties of tertiary alloys, we show that frozen transfer learning with 10-20% of the data (hundreds of datapoints) achieves similar accuracies to models trained from scratch (on thousands of datapoints). Moreover, we show that an equally accurate, but significantly more efficient surrogate model can be built using the transfer learned potential as the ground truth. In combination, we present a simulation workflow for machine learning potentials that improves data efficiency and computational efficiency.

Large language model compression has made substantial progress through pruning, quantization, and low-rank decomposition, yet a fundamental limitation persists across all existing methods: compression budgets are allocated without any representation of what individual model components functionally encode. We term this the capability-blind compression problem and argue it is a root cause of two well-documented failures -- the insensitivity of perplexity-based evaluation to reasoning capability loss, and the abrupt phase transitions in model performance recently characterized by Ma et al. (2026). We propose Capability-Guided Compression (CGC), a framework that addresses this by using Sparse Autoencoder (SAE)-derived capability density maps to allocate differential compression budgets across transformer components. Capability density is a formally defined scalar measure combining the feature breadth, activation entropy, and cross-input consistency of a component's SAE feature activation distribution. We prove theoretically that components with higher capability density exhibit lower structural redundancy and reach their individual phase transition points at lower compression ratios, providing the first pre-compression mechanism for component-level phase transition prediction. Experiments on GPT-2 Medium confirm that capability density is statistically independent of Wanda importance scores (Spearman rho = -0.054, n = 384 heads), establishing it as a genuinely novel compression signal orthogonal to all existing importance metrics. We report a negative result on PPL-based compression comparison and provide a principled diagnosis identifying GPT-2 Medium as an insufficient test bed for the full CGC hypothesis. The theoretical framework, density formalism, and orthogonality finding constitute a foundation for capability-aware compression research.

Solving the quantum many-body ground state problem remains a central challenge in computational physics. In this context, the Variational Monte Carlo (VMC) framework based on Projected Entangled Pair States (PEPS) has witnessed rapid development, establishing itself as a vital approach for investigating strongly correlated two-dimensional systems. However, standard PEPS-VMC algorithms predominantly rely on sequential local updates. This conventional approach often suffers from slow convergence and critical slowing down, particularly in the vicinity of phase transitions or within frustrated landscapes. To address these limitations, we propose an efficient autoregressive row-wise sampling algorithm for PEPS that enables direct, rejection-free sampling via single-layer contractions. By utilizing autoregressive single-layer row updates to generate collective, non-local configuration proposals, our method significantly reduces temporal correlations compared to local Metropolis moves. We benchmark the algorithm on the two-dimensional transverse-field Ising model and the quantum spin glass. Our results demonstrate that the row-wise scheme effectively mitigates critical slowing down near the Ising critical point. Furthermore, in the rugged landscape of the quantum spin glass, it yields improved optimization stability and lower ground-state energies. These findings indicate that single-layer autoregressive row updates provide a flexible and robust improvement to local PEPS-VMC sampling and may serve as a basis for more advanced sampling schemes.

A detailed study of published experimental data for a variety of materials on the incremental variation of heat capacity, thermal expansion, and compressibility at glassy freezing reveals a striking dependence of the Prigogine-Defay ratio R on the fragility index m. At high m, R approaches values of ~1, the Ehrenfest expectation for 2nd order continuous phase transitions, while R reaches values > 20 for low fragilities. We explain this correlation by the degree of separation of the glassy freezing temperature from a hidden phase transition into an ideal low-temperature glass.

Recent advances integrate physically grounded Newtonian dynamics with neural rendering frameworks, narrowing the gap between photorealistic scene reconstruction and physics-based animation. However, existing approaches focus on mechanically driven dynamics while neglecting temperature, a fundamental yet invisible physical factor underlying phenomena such as melting, solidification, and other thermomechanical processes. In this paper, we propose MeGAS, a novel framework that incorporates thermomechanical phase-change dynamics into 3D Gaussian Splatting (3DGS). Specifically, we propose a new thermomechanical dynamic Gaussian Splatting representation that augments 3DGS with temperature attributes and employs a heat advection-diffusion solver with MPM dynamics incorporating phase transitions, enabling physically plausible and visually realistic synthesis of thermophysical phenomena. Furthermore, a new topology-adaptive Gaussian rendering strategy is proposed to mitigate cracking and floaters under extreme deformation. Extensive experiments demonstrate that MeGAS produces physically consistent thermomechanical behavior while maintaining high-fidelity photorealistic rendering, advancing toward physics-integrated world models.

We quantify the impact of higher-dimensional operators in the effective theory for bubble nucleation, focusing on supercooled phase transitions in the classically conformal Abelian-Higgs model. While high-temperature dimensional reduction organizes hard thermal corrections into a tower of operators in a three-dimensional effective field theory, recent results show that dimension-six terms can dominate over higher-loop corrections to the equilibrium thermodynamics of the strongest transitions. To assess their effect on the nucleation rate and the derived near-equilibrium phase-transition observables, we develop a perturbative framework that includes them in the full one-loop nucleation rate. Including higher-dimensional operators both in the bounce action and in the fluctuation determinants, we solve the resulting Sturm-Liouville problem without a derivative expansion, using a modified Gel'fand-Yaglom method. For strongly supercooled transitions, we find that higher-dimensional operators only marginally affect the nucleation rate and the resulting observables. As a byproduct, we delineate the regime of validity of the high-temperature nucleation effective theory in supercooled phase transitions.

In this paper, we examine the thermodynamic behavior of a quantum harmonic oscillator with a position-dependent mass (PDM), where spatial inhomogeneity is modeled through a deformation parameter α. Based on the exact energy spectrum, we explore the resulting thermodynamic quantities and superstatistics. Our findings reveal that increasing α leads to a decrease in entropy and specific heat, reflecting a confinement-induced reduction in the number of accessible states. The partition function and free energy exhibit smooth behavior across all parameter regimes, indicating the absence of critical phase transitions. This study underscores the influence of mass deformation on quantum thermal responses and demonstrates that, while the overall thermodynamic trends are consistent with those reported in the literature, certain distinctive features emerge due to the specific form of the deformation.

Sampling from discrete distributions with multiple modes and energy barriers is fundamental to machine learning and computational physics. Recent discrete neural samplers like MDNS suffer from mode collapse and fail to sample high-energy barrier regions between modes, which is critical for free energy estimation and understanding phase transitions. We propose Metadynamics Discrete Neural Sampler (MetaDNS), a general framework integrating well-tempered metadynamics into discrete diffusion or autoregressive samplers. By maintaining an adaptive, history-dependent bias potential along selected low-dimensional coordinates, MetaDNS forces exploration of previously inaccessible regions, enabling free energy reconstruction infeasible with standard neural samplers due to a lack of high-energy samples. On challenging low-temperature benchmarks including Ising, Potts, and the copper-gold binary alloy, MetaDNS reproduces the thermodynamic distribution. Compared to MCMC-based metadynamics, MetaDNS also achieves comparable exploration requiring fewer bias deposition steps.

We develop a Gaussian comparison theory for posterior inference in non-Gaussian high-dimensional models. The framework allows for model misspecification and does not require the posterior distribution itself to be approximately Gaussian. Working directly with likelihood processes on separable function spaces, we establish explicit nonasymptotic free energy bounds controlled by first two moment discrepancies and local third moments. A perturbation-and-convexity argument transfers these comparisons to sandwich bounds for posterior mean squared error and posterior variance, including one-sided conclusions at nondifferentiable phase transitions. In high-dimensional product models, these conditions reduce to local moment controls and a canonical feature-radius scaling. Under weak regularity requirements, the resulting universality theory applies to a broad class of likelihood models, ranging from exponential families to more general regular local log-likelihoods. The framework is illustrated on sparse Bernoulli hypergraph inference.

We present a smoothly broken power law functional form (that we refer to as a Broken Neural Scaling Law (BNSL)) that accurately models & extrapolates the scaling behaviors of deep neural networks (i.e. how the evaluation metric of interest varies as amount of compute used for training (or inference), number of model parameters, training dataset size, model input size, number of training steps, or upstream performance varies) for various architectures & for each of various tasks within a large & diverse set of upstream & downstream tasks, in zero-shot, prompted, & finetuned settings. This set includes large-scale vision, language, audio, video, diffusion, generative modeling, multimodal learning, contrastive learning, AI alignment, AI capabilities, robotics, out-of-distribution (OOD) generalization, continual learning, transfer learning, uncertainty estimation / calibration, OOD detection, adversarial robustness, distillation, sparsity, retrieval, quantization, pruning, fairness, molecules, computer programming/coding, math word problems, "emergent phase transitions", arithmetic, supervised learning, unsupervised/self-supervised learning, & reinforcement learning (single agent & multi-agent). When compared to other functional forms for neural scaling, this functional form yields extrapolations of scaling behavior that are considerably more accurate on this set. Moreover, this functional form accurately models & extrapolates scaling behavior that other functional forms are incapable of expressing such as the nonmonotonic transitions present in the scaling behavior of phenomena such as double descent & the delayed, sharp inflection points present in the scaling behavior of tasks such as arithmetic. Lastly, we use this functional form to glean insights about the limit of the predictability of scaling behavior. Code is available at https://github.com/ethancaballero/broken_neural_scaling_laws

Online surgical phase recognition (SPR) underpins context-aware operating-room systems and requires committing to a prediction at every frame from past context alone. Surgical video poses three demands that natural-video recognizers do not jointly address: procedures span tens of thousands of frames, time flows non-uniformly as long routine stretches are punctuated by brief phase-defining transitions, and the visual domain is narrow so backbone features are strongly correlated across channels. Existing recognizers either let per-frame cost grow with elapsed length, or hold cost bounded but advance state at a uniform rate with channel-independent dynamics, leaving the latter two demands unaddressed. We present SurgicalMamba, a causal SPR model built on Mamba2's structured state-space duality (SSD) that holds per-frame cost at O(d). It introduces three SSD-compatible components, each targeting one demand: a dual-path SSD block that separates long- and short-term regimes at the level of recurrent state; intensity-modulated stepping, a continuous-time time-warp that adapts the slow path's effective rate to phase-relevant information; and state regramming, a per-chunk Cayley rotation that opens cross-channel mixing in the otherwise axis-aligned SSM recurrence. The learned rotation planes inherit a phase-aligned structure without any direct supervision, offering an interpretable internal signature of surgical workflow. Across seven public SPR benchmarks, SurgicalMamba reaches state-of-the-art accuracy and phase-level Jaccard under strict online evaluation: 94.6%/82.7% on Cholec80 (+0.7 pp/+2.2 pp over the strongest prior) and 89.5%/68.9% on AutoLaparo (+1.7 pp/+2.0 pp), at 119 fps on a single GPU. Ablations isolate the contribution of each component. The code is publicly available at https://github.com/sukjuoh/Surgical-Mamba.

Deterministic inference is a comforting ideal in classical software: the same program on the same input should always produce the same output. As large language models move into real-world deployment, this ideal has been imported wholesale into inference stacks. Recent work from the Thinking Machines Lab has presented a detailed analysis of nondeterminism in LLM inference, showing how batch-invariant kernels and deterministic attention can enforce bitwise-identical outputs, positioning deterministic inference as a prerequisite for reproducibility and enterprise reliability. In this paper, we take the opposite stance. We argue that, for LLMs, deterministic inference kills. It kills the ability to model uncertainty, suppresses emergent abilities, collapses reasoning into a single brittle path, and weakens safety alignment by hiding tail risks. LLMs implement conditional distributions over outputs, not fixed functions. Collapsing these distributions to a single canonical completion may appear reassuring, but it systematically conceals properties central to artificial cognition. We instead advocate Stochastic CHAOS, treating distributional variability as a signal to be measured and controlled. Empirically, we show that deterministic inference is systematically misleading. Single-sample deterministic evaluation underestimates both capability and fragility, masking failure probability under paraphrases and noise. Phase-like transitions associated with emergent abilities disappear under greedy decoding. Multi-path reasoning degrades when forced onto deterministic backbones, reducing accuracy and diagnostic insight. Finally, deterministic evaluation underestimates safety risk by hiding rare but dangerous behaviors that appear only under multi-sample evaluation.

The latest advancements in unsupervised learning of sentence embeddings predominantly involve employing contrastive learning-based (CL-based) fine-tuning over pre-trained language models. In this study, we analyze the latest sentence embedding methods by adopting representation rank as the primary tool of analysis. We first define Phase 1 and Phase 2 of fine-tuning based on when representation rank peaks. Utilizing these phases, we conduct a thorough analysis and obtain essential findings across key aspects, including alignment and uniformity, linguistic abilities, and correlation between performance and rank. For instance, we find that the dynamics of the key aspects can undergo significant changes as fine-tuning transitions from Phase 1 to Phase 2. Based on these findings, we experiment with a rank reduction (RR) strategy that facilitates rapid and stable fine-tuning of the latest CL-based methods. Through empirical investigations, we showcase the efficacy of RR in enhancing the performance and stability of five state-of-the-art sentence embedding methods.

Rotary positional embeddings (RoPE) are widely used in diffusion transformers (DiTs) to encode spatial relationships, yet their behavior with mixed-resolution tokens remains underexplored. A natural approach is to rescale token positions from different resolutions into a unified coordinate system before attention, but we show this fails. Our analysis shows that with RoPE, the attention similarity score is a highly structured and periodic function of token distance, so rescaling distances across resolutions moves token pairs to different regions of this periodic function, leading to incorrect attention scores. Motivated by this, we introduce Phase-Aligned Mixed-Resolution Attention (PMA), a training-free mechanism that stabilizes mixed-resolution attention. PMA modifies the RoPE position mapping to enforce a consistent positional scale for every query-key pair, ensuring that relative distances are evaluated under a single reference scale. To further improve local coherence near resolution transitions, we incorporate a lightweight boundary refinement module that softly exchanges features across adjacent scales. Experiments on image and video diffusion models validate our analysis and demonstrate consistent improvements in visual fidelity and computational efficiency.

We study finite-alphabet spin models on trees evolving under independent symmetric spin-flip dynamics. On the lattice the time-evolved plus measure of the low temperature Ising model in zero external field was shown to be non-quasilocal for all sufficiently large times in EnFeHoRe02. On the tree however the time-evolved plus phase of the Ising model behaves differently, as the quasilocal Gibbs property is first lost, but then recovered at a later time EnErIaKu12. We first extend this result by showing that large-time reentry into the quasilocal Gibbs regime on the tree happens more generally for all finite alphabet models, when the dynamics is started in f-stable Gibbs states. These are defined in terms of a time-independent sharp condition on the homogeneous recursion f describing the model, which can be checked explicitly. As our second and opposite result, we develop a method for proving large-time persistence of non-quasilocality of time-evolved measures. We show that even all configurations can become bad at large times, when the initial Gibbs measure corresponds to an f-saddle and give an explicit illustration for the Potts model. In our proofs we study the influence of spatially inhomogeneous perturbations to the solutions of a time-dependent fixed point problem.

Synchronization in one dimension displays generic scale invariance with universal properties previously observed in surface kinetic roughening and the wider context of the Kardar-Parisi-Zhang (KPZ) universality class. This has been established for phase oscillators and also for some limit-cycle oscillators, both in the presence of columnar (quenched) disorder and of time-dependent noise, by extensive numerical simulations, and has been analytically motivated by continuum approximations in the strong oscillator coupling limit. The robustness and the precise boundaries in parameter space for such critical behavior remain unclear, however, which may preclude further developments, including the extension of these results to higher dimensions and the experimental observation of nonequilibrium criticality in synchronizing (e.g.~electronic or chemical) oscillators. We here present complete numerical phase diagrams of one-dimensional synchronization, including saturation times and values, but, most importantly, also dynamical features giving insight into the gradual emergence of synchronous dynamics, based on systems of phase oscillators with either type of randomness. In the absence of synchronization, the dynamics evolves as expected for random deposition (for time-dependent noise) or linear growth (for columnar disorder), while a crossover from Edwards-Wilkinson to Kardar-Parisi-Zhang behavior (with the corresponding type of randomness) is observed as the randomness strength, or the nonoddity of the coupling among oscillators, is increased in the synchronous region -- their combined effect being partially captured by the so-called KPZ coupling. The distortion of scaling due to phase slips near the desynchronization boundary, a feature that is likely to play a role in experimental contexts, is also discussed.

We present a unified gait-conditioned reinforcement learning framework that enables humanoid robots to perform standing, walking, running, and smooth transitions within a single recurrent policy. A compact reward routing mechanism dynamically activates gait-specific objectives based on a one-hot gait ID, mitigating reward interference and supporting stable multi-gait learning. Human-inspired reward terms promote biomechanically natural motions, such as straight-knee stance and coordinated arm-leg swing, without requiring motion capture data. A structured curriculum progressively introduces gait complexity and expands command space over multiple phases. In simulation, the policy successfully achieves robust standing, walking, running, and gait transitions. On the real Unitree G1 humanoid, we validate standing, walking, and walk-to-stand transitions, demonstrating stable and coordinated locomotion. This work provides a scalable, reference-free solution toward versatile and naturalistic humanoid control across diverse modes and environments.

Brittle materials subjected to thermal shocks experience strong temperature gradients that in turn give rise to mechanical stresses that can be large enough to induce fracture. This work presents a complete model for phase-field fracture for coupled thermo-mechanical problems, wherein the bulk material properties, the material strength, and the fracture toughness are specified independently. The capabilities of the model are assessed across a wide span of scenarios in thermo-mechanical fracture, from the propagation of large pre-existing cracks to crack nucleation under spatially uniform states of stress. In particular, we revisit the controlled quenching of glass plates, and demonstrate how the model captures experimentally observed crack patterns across a range of thermal loads. Ceramic disks subjected to infrared radiation are also examined, with the model reproducing both straight cracks in notched specimens and branching in intact specimens. Finally, ceramic pellets subjected to rapid power pulses are examined, with the model explaining experimental transitions from intact to fractured pellets and the important role of material strength. The results demonstrate that the complete phase-field model unifies the treatment of distinct fracture scenarios under thermal shock, surpassing classical approaches and enabling more reliable prediction of brittle fracture in extreme environments.

Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after training for sufficiently longer, it suddenly transitions to perfect test accuracy. This paper studies the grokking phenomenon in theoretical setups and shows that it can be induced by a dichotomy of early and late phase implicit biases. Specifically, when training homogeneous neural nets with large initialization and small weight decay on both classification and regression tasks, we prove that the training process gets trapped at a solution corresponding to a kernel predictor for a long time, and then a very sharp transition to min-norm/max-margin predictors occurs, leading to a dramatic change in test accuracy.

Moiré semiconductors provide a physical realization of the Hubbard model. Bandwidth-tuned Mott transitions and complex phase diagrams mimicking those of high-temperature superconductors have been demonstrated near a weak Mott insulating state at half-band-filling. The platform also provides an opportunity to explore the physics of a partially filled Hubbard band at doping densities far away from the Mott insulator, a regime that has remained largely unexplored. Here we report the emergence of an extended strange metal (ESM), in both doping density and twist angle, in a partially filled Hubbard band of twisted bilayer WSe2. The ESM is in the clean limit, persists down to 100mK, and spans over multiple symmetry-breaking ground states; it also appears only at small twist angles, where electronic correlations are strong. These observations distinguish the state from the reported strange metals associated with quantum criticality and favor the viewpoint that it is an intrinsic state of matter. We also report the observation of a new superconducting dome being developed from the ESM but far away from both the Mott insulating state and the van Hove singularity of the material. Our work opens the door to exploring the new regime of partially filled Hubbard bands in the clean limit.

Standard game theory explains cooperation in repeated games through conditional strategies such as Tit-for-Tat (TfT), but these require continuous computation that imposes physical costs on embodied agents. We propose a three-layer Body-Reservoir Governance (BRG) architecture: (1) a body reservoir (echo state network) whose d-dimensional state performs implicit inference over interaction history, serving as both decision-maker and anomaly detector, (2) a cognitive filter providing costly strategic tools activated on demand, and (3) a metacognitive governance layer with receptivity parameter αin [0,1]. At full body governance (α=1), closed-loop dynamics satisfy a self-consistency equation: cooperation is expressed as the reservoir's fixed point, not computed. Strategy complexity cost is defined as the KL divergence between the reservoir's state distribution and its habituated baseline. Body governance reduces this cost, with action variance decreasing up to 1600times with dimension d. A dynamic sentinel generates a composite discomfort signal from the reservoir's own state, driving adaptive α(t): near baseline during cooperation, rapidly dropping upon defection to activate cognitive retaliation. Overriding the body incurs thermodynamic cost proportional to internal state distortion. The sentinel achieves the highest payoff across all conditions, outperforming static body governance, TfT, and EMA baselines. A dimension sweep (d in {5,ldots,100}) shows implicit inference scales with bodily richness (23times to 1600times variance reduction), attributable to reservoir dynamics. A phase diagram in (d, τ_{env}) space reveals governance regime transitions near d approx 20. The framework reinterprets cooperation as the minimum-dissipation response of an adapted dynamical system -- emergent from embodied dynamics rather than computed.

We present Forge-UGC (FX Optimization and Register-Graph Engine for Universal Graph Compilation), a four-phase compiler for transformer deployment on heterogeneous accelerator hardware, validated on Intel AI Boost NPU. Existing frameworks such as OpenVINO and ONNX Runtime often use opaque compilation pipelines, limited pass-level visibility, and weak buffer management, which can lead to higher compilation cost and runtime overhead. Forge-UGC addresses this with a hardware-agnostic design that separates graph capture, optimization, intermediate representation lowering, and backend scheduling. Phase 1 captures graphs with torch.export at the ATen operator level, supporting modern transformer components such as rotary position embeddings, grouped-query attention, and SwiGLU without manual decomposition. Phase 2 applies six optimization passes: dead code elimination, common subexpression elimination, constant folding, attention fusion, operator fusion, and layout optimization, reducing graph node count by 14.2 to 21.9%. Phase 3 lowers the optimized graph into a typed intermediate representation with explicit virtual register assignments. Phase 4 performs liveness analysis, linear-scan buffer allocation, reducing peak buffer count by 30 to 48%, and device-affinity scheduling, reducing NPU-CPU transitions by 42 to 65%. Across six model families ranging from 125M to 8B parameters, evaluated on WikiText-103 and GLUE, Forge-UGC delivers 6.9 to 9.2x faster compilation than OpenVINO and ONNX Runtime, 18.2 to 35.7% lower inference latency, and 30.2 to 40.9% lower energy per inference. Fidelity is preserved, with max absolute logit differences below 2.1e-5 and KL divergence below 8.4e-9. We also introduce Fusion Gain Ratio, Compilation Efficiency Index, and per-pass execution profiling for systematic evaluation of NPU compilation pipelines.

Neural networks acquire structured representations at specific moments during training, yet identifying these transitions typically relies on retrospective, label-dependent metrics. We introduce a bifurcation theory of representation dynamics to detect these moments in real time. Analyzing a passive GMM probe attached to the evolving encoder, we show the onset of structure corresponds to a supercritical pitchfork bifurcation driven by the loss Hessian. The system exhibits a theoretically predictable zero-crossing (β_c) that, compared to the network's current state (β), yields a dynamic ratio β(t)/β_c(t): a universal, label-free phase coordinate for representation dynamics, computable entirely from hidden states. We empirically validate four distinct transition regimes predicted by this coordinate across diverse settings: SAEs on language models (Pythia), SSL (CIFAR), and grokking (modular arithmetic). Crucially, under finite dissipation, macroscopic symmetry-breaking can lag the initial zero-crossing by orders of magnitude, which providing a rigorous dynamical account of the delayed escape observed in grokking. Microscopically, the bifurcation creates a shared unstable subspace, forcing collective symmetry breaking. We term this the "feature lottery" in SAE training: a feature's terminal interpretability becomes predictable remarkably early. By only 5% of training, early atom purity robustly predicts final convergence purity, with top-decile early atoms achieving over 12x the baseline purity at convergence. Beyond explaining concept emergence, β/β_c provides a practical early-warning indicator for training health, detecting the onset of usable structure, the crystallization of feature identity, and representational collapse epochs before downstream metrics react.

Bidirectional video diffusion models denoise entire videos in parallel, yet when trained on effectively unlimited in-distribution data from procedural generators, continue to violate physical laws and simple symbolic rules. We introduce Serial-to-Parallel Diffusion (S2PD), which performs autoregressive diffusion at high noise before switching to parallel diffusion at low noise. The autoregressive phase provides the serial computation needed to coordinate interdependent events and produce valid state transitions while the parallel phase jointly refines the entire video and reduces sampling time relative to fully serial generation. We implement S2PD with two architectures: a pixel-space diffusion transformer trained from scratch and a pretrained video model adapted through LoRA fine-tuning with causal attention. Across games, physical simulations, and real video, S2PD follows rules more reliably than matched bidirectional baselines and generates videos with greater temporal stability and sampling efficiency than other serial methods.

This paper presents AlphaOne (alpha1), a universal framework for modulating reasoning progress in large reasoning models (LRMs) at test time. alpha1 first introduces alpha moment, which represents the scaled thinking phase with a universal parameter alpha. Within this scaled pre-alpha moment phase, it dynamically schedules slow thinking transitions by modeling the insertion of reasoning transition tokens as a Bernoulli stochastic process. After the alpha moment, alpha1 deterministically terminates slow thinking with the end-of-thinking token, thereby fostering fast reasoning and efficient answer generation. This approach unifies and generalizes existing monotonic scaling methods by enabling flexible and dense slow-to-fast reasoning modulation. Extensive empirical studies on various challenging benchmarks across mathematical, coding, and scientific domains demonstrate alpha1's superior reasoning capability and efficiency. Project page: https://alphaone-project.github.io/

Graphical User Interface (GUI) Agents, powered by large language and vision-language models, hold promise for enabling end-to-end automation in digital environments. However, their progress is fundamentally constrained by the scarcity of scalable, high-quality trajectory data. Existing data collection strategies either rely on costly and inconsistent manual annotations or on synthetic generation methods that trade off between diversity and meaningful task coverage. To bridge this gap, we present GUI-ReWalk: a reasoning-enhanced, multi-stage framework for synthesizing realistic and diverse GUI trajectories. GUI-ReWalk begins with a stochastic exploration phase that emulates human trial-and-error behaviors, and progressively transitions into a reasoning-guided phase where inferred goals drive coherent and purposeful interactions. Moreover, it supports multi-stride task generation, enabling the construction of long-horizon workflows across multiple applications. By combining randomness for diversity with goal-aware reasoning for structure, GUI-ReWalk produces data that better reflects the intent-aware, adaptive nature of human-computer interaction. We further train Qwen2.5-VL-7B on the GUI-ReWalk dataset and evaluate it across multiple benchmarks, including Screenspot-Pro, OSWorld-G, UI-Vision, AndroidControl, and GUI-Odyssey. Results demonstrate that GUI-ReWalk enables superior coverage of diverse interaction flows, higher trajectory entropy, and more realistic user intent. These findings establish GUI-ReWalk as a scalable and data-efficient framework for advancing GUI agent research and enabling robust real-world automation.

In heterogeneous networks of coupled oscillators, phase frustration typically prevents the emergence of synchronization in the Sakaguchi--Kuramoto (SK) model. In this study, we propose an analytical framework to overcome this barrier and induce complete synchronization at a specified small coupling value in oscillators governed by phase-frustrated bi-harmonic coupling. We derive an optimal set of natural frequencies that is robust against added noise and correlated with the network degree heterogeneity, along with the parameters involved in the bi-harmonic coupling function that lead to complete synchronization (r = 1). In addition, we find complete synchronization transitions accompanied by hysteresis in scale-free networks, indicating a first-order (discontinuous) phase transition, whereas Erdős--Rényi networks exhibit complete synchronization through a second-order (continuous) phase transition. Furthermore, we use the mean-field approximation in the presence of optimal frequencies to determine the critical coupling strength associated with the synchronization transition in the pure second-harmonic Sakaguchi--Kuramoto model. Here, the obtained optimal natural frequencies scale linearly with the node degree, and the critical coupling strength for the onset of synchronization is derived analytically from the self-consistent equations. In this specific regime, we observe a perfectly ordered two-cluster synchronized state. These findings remain robust for higher-order harmonic coupling schemes, as well as across a diverse range of synthetic and empirical networks, including scale-free, Erdős--Rényi, Zachary Karate Club, and the C.~elegans neural network, demonstrating their general applicability.

We present a comprehensive numerical study of a six-state clock model with a long-range dipolar type interaction. This model is motivated by the ferroelectric orders in the multiferroic hexagonal manganites. At low temperatures, trimerization of local atomic structures leads to six distinct but energetically degenerate structural distortion, which can be modeled by a six-state clock model. Moreover, the atomic displacements in the trimerized state further produce a local electric polarization whose sign depends on whether the clock variable is even or odd. These induced electric dipoles, which can be modeled by emergent Ising degrees of freedom, interact with each other via long-range dipolar interactions. Extensive Monte Carlo simulations are carried out to investigate low temperature phases resulting from the competing interactions. Upon lowering temperature, the system undergoes two Berezinskii-Kosterlitz-Thouless (BKT) transitions, characteristic of the standard six-state clock model in two dimensions. The dipolar interaction between emergent Ising spins induces a first-order transition into a ground state characterized by a three-fold degenerate stripe order. The intermediate phase between the discontinuous and the second BKT transition corresponds to a maze-like hexagonal liquid with short-range stripe ordering. Moreover, this intermediate phase also exhibits an unusual ferromagnetic order with two adjacent clock variables occupying the two types of stripes of the labyrinthine pattern.

This paper identifies significant redundancy in the query-key interactions within self-attention mechanisms of diffusion transformer models, particularly during the early stages of denoising diffusion steps. In response to this observation, we present a novel diffusion transformer framework incorporating an additional set of mediator tokens to engage with queries and keys separately. By modulating the number of mediator tokens during the denoising generation phases, our model initiates the denoising process with a precise, non-ambiguous stage and gradually transitions to a phase enriched with detail. Concurrently, integrating mediator tokens simplifies the attention module's complexity to a linear scale, enhancing the efficiency of global attention processes. Additionally, we propose a time-step dynamic mediator token adjustment mechanism that further decreases the required computational FLOPs for generation, simultaneously facilitating the generation of high-quality images within the constraints of varied inference budgets. Extensive experiments demonstrate that the proposed method can improve the generated image quality while also reducing the inference cost of diffusion transformers. When integrated with the recent work SiT, our method achieves a state-of-the-art FID score of 2.01. The source code is available at https://github.com/LeapLabTHU/Attention-Mediators.

Current video generation techniques excel at single-shot clips but struggle to produce narrative multi-shot videos, which require flexible shot arrangement, coherent narrative, and controllability beyond text prompts. To tackle these challenges, we propose MultiShotMaster, a framework for highly controllable multi-shot video generation. We extend a pretrained single-shot model by integrating two novel variants of RoPE. First, we introduce Multi-Shot Narrative RoPE, which applies explicit phase shift at shot transitions, enabling flexible shot arrangement while preserving the temporal narrative order. Second, we design Spatiotemporal Position-Aware RoPE to incorporate reference tokens and grounding signals, enabling spatiotemporal-grounded reference injection. In addition, to overcome data scarcity, we establish an automated data annotation pipeline to extract multi-shot videos, captions, cross-shot grounding signals and reference images. Our framework leverages the intrinsic architectural properties to support multi-shot video generation, featuring text-driven inter-shot consistency, customized subject with motion control, and background-driven customized scene. Both shot count and duration are flexibly configurable. Extensive experiments demonstrate the superior performance and outstanding controllability of our framework.

We introduce the Ignition Index (I), a validated scalar metric that operationalizes Global Workspace Theory's (GWT) all-or-none ignition prediction in transformer language models. The metric fits a four-parameter sigmoid to per-layer linear probe accuracy as a function of input signal strength, extracting steepness parameter beta-hat: high values indicate abrupt, ignition-like transitions; low values indicate graded build-up. Across 11 models spanning five architecture families, shuffled-label controls demonstrate 9.6-fold selectivity for genuine linguistic structure over spurious probe capacity (p < 0.001, Mann-Whitney U-test). We find: (1) Feedforward transformers exceed SSMs by 89% in aggregate beta-hat (p < 1e-13, Cohen's d = 0.52), with Mamba exhibiting near-linear profiles consistent with absent global broadcast. (2) Huginn-3.5B exhibits 2.12-fold higher ignition along its iteration axis than its depth axis, demonstrating that recurrent architectures manifest workspace-like transitions along the recurrence dimension. (3) Pythia-410M shows a PELT-detected phase transition at training step 256 (+67%), preceding induction-head formation. (4) Hypotheses linking ignition to model scale and signal strength were not confirmed, suggesting transformer architectures may saturate available ignition mechanisms. The Ignition Index provides the first validated quantitative bridge between GWT's dynamical predictions and mechanistic interpretability, with 9.6-fold measurement selectivity and architecture-level discriminability not previously characterized in the scaling literature. Code: https://github.com/saman-rahbar/ignition-index

Long-horizon agents can fail even when their underlying models can solve the constituent steps. They may lose track of mutable state, fail to reactivate lessons from earlier executions, skip known procedures, or stop prematurely. We bet on harness scaling to improve the execution system around an agent without changing its model weights. We introduce StateM, an agent-native runtime that organizes execution around durable states, phase-local context, checked transitions, recoverable runbooks, and versioned procedural practices that agents and users can inspect together. On Terminal-Bench 2.1, StateM raises GPT-5.5 xhigh to 92.1\%, versus 83.1\% reference and GPT-5.6 Sol Ultra at 91.9\%. The runbook transfers unchanged to GPT-5.6. With GPT-5.6 Sol xhigh, StateM reaches 95.3\% raw accuracy across 445 trials and succeeds on all 89 tasks at least once. The frozen profile raises GPT-5.6 Luna from 76.7 to 85.4\%, above the 84.9\% Sol xhigh reference. Using the same runtime, runbook structure, and golden rules, less than \38 of adaptation raises DeepSeek-V4 Flash from 82.7 to 88.1% under standard timeouts and to 89.1% on an 88-task common core. Extending only the remaining latency-sensitive task matches the reported 88.8% GPT-5.6 Sol max result. Final-score API usage is about 15 versus \574.68 for the GPT reference; total DeepSeek expenditure is 52.22. On BusinessBench, family-specific runbooks built on development sets yield held-out gains of 0.55 macro and 1.34 micro points; two mechanism-matched families improve by 10.04 points. Concrete rules generalize when tasks share execution structure, while the control methodology applies broadly. StateM turns selected postmortem findings into persistent, executable preconditions and practices, making learned controls explicit and enforceable through stateful controls. Code at github.com/henryqin1997/statem.

Vision-language models (VLMs) are increasingly explored as visual critics, reward generators, and failure detectors in robotic manipulation. These roles implicitly require models to judge not only final task success, but also how a manipulation execution is physically and temporally progressing. However, existing evaluations fail to test whether VLMs possess fine-grained process understanding. To address this gap, we present RoboProcessBench, a benchmark for process-aware understanding in vision-language robotic manipulation. RoboProcessBench decomposes such capability into two complementary dimensions, static monitoring and dynamic reasoning, instantiated as 12 diagnostic question families covering phase, contact, motion, coordination, primitive-local progress, temporal order, outcome, and primitive-level transitions. Built from physically grounded execution traces, the curated benchmark corpus ProcessData contains \textasciitilde 58k question-answer pairs across 260 manipulation tasks, which is further split into ProcessData-SFT and ProcessData-Eval for post-training and evaluation purposes. Extensive evaluation of various VLMs on ProcessData-Eval reveals broad limitations across 12 diagnostic task families, suggesting current models still lack robust process-aware understanding of manipulation executions. But with ProcessData-SFT, the post-trained Qwen2.5-VL-7B and InternVL-3-8B exhibit consistent gains on local state, motion, progress, and primitive-aware cues. These results demonstrate that RoboProcessBench serves as both an evaluation benchmark and a learnable supervision source for developing VLMs capable of monitoring and evaluating robotic manipulation processes. Project webpage: https://processbench-2026.github.io/RoboProcessBench-Web/{https://processbench-2026.github.io}.

Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. Each leaf agent is summarized by a compute-performance scaling exponent β; communication is captured by a message-length fidelity curve γ(m); dependence is captured by an effective shared-error correlation ρ; and a context window W imposes hard fan-in limits that make hierarchy necessary. For binary success/failure tasks with majority aggregation, we prove a sharp phase transition for deep b-ary trees with correlated inputs and lossy communication: a single scalar α_ρ (combining γ(m), ρ, and fan-in b) determines whether weak signal is amplified to a nontrivial fixed point or washed out to chance. In the amplifying regime, we derive an organization exponent s and show that budgeted synergy, i.e., outperforming the best single agent under the same total budget, occurs exactly when s>β, yielding closed-form compute allocation rules and explicit budget thresholds. We further characterize saturation via a mixing depth and provide a conservative clipped predictor that remains accurate across growth and saturation. A continuous-performance warm-up gives closed-form risks for star, chain, and tree organizations, making correlation- and communication-induced floors explicit and exposing the core design trade-offs in a smooth setting. Finally, we validate the predicted phase boundaries in controlled synthetic simulations and show how the same mechanisms explain the dominant bottlenecks reported in recent large-scale matched-budget studies of LLM agent-system scaling.

Memory systems can store vastly different amounts of information despite similar hardware constraints. Here, we show that superior spatial memory emerges from a discrete stiffening of hippocampal population geometry-a transition from disorganized to crystalline collective coding. Comparing food-caching chickadees to non-caching zebra finches, we found that the caching hippocampus maintains a topologically rigid, "crystalline" geometry with significantly higher geometric stability (Shesha 0.245 v 0.166) and nearly two-fold greater temporal coherence (Shesha 0.393 v 0.209), while the non-caching hippocampus resembles a disorganized "mist." This stability is actively constructed by synergistic circuit dynamics: excitatory neurons form the spatial scaffold while inhibitory populations contribute orthogonal decorrelation, a circuit motif in which excitatory and inhibitory populations occupy largely non-overlapping representational subspaces. A double dissociation with Valiant's Stable Memory Allocator, a model predicting that dedicated neuron ensembles underlie each memory, confirms this advantage reflects continuous topological organization rather than discrete neuron allocation: caching networks exhibit near-zero split-half allocation reliability despite their geometric superiority. Computational modeling across 10k configurations reveals topological rigidity as the mathematical prerequisite for scale: crystalline codes sustain high-fidelity readout beyond M=1k locations while mist codes fail below M=10, a >100-fold capacity advantage. This capacity requires a 169fold representational redundancy: a "geometric tax" stabilizing the manifold against biological noise. These results establish geometric stability as a candidate organizing principle of biological memory: evolution achieves high-capacity memory not by proliferating neurons, but by engineering the geometry of the neural code itself.

The local structure of V_{2}O_{3}, an archetypal strongly correlated electron system that displays a metal-insulator transition around 160 K, has been investigated via pair distribution function (PDF) analysis of neutron and x-ray total scattering data. The rhombohedral-to-monoclinic structural phase transition manifests as an abrupt change on all length scales in the observed PDF. No monoclinic distortions of the local structure are found above the transition, although coexisting regions of phase-separated rhombohedral and monoclinic symmetry are observed between 150 K and 160 K. This lack of structural fluctuations above the transition contrasts with the known presence of magnetic fluctuations in the high-temperature state, suggesting that the lattice degree of freedom plays a secondary role behind the spin degree of freedom in the transition mechanism.

For long-range percolation on Z with translation-invariant edge kernel J, it is a classical theorem of Aizenman and Newman (1986) that the phase transition is discontinuous when J(x,y) is of order |x-y|^{-2} and that there is no phase transition at all when J(x,y)=o(|x-y|^{-2}). We prove a strengthened version of this theorem for the hierarchical lattice, where the relevant threshold is at |x-y|^{-2d} loglog |x-y| rather than |x-y|^{-2}: There is a continuous phase transition for kernels of larger order, a discontinuous phase transition for kernels of exactly this order, and no phase transition at all for kernels of smaller order. As such, |x-y|^{-2d} loglog |x-y| is essentially the only kernel that produces a discontinuous phase transition. We also prove a hierarchical analogue of the ``M^2β=1'' conjecture of Imbrie and Newman (1988), which gives an exact formula for the density of the infinite cluster at the point of discontinuous phase transition and remains open in the Euclidean setting.

Scaling laws predict loss from compute but not how capabilities interact. We measure the coupling between reasoning and truthfulness across 63 base models from 16 families and find a regime change invisible to loss curves: below a family-dependent critical scale N_c, capabilities anticorrelate; above it, they cooperate. N_c approx 3.5B parameters [2.9B, 13.4B] (bootstrap 95% CI), but model size is not the only variable that determines phase. Architecture, data curation, and training recipe each shift N_c independently: curated training eliminated the coupling dip between Qwen generations (0.025 to 0.830 at matched scale), Gemma-4 at 4B achieves coupling 0.871, characteristic of 13B+ standard-trained models, through distillation and architectural innovation, and Phi at 1B matches web-trained coupling at 10B through data curation alone. Width normalization eliminates the anticorrelation across all tested families, supporting an output-projection bottleneck. Internally, 38 of 40 models show zero competing attention heads. A sparse-regression ODE cross-predicts held-out Llama-2 at 5.6% error. The diagnostic requires no model internals -- only public benchmark scores across a model family. The cooperative regime extends to the frontier (r = +0.72, 34 models, 10 labs). Code, data, and an open-source activation-steering tool for any open-weight model are released alongside an interactive dashboard that diagnoses any model's coupling phase, suggests concrete interventions (data curation, width, benchmark rotation), and provides ODE scaling predictions, frontier diagnostics, and eigenstructure analysis: https://zehenlabs.com/cape/.

We study the Cauchy problem for the one-dimensional isothermal compressible Navier--Stokes system with the van der Waals equation of state, and analyze the well-posedness and asymptotic stability of steady-state phase-transition solutions at subcritical temperatures. Working in Lagrangian coordinates, we use variational techniques to construct piecewise smooth steady-state solutions corresponding to two-phase equilibrium states under finite-mass perturbations. Introducing artificial-viscosity regularization, we first establish existence of the global minimizer of the regularized variational problem, unique within each fixed symmetry class; passing to the vanishing artificial-viscosity limit then yields a physically admissible steady-state solution with two phase interfaces. For initial perturbations that are small with respect to energy, piecewise-gradient, total-variation, and integral norms but may exhibit large pointwise jumps across phase boundaries, we derive uniform a priori bounds for weak solutions near the two-phase equilibrium profile. We further prove that these global weak solutions converge to the steady-state two-phase equilibrium in L^infty(R) as ttoinfty, thereby characterizing their large-time asymptotic behavior. Physically, finite mass perturbations break the uniqueness of the uniform steady state and generate infinitely many piecewise constant two-phase equilibria satisfying the Maxwell equal-area rule. Artificial viscosity acts as a selection principle that singles out the physically relevant two-interface steady-state configuration, and this two-phase equilibrium is asymptotically stable under small integral perturbations that allow large-amplitude discontinuities at phase interfaces.

Water looks unchanged as it warms, then at a critical point it boils. We ask whether long-horizon language agents show an analogous transition in their implicit world models. In some parameter settings, changing state load by a small amount, or adding a single step of horizon, leaves behavior nearly unchanged; near a critical boundary, the same small change causes a sudden world collapse. We study this effect in a deterministic task family with exact per-step gold state. A large grid search over state cardinality, dependency density, horizon, branching, observation mode, and mutation rate reveals a phase diagram: a solved plateau, a narrow transition band, and a collapse floor. Per-step traces show the mechanism: world-state fidelity fails before action validity, so the agent is not merely choosing a bad action; it is acting from a corrupted world. Stronger models translate the critical boundary but do not remove the qualitative transition. These results make world-model collapse a measurable bottleneck for long-horizon agents.

Alloys with a first-order magnetic transition are central to solid-state refrigeration technology, sensors and actuators, or spintronic devices. The discontinuous nature of the transition in these materials is a consequence of the coupling between the magnetic, electronic and structural subsystems, but in a real experiment, it is difficult to observe and analyze the simultaneous evolution of all the subsystems. As a result, it is very hard to determine the main mechanisms of the transition and purposefully develop these advanced magnetic materials. To resolve this issue, we changed the existing paradigm and conducted simultaneous measurements of the macroscopic properties - magnetization, temperature change of the sample, longitudinal and transversal magnetostrictions - to reveal the rich details of the magneto-structural, first-order transition occurring in the prototypical alloy LaFe11.8Si1.2. We complement these findings with experiments on the atomistic scale, i.e., x-ray absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD) and Mössbauer spectroscopy, and then combine them with first-principles calculations to reveal the full complexity and two-stage nature of the transition. This new approach can be successfully extended to a large class of advanced magnetic materials that exhibit analogous transformations.

Motivated by the recent observation of spatially modulated screening in different paramagnetic heavy-fermion materials, we propose a theoretical mechanism for the emergence of such hybridization waves in frustrated Kondo lattices with no magnetic order. By applying a parton mean-field theory and a perturbative calculation to a minimal Kondo-Heisenberg lattice model, we demonstrate that a heavy Fermi liquid can naturally develop hybridization waves when it approaches a quantum phase transition where Kondo screening breaks down and the local magnetic moments form a Dirac spin liquid. We relate the strength of this mechanism to a kinematic condition on the electronic and spinon band structures and show that the spatial periodicity of the hybridization wave is set by a momentum Q connecting the nodes in the dispersion of the Dirac spinons to low-energy portions of the electronic band structure.

Quantum annealers are commercial devices aiming to solve very hard computational problems named spin glasses. Just like in metallurgic annealing one slowly cools a ferrous metal, quantum annealers seek good solutions by slowly removing the transverse magnetic field at the lowest possible temperature. The field removal diminishes quantum fluctuations but forces the system to traverse the critical point that separates the disordered phase (at large fields) from the spin-glass phase (at small fields). A full understanding of this phase transition is still missing. A debated, crucial question regards the closing of the energy gap separating the ground state from the first excited state. All hopes of achieving an exponential speed-up, as compared to classical computers, rest on the assumption that the gap will close algebraically with the number of qspins, but renormalization group calculations predict that the closing will be instead exponential. Here we solve this debate through extreme-scale numerical simulations, finding that both parties grasped parts of the truth. While the closing of the gap at the critical point is indeed super-algebraic, it remains algebraic if one restricts the symmetry of possible excitations. Since this symmetry restriction is experimentally achievable (at least nominally), there is still hope for the Quantum Annealing paradigm.

The Verwey transition in magnetite is a benchmark electronically driven phase transition that is highly sensitive to lattice imperfections and external perturbations. Doping, deviations from oxygen stoichiometry, and irradiation-induced point defects are known to lower the Verwey transition temperature, T_{rm V}. By contrast, the role of remanent strain fields and extended defect structures generated by uniaxial stress has remained largely unexplored. Here we combine dark-field x-ray microscopy (DFXM) and ac magnetic susceptibility to determine how strain-induced defects affect the Verwey transition in stoichiometric single-crystalline magnetite after uniaxial compression and unloading. The DFXM measurements were performed on two samples compressed along the same [011] direction: loading to 200~MPa generated stable line-like defects and remanent strain fields, whereas loading beyond the fracture threshold produced denser defect networks and mechanical fracture. To test the effect of a different loading geometry, we also measured the ac susceptibility of a sample fractured by compression along [001]. Real-space DFXM imaging, lattice-orientation mapping, and residual strain mapping show substantial remanent structural disorder after compression. Nevertheless, neither the transition temperature T_{rm V} nor the sharpness of the transition changes measurably in any of the compressed or fractured samples. This behavior contrasts with the strong suppression of T_{rm V} by point-like disorder. Our results show that extended line-like defects and remanent strain fields produced by plastic deformation do not measurably perturb the macroscopic electronic ordering responsible for the Verwey transition, thereby distinguishing the effects of point defects from those of extended slip-related defects in magnetite.

We investigate the effects of the sharpness of the phase transition between hadronic matter and quark matter on various properties of neutron stars. We construct hybrid equations of state by combining a hadronic model with a quark model using a Gaussian function. This approach introduces a smooth transition characterized by two parameters: one representing the overpressure relative to the first-order phase transition point, and the other related to the range over which the hybrid region extends in baryon chemical potential. We find that the sharpness of the phase transition significantly influences the equation of state, which can deviate by several tens of MeV fm^{-3} from the one with a sharp first-order transition. The speed of sound exhibits diverse behaviors, including drastic drops, pronounced peaks, and oscillatory patterns, depending on the sharpness parameters. In terms of stellar structure, while the maximum neutron star mass remains largely unaffected by the sharpness of the phase transition, the stellar radii can vary significantly. Smoother transitions lead to a leftward shift (up to 1 km) of the mass-radius curve segment corresponding to hybrid stars. The tidal deformability decreases with smoother transitions, especially for higher-mass stars. Our results are quite general and do not qualitatively depend on the specific hadronic and quark matter models employed. In fact, the hybrid equation of state and stellar properties derived from microscopic models of quark-hadron pasta phases display the same behavior as described above.

The Sherrington-Kirkpatrick spin-glass model used the replica symmetry method to find the phase transition of the system. In 1979-1980, Parisi proposed a solution based on replica symmetry breaking (RSB), which allowed him to identify the underlying phases of complex systems such as spin-glasses. Regardless of the method used for detection, the intrinsic phase of a system exists whether or not replicas are considered. We introduce a single replica method of spin-glass phase detection using the field's variation experienced by each spin in a system configuration. This method focuses on a single replica with quenched random couplings. Each spin inevitably observes a different field from the others. Our results show that the mean and variance of fields named "Spontaneous Configurational Field" experienced by spins are suitable indicators to explore different ferromagnetic, paramagnetic, and mixed phases. To classify different phases of the system with defined indicators we have developed an algorithm based on machine learning to analyze the desired samples.