Daily Papers

We propose JFR, a Bellman-Ford-based optimization framework leveraging frontier contraction and abstract multi-hop jump propagation to accelerate shortest-path computation while strictly preserving correctness. JFR achieves substantial reductions in relaxation operations, ranging from 25 to 99 percent, across sparse, dense, and negative-edge graphs, ensuring robust performance even under adversarial or highly connected topologies. On ultra-large graphs with up to N=20,000 nodes and 295 million edges, JFR maintains strong operational reductions and comparable or improved runtime relative to SPFA-SLF, demonstrating consistent robustness across graph size and density. Lower relaxation counts imply reduced memory-access overheads and computational effort; this normalized work reduction highlights JFR's suitability for scenarios requiring high throughput or energy-conscious operation. Future work focuses on integrating high-performance queue structures, adaptive frontier strategies, and cache-aware techniques to further reduce constant-factor overheads and fully realize JFR's practical runtime potential.

Combinatorial problems are a common challenge in business, requiring finding optimal solutions under specified constraints. While significant progress has been made with variational approaches such as QAOA, most problems addressed are unconstrained (such as Max-Cut). In this study, we investigate a hybrid quantum-classical method for constrained optimization problems, particularly those with knapsack constraints that occur frequently in financial and supply chain applications. Our proposed method relies firstly on relaxations to local quantum Hamiltonians, defined through commutative maps. Drawing inspiration from quantum random access code (QRAC) concepts, particularly Quantum Random Access Optimizer (QRAO), we explore QRAO's potential in solving large constrained optimization problems. We employ classical techniques like Linear Relaxation as a presolve mechanism to handle constraints and cope further with scalability. We compare our approach with QAOA and present the final results for a real-world procurement optimization problem: a significant sized multi-knapsack-constrained problem.

Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether this is due to fundamental limitations of convex relaxations. Initial work investigating this question focused on the simple and widely used IBP relaxation. It revealed that some univariate, convex, continuous piecewise linear (CPWL) functions cannot be encoded by any ReLU network such that its IBP-analysis is precise. To explore whether this limitation is shared by more advanced convex relaxations, we conduct the first in-depth study on the expressive power of ReLU networks across all commonly used convex relaxations. We show that: (i) more advanced relaxations allow a larger class of univariate functions to be expressed as precisely analyzable ReLU networks, (ii) more precise relaxations can allow exponentially larger solution spaces of ReLU networks encoding the same functions, and (iii) even using the most precise single-neuron relaxations, it is impossible to construct precisely analyzable ReLU networks that express multivariate, convex, monotone CPWL functions.

The thermal relaxation time of neutron stars, typically defined by a sudden drop in surface temperature, is usually on the order of 10 to 100 years. In this study, we investigate neutron star thermal relaxation by incorporating nucleon superfluidity and non-nucleonic particles, specifically considering hyperons as a representative case. We find that rapidly cooling neutron stars driven by neutron superfluidity and direct Urca processes demonstrate delayed thermal relaxation under specific physical conditions. The former acquires that the neutron ^3P_2 critical temperature is small enough, whereas the latter depends on the presence of a small core that permits direct Urca processes. To explore these scenarios, we propose simple theoretical frameworks to describe these delayed thermal relaxation behaviors and discuss how an recently-established enhanced modified Urca rate influences the relaxation time. By confronting the theoretical results with the observation of Cassiopeia A, we can effectively constrain the maximum neutron ^3P_2 critical temperature.

Understanding and interpreting dynamics of functional materials in situ is a grand challenge in physics and materials science due to the difficulty of experimentally probing materials at varied length and time scales. X-ray photon correlation spectroscopy (XPCS) is uniquely well-suited for characterizing materials dynamics over wide-ranging time scales, however spatial and temporal heterogeneity in material behavior can make interpretation of experimental XPCS data difficult. In this work we have developed an unsupervised deep learning (DL) framework for automated classification and interpretation of relaxation dynamics from experimental data without requiring any prior physical knowledge of the system behavior. We demonstrate how this method can be used to rapidly explore large datasets to identify samples of interest, and we apply this approach to directly correlate bulk properties of a model system to microscopic dynamics. Importantly, this DL framework is material and process agnostic, marking a concrete step towards autonomous materials discovery.

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification that the model is truly robust against all future attacks. Unfortunately, when faced with adversarially trained models, all existing approaches have significant trouble making certifications that are strong enough to be practically useful. Linear programming (LP) techniques in particular face a "convex relaxation barrier" that prevent them from making high-quality certifications, even after refinement with mixed-integer linear programming (MILP) and branch-and-bound (BnB) techniques. In this paper, we propose a nonconvex certification technique, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. The nonconvex relaxation makes strong certifications comparable to much more expensive SDP methods, while optimizing over dramatically fewer variables comparable to much weaker LP methods. Despite nonconvexity, we show how off-the-shelf local optimization algorithms can be used to achieve and to certify global optimality in polynomial time. Our experiments find that the nonconvex relaxation almost completely closes the gap towards exact certification of adversarially trained models.

The NMR measurements performed on a single orthorhombic crystal of superconducting ferromagnet UCoGe (Y.Ihara et al, Phys. Rev. Lett. v.105, 206403 (2010)) demonstrate strongly anisotropic magnetic properties of this material. The presented calculations allow to establish the dependence of longitudinal spin-lattice relaxation rate from temperature and magnetic field. The value 1/T_1T in field perpendicular to spontaneous magnetisation directed along c-axis has maximum in vicinity of Curie temperature whereas it does not reveal similar behaviour in field parallel to the direction of spontaneous magnetisation. Also there was shown that the longitudinal spin-lattice relaxation rate is strongly field dependent when the field directed in b-crystallographic direction but field independent if magnetic field is oriented along a-axis.

Feature selection in deep learning remains a critical challenge, particularly for high-dimensional tabular data where interpretability and computational efficiency are paramount. We present GFSNetwork, a novel neural architecture that performs differentiable feature selection through temperature-controlled Gumbel-Sigmoid sampling. Unlike traditional methods, where the user has to define the requested number of features, GFSNetwork selects it automatically during an end-to-end process. Moreover, GFSNetwork maintains constant computational overhead regardless of the number of input features. We evaluate GFSNetwork on a series of classification and regression benchmarks, where it consistently outperforms recent methods including DeepLasso, attention maps, as well as traditional feature selectors, while using significantly fewer features. Furthermore, we validate our approach on real-world metagenomic datasets, demonstrating its effectiveness in high-dimensional biological data. Concluding, our method provides a scalable solution that bridges the gap between neural network flexibility and traditional feature selection interpretability. We share our python implementation of GFSNetwork at https://github.com/wwydmanski/GFSNetwork, as well as a PyPi package (gfs_network).

Language models (LMs) are often used as zero-shot or few-shot classifiers by scoring label words, but they remain fragile to adversarial prompts. Prior work typically optimizes task- or model-specific triggers, making results difficult to compare and limiting transferability. We study universal adversarial suffixes: short token sequences (4-10 tokens) that, when appended to any input, broadly reduce accuracy across tasks and models. Our approach learns the suffix in a differentiable "soft" form using Gumbel-Softmax relaxation and then discretizes it for inference. Training maximizes calibrated cross-entropy on the label region while masking gold tokens to prevent trivial leakage, with entropy regularization to avoid collapse. A single suffix trained on one model transfers effectively to others, consistently lowering both accuracy and calibrated confidence. Experiments on sentiment analysis, natural language inference, paraphrase detection, commonsense QA, and physical reasoning with Qwen2-1.5B, Phi-1.5, and TinyLlama-1.1B demonstrate consistent attack effectiveness and transfer across tasks and model families.

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity that invalidate the exactness observed in classical (non-ordered) settings. In particular, for certain ordered problems such as the min--max case, the linear relaxation never recovers the integral solution. These results clarify the intrinsic hardness introduced by sorting and reveal that the strength of the relaxation depends critically on the ``proximity'' of the ordered problem to its classical counterpart: problems closer to the non-ordered case tend to admit tighter relaxations, while those further away exhibit substantially weaker behavior. Computational experiments on benchmark instances confirm the predictive value of the integrality conditions and demonstrate the practical implications of exact relaxations for ordered location problems.

Computational quantum chemistry plays a critical role in drug discovery, chemical synthesis, and materials science. While first-principles methods, such as density functional theory (DFT), provide high accuracy in modeling electronic structures and predicting molecular properties, they are computationally expensive. Machine learning interatomic potentials (MLIPs) have emerged as promising surrogate models that aim to achieve DFT-level accuracy while enabling efficient large-scale atomistic simulations. The development of accurate and transferable MLIPs requires large-scale, high-quality datasets with both energy and force labels. Critically, MLIPs must generalize not only to stable geometries but also to intermediate, non-equilibrium conformations encountered during atomistic simulations. In this work, we introduce PubChemQCR, a large-scale dataset of molecular relaxation trajectories curated from the raw geometry optimization outputs of the PubChemQC project. PubChemQCR is the largest publicly available dataset of DFT-based relaxation trajectories for small organic molecules, comprising approximately 3.5 million trajectories and over 300 million molecular conformations computed at various levels of theory. Each conformation is labeled with both total energy and atomic forces, making the dataset suitable for training and evaluating MLIPs. To provide baselines for future developments, we benchmark nine representative MLIP models on the dataset. Our resources are publicly available at https://huggingface.co/divelab

In this paper we introduce Feature Gradients, a gradient-based search algorithm for feature selection. Our approach extends a recent result on the estimation of learnability in the sublinear data regime by showing that the calculation can be performed iteratively (i.e., in mini-batches) and in linear time and space with respect to both the number of features D and the sample size N . This, along with a discrete-to-continuous relaxation of the search domain, allows for an efficient, gradient-based search algorithm among feature subsets for very large datasets. Crucially, our algorithm is capable of finding higher-order correlations between features and targets for both the N > D and N < D regimes, as opposed to approaches that do not consider such interactions and/or only consider one regime. We provide experimental demonstration of the algorithm in small and large sample-and feature-size settings.

Learning to Rank (LTR) algorithms are usually evaluated using Information Retrieval metrics like Normalised Discounted Cumulative Gain (NDCG) or Mean Average Precision. As these metrics rely on sorting predicted items' scores (and thus, on items' ranks), their derivatives are either undefined or zero everywhere. This makes them unsuitable for gradient-based optimisation, which is the usual method of learning appropriate scoring functions. Commonly used LTR loss functions are only loosely related to the evaluation metrics, causing a mismatch between the optimisation objective and the evaluation criterion. In this paper, we address this mismatch by proposing NeuralNDCG, a novel differentiable approximation to NDCG. Since NDCG relies on the non-differentiable sorting operator, we obtain NeuralNDCG by relaxing that operator using NeuralSort, a differentiable approximation of sorting. As a result, we obtain a new ranking loss function which is an arbitrarily accurate approximation to the evaluation metric, thus closing the gap between the training and the evaluation of LTR models. We introduce two variants of the proposed loss function. Finally, the empirical evaluation shows that our proposed method outperforms previous work aimed at direct optimisation of NDCG and is competitive with the state-of-the-art methods.

Iron inclusions embedded inside dust grains play a crucial role in both internal alignment (IA) via Barnett relaxation and external alignment via the MAgnetically Enhanced RAdiative Torque (MRAT) mechanism. Moreover, inelastic relaxation is predicted to dominate over Barnett relaxation in driving the IA of micron-sized and very large grains above 10mu m (VLGs). Yet, a detailed modeling of polarized thermal dust emission from Class 0/I Young Stellar Objects (YSOs) taking into account these effects and their observational constraints is still lacking. In this paper, we update the POLARIS code and use it to perform synthetic dust polarization modeling for MHD simulations of an intermediate-mass YSO. Results will be post-processed with CASA to confront ALMA polarimetric observations. We found that to reproduce the high polarization degree of p sim 5-30% observed in protostellar envelopes by ALMA, micron-sized and VLGs must contain iron inclusions with N_{rm cl} sim 5 - 10^{3} iron atoms per cluster, assuming 30% of iron abundance locked inside dust grains under the cluster form. Inside the inner sim 500 au region, inelastic relaxation must participate in driving the grain internal alignment, and grains must contain larger iron inclusions of N_{rm cl} sim 10^{2}-10^{4} and grow beyond geq 10mu m to reproduce sim 3-10% of dust polarization observed by ALMA. But given such a combination, the internal alignment and MRAT efficiency acting on VLGs still decrease toward the center, inducing the decrease of p(%) with increasing gas density, reaching p sim 1% inside the disk.

We investigate the impact of free speech and the relaxation of moderation on online social media platforms using Elon Musk's takeover of Twitter as a case study. By curating a dataset of over 10 million tweets, our study employs a novel framework combining content and network analysis. Our findings reveal a significant increase in the distribution of certain forms of hate content, particularly targeting the LGBTQ+ community and liberals. Network analysis reveals the formation of cohesive hate communities facilitated by influential bridge users, with substantial growth in interactions hinting at increased hate production and diffusion. By tracking the temporal evolution of PageRank, we identify key influencers, primarily self-identified far-right supporters disseminating hate against liberals and woke culture. Ironically, embracing free speech principles appears to have enabled hate speech against the very concept of freedom of expression and free speech itself. Our findings underscore the delicate balance platforms must strike between open expression and robust moderation to curb the proliferation of hate online.

A model to investigate Thermally Stimulated Depolarization Current (TSDC) peak parameters using the dipole-dipole interaction concept is proposed by the author in this work. The proposed model describe the (TSDC) peak successfully since it gives a significant peak parameters (i.e. Activation energy (E) and the per-exponential factor (\tau_0) in addition to the dipole-dipole interaction strength parameter (di). Application of this model to determine the peak parameters of polyvinyl chloride(PVC) polymer is presented . The results show how the model fit the experimental thermal sampling data. Finally the results are compared to the well know techniques; the initial rise method (IR), the half width method (HW) in addition to the Cowell and Woods analysis.

Auto-Regressive (AR) models have recently gained prominence in image generation, often matching or even surpassing the performance of diffusion models. However, one major limitation of AR models is their sequential nature, which processes tokens one at a time, slowing down generation compared to models like GANs or diffusion-based methods that operate more efficiently. While speculative decoding has proven effective for accelerating LLMs by generating multiple tokens in a single forward, its application in visual AR models remains largely unexplored. In this work, we identify a challenge in this setting, which we term token selection ambiguity, wherein visual AR models frequently assign uniformly low probabilities to tokens, hampering the performance of speculative decoding. To overcome this challenge, we propose a relaxed acceptance condition referred to as LANTERN that leverages the interchangeability of tokens in latent space. This relaxation restores the effectiveness of speculative decoding in visual AR models by enabling more flexible use of candidate tokens that would otherwise be prematurely rejected. Furthermore, by incorporating a total variation distance bound, we ensure that these speed gains are achieved without significantly compromising image quality or semantic coherence. Experimental results demonstrate the efficacy of our method in providing a substantial speed-up over speculative decoding. In specific, compared to a na\"ive application of the state-of-the-art speculative decoding, LANTERN increases speed-ups by 1.75times and 1.76times, as compared to greedy decoding and random sampling, respectively, when applied to LlamaGen, a contemporary visual AR model.

Low-bit quantization of network weights and activations can drastically reduce the memory footprint, complexity, energy consumption and latency of Deep Neural Networks (DNNs). However, low-bit quantization can also cause a considerable drop in accuracy, in particular when we apply it to complex learning tasks or lightweight DNN architectures. In this paper, we propose a training procedure that relaxes the low-bit quantization. We call this procedure DNN Quantization with Attention (DQA). The relaxation is achieved by using a learnable linear combination of high, medium and low-bit quantizations. Our learning procedure converges step by step to a low-bit quantization using an attention mechanism with temperature scheduling. In experiments, our approach outperforms other low-bit quantization techniques on various object recognition benchmarks such as CIFAR10, CIFAR100 and ImageNet ILSVRC 2012, achieves almost the same accuracy as a full precision DNN, and considerably reduces the accuracy drop when quantizing lightweight DNN architectures.

Linear relaxation based perturbation analysis (LiRPA) for neural networks, which computes provable linear bounds of output neurons given a certain amount of input perturbation, has become a core component in robustness verification and certified defense. The majority of LiRPA-based methods focus on simple feed-forward networks and need particular manual derivations and implementations when extended to other architectures. In this paper, we develop an automatic framework to enable perturbation analysis on any neural network structures, by generalizing existing LiRPA algorithms such as CROWN to operate on general computational graphs. The flexibility, differentiability and ease of use of our framework allow us to obtain state-of-the-art results on LiRPA based certified defense on fairly complicated networks like DenseNet, ResNeXt and Transformer that are not supported by prior works. Our framework also enables loss fusion, a technique that significantly reduces the computational complexity of LiRPA for certified defense. For the first time, we demonstrate LiRPA based certified defense on Tiny ImageNet and Downscaled ImageNet where previous approaches cannot scale to due to the relatively large number of classes. Our work also yields an open-source library for the community to apply LiRPA to areas beyond certified defense without much LiRPA expertise, e.g., we create a neural network with a probably flat optimization landscape by applying LiRPA to network parameters. Our opensource library is available at https://github.com/KaidiXu/auto_LiRPA.

Recent work has exposed the vulnerability of computer vision models to vector field attacks. Due to the widespread usage of such models in safety-critical applications, it is crucial to quantify their robustness against such spatial transformations. However, existing work only provides empirical robustness quantification against vector field deformations via adversarial attacks, which lack provable guarantees. In this work, we propose novel convex relaxations, enabling us, for the first time, to provide a certificate of robustness against vector field transformations. Our relaxations are model-agnostic and can be leveraged by a wide range of neural network verifiers. Experiments on various network architectures and different datasets demonstrate the effectiveness and scalability of our method.

Neural sequence-to-sequence models are currently the dominant approach in several natural language processing tasks, but require large parallel corpora. We present a sequence-to-sequence-to-sequence autoencoder (SEQ^3), consisting of two chained encoder-decoder pairs, with words used as a sequence of discrete latent variables. We apply the proposed model to unsupervised abstractive sentence compression, where the first and last sequences are the input and reconstructed sentences, respectively, while the middle sequence is the compressed sentence. Constraining the length of the latent word sequences forces the model to distill important information from the input. A pretrained language model, acting as a prior over the latent sequences, encourages the compressed sentences to be human-readable. Continuous relaxations enable us to sample from categorical distributions, allowing gradient-based optimization, unlike alternatives that rely on reinforcement learning. The proposed model does not require parallel text-summary pairs, achieving promising results in unsupervised sentence compression on benchmark datasets.

This paper presents a new mechanism to facilitate the training of mask transformers for efficient panoptic segmentation, democratizing its deployment. We observe that due to its high complexity, the training objective of panoptic segmentation will inevitably lead to much higher false positive penalization. Such unbalanced loss makes the training process of the end-to-end mask-transformer based architectures difficult, especially for efficient models. In this paper, we present ReMaX that adds relaxation to mask predictions and class predictions during training for panoptic segmentation. We demonstrate that via these simple relaxation techniques during training, our model can be consistently improved by a clear margin without any extra computational cost on inference. By combining our method with efficient backbones like MobileNetV3-Small, our method achieves new state-of-the-art results for efficient panoptic segmentation on COCO, ADE20K and Cityscapes. Code and pre-trained checkpoints will be available at https://github.com/google-research/deeplab2.

Current LLM alignment techniques use pairwise human preferences at a sample level, and as such, they do not imply an alignment on the distributional level. We propose in this paper Alignment via Optimal Transport (AOT), a novel method for distributional preference alignment of LLMs. AOT aligns LLMs on unpaired preference data by making the reward distribution of the positive samples stochastically dominant in the first order on the distribution of negative samples. We introduce a convex relaxation of this first-order stochastic dominance and cast it as an optimal transport problem with a smooth and convex cost. Thanks to the one-dimensional nature of the resulting optimal transport problem and the convexity of the cost, it has a closed-form solution via sorting on empirical measures. We fine-tune LLMs with this AOT objective, which enables alignment by penalizing the violation of the stochastic dominance of the reward distribution of the positive samples on the reward distribution of the negative samples. We analyze the sample complexity of AOT by considering the dual of the OT problem and show that it converges at the parametric rate. Empirically, we show on a diverse set of alignment datasets and LLMs that AOT leads to state-of-the-art models in the 7B family of models when evaluated with Open LLM Benchmarks and AlpacaEval.

Reward guidance has been applied to great success in the test-time adaptation of continuous diffusion models; it updates each denoising step using the gradients from a downstream reward model. We study reward guidance for discrete diffusion language models, where one cannot differentiate through the natural outputs of the model because they are discrete tokens. Existing approaches either replace these discrete tokens with continuous relaxations, or employ techniques like the straight-through estimator. In this work, we show the downsides of both these methods. The former degrades gradient feedback because the reward model has never been trained with continuous inputs. The latter involves incorrect optimization because the gradient evaluated at discrete tokens is used to update continuous logits. Our key innovation is to go beyond this tradeoff by introducing a novel mechanism called EntRGi: Entropy aware Reward Guidance that dynamically regulates the gradients from the reward model. By modulating the continuous relaxation using the model's confidence, our approach substantially improves reward guidance while providing reliable inputs to the reward model. We empirically validate our approach on a 7B-parameter diffusion language model across 3 diverse reward models and 3 multi-skill benchmarks, showing consistent improvements over state-of-the-art methods.

Vision-Language-Action (VLA) models inherit strong priors from pretrained Vision-Language Models (VLMs), but naive fine-tuning often disrupts these representations and harms generalization. Existing fixes -- freezing modules or applying uniform regularization -- either overconstrain adaptation or ignore the differing roles of VLA components. We present MAPS (Module-Wise Proximity Scheduling), the first robust fine-tuning framework for VLAs. Through systematic analysis, we uncover an empirical order in which proximity constraints should be relaxed to balance stability and flexibility. MAPS linearly schedules this relaxation, enabling visual encoders to stay close to their pretrained priors while action-oriented language layers adapt more freely. MAPS introduces no additional parameters or data, and can be seamlessly integrated into existing VLAs. Across MiniVLA-VQ, MiniVLA-OFT, OpenVLA-OFT, and challenging benchmarks such as SimplerEnv, CALVIN, LIBERO, as well as real-world evaluations on the Franka Emika Panda platform, MAPS consistently boosts both in-distribution and out-of-distribution performance (up to +30%). Our findings highlight empirically guided proximity to pretrained VLMs as a simple yet powerful principle for preserving broad generalization in VLM-to-VLA transfer.

A domain wall (DW) which moves parallel to a magnetically compensated interface between an antiferromagnetic insulator (AFMI) and a two-dimensional (2D) metal can pump spin polarization into the metal. It is assumed that localized spins of a collinear AFMI interact with itinerant electrons through their exchange interaction on the interface. We employed the formalism of Keldysh Green's functions for electrons which experience potential and spin-orbit scattering on random impurities. This formalism allows a unified analysis of spin pumping, spin diffusion and spin relaxation effects on a 2D electron gas. It is shown that the pumping of a nonstaggered magnetization into the metal film takes place in the second order with respect to the interface exchange interaction. At sufficiently weak spin relaxation this pumping effect can be much stronger than the first-order effect of the Pauli magnetism which is produced by the small nonstaggered exchange field of the DW. It is shown that the pumped polarization is sensitive to the geometry of the electron's Fermi surface and increases when the wave vector of the staggered magnetization approaches the nesting vector of the Fermi surface. In a disordered diffusive electron gas the induced spin polarization follows the motion of the domain wall. It is distributed asymmetrically around the DW over a distance which can be much larger than the DW width.

Recursive Neural Networks (RvNNs), which compose sequences according to their underlying hierarchical syntactic structure, have performed well in several natural language processing tasks compared to similar models without structural biases. However, traditional RvNNs are incapable of inducing the latent structure in a plain text sequence on their own. Several extensions have been proposed to overcome this limitation. Nevertheless, these extensions tend to rely on surrogate gradients or reinforcement learning at the cost of higher bias or variance. In this work, we propose Continuous Recursive Neural Network (CRvNN) as a backpropagation-friendly alternative to address the aforementioned limitations. This is done by incorporating a continuous relaxation to the induced structure. We demonstrate that CRvNN achieves strong performance in challenging synthetic tasks such as logical inference and ListOps. We also show that CRvNN performs comparably or better than prior latent structure models on real-world tasks such as sentiment analysis and natural language inference.

We develop an approach to growing deep network architectures over the course of training, driven by a principled combination of accuracy and sparsity objectives. Unlike existing pruning or architecture search techniques that operate on full-sized models or supernet architectures, our method can start from a small, simple seed architecture and dynamically grow and prune both layers and filters. By combining a continuous relaxation of discrete network structure optimization with a scheme for sampling sparse subnetworks, we produce compact, pruned networks, while also drastically reducing the computational expense of training. For example, we achieve 49.7% inference FLOPs and 47.4% training FLOPs savings compared to a baseline ResNet-50 on ImageNet, while maintaining 75.2% top-1 accuracy -- all without any dedicated fine-tuning stage. Experiments across CIFAR, ImageNet, PASCAL VOC, and Penn Treebank, with convolutional networks for image classification and semantic segmentation, and recurrent networks for language modeling, demonstrate that we both train faster and produce more efficient networks than competing architecture pruning or search methods.

There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling approaches, such as farthest point sampling (FPS), do not consider the downstream task. A recent work showed that learning a task-specific sampling can improve results significantly. However, the proposed technique did not deal with the non-differentiability of the sampling operation and offered a workaround instead. We introduce a novel differentiable relaxation for point cloud sampling that approximates sampled points as a mixture of points in the primary input cloud. Our approximation scheme leads to consistently good results on classification and geometry reconstruction applications. We also show that the proposed sampling method can be used as a front to a point cloud registration network. This is a challenging task since sampling must be consistent across two different point clouds for a shared downstream task. In all cases, our approach outperforms existing non-learned and learned sampling alternatives. Our code is publicly available at https://github.com/itailang/SampleNet.

The Lottery Ticket Hypothesis asserts the existence of highly sparse, trainable subnetworks ('winning tickets') within dense, randomly initialized neural networks. However, state-of-the-art methods of drawing these tickets, like Lottery Ticket Rewinding (LTR), are computationally prohibitive, while more efficient saliency-based Pruning-at-Initialization (PaI) techniques suffer from a significant accuracy-sparsity trade-off and fail basic sanity checks. In this work, we argue that PaI's reliance on first-order saliency metrics, which ignore inter-weight dependencies, contributes substantially to this performance gap, especially in the sparse regime. To address this, we introduce Concrete Ticket Search (CTS), an algorithm that frames subnetwork discovery as a holistic combinatorial optimization problem. By leveraging a Concrete relaxation of the discrete search space and a novel gradient balancing scheme (GRADBALANCE) to control sparsity, CTS efficiently identifies high-performing subnetworks near initialization without requiring sensitive hyperparameter tuning. Motivated by recent works on lottery ticket training dynamics, we further propose a knowledge distillation-inspired family of pruning objectives, finding that minimizing the reverse Kullback-Leibler divergence between sparse and dense network outputs (CTS-KL) is particularly effective. Experiments on varying image classification tasks show that CTS produces subnetworks that robustly pass sanity checks and achieve accuracy comparable to or exceeding LTR, while requiring only a small fraction of the computation. For example, on ResNet-20 on CIFAR10, it reaches 99.3% sparsity with 74.0% accuracy in 7.9 minutes, while LTR attains the same sparsity with 68.3% accuracy in 95.2 minutes. CTS's subnetworks outperform saliency-based methods across all sparsities, but its advantage over LTR is most pronounced in the highly sparse regime.

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries -- permutation, rotation, and translation -- for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions must be modified, and each layer must handle multiple data types for different harmonic orders. We present Facet, a GNN architecture for efficient ML potentials, developed through systematic analysis of steerable GNNs. Our innovations include replacing expensive multi-layer perceptrons (MLPs) for interatomic distances with splines, which match performance while cutting computational and memory demands. We also introduce a general-purpose equivariant layer that mixes node information via spherical grid projection followed by standard MLPs -- faster than tensor products and more expressive than linear or gate layers. On the MPTrj dataset, Facet matches leading models with far fewer parameters and under 10% of their training compute. On a crystal relaxation task, it runs twice as fast as MACE models. We further show SevenNet-0's parameters can be reduced by over 25% with no accuracy loss. These techniques enable more than 10x faster training of large-scale foundation models for ML potentials, potentially reshaping computational materials discovery.

In numerous artificial intelligence applications, the collaborative efforts of multiple intelligent agents are imperative for the successful attainment of target objectives. To enhance coordination among these agents, a distributed communication framework is often employed. However, indiscriminate information sharing among all agents can be resource-intensive, and the adoption of manually pre-defined communication architectures imposes constraints on inter-agent communication, thus limiting the potential for effective collaboration. Moreover, the communication framework often remains static during inference, which may result in sustained high resource consumption, as in most cases, only key decisions necessitate information sharing among agents. In this study, we introduce a novel approach wherein we conceptualize the communication architecture among agents as a learnable graph. We formulate this problem as the task of determining the communication graph while enabling the architecture parameters to update normally, thus necessitating a bi-level optimization process. Utilizing continuous relaxation of the graph representation and incorporating attention units, our proposed approach, CommFormer, efficiently optimizes the communication graph and concurrently refines architectural parameters through gradient descent in an end-to-end manner. Additionally, we introduce a temporal gating mechanism for each agent, enabling dynamic decisions on whether to receive shared information at a given time, based on current observations, thus improving decision-making efficiency. Extensive experiments on a variety of cooperative tasks substantiate the robustness of our model across diverse cooperative scenarios, where agents are able to develop more coordinated and sophisticated strategies regardless of changes in the number of agents.

Sharp, multidimensional changepoints-abrupt shifts in a regression surface whose locations and magnitudes are unknown-arise in settings as varied as gene-expression profiling, financial covariance breaks, climate-regime detection, and urban socioeconomic mapping. Despite their prevalence, there are no current approaches that jointly estimate the location and size of the discontinuity set in a one-shot approach with statistical guarantees. We therefore introduce Free Discontinuity Regression (FDR), a fully nonparametric estimator that simultaneously (i) smooths a regression surface, (ii) segments it into contiguous regions, and (iii) provably recovers the precise locations and sizes of its jumps. By extending a convex relaxation of the Mumford-Shah functional to random spatial sampling and correlated noise, FDR overcomes the fixed-grid and i.i.d. noise assumptions of classical image-segmentation approaches, thus enabling its application to real-world data of any dimension. This yields the first identification and uniform consistency results for multivariate jump surfaces: under mild SBV regularity, the estimated function, its discontinuity set, and all jump sizes converge to their true population counterparts. Hyperparameters are selected automatically from the data using Stein's Unbiased Risk Estimate, and large-scale simulations up to three dimensions validate the theoretical results and demonstrate good finite-sample performance. Applying FDR to an internet shutdown in India reveals a 25-35% reduction in economic activity around the estimated shutdown boundaries-much larger than previous estimates. By unifying smoothing, segmentation, and effect-size recovery in a general statistical setting, FDR turns free-discontinuity ideas into a practical tool with formal guarantees for modern multivariate data.

Generalization bounds which assess the difference between the true risk and the empirical risk, have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz loss function. To avoid these assumptions, in this paper, we follow an alternative approach: we relax uniform bounds assumptions by using on-average bounded loss and on-average bounded gradient norm assumptions. Following this relaxation, we propose a new generalization bound that exploits the contractivity of the log-Sobolev inequalities. These inequalities add an additional loss-gradient norm term to the generalization bound, which is intuitively a surrogate of the model complexity. We apply the proposed bound on Bayesian deep nets and empirically analyze the effect of this new loss-gradient norm term on different neural architectures.

Differentiable sorting algorithms allow training with sorting and ranking supervision, where only the ordering or ranking of samples is known. Various methods have been proposed to address this challenge, ranging from optimal transport-based differentiable Sinkhorn sorting algorithms to making classic sorting networks differentiable. One problem of current differentiable sorting methods is that they are non-monotonic. To address this issue, we propose a novel relaxation of conditional swap operations that guarantees monotonicity in differentiable sorting networks. We introduce a family of sigmoid functions and prove that they produce differentiable sorting networks that are monotonic. Monotonicity ensures that the gradients always have the correct sign, which is an advantage in gradient-based optimization. We demonstrate that monotonic differentiable sorting networks improve upon previous differentiable sorting methods.

We introduce an optical tweezer platform for assembling and individually manipulating a two-dimensional register of nuclear spin qubits. Each nuclear spin qubit is encoded in the ground ^{1}S_{0} manifold of ^{87}Sr and is individually manipulated by site-selective addressing beams. We observe that spin relaxation is negligible after 5 seconds, indicating that T_1gg5 s. Furthermore, utilizing simultaneous manipulation of subsets of qubits, we demonstrate significant phase coherence over the entire register, estimating T_2^star = left(21pm7right) s and measuring T_2^echo=left(42pm6right) s.

Despite recent efforts in Large Language Models (LLMs) safety and alignment, current adversarial attacks on frontier LLMs are still able to force harmful generations consistently. Although adversarial training has been widely studied and shown to significantly improve the robustness of traditional machine learning models, its strengths and weaknesses in the context of LLMs are less understood. Specifically, while existing discrete adversarial attacks are effective at producing harmful content, training LLMs with concrete adversarial prompts is often computationally expensive, leading to reliance on continuous relaxations. As these relaxations do not correspond to discrete input tokens, such latent training methods often leave models vulnerable to a diverse set of discrete attacks. In this work, we aim to bridge this gap by introducing MixAT, a novel method that combines stronger discrete and faster continuous attacks during training. We rigorously evaluate MixAT across a wide spectrum of state-of-the-art attacks, proposing the At Least One Attack Success Rate (ALO-ASR) metric to capture the worst-case vulnerability of models. We show MixAT achieves substantially better robustness (ALO-ASR < 20%) compared to prior defenses (ALO-ASR > 50%), while maintaining a runtime comparable to methods based on continuous relaxations. We further analyze MixAT in realistic deployment settings, exploring how chat templates, quantization, low-rank adapters, and temperature affect both adversarial training and evaluation, revealing additional blind spots in current methodologies. Our results demonstrate that MixAT's discrete-continuous defense offers a principled and superior robustness-accuracy tradeoff with minimal computational overhead, highlighting its promise for building safer LLMs. We provide our code and models at https://github.com/insait-institute/MixAT.

Large language models (LLMs) are susceptible to memorizing training data, raising concerns due to the potential extraction of sensitive information. Current methods to measure memorization rates of LLMs, primarily discoverable extraction (Carlini et al., 2022), rely on single-sequence greedy sampling, potentially underestimating the true extent of memorization. This paper introduces a probabilistic relaxation of discoverable extraction that quantifies the probability of extracting a target sequence within a set of generated samples, considering various sampling schemes and multiple attempts. This approach addresses the limitations of reporting memorization rates through discoverable extraction by accounting for the probabilistic nature of LLMs and user interaction patterns. Our experiments demonstrate that this probabilistic measure can reveal cases of higher memorization rates compared to rates found through discoverable extraction. We further investigate the impact of different sampling schemes on extractability, providing a more comprehensive and realistic assessment of LLM memorization and its associated risks. Our contributions include a new probabilistic memorization definition, empirical evidence of its effectiveness, and a thorough evaluation across different models, sizes, sampling schemes, and training data repetitions.

Recently, significant progress has been made in protein-ligand docking, especially in modern deep learning methods, and some benchmarks were proposed, e.g., PoseBench, Plinder. However, these benchmarks suffer from less practical evaluation setups (e.g., blind docking, self docking), or heavy framework that involves training, raising challenges to assess docking methods efficiently. To fill this gap, we proposed PoseX, an open-source benchmark focusing on self-docking and cross-docking, to evaluate the algorithmic advances practically and comprehensively. Specifically, first, we curate a new evaluation dataset with 718 entries for self docking and 1,312 for cross docking; second, we incorporate 22 docking methods across three methodological categories, including (1) traditional physics-based methods (e.g., Schr\"odinger Glide), (2) AI docking methods (e.g., DiffDock), (3) AI co-folding methods (e.g., AlphaFold3); third, we design a relaxation method as post-processing to minimize conformation energy and refine binding pose; fourth, we released a leaderboard to rank submitted models in real time. We draw some key insights via extensive experiments: (1) AI-based approaches have already surpassed traditional physics-based approaches in overall docking accuracy (RMSD). The longstanding generalization issues that have plagued AI molecular docking have been significantly alleviated in the latest models. (2) The stereochemical deficiencies of AI-based approaches can be greatly alleviated with post-processing relaxation. Combining AI docking methods with the enhanced relaxation method achieves the best performance to date. (3) AI co-folding methods commonly face ligand chirality issues, which cannot be resolved by relaxation. The code, curated dataset and leaderboard are released at https://github.com/CataAI/PoseX.

Vision-Language-Action (VLA) models have demonstrated remarkable generalization capabilities in robotic manipulation tasks, yet their substantial computational overhead remains a critical obstacle to real-world deployment. Improving inference efficiency is therefore essential for practical robotic applications. Existing acceleration methods often rely on heuristic or static strategies--such as rule-based token caching or pruning--that are decoupled from task objectives and fail to adapt to dynamic scene changes. In this work, we reformulate inference acceleration as a learnable policy optimization problem and propose a novel framework that integrates a dynamic, task-aware decision-making process directly into the VLA model. At its core are two lightweight, cooperative modules: a Cached Token Selector, which determines which tokens should be reused, and a Cache Ratio Predictor, which controls how many tokens to reuse. Training these modules is non-trivial due to their discrete decisions. We address this by adopting a differentiable relaxation that allows gradient-based end-to-end optimization. Extensive experiments on the LIBERO and SIMPLER benchmarks, as well as real-robot evaluations, show that our method achieves a 1.76x wall-clock inference speedup while simultaneously improving the average success rate by 1.9 percentage points (from 75.0% to 76.9%) on LIBERO and by 5.0 percentage points on real-world tasks, significantly outperforming existing baselines. This work highlights the potential of learning task-aware computational allocation policies, paving the way for VLA models that are both powerful and efficient.

In this paper, we consider the minimum submodular cost allocation (MSCA) problem. The input of MSCA is k non-negative submodular functions f_1,ldots,f_k on the ground set N given by evaluation oracles, and the goal is to partition N into k (possibly empty) sets X_1,ldots,X_k so that sum_{i=1}^k f_i(X_i) is minimized. In this paper, we focus on the case when f_1,ldots,f_k are monotone (denoted by Mono-MSCA). We provide a natural LP-relaxation for Mono-MSCA, which is equivalent to the convex program relaxation introduced by Chekuri and Ene. We show that the integrality gap of the LP-relaxation is at most k/2, which yields a k/2-approximation algorithm for Mono-MSCA. We also show that the integrality gap of the LP-relaxation is at least k/2-epsilon for any constant epsilon>0 when k is fixed.

Current high-performance semantic segmentation models are purely data-driven sub-symbolic approaches and blind to the structured nature of the visual world. This is in stark contrast to human cognition which abstracts visual perceptions at multiple levels and conducts symbolic reasoning with such structured abstraction. To fill these fundamental gaps, we devise LOGICSEG, a holistic visual semantic parser that integrates neural inductive learning and logic reasoning with both rich data and symbolic knowledge. In particular, the semantic concepts of interest are structured as a hierarchy, from which a set of constraints are derived for describing the symbolic relations and formalized as first-order logic rules. After fuzzy logic-based continuous relaxation, logical formulae are grounded onto data and neural computational graphs, hence enabling logic-induced network training. During inference, logical constraints are packaged into an iterative process and injected into the network in a form of several matrix multiplications, so as to achieve hierarchy-coherent prediction with logic reasoning. These designs together make LOGICSEG a general and compact neural-logic machine that is readily integrated into existing segmentation models. Extensive experiments over four datasets with various segmentation models and backbones verify the effectiveness and generality of LOGICSEG. We believe this study opens a new avenue for visual semantic parsing.

We propose nabla-RANSAC, a generalized differentiable RANSAC that allows learning the entire randomized robust estimation pipeline. The proposed approach enables the use of relaxation techniques for estimating the gradients in the sampling distribution, which are then propagated through a differentiable solver. The trainable quality function marginalizes over the scores from all the models estimated within nabla-RANSAC to guide the network learning accurate and useful inlier probabilities or to train feature detection and matching networks. Our method directly maximizes the probability of drawing a good hypothesis, allowing us to learn better sampling distribution. We test nabla-RANSAC on a number of real-world scenarios on fundamental and essential matrix estimation, both outdoors and indoors, with handcrafted and learning-based features. It is superior to the state-of-the-art in terms of accuracy while running at a similar speed to its less accurate alternatives. The code and trained models are available at https://github.com/weitong8591/differentiable_ransac.

A distribution shift can have fundamental consequences such as signaling a change in the operating environment or significantly reducing the accuracy of downstream models. Thus, understanding distribution shifts is critical for examining and hopefully mitigating the effect of such a shift. Most prior work focuses on merely detecting if a shift has occurred and assumes any detected shift can be understood and handled appropriately by a human operator. We hope to aid in these manual mitigation tasks by explaining the distribution shift using interpretable transportation maps from the original distribution to the shifted one. We derive our interpretable mappings from a relaxation of optimal transport, where the candidate mappings are restricted to a set of interpretable mappings. We then inspect multiple quintessential use-cases of distribution shift in real-world tabular, text, and image datasets to showcase how our explanatory mappings provide a better balance between detail and interpretability than baseline explanations by both visual inspection and our PercentExplained metric.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of L-smooth and mu-strongly convex functions distributed over a given network of size n. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous, leading to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix chi_1 and the maximal resistance chi_2leq chi_1 of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires O(nfrac{L{mu}}log(1{epsilon})) local gradients and only O(nchi_1chi_2frac{L{mu}}log(1{epsilon})) communications to reach a precision epsilon, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method. We also propose a SDP relaxation to find the optimal gossip rate of each edge minimizing the total number of communications for a given graph, resulting in faster convergence compared to standard approaches relying on uniform communication weights. Our source code is released on a public repository.

We investigate a general formulation for clustering and transductive few-shot learning, which integrates prototype-based objectives, Laplacian regularization and supervision constraints from a few labeled data points. We propose a concave-convex relaxation of the problem, and derive a computationally efficient block-coordinate bound optimizer, with convergence guarantee. At each iteration,our optimizer computes independent (parallel) updates for each point-to-cluster assignment. Therefore, it could be trivially distributed for large-scale clustering and few-shot tasks. Furthermore, we provides a thorough convergence analysis based on point-to-set maps. Were port comprehensive clustering and few-shot learning experiments over various data sets, showing that our method yields competitive performances, in term of accuracy and optimization quality, while scaling up to large problems. Using standard training on the base classes, without resorting to complex meta-learning and episodic-training strategies, our approach outperforms state-of-the-art few-shot methods by significant margins, across various models, settings and data sets. Surprisingly, we found that even standard clustering procedures (e.g., K-means), which correspond to particular, non-regularized cases of our general model, already achieve competitive performances in comparison to the state-of-the-art in few-shot learning. These surprising results point to the limitations of the current few-shot benchmarks, and question the viability of a large body of convoluted few-shot learning techniques in the recent literature.

Certified defenses based on convex relaxations are an established technique for training provably robust models. The key component is the choice of relaxation, varying from simple intervals to tight polyhedra. Counterintuitively, loose interval-based training often leads to higher certified robustness than what can be achieved with tighter relaxations, which is a well-known but poorly understood paradox. While recent works introduced various improvements aiming to circumvent this issue in practice, the fundamental problem of training models with high certified robustness remains unsolved. In this work, we investigate the underlying reasons behind the paradox and identify two key properties of relaxations, beyond tightness, that impact certified training dynamics: continuity and sensitivity. Our extensive experimental evaluation with a number of popular convex relaxations provides strong evidence that these factors can explain the drop in certified robustness observed for tighter relaxations. We also systematically explore modifications of existing relaxations and discover that improving unfavorable properties is challenging, as such attempts often harm other properties, revealing a complex tradeoff. Our findings represent an important first step towards understanding the intricate optimization challenges involved in certified training.

Despite their great success, there is still no comprehensive theoretical understanding of learning with Deep Neural Networks (DNNs) or their inner organization. Previous work proposed to analyze DNNs in the Information Plane; i.e., the plane of the Mutual Information values that each layer preserves on the input and output variables. They suggested that the goal of the network is to optimize the Information Bottleneck (IB) tradeoff between compression and prediction, successively, for each layer. In this work we follow up on this idea and demonstrate the effectiveness of the Information-Plane visualization of DNNs. Our main results are: (i) most of the training epochs in standard DL are spent on {\emph compression} of the input to efficient representation and not on fitting the training labels. (ii) The representation compression phase begins when the training errors becomes small and the Stochastic Gradient Decent (SGD) epochs change from a fast drift to smaller training error into a stochastic relaxation, or random diffusion, constrained by the training error value. (iii) The converged layers lie on or very close to the Information Bottleneck (IB) theoretical bound, and the maps from the input to any hidden layer and from this hidden layer to the output satisfy the IB self-consistent equations. This generalization through noise mechanism is unique to Deep Neural Networks and absent in one layer networks. (iv) The training time is dramatically reduced when adding more hidden layers. Thus the main advantage of the hidden layers is computational. This can be explained by the reduced relaxation time, as this it scales super-linearly (exponentially for simple diffusion) with the information compression from the previous layer.

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimization, strongly influenced by Nesterov's seminal book and Nemirovski's lecture notes, includes the analysis of cutting plane methods, as well as (accelerated) gradient descent schemes. We also pay special attention to non-Euclidean settings (relevant algorithms include Frank-Wolfe, mirror descent, and dual averaging) and discuss their relevance in machine learning. We provide a gentle introduction to structural optimization with FISTA (to optimize a sum of a smooth and a simple non-smooth term), saddle-point mirror prox (Nemirovski's alternative to Nesterov's smoothing), and a concise description of interior point methods. In stochastic optimization we discuss stochastic gradient descent, mini-batches, random coordinate descent, and sublinear algorithms. We also briefly touch upon convex relaxation of combinatorial problems and the use of randomness to round solutions, as well as random walks based methods.

The development of accurate and efficient machine learning models for predicting the structure and properties of molecular crystals has been hindered by the scarcity of publicly available datasets of structures with property labels. To address this challenge, we introduce the Open Molecular Crystals 2025 (OMC25) dataset, a collection of over 27 million molecular crystal structures containing 12 elements and up to 300 atoms in the unit cell. The dataset was generated from dispersion-inclusive density functional theory (DFT) relaxation trajectories of over 230,000 randomly generated molecular crystal structures of around 50,000 organic molecules. OMC25 comprises diverse chemical compounds capable of forming different intermolecular interactions and a wide range of crystal packing motifs. We provide detailed information on the dataset's construction, composition, structure, and properties. To demonstrate the quality and use cases of OMC25, we further trained and evaluated state-of-the-art open-source machine learning interatomic potentials. By making this dataset publicly available, we aim to accelerate the development of more accurate and efficient machine learning models for molecular crystals.

Conversational Search (CS) is the task of retrieving relevant documents from a corpus within a conversational context, combining retrieval with conversational context modeling. With the explosion of Large Language Models (LLMs), the CS field has seen major improvements with LLMs rewriting user queries, accounting for conversational context. However, engaging LLMs at inference time harms efficiency. Current methods address this by distilling embeddings from human-rewritten queries to learn the context modeling task. Yet, these approaches predominantly focus on context modeling, and only treat the contrastive component of the retrieval task within a distillation-independent loss term. To address these limitations, we propose a new distillation method, as a relaxation of the previous objective, unifying retrieval and context modeling. We relax the existing training objectives by distilling similarity scores between conversations and documents, rather than relying solely on representation learning. Our proposed distillation objective allows for more freedom in the representation space and leverages the contrastive nature of document relevance. Through experiments on Learned Sparse Retrieval (LSR) across 5 CS datasets, our approach demonstrates substantial improvements in both in-domain and out-of-domain retrieval performance, outperforming state-of-the-art with gains of up to 6 points in recall for out-of-domain datasets. Additionally, through the relaxation of the objective, we propose a multi-teacher distillation, using multiple LLMs as teachers, yielding additional gains, and outperforming the teachers themselves in in-domain experiments. Finally, analysis of the sparsity of the models reveals that our distillation allows for better control over the sparsity of the trained models.

We propose Beam Tree Recursive Cell (BT-Cell) - a backpropagation-friendly framework to extend Recursive Neural Networks (RvNNs) with beam search for latent structure induction. We further extend this framework by proposing a relaxation of the hard top-k operators in beam search for better propagation of gradient signals. We evaluate our proposed models in different out-of-distribution splits in both synthetic and realistic data. Our experiments show that BTCell achieves near-perfect performance on several challenging structure-sensitive synthetic tasks like ListOps and logical inference while maintaining comparable performance in realistic data against other RvNN-based models. Additionally, we identify a previously unknown failure case for neural models in generalization to unseen number of arguments in ListOps. The code is available at: https://github.com/JRC1995/BeamTreeRecursiveCells.

Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster assignments by optimizing a tighter relaxation of the minimum cut based on graph total variation (GTV). The cluster assignments can be used directly to perform vertex clustering or to implement graph pooling in a graph classification framework. Our model consists of two core components: i) a message-passing layer that minimizes the ell_1 distance in the features of adjacent vertices, which is key to achieving sharp transitions between clusters; ii) an unsupervised loss function that minimizes the GTV of the cluster assignments while ensuring balanced partitions. Experimental results show that our model outperforms other GNNs for vertex clustering and graph classification.

Deep residual networks (ResNets) have demonstrated outstanding success in computer vision tasks, attributed to their ability to maintain gradient flow through deep architectures. Simultaneously, controlling the Lipschitz constant in neural networks has emerged as an essential area of research to enhance adversarial robustness and network certifiability. This paper presents a rigorous approach to the general design of L-Lipschitz deep residual networks using a Linear Matrix Inequality (LMI) framework. Initially, the ResNet architecture was reformulated as a cyclic tridiagonal LMI, and closed-form constraints on network parameters were derived to ensure L-Lipschitz continuity; however, using a new LDL^top decomposition approach for certifying LMI feasibility, we extend the construction of L-Lipchitz networks to any other nonlinear architecture. Our contributions include a provable parameterization methodology for constructing Lipschitz-constrained residual networks and other hierarchical architectures. Cholesky decomposition is also used for efficient parameterization. These findings enable robust network designs applicable to adversarial robustness, certified training, and control systems. The LDL^top formulation is shown to be a tight relaxation of the SDP-based network, maintaining full expressiveness and achieving 3\%-13\% accuracy gains over SLL Layers on 121 UCI data sets.

We present a structural analysis of the young massive star cluster Westerlund 1 (Wd 1). With multi-epoch Hubble Space Telescope (HST) observations, we measure the proper motions of 10346 stars and determine their kinematic memberships by fitting a Gaussian mixture model to their proper motions. After correcting for extinction and completeness, we model the stellar density distribution and confirm the presence of an elongation with an eccentricity of 0.71. The eccentricity decreases slightly with increasing mass. We fit the radial profile with the Elson, Fall, and Freeman model, observing a decrease in the core radius with increasing mass, indicative of weak but detectable mass segregation. This finding is further supported by a measured mass segregation ratio of Lambda_rm MSR=1.11pm0.11, only above 1 by 1sigma, and slightly shorter minimum spanning tree length for higher mass bins. The cluster has a 1D velocity dispersion of 3.42 pm 0.10~km,s^{-1}, suggesting it is subvirial. The subvirial state implies either exceptionally high star formation efficiency or inefficient stellar feedback caused by local gas expulsion before stars reach the cluster. The crossing time is 0.30 Myr and the relaxation time is 0.26 Gyr. Given the age of Wd 1 of 10.7 Myr, we expect evident mass segregation for stars more massive than 10~M_odot, which accounts for the minor mass segregation found in the mass range of 1.00x201312.14~M_odot in this work. This suggests the overall mass segregation in Wd 1 is not primordial.

This paper investigates a Stacked Intelligent Metasurfaces (SIM)-assisted Integrated Sensing and Communications (ISAC) system. An extended target model is considered, where the BS aims to estimate the complete target response matrix relative to the SIM. Under the constraints of minimum Signal-to-Interference-plus-Noise Ratio (SINR) for the communication users (CUs) and maximum transmit power, we jointly optimize the transmit beamforming at the base station (BS) and the end-to-end transmission matrix of the SIM, to minimize the Cramér-Rao Bound (CRB) for target estimation. Effective algorithms such as the alternating optimization (AO) and semidefinite relaxation (SDR) are employed to solve the non-convex SINR-constrained CRB minimization problem. Finally, we design and build an experimental platform for SIM, and evaluate the performance of the proposed algorithms for communication and sensing tasks.

Solving a linear system Ax=b is a fundamental scientific computing primitive for which numerous solvers and preconditioners have been developed. These come with parameters whose optimal values depend on the system being solved and are often impossible or too expensive to identify; thus in practice sub-optimal heuristics are used. We consider the common setting in which many related linear systems need to be solved, e.g. during a single numerical simulation. In this scenario, can we sequentially choose parameters that attain a near-optimal overall number of iterations, without extra matrix computations? We answer in the affirmative for Successive Over-Relaxation (SOR), a standard solver whose parameter omega has a strong impact on its runtime. For this method, we prove that a bandit online learning algorithm--using only the number of iterations as feedback--can select parameters for a sequence of instances such that the overall cost approaches that of the best fixed omega as the sequence length increases. Furthermore, when given additional structural information, we show that a contextual bandit method asymptotically achieves the performance of the instance-optimal policy, which selects the best omega for each instance. Our work provides the first learning-theoretic treatment of high-precision linear system solvers and the first end-to-end guarantees for data-driven scientific computing, demonstrating theoretically the potential to speed up numerical methods using well-understood learning algorithms.

Training classifiers is difficult with severe class imbalance, but many rare events are the culmination of a sequence with much more common intermediate outcomes. For example, in online marketing a user first sees an ad, then may click on it, and finally may make a purchase; estimating the probability of purchases is difficult because of their rarity. We show both theoretically and through data experiments that the more abundant data in earlier steps may be leveraged to improve estimation of probabilities of rare events. We present PRESTO, a relaxation of the proportional odds model for ordinal regression. Instead of estimating weights for one separating hyperplane that is shifted by separate intercepts for each of the estimated Bayes decision boundaries between adjacent pairs of categorical responses, we estimate separate weights for each of these transitions. We impose an L1 penalty on the differences between weights for the same feature in adjacent weight vectors in order to shrink towards the proportional odds model. We prove that PRESTO consistently estimates the decision boundary weights under a sparsity assumption. Synthetic and real data experiments show that our method can estimate rare probabilities in this setting better than both logistic regression on the rare category, which fails to borrow strength from more abundant categories, and the proportional odds model, which is too inflexible.

We investigate the fidelity of Grover's search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence of its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms and we find that there exists a competition between them, leading to an optimum value of the drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.

The use of deep 3D point cloud models in safety-critical applications, such as autonomous driving, dictates the need to certify the robustness of these models to real-world transformations. This is technically challenging, as it requires a scalable verifier tailored to point cloud models that handles a wide range of semantic 3D transformations. In this work, we address this challenge and introduce 3DCertify, the first verifier able to certify the robustness of point cloud models. 3DCertify is based on two key insights: (i) a generic relaxation based on first-order Taylor approximations, applicable to any differentiable transformation, and (ii) a precise relaxation for global feature pooling, which is more complex than pointwise activations (e.g., ReLU or sigmoid) but commonly employed in point cloud models. We demonstrate the effectiveness of 3DCertify by performing an extensive evaluation on a wide range of 3D transformations (e.g., rotation, twisting) for both classification and part segmentation tasks. For example, we can certify robustness against rotations by pm60{\deg} for 95.7% of point clouds, and our max pool relaxation increases certification by up to 15.6%.

We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. These assumptions can be thought of as a relaxation of faithfulness, and most of them can be directly tested from (the underlying distribution) of the data, particularly when one focuses on structural causal models. We specialize the definitions and results for structural causal models.

This paper addresses the scalability challenge of architecture search by formulating the task in a differentiable manner. Unlike conventional approaches of applying evolution or reinforcement learning over a discrete and non-differentiable search space, our method is based on the continuous relaxation of the architecture representation, allowing efficient search of the architecture using gradient descent. Extensive experiments on CIFAR-10, ImageNet, Penn Treebank and WikiText-2 show that our algorithm excels in discovering high-performance convolutional architectures for image classification and recurrent architectures for language modeling, while being orders of magnitude faster than state-of-the-art non-differentiable techniques. Our implementation has been made publicly available to facilitate further research on efficient architecture search algorithms.

Elucidating quantum coherence effects and geometrical factors for efficient energy transfer in photosynthesis has the potential to uncover non-classical design principles for advanced organic materials. We study energy transfer in a linear light-harvesting model to reveal that dimerized geometries with strong electronic coherences within donor and acceptor pairs exhibit significantly improved efficiency, which is in marked contrast to predictions of the classical F\"orster theory. We reveal that energy tuning due to coherent delocalization of photoexcitations is mainly responsible for the efficiency optimization. This coherence-assisted energy-tuning mechanism also explains the energetics and chlorophyll arrangements in the widely-studied Fenna-Matthews-Olson complex. We argue that a clustered network with rapid energy relaxation among donors and resonant energy transfer from donor to acceptor states provides a basic formula for constructing efficient light-harvesting systems, and the general principles revealed here can be generalized to larger systems and benefit future innovation of efficient molecular light-harvesting materials.

Seven years ago, researchers proposed a postprocessing method to equalize the error rates of a model across different demographic groups. The work launched hundreds of papers purporting to improve over the postprocessing baseline. We empirically evaluate these claims through thousands of model evaluations on several tabular datasets. We find that the fairness-accuracy Pareto frontier achieved by postprocessing contains all other methods we were feasibly able to evaluate. In doing so, we address two common methodological errors that have confounded previous observations. One relates to the comparison of methods with different unconstrained base models. The other concerns methods achieving different levels of constraint relaxation. At the heart of our study is a simple idea we call unprocessing that roughly corresponds to the inverse of postprocessing. Unprocessing allows for a direct comparison of methods using different underlying models and levels of relaxation.

Constrained Markov Decision Processes (CMDPs) are critical in many high-stakes applications, where decisions must optimize cumulative rewards while strictly adhering to complex nonlinear constraints. In domains such as power systems, finance, supply chains, and precision robotics, violating these constraints can result in significant financial or societal costs. Existing Reinforcement Learning (RL) methods often struggle with sample efficiency and effectiveness in finding feasible policies for highly and strictly constrained CMDPs, limiting their applicability in these environments. Stochastic dual dynamic programming is often used in practice on convex relaxations of the original problem, but they also encounter computational challenges and loss of optimality. This paper introduces a novel approach, Two-Stage Deep Decision Rules (TS-DDR), to efficiently train parametric actor policies using Lagrangian Duality. TS-DDR is a self-supervised learning algorithm that trains general decision rules (parametric policies) using stochastic gradient descent (SGD); its forward passes solve {\em deterministic} optimization problems to find feasible policies, and its backward passes leverage duality theory to train the parametric policy with closed-form gradients. TS-DDR inherits the flexibility and computational performance of deep learning methodologies to solve CMDP problems. Applied to the Long-Term Hydrothermal Dispatch (LTHD) problem using actual power system data from Bolivia, TS-DDR is shown to enhance solution quality and to reduce computation times by several orders of magnitude when compared to current state-of-the-art methods.

The Parameter-Efficient Fine-Tuning (PEFT) methods have been extensively researched for large language models in the downstream tasks. Among all the existing approaches, the Low-Rank Adaptation (LoRA) has gained popularity for its streamlined design by incorporating low-rank matrices into existing pre-trained models. Though effective, LoRA allocates every module an identical low-rank matrix, which ignores the varying properties and contributions across different components. Moreover, the existing adaptive LoRA solutions rely highly on intuitive importance scoring indicators to adjust the interior rank of the decomposition matrices. In this paper, we propose a new PEFT scheme called DiffoRA, which is theoretically grounded and enables module-wise adoption of LoRA. At the core of our DiffoRA lies a Differential Adaptation Matrix (DAM) to determine which module is the most suitable and essential for fine-tuning. We explain how the designed matrix impacts the convergence rate and generalization capability of a pre-trained model. Furthermore, we construct the DAM via continuous relaxation and discretization with weight-sharing optimizations. We fully implement our DiffoRA and design comprehensive experiments to evaluate its performance. The experimental results demonstrate that our approach achieves the best model accuracy over all the state-of-the-art baselines across various benchmarks.

Nonlinear elastic properties of polymers and polymeric composites are essential for accurate prediction of their response to dynamic loads, which is crucial in a wide range of applications. These properties can be affected by strain rate, temperature, and pressure. The temperature susceptibility of nonlinear elastic moduli of polymers remains poorly understood. We have recently observed a significant frequency dependence of the nonlinear elastic (Murnaghan) moduli of polystyrene. In this paper we expand this analysis by the temperature dependence. The measurement methodology was based on the acousto-elastic effect, and involved analysis of the dependencies of velocities of longitudinal and shear single-frequency ultrasonic waves in the sample on the applied static pressure. Measurements were performed at different temperatures in the range of 25-65 {\deg}C and at different frequencies in the range of 0.75-3 MHz. The temperature susceptibility of the nonlinear moduli l and m was found to be two orders of magnitude larger than that of linear moduli lambda and mu. At the same time, the observed variations of n modulus with temperature were low and within the measurement tolerance. The observed tendencies can be explained by different influence of pressure on relaxation processes in the material at different temperatures.

In this paper, we develop and implement an efficient asymptotic-preserving (AP) scheme to solve the gas mixture of Boltzmann equations under the disparate mass scaling relevant to the so-called "epochal relaxation" phenomenon. The disparity in molecular masses, ranging across several orders of magnitude, leads to significant challenges in both the evaluation of collision operators and the designing of time-stepping schemes to capture the multi-scale nature of the dynamics. A direct implementation of the spectral method faces prohibitive computational costs as the mass ratio increases due to the need to resolve vastly different thermal velocities. Unlike [I. M. Gamba, S. Jin, and L. Liu, Commun. Math. Sci., 17 (2019), pp. 1257-1289], we propose an alternative approach based on proper truncation of asymptotic expansions of the collision operators, which significantly reduces the computational complexity and works well for small varepsilon. By incorporating the separation of three time scales in the model's relaxation process [P. Degond and B. Lucquin-Desreux, Math. Models Methods Appl. Sci., 6 (1996), pp. 405-436], we design an AP scheme that captures the specific dynamics of the disparate mass model while maintaining computational efficiency. Numerical experiments demonstrate the effectiveness of the proposed scheme in handling large mass ratios of heavy and light species, as well as capturing the epochal relaxation phenomenon.

Parameter-efficient finetuning (PEFT) has become ubiquitous to adapt foundation models to downstream task requirements while retaining their generalization ability. However, the amount of additionally introduced parameters and compute for successful adaptation and hyperparameter searches can explode quickly, especially when deployed at scale to serve numerous individual requests. To ensure effective, parameter-efficient, and hyperparameter-robust adaptation, we propose the ETHER transformation family, which performs Efficient fineTuning via HypErplane Reflections. By design, ETHER transformations require a minimal number of parameters, are less likely to deteriorate model performance, and exhibit robustness to hyperparameter and learning rate choices. In particular, we introduce ETHER and its relaxation ETHER+, which match or outperform existing PEFT methods with significantly fewer parameters (sim10-100 times lower than LoRA or OFT) across multiple image synthesis and natural language tasks without exhaustive hyperparameter tuning. Finally, we investigate the recent emphasis on Hyperspherical Energy retention for adaptation and raise questions on its practical utility. The code is available at https://github.com/mwbini/ether.

Merging models fine-tuned from a common, extensively pre-trained large model but specialized for different tasks has been demonstrated as a cheap and scalable strategy to construct a multi-task model that performs well across diverse tasks. Recent research, exemplified by task arithmetic, highlights that this multi-task model can be derived through arithmetic operations on task vectors. Nevertheless, current merging techniques frequently resolve potential conflicts among parameters from task-specific models by evaluating individual attributes, such as the parameters' magnitude or sign, overlooking their collective impact on the overall functionality of the model. In this work, we propose the CONtinuous relaxation of disCRETE (Concrete) subspace learning method to identify a common low-dimensional subspace and utilize its shared information to track the interference problem without sacrificing much performance. Specifically, we model the problem as a bi-level optimization problem and introduce a meta-learning framework to find the Concrete subspace mask through gradient-based techniques. At the upper level, we focus on learning a shared Concrete mask to identify the subspace, while at the inner level, model merging is performed to maximize the performance of the merged model. We conduct extensive experiments on both vision domain and language domain, and the results demonstrate the effectiveness of our method. The code is available at https://github.com/tanganke/subspace_fusion

Proprioception is the "sixth sense" that detects limb postures with motor neurons. It requires a natural integration between the musculoskeletal systems and sensory receptors, which is challenging among modern robots that aim for lightweight, adaptive, and sensitive designs at a low cost. Here, we present the Soft Polyhedral Network with an embedded vision for physical interactions, capable of adaptive kinesthesia and viscoelastic proprioception by learning kinetic features. This design enables passive adaptations to omni-directional interactions, visually captured by a miniature high-speed motion tracking system embedded inside for proprioceptive learning. The results show that the soft network can infer real-time 6D forces and torques with accuracies of 0.25/0.24/0.35 N and 0.025/0.034/0.006 Nm in dynamic interactions. We also incorporate viscoelasticity in proprioception during static adaptation by adding a creep and relaxation modifier to refine the predicted results. The proposed soft network combines simplicity in design, omni-adaptation, and proprioceptive sensing with high accuracy, making it a versatile solution for robotics at a low cost with more than 1 million use cycles for tasks such as sensitive and competitive grasping, and touch-based geometry reconstruction. This study offers new insights into vision-based proprioception for soft robots in adaptive grasping, soft manipulation, and human-robot interaction.

It is often advantageous to train models on a subset of the available train examples, because the examples are of variable quality or because one would like to train with fewer examples, without sacrificing performance. We present Gradient Information Optimization (GIO), a scalable, task-agnostic approach to this data selection problem that requires only a small set of (unlabeled) examples representing a target distribution. GIO begins from a natural, information-theoretic objective that is intractable in practice. Our contribution is in showing that it can be made highly scalable through a simple relaxation of the objective and a highly efficient implementation. In experiments with machine translation, spelling correction, and image recognition, we show that GIO delivers outstanding results with very small train sets. These findings are robust to different representation models and hyperparameters for GIO itself. GIO is task- and domain-agnostic and can be applied out-of-the-box to new datasets and domains.

One prominent approach toward resolving the adversarial vulnerability of deep neural networks is the two-player zero-sum paradigm of adversarial training, in which predictors are trained against adversarially chosen perturbations of data. Despite the promise of this approach, algorithms based on this paradigm have not engendered sufficient levels of robustness and suffer from pathological behavior like robust overfitting. To understand this shortcoming, we first show that the commonly used surrogate-based relaxation used in adversarial training algorithms voids all guarantees on the robustness of trained classifiers. The identification of this pitfall informs a novel non-zero-sum bilevel formulation of adversarial training, wherein each player optimizes a different objective function. Our formulation yields a simple algorithmic framework that matches and in some cases outperforms state-of-the-art attacks, attains comparable levels of robustness to standard adversarial training algorithms, and does not suffer from robust overfitting.

A popular approach for sequential decision-making is to perform simulator-based search guided with Machine Learning (ML) methods like policy learning. On the other hand, model-relaxation heuristics can guide the search effectively if a full declarative model is available. In this work, we consider how a practitioner can improve ML-based black-box planning on settings where a complete symbolic model is not available. We show that specifying an incomplete STRIPS model that describes only part of the problem enables the use of relaxation heuristics. Our findings on several planning domains suggest that this is an effective way to improve ML-based black-box planning beyond collecting more data or tuning ML architectures.

Reinforcement Learning from Human Feedback (RLHF) is widely used for aligning large language models, yet practitioners face a persistent puzzle: improving safety often reduces fairness, scaling to diverse populations becomes computationally intractable, and making systems robust often amplifies majority biases. We formalize this tension as the Alignment Trilemma: no RLHF system can simultaneously achieve (i) epsilon-representativeness across diverse human values, (ii) polynomial tractability in sample and compute complexity, and (iii) delta-robustness against adversarial perturbations and distribution shift. Through a complexity-theoretic analysis integrating statistical learning theory and robust optimization, we prove that achieving both representativeness (epsilon <= 0.01) and robustness (delta <= 0.001) for global-scale populations requires Omega(2^{d_context}) operations, which is super-polynomial in the context dimensionality. We show that current RLHF implementations resolve this trilemma by sacrificing representativeness: they collect only 10^3--10^4 samples from homogeneous annotator pools while 10^7--10^8 samples are needed for true global representation. Our framework provides a unified explanation for documented RLHF pathologies including preference collapse, sycophancy, and systematic bias amplification. We conclude with concrete directions for navigating these fundamental trade-offs through strategic relaxations of alignment requirements.

We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving graph spectra, which are also computationally expensive due to the temporal aspect along with the graph vertex domain. We view the problem as an optimization over the Laplacian of the continuous time dynamic graph. Additionally, we propose pseudo-spectrum relaxations that decompose the transformation process, making it highly computationally efficient. The EFT method adeptly captures the evolving graph's structural and positional properties, making it effective for downstream tasks on evolving graphs. Hence, as a reference implementation, we develop a simple neural model induced with EFT for capturing evolving graph spectra. We empirically validate our theoretical findings on a number of large-scale and standard temporal graph benchmarks and demonstrate that our model achieves state-of-the-art performance.

Methods of computational quantum chemistry provide accurate approximations of molecular properties crucial for computer-aided drug discovery and other areas of chemical science. However, high computational complexity limits the scalability of their applications. Neural network potentials (NNPs) are a promising alternative to quantum chemistry methods, but they require large and diverse datasets for training. This work presents a new dataset and benchmark called nabla^2DFT that is based on the nablaDFT. It contains twice as much molecular structures, three times more conformations, new data types and tasks, and state-of-the-art models. The dataset includes energies, forces, 17 molecular properties, Hamiltonian and overlap matrices, and a wavefunction object. All calculations were performed at the DFT level (omegaB97X-D/def2-SVP) for each conformation. Moreover, nabla^2DFT is the first dataset that contains relaxation trajectories for a substantial number of drug-like molecules. We also introduce a novel benchmark for evaluating NNPs in molecular property prediction, Hamiltonian prediction, and conformational optimization tasks. Finally, we propose an extendable framework for training NNPs and implement 10 models within it.

We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. In contrast to the ubiquitous Empirical Risk Minimization (ERM) framework, which optimizes for average performance, FL demands satisfactory performance on every individual data point. Since any model that meets the prescribed performance threshold is a valid FL solution, the choice of optimization algorithm and its dynamics play a crucial role in shaping the properties of the resulting solutions. In particular, we study a primal-dual approach which dynamically re-weights the importance of each sample during training. To address the challenge of setting a meaningful threshold in practice, we introduce a relaxation of FL that incorporates slack variables of minimal norm. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.

Magnetic Resonance Imaging with tagging (tMRI) has long been utilized for quantifying tissue motion and strain during deformation. However, a phenomenon known as tag fading, a gradual decrease in tag visibility over time, often complicates post-processing. The first contribution of this study is to model tag fading by considering the interplay between T_1 relaxation and the repeated application of radio frequency (RF) pulses during serial imaging sequences. This is a factor that has been overlooked in prior research on tMRI post-processing. Further, we have observed an emerging trend of utilizing raw tagged MRI within a deep learning-based (DL) registration framework for motion estimation. In this work, we evaluate and analyze the impact of commonly used image similarity objectives in training DL registrations on raw tMRI. This is then compared with the Harmonic Phase-based approach, a traditional approach which is claimed to be robust to tag fading. Our findings, derived from both simulated images and an actual phantom scan, reveal the limitations of various similarity losses in raw tMRI and emphasize caution in registration tasks where image intensity changes over time.

Model predictive control (MPC)-based energy management systems (EMS) are essential for ensuring optimal, secure, and stable operation in microgrids with high penetrations of distributed energy resources. However, due to the high computational cost for the decision-making, the conventional MPC-based EMS typically adopts a simplified integrated-bus power balance model. While this simplification is effective for small networks, large-scale systems require a more detailed branch flow model to account for the increased impact of grid power losses and security constraints. This work proposes an efficient and reliable MPC-based EMS that incorporates power-loss effects and grid-security constraints. %, while adaptively shaping the battery power profile in response to online renewable inputs, achieving reduced operational costs. It enhances system reliability, reduces operational costs, and shows strong potential for online implementation due to its reduced computational effort. Specifically, a second-order cone program (SOCP) branch flow relaxation is integrated into the constraint set, yielding a convex formulation that guarantees globally optimal solutions with high computational efficiency. Owing to the radial topology of the microgrid, this relaxation is practically tight, ensuring equivalence to the original problem. Building on this foundation, an online demand response (DR) module is designed to further reduce the operation cost through peak shaving. To the best of our knowledge, no prior MPC-EMS framework has simultaneously modeled losses and security constraints while coordinating flexible loads within a unified architecture. The developed framework enables secure operation with effective peak shaving and reduced total cost. The effectiveness of the proposed method is validated on 10-bus, 18-bus, and 33-bus systems.

SO(3)-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks in which CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of SO(3)-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the O(L^3) CG paths into a single shared parameter set without compromising equivariance, where L is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from O(L^6) to O(L^4). We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS/tree/main/OpenMol/TDN{https://github.com/divelab/AIRS/}).

Accurate potential energy surface (PES) descriptions are essential for atomistic simulations of materials. Universal machine learning interatomic potentials (UMLIPs)^{1-3} offer a computationally efficient alternative to density functional theory (DFT)^4 for PES modeling across the periodic table. However, their accuracy today is fundamentally constrained due to a reliance on DFT relaxation data.^{5,6} Here, we introduce MatPES, a foundational PES dataset comprising sim 400,000 structures carefully sampled from 281 million molecular dynamics snapshots that span 16 billion atomic environments. We demonstrate that UMLIPs trained on the modestly sized MatPES dataset can rival, or even outperform, prior models trained on much larger datasets across a broad range of equilibrium, near-equilibrium, and molecular dynamics property benchmarks. We also introduce the first high-fidelity PES dataset based on the revised regularized strongly constrained and appropriately normed (r^2SCAN) functional^7 with greatly improved descriptions of interatomic bonding. The open source MatPES initiative emphasizes the importance of data quality over quantity in materials science and enables broad community-driven advancements toward more reliable, generalizable, and efficient UMLIPs for large-scale materials discovery and design.

The properties of the stellar cluster surrounding Sagittarius A* can be assessed indirectly through the motion of the S-stars. Specifically, the current accuracy to which the prograde precession of the S2 star is measured allows to place significant constraints on the extended mass enclosed by its orbit. We suggest that high velocity destructive collisions (DCs) offer a natural mechanism for depleting the mass inside the S2 orbit, thus allowing to reconcile the measured precession and the existence of a dense stellar cluster. Such a solution is especially necessary when considering that stars are supplied to the inner part of the cluster by both dynamical relaxation and by stars being captured in tight orbits during tidal disruption of binaries. We use analytic arguments and results from simulations to demonstrate that in order to obtain a precession that is consistent with observations, collisional depletion is necessary if the capture rate is greater than a few 10^{-6} yr^{-1}. We also show that fluctuations arising from the finite number of stars cannot serve as an alternative to DCs for generating consistency with the observed S2 precession. We conclude that astrometric observations of the S-stars provide a meaningful indication that the inner part of our galactic center is shaped by collisional depletion, supporting the hypothesis that DCs occur in galactic nuclei at an astrophysically significant rate.

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize the optimization problem using a continuous relaxation of the acyclicity property. The computational cost of evaluating graph acyclicity is cubic on the number of nodes and significantly affects scalability. In this paper we introduce COSMO, a constraint-free continuous optimization scheme for acyclic structure learning. At the core of our method, we define a differentiable approximation of an orientation matrix parameterized by a single priority vector. Differently from previous work, our parameterization fits a smooth orientation matrix and the resulting acyclic adjacency matrix without evaluating acyclicity at any step. Despite the absence of explicit constraints, we prove that COSMO always converges to an acyclic solution. In addition to being asymptotically faster, our empirical analysis highlights how COSMO performance on graph reconstruction compares favorably with competing structure learning methods.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

This paper studies the online node classification problem under a transductive learning setting. Current methods either invert a graph kernel matrix with O(n^3) runtime and O(n^2) space complexity or sample a large volume of random spanning trees, thus are difficult to scale to large graphs. In this work, we propose an improvement based on the online relaxation technique introduced by a series of works (Rakhlin et al.,2012; Rakhlin and Sridharan, 2015; 2017). We first prove an effective regret O(n^{1+gamma}) when suitable parameterized graph kernels are chosen, then propose an approximate algorithm FastONL enjoying O(kn^{1+gamma}) regret based on this relaxation. The key of FastONL is a generalized local push method that effectively approximates inverse matrix columns and applies to a series of popular kernels. Furthermore, the per-prediction cost is O(vol({S})log 1/epsilon) locally dependent on the graph with linear memory cost. Experiments show that our scalable method enjoys a better tradeoff between local and global consistency.

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.

Vector font synthesis is a challenging and ongoing problem in the fields of Computer Vision and Computer Graphics. The recently-proposed DeepVecFont achieved state-of-the-art performance by exploiting information of both the image and sequence modalities of vector fonts. However, it has limited capability for handling long sequence data and heavily relies on an image-guided outline refinement post-processing. Thus, vector glyphs synthesized by DeepVecFont still often contain some distortions and artifacts and cannot rival human-designed results. To address the above problems, this paper proposes an enhanced version of DeepVecFont mainly by making the following three novel technical contributions. First, we adopt Transformers instead of RNNs to process sequential data and design a relaxation representation for vector outlines, markedly improving the model's capability and stability of synthesizing long and complex outlines. Second, we propose to sample auxiliary points in addition to control points to precisely align the generated and target B\'ezier curves or lines. Finally, to alleviate error accumulation in the sequential generation process, we develop a context-based self-refinement module based on another Transformer-based decoder to remove artifacts in the initially synthesized glyphs. Both qualitative and quantitative results demonstrate that the proposed method effectively resolves those intrinsic problems of the original DeepVecFont and outperforms existing approaches in generating English and Chinese vector fonts with complicated structures and diverse styles.

The two-stage object pose estimation paradigm first detects semantic keypoints on the image and then estimates the 6D pose by minimizing reprojection errors. Despite performing well on standard benchmarks, existing techniques offer no provable guarantees on the quality and uncertainty of the estimation. In this paper, we inject two fundamental changes, namely conformal keypoint detection and geometric uncertainty propagation, into the two-stage paradigm and propose the first pose estimator that endows an estimation with provable and computable worst-case error bounds. On one hand, conformal keypoint detection applies the statistical machinery of inductive conformal prediction to convert heuristic keypoint detections into circular or elliptical prediction sets that cover the groundtruth keypoints with a user-specified marginal probability (e.g., 90%). Geometric uncertainty propagation, on the other, propagates the geometric constraints on the keypoints to the 6D object pose, leading to a Pose UnceRtainty SEt (PURSE) that guarantees coverage of the groundtruth pose with the same probability. The PURSE, however, is a nonconvex set that does not directly lead to estimated poses and uncertainties. Therefore, we develop RANdom SAmple averaGing (RANSAG) to compute an average pose and apply semidefinite relaxation to upper bound the worst-case errors between the average pose and the groundtruth. On the LineMOD Occlusion dataset we demonstrate: (i) the PURSE covers the groundtruth with valid probabilities; (ii) the worst-case error bounds provide correct uncertainty quantification; and (iii) the average pose achieves better or similar accuracy as representative methods based on sparse keypoints.

Modern neural models trained on textual data rely on pre-trained representations that emerge without direct supervision. As these representations are increasingly being used in real-world applications, the inability to control their content becomes an increasingly important problem. We formulate the problem of identifying and erasing a linear subspace that corresponds to a given concept, in order to prevent linear predictors from recovering the concept. We model this problem as a constrained, linear maximin game, and show that existing solutions are generally not optimal for this task. We derive a closed-form solution for certain objectives, and propose a convex relaxation, \method, that works well for others. When evaluated in the context of binary gender removal, the method recovers a low-dimensional subspace whose removal mitigates bias by intrinsic and extrinsic evaluation. We show that the method is highly expressive, effectively mitigating bias in deep nonlinear classifiers while maintaining tractability and interpretability.

Differentiable Architecture Search (DARTS) has attracted a lot of attention due to its simplicity and small search costs achieved by a continuous relaxation and an approximation of the resulting bi-level optimization problem. However, DARTS does not work robustly for new problems: we identify a wide range of search spaces for which DARTS yields degenerate architectures with very poor test performance. We study this failure mode and show that, while DARTS successfully minimizes validation loss, the found solutions generalize poorly when they coincide with high validation loss curvature in the architecture space. We show that by adding one of various types of regularization we can robustify DARTS to find solutions with less curvature and better generalization properties. Based on these observations, we propose several simple variations of DARTS that perform substantially more robustly in practice. Our observations are robust across five search spaces on three image classification tasks and also hold for the very different domains of disparity estimation (a dense regression task) and language modelling.

Speculative decoding accelerates autoregressive speech generation by letting a fast draft model propose tokens that a larger target model verifies. However, for speech LLMs that generate acoustic tokens, exact token matching is overly restrictive: many discrete tokens are acoustically or semantically interchangeable, reducing acceptance rates and limiting speedups. We introduce Principled Coarse-Graining (PCG), which verifies proposals at the level of Acoustic Similarity Groups (ASGs) derived from the target model's embedding space. By splitting each token's probability mass across the overlapping groups that contain it, we define an overlap-aware coarse-grained distribution and perform rejection sampling on the resulting group variable. This yields an exactness guarantee at the group level while allowing the accepted draft token to stand in for any member of the group in practice. On LibriTTS, PCG increases acceptance and throughput relative to standard speculative decoding and prior speech-specific relaxations while maintaining intelligibility and speaker similarity. These results suggest acoustically aware, group-level acceptance as a simple and general way to accelerate speech token generation while maintaining speech quality.

Lipschitz constants are connected to many properties of neural networks, such as robustness, fairness, and generalization. Existing methods for computing Lipschitz constants either produce relatively loose upper bounds or are limited to small networks. In this paper, we develop an efficient framework for computing the ell_infty local Lipschitz constant of a neural network by tightly upper bounding the norm of Clarke Jacobian via linear bound propagation. We formulate the computation of local Lipschitz constants with a linear bound propagation process on a high-order backward graph induced by the chain rule of Clarke Jacobian. To enable linear bound propagation, we derive tight linear relaxations for specific nonlinearities in Clarke Jacobian. This formulate unifies existing ad-hoc approaches such as RecurJac, which can be seen as a special case of ours with weaker relaxations. The bound propagation framework also allows us to easily borrow the popular Branch-and-Bound (BaB) approach from neural network verification to further tighten Lipschitz constants. Experiments show that on tiny models, our method produces comparable bounds compared to exact methods that cannot scale to slightly larger models; on larger models, our method efficiently produces tighter results than existing relaxed or naive methods, and our method scales to much larger practical models that previous works could not handle. We also demonstrate an application on provable monotonicity analysis. Code is available at https://github.com/shizhouxing/Local-Lipschitz-Constants.

We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters. Our learnable geometric scattering (LEGS) module enables adaptive tuning of the wavelets to encourage band-pass features to emerge in learned representations. The incorporation of our LEGS-module in GNNs enables the learning of longer-range graph relations compared to many popular GNNs, which often rely on encoding graph structure via smoothness or similarity between neighbors. Further, its wavelet priors result in simplified architectures with significantly fewer learned parameters compared to competing GNNs. We demonstrate the predictive performance of LEGS-based networks on graph classification benchmarks, as well as the descriptive quality of their learned features in biochemical graph data exploration tasks. Our results show that LEGS-based networks match or outperforms popular GNNs, as well as the original geometric scattering construction, on many datasets, in particular in biochemical domains, while retaining certain mathematical properties of handcrafted (non-learned) geometric scattering.

Catalyst discovery and optimization is key to solving many societal and energy challenges including solar fuels synthesis, long-term energy storage, and renewable fertilizer production. Despite considerable effort by the catalysis community to apply machine learning models to the computational catalyst discovery process, it remains an open challenge to build models that can generalize across both elemental compositions of surfaces and adsorbate identity/configurations, perhaps because datasets have been smaller in catalysis than related fields. To address this we developed the OC20 dataset, consisting of 1,281,040 Density Functional Theory (DFT) relaxations (~264,890,000 single point evaluations) across a wide swath of materials, surfaces, and adsorbates (nitrogen, carbon, and oxygen chemistries). We supplemented this dataset with randomly perturbed structures, short timescale molecular dynamics, and electronic structure analyses. The dataset comprises three central tasks indicative of day-to-day catalyst modeling and comes with pre-defined train/validation/test splits to facilitate direct comparisons with future model development efforts. We applied three state-of-the-art graph neural network models (CGCNN, SchNet, Dimenet++) to each of these tasks as baseline demonstrations for the community to build on. In almost every task, no upper limit on model size was identified, suggesting that even larger models are likely to improve on initial results. The dataset and baseline models are both provided as open resources, as well as a public leader board to encourage community contributions to solve these important tasks.

When quantizing neural networks, assigning each floating-point weight to its nearest fixed-point value is the predominant approach. We find that, perhaps surprisingly, this is not the best we can do. In this paper, we propose AdaRound, a better weight-rounding mechanism for post-training quantization that adapts to the data and the task loss. AdaRound is fast, does not require fine-tuning of the network, and only uses a small amount of unlabelled data. We start by theoretically analyzing the rounding problem for a pre-trained neural network. By approximating the task loss with a Taylor series expansion, the rounding task is posed as a quadratic unconstrained binary optimization problem. We simplify this to a layer-wise local loss and propose to optimize this loss with a soft relaxation. AdaRound not only outperforms rounding-to-nearest by a significant margin but also establishes a new state-of-the-art for post-training quantization on several networks and tasks. Without fine-tuning, we can quantize the weights of Resnet18 and Resnet50 to 4 bits while staying within an accuracy loss of 1%.

We introduce a novel approach to large language model (LLM) distillation by formulating it as a constrained reinforcement learning problem. While recent work has begun exploring the integration of task-specific rewards into distillation processes, existing methods typically rely on ad-hoc reward weighting. We propose a principled optimization framework that maximizes task-specific rewards while constraining the divergence from the teacher model to remain below a specified threshold. Our approach adapts constrained state augmented reinforcement learning to the distillation setting, introducing a modified reward function that maintains theoretical guarantees of constraint satisfaction without requiring state augmentation or teacher model access during deployment and without the computational overhead of the dual Lagrangian methods. Through extensive experiments on mathematical reasoning tasks, we demonstrate that our method achieves better constraint satisfaction rates and better reasoning compared to the soft Lagrangian relaxation baselines while maintaining competitive task performance. Our framework provides a theoretically grounded and practically efficient solution for reward-aware distillation in resource-constrained settings.

Machine learning-based interatomic potentials and force fields depend critically on accurate atomic structures, yet such data are scarce due to the limited availability of experimentally resolved crystals. Although atomic-resolution electron microscopy offers a potential source of structural data, converting these images into simulation-ready formats remains labor-intensive and error-prone, creating a bottleneck for model training and validation. We introduce AutoMat, an end-to-end, agent-assisted pipeline that automatically transforms scanning transmission electron microscopy (STEM) images into atomic crystal structures and predicts their physical properties. AutoMat combines pattern-adaptive denoising, physics-guided template retrieval, symmetry-aware atomic reconstruction, fast relaxation and property prediction via MatterSim, and coordinated orchestration across all stages. We propose the first dedicated STEM2Mat-Bench for this task and evaluate performance using lattice RMSD, formation energy MAE, and structure-matching success rate. By orchestrating external tool calls, AutoMat enables a text-only LLM to outperform vision-language models in this domain, achieving closed-loop reasoning throughout the pipeline. In large-scale experiments over 450 structure samples, AutoMat substantially outperforms existing multimodal large language models and tools. These results validate both AutoMat and STEM2Mat-Bench, marking a key step toward bridging microscopy and atomistic simulation in materials science.The code and dataset are publicly available at https://github.com/yyt-2378/AutoMat and https://huggingface.co/datasets/yaotianvector/STEM2Mat.

On-policy reinforcement learning (RL), particularly Proximal Policy Optimization (PPO) and Group Relative Policy Optimization (GRPO), has become the dominant paradigm for fine-tuning large language models (LLMs). While policy ratio clipping stabilizes training, this heuristic hard constraint incurs a fundamental cost: it indiscriminately truncates gradients from high-return yet high-divergence actions, suppressing rare but highly informative "eureka moments" in complex reasoning. Moreover, once data becomes slightly stale, hard clipping renders it unusable, leading to severe sample inefficiency. In this work, we revisit the trust-region objective in policy optimization and show that explicitly constraining the variance (second central moment) of the policy ratio provides a principled and smooth relaxation of hard clipping. This distributional constraint stabilizes policy updates while preserving gradient signals from valuable trajectories. Building on this insight, we propose R^2VPO (Ratio-Variance Regularized Policy Optimization), a novel primal-dual framework that supports stable on-policy learning and enables principled off-policy data reuse by dynamically reweighting stale samples rather than discarding them. We extensively evaluate R^2VPO on fine-tuning state-of-the-art LLMs, including DeepSeek-Distill-Qwen-1.5B and the openPangu-Embedded series (1B and 7B), across challenging mathematical reasoning benchmarks. Experimental results show that R^2VPO consistently achieves superior asymptotic performance, with average relative gains of up to 17% over strong clipping-based baselines, while requiring approximately 50% fewer rollouts to reach convergence. These findings establish ratio-variance control as a promising direction for improving both stability and data efficiency in RL-based LLM alignment.

Modern deep residual networks perform substantial redundant computation by evaluating all residual blocks for every input, even when identity mappings suffice. We introduce CosineGate, an end-to-end differentiable architecture for dynamic routing in residual networks that uses cosine incompatibility between identity and residual feature representations as a self-supervised skip signal. CosineGate measures semantic redundancy through the Cosine Incompatibility Ratio (CIR), defined as 1 - cos(x, F(x)), and uses Gumbel-Softmax relaxation to enable per-sample, per-block gating during training. A progressive FLOPs regularization term controls average compute usage without destabilizing optimization. On CIFAR-10, CosineGate spans the accuracy-efficiency Pareto frontier: an aggressive configuration achieves 89.9 percent accuracy with 24.1 percent FLOPs savings, a balanced configuration achieves 91.3 percent accuracy with 28.5 percent savings at epoch 160, and a conservative configuration reaches a peak of 93.2 percent accuracy with minimal compute reduction. These results match or exceed ResNet-20 (91.3 percent) while reducing computation, without auxiliary supervision, distillation, or task-specific heuristics. Our results demonstrate that simple geometric measures of feature incompatibility provide a principled and effective signal for dynamic residual routing.

Computer vision methods that explicitly detect object parts and reason on them are a step towards inherently interpretable models. Existing approaches that perform part discovery driven by a fine-grained classification task make very restrictive assumptions on the geometric properties of the discovered parts; they should be small and compact. Although this prior is useful in some cases, in this paper we show that pre-trained transformer-based vision models, such as self-supervised DINOv2 ViT, enable the relaxation of these constraints. In particular, we find that a total variation (TV) prior, which allows for multiple connected components of any size, substantially outperforms previous work. We test our approach on three fine-grained classification benchmarks: CUB, PartImageNet and Oxford Flowers, and compare our results to previously published methods as well as a re-implementation of the state-of-the-art method PDiscoNet with a transformer-based backbone. We consistently obtain substantial improvements across the board, both on part discovery metrics and the downstream classification task, showing that the strong inductive biases in self-supervised ViT models require to rethink the geometric priors that can be used for unsupervised part discovery.

Vision-Language Models (VLMs) achieve strong multimodal performance but are costly to deploy, and post-training quantization often causes significant accuracy loss. Despite its potential, quantization-aware training for VLMs remains underexplored. We propose GRACE, a framework unifying knowledge distillation and QAT under the Information Bottleneck principle: quantization constrains information capacity while distillation guides what to preserve within this budget. Treating the teacher as a proxy for task-relevant information, we introduce confidence-gated decoupled distillation to filter unreliable supervision, relational centered kernel alignment to transfer visual token structures, and an adaptive controller via Lagrangian relaxation to balance fidelity against capacity constraints. Across extensive benchmarks on LLaVA and Qwen families, our INT4 models consistently outperform FP16 baselines (e.g., LLaVA-1.5-7B: 70.1 vs. 66.8 on SQA; Qwen2-VL-2B: 76.9 vs. 72.6 on MMBench), nearly matching teacher performance. Using real INT4 kernel, we achieve 3times throughput with 54% memory reduction. This principled framework significantly outperforms existing quantization methods, making GRACE a compelling solution for resource-constrained deployment.

We propose an abstract framework to establish the convergence of the iterates of stochastic versions of a broad range of monotone operator splitting methods in Hilbert spaces. This framework allows for the introduction of stochasticity at several levels: approximation of operators, selection of coordinates and operators in block-iterative implementations, and relaxation parameters. The proposed analysis involves a reduced inclusion model with two operators. At each iteration, stochastic approximations to points in the graphs of these two operators are used to form the update. The results are applied to derive the almost sure and L^2 convergence of stochastic versions of the proximal point algorithm, as well as of randomized block-iterative projective splitting methods for solving systems of coupled inclusions involving a mix of set-valued, cocoercive, and Lipschitzian monotone operators combined via various monotonicity-preserving operations.

The core of Transferable Utility (T.U.) games is a well-known solution concept from cooperative game theory yielding a cost allocation among n agents (called players) forming a coalition that is stable (i.e. no subset of players has an interest to deviate). In this paper, inspired by a practical application in the context of a decision support system for collaborative transportation in a Short Food Supply Chain (SFSC), we mainly focus on Traveling Salesman Games (TSGs), where the objective is to allocate the cost of a Traveling Salesman Problem (TSP) with n locations and 1 depot to n players, each linked to exactly one of the locations. Given the computational complexity of computing an element of the core and the cost of a TSP, we study semicore allocations: a relaxation of the core that only requires that the subsets of size n -1 and of size 1 do not wish to deviate from the coalition. In the literature, instances of TSGs with empty cores and semicores are found. Hence, this paper first surveys the methods to approximate stability whenever the core is empty, such as the cost of stability (computing the minimum amount of money to subsidize the coalition with to attain stability) and the ε-core (which is a set of allocations that allow subsets of players to exceed their actual cost, but at most of a value of ε). We prove that these two solution

We introduce a simple yet effective approach for separating transmitted and reflected light. Our key insight is that the powerful novel view synthesis capabilities provided by modern inverse rendering methods (e.g.,~3D Gaussian splatting) allow one to perform flash/no-flash reflection separation using unpaired measurements -- this relaxation dramatically simplifies image acquisition over conventional paired flash/no-flash reflection separation methods. Through extensive real-world experiments, we demonstrate our method, Flash-Splat, accurately reconstructs both transmitted and reflected scenes in 3D. Our method outperforms existing 3D reflection separation methods, which do not leverage illumination control, by a large margin. Our project webpage is at https://flash-splat.github.io/.

Chronotype compares individuals' circadian phase to others. It contextualizes mental health risk assessments and detection of social jet lag, which can hamper mental health and cognitive performance. Existing ways of determining chronotypes, such as Dim Light Melatonin Onset (DLMO) or the Morningness-Eveningness Questionnaire (MEQ), are limited by being discrete in time and time-intensive to update, meaning they rarely capture real-world variability across time. Chronotyping users based on a daily planner app might augment existing methods to enable assessment continuously and at scale. This paper reports the construction of a supervised binary classifier that attempts to demonstrate the feasibility of this approach. 1,460 registered users from the Owaves app opted in by filling out the MEQ survey between July 14, 2022, and May 1, 2023. 142 met the eligibility criteria. We used multimodal app data from individuals identified as morning and evening types from MEQ data, basing the classifier on app time series data. This included daily timing for 8 main lifestyle activity types: exercise, sleep, social interactions, meal times, relaxation, work, play, and miscellaneous, as defined in the app. The timing of activities showed substantial change across time, as well as heterogeneity by activity type. Our novel chronotyping classifier was able to predict the morningness and eveningness of its users with an ROC AUC of 0.70. Our findings demonstrate the feasibility of chronotype classification from multimodal, real-world app data, while highlighting fundamental challenges to applying discrete and fixed labels to complex, dynamic, multimodal behaviors. Our findings suggest a potential for real-time monitoring of shifts in chronotype specific to different causes (i.e. types of activity), which could feasibly be used to support future, prospective mental health support research.

In this work, we address the issue of quality of experience (QoE) in unmanned aerial vehicle (UAV) aided multiuser rate-splitting multiple access (RSMA) networks under secrecy constraints. The problem is formulated as maximization of sum mean opinion scores (MOSs) of the users. The problem is decomposed into two subproblems, beamforming and rate allocation and UAV trajectory subproblem. For, beamforming and rate allocation subproblem, we use the epigraph method, property of polynomials, and the norm-bounded error of channels, we linearize the objective function. Then, applying second-order conic (SOC) and first Taylor expansion, we convexify the remaining nonconvex constraints. For the highly nonconvex UAV trajectory, we unroll the constraints and we apply first Taylor expansion on the unrolled constraints. The simulation results demonstrate the efficiency of the proposed framework.

New methods for carbon dioxide removal are urgently needed to combat global climate change. Direct air capture (DAC) is an emerging technology to capture carbon dioxide directly from ambient air. Metal-organic frameworks (MOFs) have been widely studied as potentially customizable adsorbents for DAC. However, discovering promising MOF sorbents for DAC is challenging because of the vast chemical space to explore and the need to understand materials as functions of humidity and temperature. We explore a computational approach benefiting from recent innovations in machine learning (ML) and present a dataset named Open DAC 2023 (ODAC23) consisting of more than 38M density functional theory (DFT) calculations on more than 8,400 MOF materials containing adsorbed CO_2 and/or H_2O. ODAC23 is by far the largest dataset of MOF adsorption calculations at the DFT level of accuracy currently available. In addition to probing properties of adsorbed molecules, the dataset is a rich source of information on structural relaxation of MOFs, which will be useful in many contexts beyond specific applications for DAC. A large number of MOFs with promising properties for DAC are identified directly in ODAC23. We also trained state-of-the-art ML models on this dataset to approximate calculations at the DFT level. This open-source dataset and our initial ML models will provide an important baseline for future efforts to identify MOFs for a wide range of applications, including DAC.

Equilibrium propagation (EP) is a compelling alternative to the backpropagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to estimate unbiased gradients efficiently. Both requirements are challenging to implement in physical systems. Yet, whether and how weight asymmetry affects its applicability is unknown because, in practice, it may be masked by biases introduced through the finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias. For complex-differentiable non-symmetric networks, we show that the finite nudge does not pose a problem, as exact derivatives can still be estimated via a Cauchy integral. In contrast, weight asymmetry introduces bias resulting in low task performance due to poor alignment of EP's neuronal error vectors compared to BP. To mitigate this issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32x32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

In this paper we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free optimization method, as a stochastic relaxation of gradient descent. Remarkably, we observe that through communication of the particles, CBO exhibits a stochastic gradient descent (SGD)-like behavior despite solely relying on evaluations of the objective function. The fundamental value of such link between CBO and SGD lies in the fact that CBO is provably globally convergent to global minimizers for ample classes of nonsmooth and nonconvex objective functions, hence, on the one side, offering a novel explanation for the success of stochastic relaxations of gradient descent. On the other side, contrary to the conventional wisdom for which zero-order methods ought to be inefficient or not to possess generalization abilities, our results unveil an intrinsic gradient descent nature of such heuristics. This viewpoint furthermore complements previous insights into the working principles of CBO, which describe the dynamics in the mean-field limit through a nonlinear nonlocal partial differential equation that allows to alleviate complexities of the nonconvex function landscape. Our proofs leverage a completely nonsmooth analysis, which combines a novel quantitative version of the Laplace principle (log-sum-exp trick) and the minimizing movement scheme (proximal iteration). In doing so, we furnish useful and precise insights that explain how stochastic perturbations of gradient descent overcome energy barriers and reach deep levels of nonconvex functions. Instructive numerical illustrations support the provided theoretical insights.

In a recent work, Laforgue et al. introduce the model of last switch dependent (LSD) bandits, in an attempt to capture nonstationary phenomena induced by the interaction between the player and the environment. Examples include satiation, where consecutive plays of the same action lead to decreased performance, or deprivation, where the payoff of an action increases after an interval of inactivity. In this work, we take a step towards understanding the approximability of planning LSD bandits, namely, the (NP-hard) problem of computing an optimal arm-pulling strategy under complete knowledge of the model. In particular, we design the first efficient constant approximation algorithm for the problem and show that, under a natural monotonicity assumption on the payoffs, its approximation guarantee (almost) matches the state-of-the-art for the special and well-studied class of recharging bandits (also known as delay-dependent). In this attempt, we develop new tools and insights for this class of problems, including a novel higher-dimensional relaxation and the technique of mirroring the evolution of virtual states. We believe that these novel elements could potentially be used for approaching richer classes of action-induced nonstationary bandits (e.g., special instances of restless bandits). In the case where the model parameters are initially unknown, we develop an online learning adaptation of our algorithm for which we provide sublinear regret guarantees against its full-information counterpart.

Dynamic Mode Decomposition (DMD) is an equation-free method that aims at reconstructing the best linear fit from temporal datasets. In this paper, we show that DMD does not provide accurate approximation for datasets describing oscillatory dynamics, like spiral waves and relaxation oscillations, or spatio-temporal Turing instability. Inspired from the classical "divide and conquer" approach, we propose a piecewise version of DMD (pDMD) to overcome this problem. The main idea is to split the original dataset in N submatrices and then apply the exact (randomized) DMD method in each subset of the obtained partition. We describe the pDMD algorithm in detail and we introduce some error indicators to evaluate its performance when N is increased. Numerical experiments show that very accurate reconstructions are obtained by pDMD for datasets arising from time snapshots of some reaction-diffusion PDE systems, like the FitzHugh-Nagumo model, the lambda-omega system and the DIB morpho-chemical system for battery modeling.

The simulation of large-scale systems with complex electron interactions remains one of the greatest challenges for the atomistic modeling of materials. Although classical force fields often fail to describe the coupling between electronic states and ionic rearrangements, the more accurate ab-initio molecular dynamics suffers from computational complexity that prevents long-time and large-scale simulations, which are essential to study many technologically relevant phenomena, such as reactions, ion migrations, phase transformations, and degradation. In this work, we present the Crystal Hamiltonian Graph neural Network (CHGNet) as a novel machine-learning interatomic potential (MLIP), using a graph-neural-network-based force field to model a universal potential energy surface. CHGNet is pretrained on the energies, forces, stresses, and magnetic moments from the Materials Project Trajectory Dataset, which consists of over 10 years of density functional theory static and relaxation trajectories of sim 1.5 million inorganic structures. The explicit inclusion of magnetic moments enables CHGNet to learn and accurately represent the orbital occupancy of electrons, enhancing its capability to describe both atomic and electronic degrees of freedom. We demonstrate several applications of CHGNet in solid-state materials, including charge-informed molecular dynamics in Li_xMnO_2, the finite temperature phase diagram for Li_xFePO_4 and Li diffusion in garnet conductors. We critically analyze the significance of including charge information for capturing appropriate chemistry, and we provide new insights into ionic systems with additional electronic degrees of freedom that can not be observed by previous MLIPs.

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium -- such as Nash equilibrium and (Coarse) Correlated Equilibrium -- from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed "unilateral concentrability". Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

Hyperbolic neural networks have shown great potential for modeling complex data. However, existing hyperbolic networks are not completely hyperbolic, as they encode features in a hyperbolic space yet formalize most of their operations in the tangent space (a Euclidean subspace) at the origin of the hyperbolic space. This hybrid method greatly limits the modeling ability of networks. In this paper, we propose a fully hyperbolic framework to build hyperbolic networks based on the Lorentz model by adapting the Lorentz transformations (including boost and rotation) to formalize essential operations of neural networks. Moreover, we also prove that linear transformation in tangent spaces used by existing hyperbolic networks is a relaxation of the Lorentz rotation and does not include the boost, implicitly limiting the capabilities of existing hyperbolic networks. The experimental results on four NLP tasks show that our method has better performance for building both shallow and deep networks. Our code will be released to facilitate follow-up research.

This paper presents a novel preconditioning strategy for the classic 8-point algorithm (8-PA) for estimating an essential matrix from 360-FoV images (i.e., equirectangular images) in spherical projection. To alleviate the effect of uneven key-feature distributions and outlier correspondences, which can potentially decrease the accuracy of an essential matrix, our method optimizes a non-rigid transformation to deform a spherical camera into a new spatial domain, defining a new constraint and a more robust and accurate solution for an essential matrix. Through several experiments using random synthetic points, 360-FoV, and fish-eye images, we demonstrate that our normalization can increase the camera pose accuracy by about 20% without significantly overhead the computation time. In addition, we present further benefits of our method through both a constant weighted least-square optimization that improves further the well known Gold Standard Method (GSM) (i.e., the non-linear optimization by using epipolar errors); and a relaxation of the number of RANSAC iterations, both showing that our normalization outcomes a more reliable, robust, and accurate solution.

We present Vx2Text, a framework for text generation from multimodal inputs consisting of video plus text, speech, or audio. In order to leverage transformer networks, which have been shown to be effective at modeling language, each modality is first converted into a set of language embeddings by a learnable tokenizer. This allows our approach to perform multimodal fusion in the language space, thus eliminating the need for ad-hoc cross-modal fusion modules. To address the non-differentiability of tokenization on continuous inputs (e.g., video or audio), we utilize a relaxation scheme that enables end-to-end training. Furthermore, unlike prior encoder-only models, our network includes an autoregressive decoder to generate open-ended text from the multimodal embeddings fused by the language encoder. This renders our approach fully generative and makes it directly applicable to different "video+x to text" problems without the need to design specialized network heads for each task. The proposed framework is not only conceptually simple but also remarkably effective: experiments demonstrate that our approach based on a single architecture outperforms the state-of-the-art on three video-based text-generation tasks -- captioning, question answering and audio-visual scene-aware dialog.

Latent factor models are the driving forces of the state-of-the-art recommender systems, with an important insight of vectorizing raw input features into dense embeddings. The dimensions of different feature embeddings are often set to a same value empirically, which limits the predictive performance of latent factor models. Existing works have proposed heuristic or reinforcement learning-based methods to search for mixed feature embedding dimensions. For efficiency concern, these methods typically choose embedding dimensions from a restricted set of candidate dimensions. However, this restriction will hurt the flexibility of dimension selection, leading to suboptimal performance of search results. In this paper, we propose Differentiable Neural Input Search (DNIS), a method that searches for mixed feature embedding dimensions in a more flexible space through continuous relaxation and differentiable optimization. The key idea is to introduce a soft selection layer that controls the significance of each embedding dimension, and optimize this layer according to model's validation performance. DNIS is model-agnostic and thus can be seamlessly incorporated with existing latent factor models for recommendation. We conduct experiments with various architectures of latent factor models on three public real-world datasets for rating prediction, Click-Through-Rate (CTR) prediction, and top-k item recommendation. The results demonstrate that our method achieves the best predictive performance compared with existing neural input search approaches with fewer embedding parameters and less time cost.

Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging. Approximate methods based on learning compact representations, have been widely explored for this problem, such as locality sensitive hashing, product quantization, and PCA. In this work, in contrast to learning compact representations, we propose to learn high dimensional and sparse representations that have similar representational capacity as dense embeddings while being more efficient due to sparse matrix multiplication operations which can be much faster than dense multiplication. Following the key insight that the number of operations decreases quadratically with the sparsity of embeddings provided the non-zero entries are distributed uniformly across dimensions, we propose a novel approach to learn such distributed sparse embeddings via the use of a carefully constructed regularization function that directly minimizes a continuous relaxation of the number of floating-point operations (FLOPs) incurred during retrieval. Our experiments show that our approach is competitive to the other baselines and yields a similar or better speed-vs-accuracy tradeoff on practical datasets.

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the Generalized Gibbs Ensemble description for this infinite dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve towards the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a Generalized Gibbs Ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states which would potentially not be described by the Gibbs Generalized Ensemble description.