Daily Papers

Graph neural networks (GNNs) have achieved impressive performance in graph domain adaptation. However, extensive source graphs could be unavailable in real-world scenarios due to privacy and storage concerns. To this end, we investigate an underexplored yet practical problem of source-free graph domain adaptation, which transfers knowledge from source models instead of source graphs to a target domain. To solve this problem, we introduce a novel GNN-based approach called Rank and Align (RNA), which ranks graph similarities with spectral seriation for robust semantics learning, and aligns inharmonic graphs with harmonic graphs which close to the source domain for subgraph extraction. In particular, to overcome label scarcity, we employ the spectral seriation algorithm to infer the robust pairwise rankings, which can guide semantic learning using a similarity learning objective. To depict distribution shifts, we utilize spectral clustering and the silhouette coefficient to detect harmonic graphs, which the source model can easily classify. To reduce potential domain discrepancy, we extract domain-invariant subgraphs from inharmonic graphs by an adversarial edge sampling process, which guides the invariant learning of GNNs. Extensive experiments on several benchmark datasets demonstrate the effectiveness of our proposed RNA.

Graphs can be leveraged to model polyphonic multitrack symbolic music, where notes, chords and entire sections may be linked at different levels of the musical hierarchy by tonal and rhythmic relationships. Nonetheless, there is a lack of works that consider graph representations in the context of deep learning systems for music generation. This paper bridges this gap by introducing a novel graph representation for music and a deep Variational Autoencoder that generates the structure and the content of musical graphs separately, one after the other, with a hierarchical architecture that matches the structural priors of music. By separating the structure and content of musical graphs, it is possible to condition generation by specifying which instruments are played at certain times. This opens the door to a new form of human-computer interaction in the context of music co-creation. After training the model on existing MIDI datasets, the experiments show that the model is able to generate appealing short and long musical sequences and to realistically interpolate between them, producing music that is tonally and rhythmically consistent. Finally, the visualization of the embeddings shows that the model is able to organize its latent space in accordance with known musical concepts.

This paper presents a deep machine learning architecture, the "polyharmonic cascade" -- a sequence of packages of polyharmonic splines, where each layer is rigorously derived from the theory of random functions and the principles of indifference. This makes it possible to approximate nonlinear functions of arbitrary complexity while preserving global smoothness and a probabilistic interpretation. For the polyharmonic cascade, a training method alternative to gradient descent is proposed: instead of directly optimizing the coefficients, one solves a single global linear system on each batch with respect to the function values at fixed "constellations" of nodes. This yields synchronized updates of all layers, preserves the probabilistic interpretation of individual layers and theoretical consistency with the original model, and scales well: all computations reduce to 2D matrix operations efficiently executed on a GPU. Fast learning without overfitting on MNIST is demonstrated.

This paper approaches the problem of separating the notes from a quantized symbolic music piece (e.g., a MIDI file) into multiple voices and staves. This is a fundamental part of the larger task of music score engraving (or score typesetting), which aims to produce readable musical scores for human performers. We focus on piano music and support homophonic voices, i.e., voices that can contain chords, and cross-staff voices, which are notably difficult tasks that have often been overlooked in previous research. We propose an end-to-end system based on graph neural networks that clusters notes that belong to the same chord and connects them with edges if they are part of a voice. Our results show clear and consistent improvements over a previous approach on two datasets of different styles. To aid the qualitative analysis of our results, we support the export in symbolic music formats and provide a direct visualization of our outputs graph over the musical score. All code and pre-trained models are available at https://github.com/CPJKU/piano_svsep

Chord progressions encapsulate important information about music, pertaining to its structure and conveyed emotions. They serve as the backbone of musical composition, and in many cases, they are the sole information required for a musician to play along and follow the music. Despite their importance, chord progressions as a data domain remain underexplored. There is a lack of large-scale datasets suitable for deep learning applications, and limited research exploring chord progressions as an input modality. In this work, we present Chordonomicon, a dataset of over 666,000 songs and their chord progressions, annotated with structural parts, genre, and release date - created by scraping various sources of user-generated progressions and associated metadata. We demonstrate the practical utility of the Chordonomicon dataset for classification and generation tasks, and discuss its potential to provide valuable insights to the research community. Chord progressions are unique in their ability to be represented in multiple formats (e.g. text, graph) and the wealth of information chords convey in given contexts, such as their harmonic function . These characteristics make the Chordonomicon an ideal testbed for exploring advanced machine learning techniques, including transformers, graph machine learning, and hybrid systems that combine knowledge representation and machine learning.

We introduce materiomusic as a generative framework linking the hierarchical structures of matter with the compositional logic of music. Across proteins, spider webs and flame dynamics, vibrational and architectural principles recur as tonal hierarchies, harmonic progressions, and long-range musical form. Using reversible mappings, from molecular spectra to musical tones and from three-dimensional networks to playable instruments, we show how sound functions as a scientific probe, an epistemic inversion where listening becomes a mode of seeing and musical composition becomes a blueprint for matter. These mappings excavate deep time: patterns originating in femtosecond molecular vibrations or billion-year evolutionary histories become audible. We posit that novelty in science and art emerges when constraints cannot be satisfied within existing degrees of freedom, forcing expansion of the space of viable configurations. Selective imperfection provides the mechanism restoring balance between coherence and adaptability. Quantitative support comes from exhaustive enumeration of all 2^12 musical scales, revealing that culturally significant systems cluster in a mid-entropy, mid-defect corridor, directly paralleling the Hall-Petch optimum where intermediate defect densities maximize material strength. Iterating these mappings creates productive collisions between human creativity and physics, generating new information as musical structures encounter evolutionary constraints. We show how swarm-based AI models compose music exhibiting human-like structural signatures such as small-world connectivity, modular integration, long-range coherence, suggesting a route beyond interpolation toward invention. We show that science and art are generative acts of world-building under constraint, with vibration as a shared grammar organizing structure across scales.

Graph Neural Networks (GNNs) have recently gained traction in symbolic music tasks, yet a lack of a unified framework impedes progress. Addressing this gap, we present GraphMuse, a graph processing framework and library that facilitates efficient music graph processing and GNN training for symbolic music tasks. Central to our contribution is a new neighbor sampling technique specifically targeted toward meaningful behavior in musical scores. Additionally, GraphMuse integrates hierarchical modeling elements that augment the expressivity and capabilities of graph networks for musical tasks. Experiments with two specific musical prediction tasks -- pitch spelling and cadence detection -- demonstrate significant performance improvement over previous methods. Our hope is that GraphMuse will lead to a boost in, and standardization of, symbolic music processing based on graph representations. The library is available at https://github.com/manoskary/graphmuse

Recent advancements in deep learning have led to drastic improvements in speech segregation models. Despite their success and growing applicability, few efforts have been made to analyze the underlying principles that these networks learn to perform segregation. Here we analyze the role of harmonicity on two state-of-the-art Deep Neural Networks (DNN)-based models- Conv-TasNet and DPT-Net. We evaluate their performance with mixtures of natural speech versus slightly manipulated inharmonic speech, where harmonics are slightly frequency jittered. We find that performance deteriorates significantly if one source is even slightly harmonically jittered, e.g., an imperceptible 3% harmonic jitter degrades performance of Conv-TasNet from 15.4 dB to 0.70 dB. Training the model on inharmonic speech does not remedy this sensitivity, instead resulting in worse performance on natural speech mixtures, making inharmonicity a powerful adversarial factor in DNN models. Furthermore, additional analyses reveal that DNN algorithms deviate markedly from biologically inspired algorithms that rely primarily on timing cues and not harmonicity to segregate speech.

We investigate a dynamically adapting tuning scheme for microtonal tuning of musical instruments, allowing the performer to play music in just intonation in any key. Unlike other methods, which are based on a procedural analysis of the chordal structure, the tuning scheme continually solves a system of linear equations without making explicit decisions. In complex situations, where not all intervals of a chord can be tuned according to just frequency ratios, the method automatically yields a tempered compromise. We outline the implementation of the algorithm in an open-source software project that we have provided in order to demonstrate the feasibility of the tuning method.

We present Symphony, an E(3)-equivariant autoregressive generative model for 3D molecular geometries that iteratively builds a molecule from molecular fragments. Existing autoregressive models such as G-SchNet and G-SphereNet for molecules utilize rotationally invariant features to respect the 3D symmetries of molecules. In contrast, Symphony uses message-passing with higher-degree E(3)-equivariant features. This allows a novel representation of probability distributions via spherical harmonic signals to efficiently model the 3D geometry of molecules. We show that Symphony is able to accurately generate small molecules from the QM9 dataset, outperforming existing autoregressive models and approaching the performance of diffusion models.

We propose a new graph convolutional block, called MusGConv, specifically designed for the efficient processing of musical score data and motivated by general perceptual principles. It focuses on two fundamental dimensions of music, pitch and rhythm, and considers both relative and absolute representations of these components. We evaluate our approach on four different musical understanding problems: monophonic voice separation, harmonic analysis, cadence detection, and composer identification which, in abstract terms, translate to different graph learning problems, namely, node classification, link prediction, and graph classification. Our experiments demonstrate that MusGConv improves the performance on three of the aforementioned tasks while being conceptually very simple and efficient. We interpret this as evidence that it is beneficial to include perception-informed processing of fundamental musical concepts when developing graph network applications on musical score data.

This paper targets the perceptual task of separating the different interacting voices, i.e., monophonic melodic streams, in a polyphonic musical piece. We target symbolic music, where notes are explicitly encoded, and model this task as a Multi-Trajectory Tracking (MTT) problem from discrete observations, i.e., notes in a pitch-time space. Our approach builds a graph from a musical piece, by creating one node for every note, and separates the melodic trajectories by predicting a link between two notes if they are consecutive in the same voice/stream. This kind of local, greedy prediction is made possible by node embeddings created by a heterogeneous graph neural network that can capture inter- and intra-trajectory information. Furthermore, we propose a new regularization loss that encourages the output to respect the MTT premise of at most one incoming and one outgoing link for every node, favouring monophonic (voice) trajectories; this loss function might also be useful in other general MTT scenarios. Our approach does not use domain-specific heuristics, is scalable to longer sequences and a higher number of voices, and can handle complex cases such as voice inversions and overlaps. We reach new state-of-the-art results for the voice separation task in classical music of different styles.

In this paper, we study the flow of signals through linear paths with the nonlinear condition that a node emits a signal when it receives external stimuli or when two incoming signals from other nodes arrive coincidentally with a combined amplitude above a fixed threshold. Sets of such nodes form a polychrony group and can sometimes lead to cascades. In the context of this work, cascades are polychrony groups in which the number of nodes activated as a consequence of other nodes is greater than the number of externally activated nodes. The difference between these two numbers is the so-called profit. Given the initial conditions, we predict the conditions for a vertex to activate at a prescribed time and provide an algorithm to efficiently reconstruct a cascade. We develop a dictionary between polychrony groups and graph theory. We call the graph corresponding to a cascade a chinampa. This link leads to a topological classification of chinampas. We enumerate the chinampas of profits zero and one and the description of a family of chinampas isomorphic to a family of partially ordered sets, which implies that the enumeration problem of this family is equivalent to computing the Stanley-order polynomials of those partially ordered sets.

Generating musical audio directly with neural networks is notoriously difficult because it requires coherently modeling structure at many different timescales. Fortunately, most music is also highly structured and can be represented as discrete note events played on musical instruments. Herein, we show that by using notes as an intermediate representation, we can train a suite of models capable of transcribing, composing, and synthesizing audio waveforms with coherent musical structure on timescales spanning six orders of magnitude (~0.1 ms to ~100 s), a process we call Wave2Midi2Wave. This large advance in the state of the art is enabled by our release of the new MAESTRO (MIDI and Audio Edited for Synchronous TRacks and Organization) dataset, composed of over 172 hours of virtuosic piano performances captured with fine alignment (~3 ms) between note labels and audio waveforms. The networks and the dataset together present a promising approach toward creating new expressive and interpretable neural models of music.

Modeling the natural contour of fundamental frequency (F0) plays a critical role in music audio synthesis. However, transcribing and managing multiple F0 contours in polyphonic music is challenging, and explicit F0 contour modeling has not yet been explored for polyphonic instrumental synthesis. In this paper, we present ViolinDiff, a two-stage diffusion-based synthesis framework. For a given violin MIDI file, the first stage estimates the F0 contour as pitch bend information, and the second stage generates mel spectrogram incorporating these expressive details. The quantitative metrics and listening test results show that the proposed model generates more realistic violin sounds than the model without explicit pitch bend modeling. Audio samples are available online: daewoung.github.io/ViolinDiff-Demo.

In recent years, graphs have gained prominence across various domains, especially in recommendation systems. Within the realm of music recommendation, graphs play a crucial role in enhancing genre-based recommendations by integrating Mel-Frequency Cepstral Coefficients (MFCC) with advanced graph embeddings. This study explores the efficacy of Graph Convolutional Networks (GCN), GraphSAGE, and Graph Transformer (GT) models in learning embeddings that effectively capture intricate relationships between music items and genres represented within graph structures. Through comprehensive empirical evaluations on diverse real-world music datasets, our findings consistently demonstrate that these graph-based approaches outperform traditional methods that rely solely on MFCC features or collaborative filtering techniques. Specifically, the graph-enhanced models achieve notably higher accuracy in predicting genre-specific preferences and offering relevant music suggestions to users. These results underscore the effectiveness of utilizing graph embeddings to enrich feature representations and exploit latent associations within music data, thereby illustrating their potential to advance the capabilities of personalized and context-aware music recommendation systems. Keywords: graphs, recommendation systems, neural networks, MFCC

In this work, we present Score MUsic Graph (SMUG)-Explain, a framework for generating and visualizing explanations of graph neural networks applied to arbitrary prediction tasks on musical scores. Our system allows the user to visualize the contribution of input notes (and note features) to the network output, directly in the context of the musical score. We provide an interactive interface based on the music notation engraving library Verovio. We showcase the usage of SMUG-Explain on the task of cadence detection in classical music. All code is available on https://github.com/manoskary/SMUG-Explain.

We present a novel music generation framework for music infilling, with a user friendly interface. Infilling refers to the task of generating musical sections given the surrounding multi-track music. The proposed transformer-based framework is extensible for new control tokens as the added music control tokens such as tonal tension per bar and track polyphony level in this work. We explore the effects of including several musically meaningful control tokens, and evaluate the results using objective metrics related to pitch and rhythm. Our results demonstrate that adding additional control tokens helps to generate music with stronger stylistic similarities to the original music. It also provides the user with more control to change properties like the music texture and tonal tension in each bar compared to previous research which only provided control for track density. We present the model in a Google Colab notebook to enable interactive generation.

For a graph G with n vertices and m edges, Lin et al. Lin define the atom--bond sum-connectivity (ABS) matrix of G such that the (i,j)^{th} entry is \[ 1 - \frac{2{d_i + d_j}} \] if vertex v_i is adjacent to the vertex v_j, and 0 otherwise. In this article, we determine the characteristic polynomial of the ABS matrix for certain specific classes of graphs. Furthermore, we compute the ABS eigenvalues and the ABS energy for these classes.

In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding with a polyharmonic spline. However, a direct application of that solution is limited by O(N^3) computational cost and by a breakdown of the original theoretical assumptions when the input space has excessive dimensionality. This paper proposes a cascade architecture built from packages of polyharmonic splines that simultaneously addresses scalability and is theoretically justified for problems with unknown intrinsic low dimensionality. Efficient matrix procedures are presented for forward computation and end-to-end differentiation through the cascade.

Roman Numeral analysis is the important task of identifying chords and their functional context in pieces of tonal music. This paper presents a new approach to automatic Roman Numeral analysis in symbolic music. While existing techniques rely on an intermediate lossy representation of the score, we propose a new method based on Graph Neural Networks (GNNs) that enable the direct description and processing of each individual note in the score. The proposed architecture can leverage notewise features and interdependencies between notes but yield onset-wise representation by virtue of our novel edge contraction algorithm. Our results demonstrate that ChordGNN outperforms existing state-of-the-art models, achieving higher accuracy in Roman Numeral analysis on the reference datasets. In addition, we investigate variants of our model using proposed techniques such as NADE, and post-processing of the chord predictions. The full source code for this work is available at https://github.com/manoskary/chordgnn

We present and release MIDI-GPT, a generative system based on the Transformer architecture that is designed for computer-assisted music composition workflows. MIDI-GPT supports the infilling of musical material at the track and bar level, and can condition generation on attributes including: instrument type, musical style, note density, polyphony level, and note duration. In order to integrate these features, we employ an alternative representation for musical material, creating a time-ordered sequence of musical events for each track and concatenating several tracks into a single sequence, rather than using a single time-ordered sequence where the musical events corresponding to different tracks are interleaved. We also propose a variation of our representation allowing for expressiveness. We present experimental results that demonstrate that MIDI-GPT is able to consistently avoid duplicating the musical material it was trained on, generate music that is stylistically similar to the training dataset, and that attribute controls allow enforcing various constraints on the generated material. We also outline several real-world applications of MIDI-GPT, including collaborations with industry partners that explore the integration and evaluation of MIDI-GPT into commercial products, as well as several artistic works produced using it.

We show that coherent, long-form musical composition can emerge from a decentralized swarm of identical, frozen foundation models that coordinate via stigmergic, peer-to-peer signals, without any weight updates. We compare a centralized multi-agent system with a global critic to a fully decentralized swarm in which bar-wise agents sense and deposit harmonic, rhythmic, and structural cues, adapt short-term memory, and reach consensus. Across symbolic, audio, and graph-theoretic analyses, the swarm yields superior quality while delivering greater diversity and structural variety and leads across creativity metrics. The dynamics contract toward a stable configuration of complementary roles, and self-similarity networks reveal a small-world architecture with efficient long-range connectivity and specialized bridging motifs, clarifying how local novelties consolidate into global musical form. By shifting specialization from parameter updates to interaction rules, shared memory, and dynamic consensus, MusicSwarm provides a compute- and data-efficient route to long-horizon creative structure that is immediately transferable beyond music to collaborative writing, design, and scientific discovery.

Automatic music generation systems have gained in popularity and sophistication as advances in cloud computing have enabled large-scale complex computations such as deep models and optimization algorithms on personal devices. Yet, they still face an important challenge, that of long-term structure, which is key to conveying a sense of musical coherence. We present the MorpheuS music generation system designed to tackle this problem. MorpheuS' novel framework has the ability to generate polyphonic pieces with a given tension profile and long- and short-term repeated pattern structures. A mathematical model for tonal tension quantifies the tension profile and state-of-the-art pattern detection algorithms extract repeated patterns in a template piece. An efficient optimization metaheuristic, variable neighborhood search, generates music by assigning pitches that best fit the prescribed tension profile to the template rhythm while hard constraining long-term structure through the detected patterns. This ability to generate affective music with specific tension profile and long-term structure is particularly useful in a game or film music context. Music generated by the MorpheuS system has been performed live in concerts.

The aim of this work is to define a model based on deep learning that is able to identify different instrument timbres with as few parameters as possible. For this purpose, we have worked with classical orchestral instruments played with different dynamics, which are part of a few instrument families and which play notes in the same pitch range. It has been possible to assess the ability to classify instruments by timbre even if the instruments are playing the same note with the same intensity. The network employed uses a multi-head attention mechanism, with 8 heads and a dense network at the output taking as input the log-mel magnitude spectrograms of the sound samples. This network allows the identification of 20 instrument classes of the classical orchestra, achieving an overall F_1 value of 0.62. An analysis of the weights of the attention layer has been performed and the confusion matrix of the model is presented, allowing us to assess the ability of the proposed architecture to distinguish timbre and to establish the aspects on which future work should focus.

Modern music producers commonly use MIDI (Musical Instrument Digital Interface) to store their musical compositions. However, MIDI files created with digital software may lack the expressive characteristics of human performances, essentially leaving the velocity parameter - a control for note loudness - undefined, which defaults to a flat value. The task of filling MIDI velocity is termed MIDI velocity prediction, which uses regression models to enhance music expressiveness by adjusting only this parameter. In this paper, we introduce the U-Net, a widely adopted architecture in image colorization, to this task. By conceptualizing MIDI data as images, we adopt window attention and develop a custom loss function to address the sparsity of MIDI-converted images. Current dataset availability restricts our experiments to piano data. Evaluated on the MAESTRO v3 and SMD datasets, our proposed method for filling MIDI velocity outperforms previous approaches in both quantitative metrics and qualitative listening tests.

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.

We explore the potential of a popular distributional semantics vector space model, word2vec, for capturing meaningful relationships in ecological (complex polyphonic) music. More precisely, the skip-gram version of word2vec is used to model slices of music from a large corpus spanning eight musical genres. In this newly learned vector space, a metric based on cosine distance is able to distinguish between functional chord relationships, as well as harmonic associations in the music. Evidence, based on cosine distance between chord-pair vectors, suggests that an implicit circle-of-fifths exists in the vector space. In addition, a comparison between pieces in different keys reveals that key relationships are represented in word2vec space. These results suggest that the newly learned embedded vector representation does in fact capture tonal and harmonic characteristics of music, without receiving explicit information about the musical content of the constituent slices. In order to investigate whether proximity in the discovered space of embeddings is indicative of `semantically-related' slices, we explore a music generation task, by automatically replacing existing slices from a given piece of music with new slices. We propose an algorithm to find substitute slices based on spatial proximity and the pitch class distribution inferred in the chosen subspace. The results indicate that the size of the subspace used has a significant effect on whether slices belonging to the same key are selected. In sum, the proposed word2vec model is able to learn music-vector embeddings that capture meaningful tonal and harmonic relationships in music, thereby providing a useful tool for exploring musical properties and comparisons across pieces, as a potential input representation for deep learning models, and as a music generation device.

Developing generative models to create or conditionally create symbolic music presents unique challenges due to the combination of limited data availability and the need for high precision in note pitch. To address these challenges, we introduce an efficient Fine-Grained Guidance (FGG) approach within diffusion models. FGG guides the diffusion models to generate music that aligns more closely with the control and intent of expert composers, which is critical to improve the accuracy, listenability, and quality of generated music. This approach empowers diffusion models to excel in advanced applications such as improvisation, and interactive music creation. We derive theoretical characterizations for both the challenges in symbolic music generation and the effects of the FGG approach. We provide numerical experiments and subjective evaluation to demonstrate the effectiveness of our approach. We have published a demo page to showcase performances, as one of the first in the symbolic music literature's demo pages that enables real-time interactive generation.

Even with strong sequence models like Transformers, generating expressive piano performances with long-range musical structures remains challenging. Meanwhile, methods to compose well-structured melodies or lead sheets (melody + chords), i.e., simpler forms of music, gained more success. Observing the above, we devise a two-stage Transformer-based framework that Composes a lead sheet first, and then Embellishes it with accompaniment and expressive touches. Such a factorization also enables pretraining on non-piano data. Our objective and subjective experiments show that Compose & Embellish shrinks the gap in structureness between a current state of the art and real performances by half, and improves other musical aspects such as richness and coherence as well.

Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which limits generation scalability and hinders accurate modeling of the underlying distribution. To overcome these limitations, we propose a novel approach that significantly reduces the output space of existing graph generative models. Specifically, starting from the observation that many real-world graphs have low graph bandwidth, we restrict graph bandwidth during training and generation. Our strategy improves both generation scalability and quality without increasing architectural complexity or reducing expressiveness. Our approach is compatible with existing graph generative methods, and we describe its application to both autoregressive and one-shot models. We extensively validate our strategy on synthetic and real datasets, including molecular graphs. Our experiments show that, in addition to improving generation efficiency, our approach consistently improves generation quality and reconstruction accuracy. The implementation is made available.

This work investigates a case study of using physical-based sonification of Quadratic Unconstrained Binary Optimization (QUBO) problems, optimized by the Variational Quantum Eigensolver (VQE) algorithm. The VQE approximates the solution of the problem by using an iterative loop between the quantum computer and a classical optimization routine. This work explores the intermediary statevectors found in each VQE iteration as the means of sonifying the optimization process itself. The implementation was realised in the form of a musical interface prototype named Variational Quantum Harmonizer (VQH), providing potential design strategies for musical applications, focusing on chords, chord progressions, and arpeggios. The VQH can be used both to enhance data visualization or to create artistic pieces. The methodology is also relevant in terms of how an artist would gain intuition towards achieving a desired musical sound by carefully designing QUBO cost functions. Flexible mapping strategies could supply a broad portfolio of sounds for QUBO and quantum-inspired musical compositions, as demonstrated in a case study composition, "Dependent Origination" by Peter Thomas and Paulo Itaborai.

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small outer conductance. Such graphs have widespread application as a benchmark in the theoretical analysis of spectral clustering. We provide an efficient (epsilon,delta)-DP algorithm tailored specifically for such graphs. Our algorithm draws inspiration from the recent work of Chen et al., who developed DP algorithms for recovery of stochastic block models in cases where the graph comprises exactly two nearly-balanced clusters. Our algorithm works for well-clustered graphs with k nearly-balanced clusters, and the misclassification ratio almost matches the one of the best-known non-private algorithms. We conduct experimental evaluations on datasets with known ground truth clusters to substantiate the prowess of our algorithm. We also show that any (pure) epsilon-DP algorithm would result in substantial error.

This paper presents the Jazz Transformer, a generative model that utilizes a neural sequence model called the Transformer-XL for modeling lead sheets of Jazz music. Moreover, the model endeavors to incorporate structural events present in the Weimar Jazz Database (WJazzD) for inducing structures in the generated music. While we are able to reduce the training loss to a low value, our listening test suggests however a clear gap between the average ratings of the generated and real compositions. We therefore go one step further and conduct a series of computational analysis of the generated compositions from different perspectives. This includes analyzing the statistics of the pitch class, grooving, and chord progression, assessing the structureness of the music with the help of the fitness scape plot, and evaluating the model's understanding of Jazz music through a MIREX-like continuation prediction task. Our work presents in an analytical manner why machine-generated music to date still falls short of the artwork of humanity, and sets some goals for future work on automatic composition to further pursue.

We study Helly graphs of finite combinatorial dimension, i.e. whose injective hull is finite-dimensional. We describe very simple fine simplicial subdivisions of the injective hull of a Helly graph, following work of Lang. We also give a very explicit simplicial model of the injective hull of a Helly graphs, in terms of cliques which are intersections of balls. We use these subdivisions to prove that any automorphism of a Helly graph with finite combinatorial dimension is either elliptic or hyperbolic. Moreover, every such hyperbolic automorphism has an axis in an appropriate Helly subdivision, and its translation length is rational with uniformly bounded denominator.

Recent years have witnessed significant progress in generative models for music, featuring diverse architectures that balance output quality, diversity, speed, and user control. This study explores a user-friendly graphical interface enabling the drawing of masked regions for inpainting by an Hourglass Diffusion Transformer (HDiT) model trained on MIDI piano roll images. To enhance note generation in specified areas, masked regions can be "repainted" with extra noise. The non-latent HDiTs linear scaling with pixel count allows efficient generation in pixel space, providing intuitive and interpretable controls such as masking throughout the network and removing the need to operate in compressed latent spaces such as those provided by pretrained autoencoders. We demonstrate that, in addition to inpainting of melodies, accompaniment, and continuations, the use of repainting can help increase note density yielding musical structures closely matching user specifications such as rising, falling, or diverging melody and/or accompaniment, even when these lie outside the typical training data distribution. We achieve performance on par with prior results while operating at longer context windows, with no autoencoder, and can enable complex geometries for inpainting masks, increasing the options for machine-assisted composers to control the generated music.

We study the H-chromatic symmetric functions X_G^H (introduced in (arXiv:2011.06063) as a generalization of the chromatic symmetric function (CSF) X_G), which track homomorphisms from the graph G to the graph H. We focus first on the case of self-chromatic symmetric functions (self-CSFs) X_G^G, making some progress toward a conjecture from (arXiv:2011.06063) that the self-CSF, like the normal CSF, is always different for different trees. In particular, we show that the self-CSF distinguishes trees from non-trees with just one exception, we check using Sage that it distinguishes all trees on up to 12 vertices, and we show that it determines the number of legs of a spider and the degree sequence of a caterpillar given its spine length. We also show that the self-CSF detects the number of connected components of a forest, again with just one exception. Then we prove some results about the power sum expansions for H-CSFs when H is a complete bipartite graph, in particular proving that the conjecture from (arXiv:2011.06063) about p-monotonicity of ω(X_G^H) for H a star holds as long as H is sufficiently large compared to G. We also show that the self-CSFs of complete multipartite graphs form a basis for the ring Λ of symmetric functions, and we give some construction of bases for the vector space Λ^n of degree n symmetric functions using H-CSFs X_G^H where H is a fixed graph that is not a complete graph, answering a question from (arXiv:2011.06063) about whether such bases exist. However, we show that there generally do not exist such bases with G fixed, even with loops, answering another question from (arXiv:2011.06063). We also define the H-chromatic polynomial as an analogue of the chromatic polynomial, and ask when it is the same for different graphs.

Melody harmonization has long been closely associated with chorales composed by Johann Sebastian Bach. Previous works rarely emphasised chorale generation conditioned on chord progressions, and there has been a lack of focus on assistive compositional tools. In this paper, we first designed a music representation that encoded chord symbols for chord conditioning, and then proposed DeepChoir, a melody harmonization system that can generate a four-part chorale for a given melody conditioned on a chord progression. With controllable harmonicity, users can control the extent of harmonicity for generated chorales. Experimental results reveal the effectiveness of the music representation and the controllability of DeepChoir.

Recent advances in generative AI for music have achieved remarkable fidelity and stylistic diversity, yet these systems often fail to align with nuanced human preferences due to the specific loss functions they use. This paper advocates for the systematic application of preference alignment techniques to music generation, addressing the fundamental gap between computational optimization and human musical appreciation. Drawing on recent breakthroughs including MusicRL's large-scale preference learning, multi-preference alignment frameworks like diffusion-based preference optimization in DiffRhythm+, and inference-time optimization techniques like Text2midi-InferAlign, we discuss how these techniques can address music's unique challenges: temporal coherence, harmonic consistency, and subjective quality assessment. We identify key research challenges including scalability to long-form compositions, reliability amongst others in preference modelling. Looking forward, we envision preference-aligned music generation enabling transformative applications in interactive composition tools and personalized music services. This work calls for sustained interdisciplinary research combining advances in machine learning, music-theory to create music AI systems that truly serve human creative and experiential needs.

Music foundation models possess impressive music generation capabilities. When people compose music, they may infuse their understanding of music into their work, by using notes and intervals to craft melodies, chords to build progressions, and tempo to create a rhythmic feel. To what extent is this true of music generation models? More specifically, are fundamental Western music theory concepts observable within the "inner workings" of these models? Recent work proposed leveraging latent audio representations from music generation models towards music information retrieval tasks (e.g. genre classification, emotion recognition), which suggests that high-level musical characteristics are encoded within these models. However, probing individual music theory concepts (e.g. tempo, pitch class, chord quality) remains under-explored. Thus, we introduce SynTheory, a synthetic MIDI and audio music theory dataset, consisting of tempos, time signatures, notes, intervals, scales, chords, and chord progressions concepts. We then propose a framework to probe for these music theory concepts in music foundation models (Jukebox and MusicGen) and assess how strongly they encode these concepts within their internal representations. Our findings suggest that music theory concepts are discernible within foundation models and that the degree to which they are detectable varies by model size and layer.

In this paper, we explore the application of Large Language Models (LLMs) to the pre-training of music. While the prevalent use of MIDI in music modeling is well-established, our findings suggest that LLMs are inherently more compatible with ABC Notation, which aligns more closely with their design and strengths, thereby enhancing the model's performance in musical composition. To address the challenges associated with misaligned measures from different tracks during generation, we propose the development of a Synchronized Multi-Track ABC Notation (SMT-ABC Notation), which aims to preserve coherence across multiple musical tracks. Our contributions include a series of models capable of handling up to 8192 tokens, covering 90\% of the symbolic music data in our training set. Furthermore, we explore the implications of the Symbolic Music Scaling Law (SMS Law) on model performance. The results indicate a promising direction for future research in music generation, offering extensive resources for community-led research through our open-source contributions.

Graphs have often been used to answer questions about the interaction between real-world entities by taking advantage of their capacity to represent complex topologies. Complex networks are known to be graphs that capture such non-trivial topologies; they are able to represent human phenomena such as epidemic processes, the dynamics of populations, and the urbanization of cities. The investigation of complex networks has been extrapolated to many fields of science, with particular emphasis on computing techniques, including artificial intelligence. In such a case, the analysis of the interaction between entities of interest is transposed to the internal learning of algorithms, a paradigm whose investigation is able to expand the state of the art in Computer Science. By exploring this paradigm, this thesis puts together complex networks and machine learning techniques to improve the understanding of the human phenomena observed in pandemics, pendular migration, and street networks. Accordingly, we contribute with: (i) a new neural network architecture capable of modeling dynamic processes observed in spatial and temporal data with applications in epidemics propagation, weather forecasting, and patient monitoring in intensive care units; (ii) a machine-learning methodology for analyzing and predicting links in the scope of human mobility between all the cities of Brazil; and, (iii) techniques for identifying inconsistencies in the urban planning of cities while tracking the most influential vertices, with applications over Brazilian and worldwide cities. We obtained results sustained by sound evidence of advances to the state of the art in artificial intelligence, rigorous formalisms, and ample experimentation. Our findings rely upon real-world applications in a range of domains, demonstrating the applicability of our methodologies.

Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this hierarchy has propelled significant advances in GNN analysis and architecture developments, it suffers from several significant limitations. These include a complex definition that lacks direct guidance for model improvement and a WL hierarchy that is too coarse to study current GNNs. This paper introduces an alternative expressive power hierarchy based on the ability of GNNs to calculate equivariant polynomials of a certain degree. As a first step, we provide a full characterization of all equivariant graph polynomials by introducing a concrete basis, significantly generalizing previous results. Each basis element corresponds to a specific multi-graph, and its computation over some graph data input corresponds to a tensor contraction problem. Second, we propose algorithmic tools for evaluating the expressiveness of GNNs using tensor contraction sequences, and calculate the expressive power of popular GNNs. Finally, we enhance the expressivity of common GNN architectures by adding polynomial features or additional operations / aggregations inspired by our theory. These enhanced GNNs demonstrate state-of-the-art results in experiments across multiple graph learning benchmarks.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

Gross, Mansour, and Tucker introduced the partial-duality polynomial of a ribbon graph [Distributions, European J. Combin. 86, 1--20, 2020], the generating function enumerating partial duals by the Euler genus. Chmutov and Vignes-Tourneret wondered if this polynomial and its conjectured properties would hold for general delta-matroids, which are combinatorial abstractions of ribbon graphs. Yan and Jin contributed to this inquiry by identifying a subset of delta-matroids-specifically, even normal binary ones-whose twist polynomials are characterized by a singular term. Building upon this foundation, the current paper expands the scope of the investigation to encompass even non-binary delta-matroids, revealing that none of them have width-changing twists.

A Harris Graph is a tough, Eulerian, non-Hamiltonian graph. Several approaches to creating new Harris graphs from existing ones are explored, including creating families of Harris graphs and combining Harris graphs. Pictures of all Harris Graphs through order 9 and the number of Harris graphs through order 12 are included. We also prove a result about barnacle-free Harris graphs.

Indian classical music relies on a sophisticated microtonal system of 22 shrutis (pitch intervals), which provides expressive nuance beyond the 12-tone equal temperament system. Existing symbolic music processing tools fail to account for these microtonal distinctions and culturally specific raga grammars that govern melodic movement. We present ShrutiSense, a comprehensive symbolic pitch processing system designed for Indian classical music, addressing two critical tasks: (1) correcting westernized or corrupted pitch sequences, and (2) completing melodic sequences with missing values. Our approach employs complementary models for different tasks: a Shruti-aware finite-state transducer (FST) that performs contextual corrections within the 22-shruti framework and a grammar-constrained Shruti hidden Markov model (GC-SHMM) that incorporates raga-specific transition rules for contextual completions. Comprehensive evaluation on simulated data across five ragas demonstrates that ShrutiSense (FST model) achieves 91.3% shruti classification accuracy for correction tasks, with example sequences showing 86.7-90.0% accuracy at corruption levels of 0.2 to 0.4. The system exhibits robust performance under pitch noise up to +/-50 cents, maintaining consistent accuracy across ragas (90.7-91.8%), thus preserving the cultural authenticity of Indian classical music expression.

Let G be a graph with adjacency matrix A(G). We conjecture that \[2n^+(G) \le n^-(G)(n^-(G) + 1),\] where n^+(G) and n^-(G) denote the number of positive and negative eigenvalues of A(G), respectively. This conjecture generalizes to all graphs the well-known absolute bound for strongly regular graphs. The conjecture also relates to a question posed by Torgasev. We prove the conjecture for special graph families, including line graphs and planar graphs, and provide examples where the conjecture is exact. We also conjecture that for any connected graph G, its line graph L(G) satisfies n^+(L(G)) le n^-(L(G)) + 1 and obtain partial results.

We present Text2midi-InferAlign, a novel technique for improving symbolic music generation at inference time. Our method leverages text-to-audio alignment and music structural alignment rewards during inference to encourage the generated music to be consistent with the input caption. Specifically, we introduce two objectives scores: a text-audio consistency score that measures rhythmic alignment between the generated music and the original text caption, and a harmonic consistency score that penalizes generated music containing notes inconsistent with the key. By optimizing these alignment-based objectives during the generation process, our model produces symbolic music that is more closely tied to the input captions, thereby improving the overall quality and coherence of the generated compositions. Our approach can extend any existing autoregressive model without requiring further training or fine-tuning. We evaluate our work on top of Text2midi - an existing text-to-midi generation model, demonstrating significant improvements in both objective and subjective evaluation metrics.

Controllable music generation promotes the interaction between humans and composition systems by projecting the users' intent on their desired music. The challenge of introducing controllability is an increasingly important issue in the symbolic music generation field. When building controllable generative popular multi-instrument music systems, two main challenges typically present themselves, namely weak controllability and poor music quality. To address these issues, we first propose spatiotemporal features as powerful and fine-grained controls to enhance the controllability of the generative model. In addition, an efficient music representation called REMI_Track is designed to convert multitrack music into multiple parallel music sequences and shorten the sequence length of each track with Byte Pair Encoding (BPE) techniques. Subsequently, we release BandControlNet, a conditional model based on parallel Transformers, to tackle the multiple music sequences and generate high-quality music samples that are conditioned to the given spatiotemporal control features. More concretely, the two specially designed modules of BandControlNet, namely structure-enhanced self-attention (SE-SA) and Cross-Track Transformer (CTT), are utilized to strengthen the resulting musical structure and inter-track harmony modeling respectively. Experimental results tested on two popular music datasets of different lengths demonstrate that the proposed BandControlNet outperforms other conditional music generation models on most objective metrics in terms of fidelity and inference speed and shows great robustness in generating long music samples. The subjective evaluations show BandControlNet trained on short datasets can generate music with comparable quality to state-of-the-art models, while outperforming them significantly using longer datasets.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

We present Brain Harmony (BrainHarmonix), the first multimodal brain foundation model that unifies structural morphology and functional dynamics into compact 1D token representations. The model was pretrained on two of the largest neuroimaging datasets to date, encompassing 64,594 T1-weighted structural MRI 3D volumes (~ 14 million images) and 70,933 functional MRI (fMRI) time series. BrainHarmonix is grounded in two foundational neuroscience principles: structure complements function - structural and functional modalities offer distinct yet synergistic insights into brain organization; function follows structure - brain functional dynamics are shaped by cortical morphology. The modular pretraining process involves single-modality training with geometric pre-alignment followed by modality fusion through shared brain hub tokens. Notably, our dynamics encoder uniquely handles fMRI time series with heterogeneous repetition times (TRs), addressing a major limitation in existing models. BrainHarmonix is also the first to deeply compress high-dimensional neuroimaging signals into unified, continuous 1D tokens, forming a compact latent space of the human brain. BrainHarmonix achieves strong generalization across diverse downstream tasks, including neurodevelopmental and neurodegenerative disorder classification and cognition prediction - consistently outperforming previous approaches. Our models - pretrained on 8 H100 GPUs - aim to catalyze a new era of AI-driven neuroscience powered by large-scale multimodal neuroimaging.

This tutorial serves as a comprehensive guide for understanding graph databases, focusing on the fundamentals of graph theory while showcasing practical applications across various fields. It starts by introducing foundational concepts and delves into the structure of graphs through nodes and edges, covering different types such as undirected, directed, weighted, and unweighted graphs. Key graph properties, terminologies, and essential algorithms for network analysis are outlined, including Dijkstras shortest path algorithm and methods for calculating node centrality and graph connectivity. The tutorial highlights the advantages of graph databases over traditional relational databases, particularly in efficiently managing complex, interconnected data. It examines leading graph database systems such as Neo4j, Amazon Neptune, and ArangoDB, emphasizing their unique features for handling large datasets. Practical instructions on graph operations using NetworkX and Neo4j are provided, covering node and edge creation, attribute assignment, and advanced queries with Cypher. Additionally, the tutorial explores common graph visualization techniques using tools like Plotly and Neo4j Bloom, which enhance the interpretation and usability of graph data. It also delves into community detection algorithms, including the Louvain method, which facilitates clustering in large networks. Finally, the paper concludes with recommendations for researchers interested in exploring the vast potential of graph technologies.

Many of the music generation systems based on neural networks are fully autonomous and do not offer control over the generation process. In this research, we present a controllable music generation system in terms of tonal tension. We incorporate two tonal tension measures based on the Spiral Array Tension theory into a variational autoencoder model. This allows us to control the direction of the tonal tension throughout the generated piece, as well as the overall level of tonal tension. Given a seed musical fragment, stemming from either the user input or from directly sampling from the latent space, the model can generate variations of this original seed fragment with altered tonal tension. This altered music still resembles the seed music rhythmically, but the pitch of the notes are changed to match the desired tonal tension as conditioned by the user.

Estimating piano dynamic from audio recordings is a fundamental challenge in computational music analysis. In this paper, we propose an efficient multi-task network that jointly predicts dynamic levels, change points, beats, and downbeats from a shared latent representation. These four targets form the metrical structure of dynamics in the music score. Inspired by recent vocal dynamic research, we use a multi-scale network as the backbone, which takes Bark-scale specific loudness as the input feature. Compared to log-Mel as input, this reduces model size from 14.7 M to 0.5 M, enabling long sequential input. We use a 60-second audio length in audio segmentation, which doubled the length of beat tracking commonly used. Evaluated on the public MazurkaBL dataset, our model achieves state-of-the-art results across all tasks. This work sets a new benchmark for piano dynamic estimation and delivers a powerful and compact tool, paving the way for large-scale, resource-efficient analysis of musical expression.

This work studies a central extremal graph theory problem inspired by a 1975 conjecture of Erdos, which aims to find graphs with a given size (number of nodes) that maximize the number of edges without having 3- or 4-cycles. We formulate this problem as a sequential decision-making problem and compare AlphaZero, a neural network-guided tree search, with tabu search, a heuristic local search method. Using either method, by introducing a curriculum -- jump-starting the search for larger graphs using good graphs found at smaller sizes -- we improve the state-of-the-art lower bounds for several sizes. We also propose a flexible graph-generation environment and a permutation-invariant network architecture for learning to search in the space of graphs.

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph G=(V, D,B) is parameterized by a rational function with parameters for each vertex and edge in G. This rational parametrization naturally allows for the study of these models from an algebraic and combinatorial point of view. Indeed, this point of view has led to a collection of results in the literature, mainly focusing on questions related to identifiability and determining relationships between covariances (i.e., finding polynomials in the Gaussian vanishing ideal). So far, a large proportion of these results has focused on the case when D, the directed part of the mixed graph G, is acyclic. This is due to the fact that in the acyclic case, the parametrization becomes polynomial and there is a description of the entries of the covariance matrices in terms of a finite sum. We move beyond the acyclic case and give a closed form expression for the entries of the covariance matrices in terms of the one-connections in a graph obtained from D through some small operations. This closed form expression then allows us to show that if G is simple, then the parametrization map is generically finite-to-one. Finally, having a closed form expression for the covariance matrices allows for the development of an algorithm for systematically exploring possible polynomials in the Gaussian vanishing ideal.

Let L denote the Laplacian matrix of a graph G. We study continuous quantum walks on G defined by the transition matrix U(t)=expleft(itLright). The initial state is of the pair state form, e_a-e_b with a,b being any two vertices of G. We provide two ways to construct infinite families of graphs that have perfect pair transfer. We study a "transitivity" phenomenon which cannot occur in vertex state transfer. We characterize perfect pair state transfer on paths and cycles. We also study the case when quantum walks are generated by the unsigned Laplacians of underlying graphs and the initial states are of the plus state form, e_a+e_b. When the underlying graphs are bipartite, plus state transfer is equivalent to pair state transfer.

Despite progress in controllable symbolic music generation, data scarcity remains a challenge for certain control modalities. Composer-style music generation is a prime example, as only a few pieces per composer are available, limiting the modeling of both styles and fundamental music elements (e.g., melody, chord, rhythm). In this paper, we investigate how general music knowledge learned from a broad corpus can enhance the mastery of specific composer styles, with a focus on piano piece generation. Our approach follows a two-stage training paradigm. First, we pre-train a REMI-based music generation model on a large corpus of pop, folk, and classical music. Then, we fine-tune it on a small, human-verified dataset from four renowned composers, namely Bach, Mozart, Beethoven, and Chopin, using a lightweight adapter module to condition the model on style indicators. To evaluate the effectiveness of our approach, we conduct both objective and subjective evaluations on style accuracy and musicality. Experimental results demonstrate that our method outperforms ablations and baselines, achieving more precise composer-style modeling and better musical aesthetics. Additionally, we provide observations on how the model builds music concepts from the generality pre-training and refines its stylistic understanding through the mastery fine-tuning.

Leveraging generative Artificial Intelligence (AI), we have transformed a dataset comprising 1,000 scientific papers into an ontological knowledge graph. Through an in-depth structural analysis, we have calculated node degrees, identified communities and connectivities, and evaluated clustering coefficients and betweenness centrality of pivotal nodes, uncovering fascinating knowledge architectures. The graph has an inherently scale-free nature, is highly connected, and can be used for graph reasoning by taking advantage of transitive and isomorphic properties that reveal unprecedented interdisciplinary relationships that can be used to answer queries, identify gaps in knowledge, propose never-before-seen material designs, and predict material behaviors. We compute deep node embeddings for combinatorial node similarity ranking for use in a path sampling strategy links dissimilar concepts that have previously not been related. One comparison revealed structural parallels between biological materials and Beethoven's 9th Symphony, highlighting shared patterns of complexity through isomorphic mapping. In another example, the algorithm proposed a hierarchical mycelium-based composite based on integrating path sampling with principles extracted from Kandinsky's 'Composition VII' painting. The resulting material integrates an innovative set of concepts that include a balance of chaos/order, adjustable porosity, mechanical strength, and complex patterned chemical functionalization. We uncover other isomorphisms across science, technology and art, revealing a nuanced ontology of immanence that reveal a context-dependent heterarchical interplay of constituents. Graph-based generative AI achieves a far higher degree of novelty, explorative capacity, and technical detail, than conventional approaches and establishes a widely useful framework for innovation by revealing hidden connections.

The paper is a continuation of the study started in Yorzh1. Schrodinger operators on finite compact metric graphs are considered under the assumption that the matching conditions at the graph vertices are of delta type. Either an infinite series of trace formulae (provided that edge potentials are infinitely smooth) or a finite number of such formulae (in the cases of L_1 and C^M edge potentials) are obtained which link together two different quantum graphs under the assumption that their spectra coincide. Applications are given to the problem of recovering matching conditions for a quantum graph based on its spectrum.

The rise of deep learning technologies has quickly advanced many fields, including that of generative music systems. There exist a number of systems that allow for the generation of good sounding short snippets, yet, these generated snippets often lack an overarching, longer-term structure. In this work, we propose CM-HRNN: a conditional melody generation model based on a hierarchical recurrent neural network. This model allows us to generate melodies with long-term structures based on given chord accompaniments. We also propose a novel, concise event-based representation to encode musical lead sheets while retaining the notes' relative position within the bar with respect to the musical meter. With this new data representation, the proposed architecture can simultaneously model the rhythmic, as well as the pitch structures in an effective way. Melodies generated by the proposed model were extensively evaluated in quantitative experiments as well as a user study to ensure the musical quality of the output as well as to evaluate if they contain repeating patterns. We also compared the system with the state-of-the-art AttentionRNN. This comparison shows that melodies generated by CM-HRNN contain more repeated patterns (i.e., higher compression ratio) and a lower tonal tension (i.e., more tonally concise). Results from our listening test indicate that CM-HRNN outperforms AttentionRNN in terms of long-term structure and overall rating.

We introduce ACE-Step, a novel open-source foundation model for music generation that overcomes key limitations of existing approaches and achieves state-of-the-art performance through a holistic architectural design. Current methods face inherent trade-offs between generation speed, musical coherence, and controllability. For example, LLM-based models (e.g. Yue, SongGen) excel at lyric alignment but suffer from slow inference and structural artifacts. Diffusion models (e.g. DiffRhythm), on the other hand, enable faster synthesis but often lack long-range structural coherence. ACE-Step bridges this gap by integrating diffusion-based generation with Sana's Deep Compression AutoEncoder (DCAE) and a lightweight linear transformer. It also leverages MERT and m-hubert to align semantic representations (REPA) during training, allowing rapid convergence. As a result, our model synthesizes up to 4 minutes of music in just 20 seconds on an A100 GPU-15x faster than LLM-based baselines-while achieving superior musical coherence and lyric alignment across melody, harmony, and rhythm metrics. Moreover, ACE-Step preserves fine-grained acoustic details, enabling advanced control mechanisms such as voice cloning, lyric editing, remixing, and track generation (e.g. lyric2vocal, singing2accompaniment). Rather than building yet another end-to-end text-to-music pipeline, our vision is to establish a foundation model for music AI: a fast, general-purpose, efficient yet flexible architecture that makes it easy to train subtasks on top of it. This paves the way for the development of powerful tools that seamlessly integrate into the creative workflows of music artists, producers, and content creators. In short, our goal is to build a stable diffusion moment for music. The code, the model weights and the demo are available at: https://ace-step.github.io/.

This is the third paper of the CayleyPy project applying artificial intelligence to problems in group theory. We announce the first public release of CayleyPy, an open source Python library for computations with Cayley and Schreier graphs. Compared with systems such as GAP and Sage, CayleyPy handles much larger graphs and performs several orders of magnitude faster. Using CayleyPy we obtained about 200 new conjectures on Cayley and Schreier graphs, focused on diameters and growth. For many Cayley graphs of symmetric groups Sn we observe quasi polynomial diameter formulas: a small set of quadratic or linear polynomials indexed by n mod s. We conjecture that this is a general phenomenon, giving efficient diameter computation despite the problem being NP hard. We propose a refinement of the Babai type conjecture on diameters of Sn: n^2/2 + 4n upper bounds in the undirected case, compared to previous O(n^2) bounds. We also provide explicit generator families, related to involutions in a square with whiskers pattern, conjectured to maximize the diameter; search confirms this for all n up to 15. We further conjecture an answer to a question posed by V M Glushkov in 1968 on directed Cayley graphs generated by a cyclic shift and a transposition. For nilpotent groups we conjecture an improvement of J S Ellenberg's results on upper unitriangular matrices over Z/pZ, showing linear dependence of diameter on p. Moreover. Some conjectures are LLM friendly, naturally stated as sorting problems verifiable by algorithms or Python code. To benchmark path finding we created more than 10 Kaggle datasets. CayleyPy works with arbitrary permutation or matrix groups and includes over 100 predefined generators. Our growth computation code outperforms GAP and Sage up to 1000 times in speed and size.

In recent years, many large directed networks such as online social networks are collected with the help of powerful data engineering and data storage techniques. Analyses of such networks attract significant attention from both the academics and industries. However, analyses of large directed networks are often time-consuming and expensive because the complexities of a lot of graph algorithms are often polynomial with the size of the graph. Hence, sampling algorithms that can generate graphs preserving properties of original graph are of great importance because they can speed up the analysis process. We propose a promising framework to sample directed graphs: Construct a sample graph with linearly rescaled Joint Degree Matrix (JDM) and Degree Correlation Matrix (DCM). Previous work shows that graphs with the same JDM and DCM will have a range of very similar graph properties. We also conduct experiments on real-world datasets to show that the numbers of non-zero entries in JDM and DCM are quite small compared to the number of edges and nodes. Adopting this framework, we propose a novel graph sampling algorithm that can provably preserves in-degree and out-degree distributions, which are two most fundamental properties of a graph. We also prove the upper bound for deviations in the joint degree distribution and degree correlation distribution, which correspond to JDM and DCM. Besides, we prove that the deviations in these distributions are negatively correlated with the sparsity of the JDM and DCM. Considering that these two matrices are always quite sparse, we believe that proposed algorithm will have a better-than-theory performance on real-world large directed networks.

Deep learning has recently empowered and democratized generative modeling of images and text, with additional concurrent works exploring the possibility of generating more complex forms of data, such as audio. However, the high dimensionality, long-range dependencies, and lack of standardized datasets currently makes generative modeling of audio and music very challenging. We propose to model music as a series of discrete notes upon which we can use autoregressive natural language processing techniques for successful generative modeling. While previous works used similar pipelines on data such as sheet music and MIDI, we aim to extend such approaches to the under-studied medium of guitar tablature. Specifically, we develop the first work to our knowledge that models one specific genre as guitar tablature: heavy rock. Unlike other works in guitar tablature generation, we have a freely available public demo at https://huggingface.co/spaces/josuelmet/Metal_Music_Interpolator

The field of automatic music composition has seen great progress in the last few years, much of which can be attributed to advances in deep neural networks. There are numerous studies that present different strategies for generating sheet music from scratch. The inclusion of high-level musical characteristics (e.g., perceived emotional qualities), however, as conditions for controlling the generation output remains a challenge. In this paper, we present a novel approach for calculating the valence (the positivity or negativity of the perceived emotion) of a chord progression within a lead sheet, using pre-defined mood tags proposed by music experts. Based on this approach, we propose a novel strategy for conditional lead sheet generation that allows us to steer the music generation in terms of valence, phrasing, and time signature. Our approach is similar to a Neural Machine Translation (NMT) problem, as we include high-level conditions in the encoder part of the sequence-to-sequence architectures used (i.e., long-short term memory networks, and a Transformer network). We conducted experiments to thoroughly analyze these two architectures. The results show that the proposed strategy is able to generate lead sheets in a controllable manner, resulting in distributions of musical attributes similar to those of the training dataset. We also verified through a subjective listening test that our approach is effective in controlling the valence of a generated chord progression.

Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph representation learning. Specifically, constructing graphs that effectively capture the complete geometric information of crystals and handle chiral crystals remains an unsolved and challenging problem. In this paper, we introduce a novel approach that utilizes the periodic patterns of unit cells to establish the lattice-based representation for each atom, enabling efficient and expressive graph representations of crystals. Furthermore, we propose ComFormer, a SE(3) transformer designed specifically for crystalline materials. ComFormer includes two variants; namely, iComFormer that employs invariant geometric descriptors of Euclidean distances and angles, and eComFormer that utilizes equivariant vector representations. Experimental results demonstrate the state-of-the-art predictive accuracy of ComFormer variants on various tasks across three widely-used crystal benchmarks. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Text-to-music generation models are now capable of generating high-quality music audio in broad styles. However, text control is primarily suitable for the manipulation of global musical attributes like genre, mood, and tempo, and is less suitable for precise control over time-varying attributes such as the positions of beats in time or the changing dynamics of the music. We propose Music ControlNet, a diffusion-based music generation model that offers multiple precise, time-varying controls over generated audio. To imbue text-to-music models with time-varying control, we propose an approach analogous to pixel-wise control of the image-domain ControlNet method. Specifically, we extract controls from training audio yielding paired data, and fine-tune a diffusion-based conditional generative model over audio spectrograms given melody, dynamics, and rhythm controls. While the image-domain Uni-ControlNet method already allows generation with any subset of controls, we devise a new strategy to allow creators to input controls that are only partially specified in time. We evaluate both on controls extracted from audio and controls we expect creators to provide, demonstrating that we can generate realistic music that corresponds to control inputs in both settings. While few comparable music generation models exist, we benchmark against MusicGen, a recent model that accepts text and melody input, and show that our model generates music that is 49% more faithful to input melodies despite having 35x fewer parameters, training on 11x less data, and enabling two additional forms of time-varying control. Sound examples can be found at https://MusicControlNet.github.io/web/.

We study a new connection between a technical measure called mu-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of mu-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal mu-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

Even though they differ in the physical domain, digital video and audio share many characteristics. Both are temporal data streams often stored in buffers with 8-bit values. This paper investigates a method for creating harmonic sounds with a video signal as input. A musical instrument is proposed, that utilizes video in both a sound synthesis method, and in a controller interface for selecting musical notes at specific velocities. The resulting instrument was informally determined by the author to sound both pleasant and interesting, but hard to control, and therefore suited for synth pad sounds.

We train an object detector built from convolutional neural networks to count interference fringes in elliptical antinode regions in frames of high-speed video recordings of transient oscillations in Caribbean steelpan drums illuminated by electronic speckle pattern interferometry (ESPI). The annotations provided by our model aim to contribute to the understanding of time-dependent behavior in such drums by tracking the development of sympathetic vibration modes. The system is trained on a dataset of crowdsourced human-annotated images obtained from the Zooniverse Steelpan Vibrations Project. Due to the small number of human-annotated images and the ambiguity of the annotation task, we also evaluate the model on a large corpus of synthetic images whose properties have been matched to the real images by style transfer using a Generative Adversarial Network. Applying the model to thousands of unlabeled video frames, we measure oscillations consistent with audio recordings of these drum strikes. One unanticipated result is that sympathetic oscillations of higher-octave notes significantly precede the rise in sound intensity of the corresponding second harmonic tones; the mechanism responsible for this remains unidentified. This paper primarily concerns the development of the predictive model; further exploration of the steelpan images and deeper physical insights await its further application.

Recent years have seen the rapid development of large generative models for text; however, much less research has explored the connection between text and another "language" of communication -- music. Music, much like text, can convey emotions, stories, and ideas, and has its own unique structure and syntax. In our work, we bridge text and music via a text-to-music generation model that is highly efficient, expressive, and can handle long-term structure. Specifically, we develop Mo\^usai, a cascading two-stage latent diffusion model that can generate multiple minutes of high-quality stereo music at 48kHz from textual descriptions. Moreover, our model features high efficiency, which enables real-time inference on a single consumer GPU with a reasonable speed. Through experiments and property analyses, we show our model's competence over a variety of criteria compared with existing music generation models. Lastly, to promote the open-source culture, we provide a collection of open-source libraries with the hope of facilitating future work in the field. We open-source the following: Codes: https://github.com/archinetai/audio-diffusion-pytorch; music samples for this paper: http://bit.ly/44ozWDH; all music samples for all models: https://bit.ly/audio-diffusion.

Deep graph learning has gained grand popularity over the past years due to its versatility and success in representing graph data across a wide range of domains. However, the pervasive issue of imbalanced graph data distributions, where certain parts exhibit disproportionally abundant data while others remain sparse, undermines the efficacy of conventional graph learning algorithms, leading to biased outcomes. To address this challenge, Imbalanced Graph Learning (IGL) has garnered substantial attention, enabling more balanced data distributions and better task performance. Despite the proliferation of IGL algorithms, the absence of consistent experimental protocols and fair performance comparisons pose a significant barrier to comprehending advancements in this field. To bridge this gap, we introduce IGL-Bench, a foundational comprehensive benchmark for imbalanced graph learning, embarking on 16 diverse graph datasets and 24 distinct IGL algorithms with uniform data processing and splitting strategies. Specifically, IGL-Bench systematically investigates state-of-the-art IGL algorithms in terms of effectiveness, robustness, and efficiency on node-level and graph-level tasks, with the scope of class-imbalance and topology-imbalance. Extensive experiments demonstrate the potential benefits of IGL algorithms on various imbalanced conditions, offering insights and opportunities in the IGL field. Further, we have developed an open-sourced and unified package to facilitate reproducible evaluation and inspire further innovative research, which is available at https://github.com/RingBDStack/IGL-Bench.

We present a keyframe-based framework for generating music-synchronized, choreography aware animal dance videos. Starting from a few keyframes representing distinct animal poses -- generated via text-to-image prompting or GPT-4o -- we formulate dance synthesis as a graph optimization problem: find the optimal keyframe structure that satisfies a specified choreography pattern of beats, which can be automatically estimated from a reference dance video. We also introduce an approach for mirrored pose image generation, essential for capturing symmetry in dance. In-between frames are synthesized using an video diffusion model. With as few as six input keyframes, our method can produce up to 30 second dance videos across a wide range of animals and music tracks.

Recent advancements in music generation have garnered significant attention, yet existing approaches face critical limitations. Some current generative models can only synthesize either the vocal track or the accompaniment track. While some models can generate combined vocal and accompaniment, they typically rely on meticulously designed multi-stage cascading architectures and intricate data pipelines, hindering scalability. Additionally, most systems are restricted to generating short musical segments rather than full-length songs. Furthermore, widely used language model-based methods suffer from slow inference speeds. To address these challenges, we propose DiffRhythm, the first latent diffusion-based song generation model capable of synthesizing complete songs with both vocal and accompaniment for durations of up to 4m45s in only ten seconds, maintaining high musicality and intelligibility. Despite its remarkable capabilities, DiffRhythm is designed to be simple and elegant: it eliminates the need for complex data preparation, employs a straightforward model structure, and requires only lyrics and a style prompt during inference. Additionally, its non-autoregressive structure ensures fast inference speeds. This simplicity guarantees the scalability of DiffRhythm. Moreover, we release the complete training code along with the pre-trained model on large-scale data to promote reproducibility and further research.

The Berge-Fulkerson conjecture states that every bridgeless cubic graph can be covered with six perfect matchings such that each edge is covered exactly twice. An equivalent reformulation is that it's possible to find a 6-cycle 4-cover. In this paper we discuss the oriented version (o6c4c) of the latter statement, pose it as a conjecture and prove it for the family of Isaacs flower snarks. Similarly to the case of oriented cycle double cover, we can always construct an orientable surface (possibly with boundary) from an o6c4c solution. If the o6c4c solution itself splits into two (not necessarily oriented) cycle double covers, then it's also possible to build another pair of orientable surfaces (also possibly with boundaries). Finally we show how to build a ribbon graph, and for some special o6c4c cases we show that this ribbon graph corresponds to an oriented 6-cycle double cover. Github: https://github.com/gexahedron/cycle-double-covers

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or cannot sufficiently model the complex dependency between nodes and edges, which is crucial for generating real-world graphs such as molecules. To overcome such limitations, we propose a novel score-based generative model for graphs with a continuous-time framework. Specifically, we propose a new graph diffusion process that models the joint distribution of the nodes and edges through a system of stochastic differential equations (SDEs). Then, we derive novel score matching objectives tailored for the proposed diffusion process to estimate the gradient of the joint log-density with respect to each component, and introduce a new solver for the system of SDEs to efficiently sample from the reverse diffusion process. We validate our graph generation method on diverse datasets, on which it either achieves significantly superior or competitive performance to the baselines. Further analysis shows that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule, demonstrating the effectiveness of the system of SDEs in modeling the node-edge relationships. Our code is available at https://github.com/harryjo97/GDSS.

The electrocardiogram (ECG) is a dependable instrument for assessing the function of the cardiovascular system. There has recently been much emphasis on precisely classifying ECGs. While ECG situations have numerous similarities, little attention has been paid to categorizing ECGs using graph neural networks. In this study, we offer three distinct techniques for classifying heartbeats using deep graph neural networks to classify the ECG signals accurately. We suggest using different methods to extract topological features from the ECG signal and then using a branch of the graph neural network named graph isomorphism network for classifying the ECGs. On the PTB Diagnostics data set, we tested the three proposed techniques. According to the findings, the three proposed techniques are capable of making arrhythmia classification predictions with the accuracy of 99.38, 98.76, and 91.93 percent, respectively.

We introduce anticipation: a method for constructing a controllable generative model of a temporal point process (the event process) conditioned asynchronously on realizations of a second, correlated process (the control process). We achieve this by interleaving sequences of events and controls, such that controls appear following stopping times in the event sequence. This work is motivated by problems arising in the control of symbolic music generation. We focus on infilling control tasks, whereby the controls are a subset of the events themselves, and conditional generation completes a sequence of events given the fixed control events. We train anticipatory infilling models using the large and diverse Lakh MIDI music dataset. These models match the performance of autoregressive models for prompted music generation, with the additional capability to perform infilling control tasks, including accompaniment. Human evaluators report that an anticipatory model produces accompaniments with similar musicality to even music composed by humans over a 20-second clip.

While recent generative models can produce engaging music, their utility is limited. The variation in the music is often left to chance, resulting in compositions that lack structure. Pieces extending beyond a minute can become incoherent or repetitive. This paper introduces an approach for generating structured, arbitrarily long musical pieces. Central to this approach is the creation of musical segments using a conditional generative model, with transitions between these segments. The generation of prompts that determine the high-level composition is distinct from the creation of finer, lower-level details. A large language model is then used to suggest the musical form.

We present the Melody Guided Music Generation (MMGen) model, the first novel approach using melody to guide the music generation that, despite a pretty simple method and extremely limited resources, achieves excellent performance. Specifically, we first align the melody with audio waveforms and their associated descriptions using the multimodal alignment module. Subsequently, we condition the diffusion module on the learned melody representations. This allows MMGen to generate music that matches the style of the provided audio while also producing music that reflects the content of the given text description. To address the scarcity of high-quality data, we construct a multi-modal dataset, MusicSet, which includes melody, text, and audio, and will be made publicly available. We conduct extensive experiments which demonstrate the superiority of the proposed model both in terms of experimental metrics and actual performance quality.

The Markov numbers are positive integers appearing as solutions to the Diophantine equation x^2 + y^2 + z^2 = 3xyz. These numbers are very well-studied and have many combinatorial properties, as well as being the source of the long-standing unicity conjecture. In 2018, Canakc{\i} and Schiffler showed that the Markov number m_{a{b}} is the number of perfect matchings of a certain snake graph corresponding to the Christoffel path from (0,0) to (a,b). Based on this correspondence, Schiffler in 2023 introduced two orderings on lattice paths. For any path omega, associate a snake graph G(omega) and a continued fraction g(omega). The ordering <_M is given by the number of perfect matchings on G(omega), and the ordering <_L is given by the Lagrange number of g(omega). In this work, we settle two conjectures of Schiffler. First, we show that the path omega(a,b) = RRcdots R UU cdots U is the unique maximum over all lattice paths from (0,0) to (a,b) with respect to both orderings <_M and <_L. We then use this result to prove that sup L(omega) over all lattice paths is exactly 1+sqrt5.

We introduce HiFi-HARP, a large-scale dataset of 7th-order Higher-Order Ambisonic Room Impulse Responses (HOA-RIRs) consisting of more than 100,000 RIRs generated via a hybrid acoustic simulation in realistic indoor scenes. HiFi-HARP combines geometrically complex, furnished room models from the 3D-FRONT repository with a hybrid simulation pipeline: low-frequency wave-based simulation (finite-difference time-domain) up to 900 Hz is used, while high frequencies above 900 Hz are simulated using a ray-tracing approach. The combined raw RIRs are encoded into the spherical-harmonic domain (AmbiX ACN) for direct auralization. Our dataset extends prior work by providing 7th-order Ambisonic RIRs that combine wave-theoretic accuracy with realistic room content. We detail the generation pipeline (scene and material selection, array design, hybrid simulation, ambisonic encoding) and provide dataset statistics (room volumes, RT60 distributions, absorption properties). A comparison table highlights the novelty of HiFi-HARP relative to existing RIR collections. Finally, we outline potential benchmarks such as FOA-to-HOA upsampling, source localization, and dereverberation. We discuss machine learning use cases (spatial audio rendering, acoustic parameter estimation) and limitations (e.g., simulation approximations, static scenes). Overall, HiFi-HARP offers a rich resource for developing spatial audio and acoustics algorithms in complex environments.

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on many tasks, their foundation on pairwise interaction networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art (SOTA) performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs.

Despite significant recent progress across multiple subtasks of audio source separation, few music source separation systems support separation beyond the four-stem vocals, drums, bass, and other (VDBO) setup. Of the very few current systems that support source separation beyond this setup, most continue to rely on an inflexible decoder setup that can only support a fixed pre-defined set of stems. Increasing stem support in these inflexible systems correspondingly requires increasing computational complexity, rendering extensions of these systems computationally infeasible for long-tail instruments. In this work, we propose Banquet, a system that allows source separation of multiple stems using just one decoder. A bandsplit source separation model is extended to work in a query-based setup in tandem with a music instrument recognition PaSST model. On the MoisesDB dataset, Banquet, at only 24.9 M trainable parameters, approached the performance level of the significantly more complex 6-stem Hybrid Transformer Demucs on VDBO stems and outperformed it on guitar and piano. The query-based setup allows for the separation of narrow instrument classes such as clean acoustic guitars, and can be successfully applied to the extraction of less common stems such as reeds and organs. Implementation is available at https://github.com/kwatcharasupat/query-bandit.

We study the problem of symbolic music generation (e.g., generating piano rolls), with a technical focus on non-differentiable rule guidance. Musical rules are often expressed in symbolic form on note characteristics, such as note density or chord progression, many of which are non-differentiable which pose a challenge when using them for guided diffusion. We propose Stochastic Control Guidance (SCG), a novel guidance method that only requires forward evaluation of rule functions that can work with pre-trained diffusion models in a plug-and-play way, thus achieving training-free guidance for non-differentiable rules for the first time. Additionally, we introduce a latent diffusion architecture for symbolic music generation with high time resolution, which can be composed with SCG in a plug-and-play fashion. Compared to standard strong baselines in symbolic music generation, this framework demonstrates marked advancements in music quality and rule-based controllability, outperforming current state-of-the-art generators in a variety of settings. For detailed demonstrations, code and model checkpoints, please visit our project website: https://scg-rule-guided-music.github.io/.

Recent progress in text-to-music generation has enabled models to synthesize high-quality musical segments, full compositions, and even respond to fine-grained control signals, e.g. chord progressions. State-of-the-art (SOTA) systems differ significantly across many dimensions, such as training datasets, modeling paradigms, and architectural choices. This diversity complicates efforts to evaluate models fairly and pinpoint which design choices most influence performance. While factors like data and architecture are important, in this study we focus exclusively on the modeling paradigm. We conduct a systematic empirical analysis to isolate its effects, offering insights into associated trade-offs and emergent behaviors that can guide future text-to-music generation systems. Specifically, we compare the two arguably most common modeling paradigms: Auto-Regressive decoding and Conditional Flow-Matching. We conduct a controlled comparison by training all models from scratch using identical datasets, training configurations, and similar backbone architectures. Performance is evaluated across multiple axes, including generation quality, robustness to inference configurations, scalability, adherence to both textual and temporally aligned conditioning, and editing capabilities in the form of audio inpainting. This comparative study sheds light on distinct strengths and limitations of each paradigm, providing actionable insights that can inform future architectural and training decisions in the evolving landscape of text-to-music generation. Audio sampled examples are available at: https://huggingface.co/spaces/ortal1602/ARvsFM

Recently, symbolic music generation has become a focus of numerous deep learning research. Structure as an important part of music, contributes to improving the quality of music, and an increasing number of works start to study the hierarchical structure. In this study, we delve into the multi-level structures within music from macro-level and micro-level hierarchies. At the macro-level hierarchy, we conduct phrase segmentation algorithm to explore how phrases influence the overall development of music, and at the micro-level hierarchy, we design skeleton notes extraction strategy to explore how skeleton notes within each phrase guide the melody generation. Furthermore, we propose a novel Phrase-level Cross-Attention mechanism to capture the intrinsic relationship between macro-level hierarchy and micro-level hierarchy. Moreover, in response to the current lack of research on Chinese-style music, we construct our Small Tunes Dataset: a substantial collection of MIDI files comprising 10088 Small Tunes, a category of traditional Chinese Folk Songs. This dataset serves as the focus of our study. We generate Small Tunes songs utilizing the extracted skeleton notes as conditions, and experiment results indicate that our proposed model, Small Tunes Transformer, outperforms other state-of-the-art models. Besides, we design three novel objective evaluation metrics to evaluate music from both rhythm and melody dimensions.

Multivariate time series is prevalent in many scientific and industrial domains. Modeling multivariate signals is challenging due to their long-range temporal dependencies and intricate interactions--both direct and indirect. To confront these complexities, we introduce a method of representing multivariate signals as nodes in a graph with edges indicating interdependency between them. Specifically, we leverage graph neural networks (GNN) and attention mechanisms to efficiently learn the underlying relationships within the time series data. Moreover, we suggest employing hierarchical signal decompositions running over the graphs to capture multiple spatial dependencies. The effectiveness of our proposed model is evaluated across various real-world benchmark datasets designed for long-term forecasting tasks. The results consistently showcase the superiority of our model, achieving an average 23\% reduction in mean squared error (MSE) compared to existing models.

Music Emotion Recognition involves the automatic identification of emotional elements within music tracks, and it has garnered significant attention due to its broad applicability in the field of Music Information Retrieval. It can also be used as the upstream task of many other human-related tasks such as emotional music generation and music recommendation. Due to existing psychology research, music emotion is determined by multiple factors such as the Timbre, Velocity, and Structure of the music. Incorporating multiple factors in MER helps achieve more interpretable and finer-grained methods. However, most prior works were uni-domain and showed weak consistency between arousal modeling performance and valence modeling performance. Based on this background, we designed a multi-domain emotion modeling method for instrumental music that combines symbolic analysis and acoustic analysis. At the same time, because of the rarity of music data and the difficulty of labeling, our multi-domain approach can make full use of limited data. Our approach was implemented and assessed using the publicly available piano dataset EMOPIA, resulting in a notable improvement over our baseline model with a 2.4% increase in overall accuracy, establishing its state-of-the-art performance.

This paper concludes a series of studies on the polyharmonic cascade, a deep machine learning architecture theoretically derived from indifference principles and the theory of random functions. A universal initialization procedure is proposed, based on symmetric constellations in the form of hyperoctahedra with a central point. This initialization not only ensures stable training of cascades with tens and hundreds of layers (up to 500 layers without skip connections), but also radically simplifies the computations. Scalability and robustness are demonstrated on MNIST (98.3% without convolutions or augmentations), HIGGS (AUC approximately 0.885 on 11M examples), and Epsilon (AUC approximately 0.963 with 2000 features). All linear algebra is reduced to 2D operations and is efficiently executed on GPUs. A public repository and an archived snapshot are provided for full reproducibility.

Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so that information may be translated between spatial- and spectral domains. Here we show this traditional reliance on the graph Fourier transform to be superfluous and -- making use of certain advanced tools from complex analysis and spectral theory -- extend spectral convolutions to directed graphs. We provide a frequency-response interpretation of newly developed filters, investigate the influence of the basis used to express filters and discuss the interplay with characteristic operators on which networks are based. In order to thoroughly test the developed theory, we conduct experiments in real world settings, showcasing that directed spectral convolutional networks provide new state of the art results for heterophilic node classification on many datasets and -- as opposed to baselines -- may be rendered stable to resolution-scale varying topological perturbations.

We introduce a new class of generative models for music called live music models that produce a continuous stream of music in real-time with synchronized user control. We release Magenta RealTime, an open-weights live music model that can be steered using text or audio prompts to control acoustic style. On automatic metrics of music quality, Magenta RealTime outperforms other open-weights music generation models, despite using fewer parameters and offering first-of-its-kind live generation capabilities. We also release Lyria RealTime, an API-based model with extended controls, offering access to our most powerful model with wide prompt coverage. These models demonstrate a new paradigm for AI-assisted music creation that emphasizes human-in-the-loop interaction for live music performance.

Artificial intelligence has made great strides in the last decade but still falls short of the human brain, the best-known example of intelligence. Not much is known of the neural processes that allow the brain to make the leap to achieve so much from so little beyond its ability to create knowledge structures that can be flexibly and dynamically combined, recombined, and applied in new and novel ways. This paper proposes a mathematical approach using graph theory and spectral graph theory, to hypothesize how to constrain these neural clusters of information based on eigen-relationships. This same hypothesis is hierarchically applied to scale up from the smallest to the largest clusters of knowledge that eventually lead to model building and reasoning.

This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of indifference. It is shown that if a probability measure on an infinite-dimensional function space possesses natural symmetries (invariance under translation, rotation, scaling, and Gaussianity), then the entire solution scheme, including the kernel form, the type of regularization, and the noise parameterization, follows analytically from these postulates. The resulting kernel coincides with a generalized polyharmonic spline; however, unlike existing approaches, it is not chosen empirically but arises as a consequence of the indifference principle. This result provides a theoretical foundation for a broad class of smoothing and interpolation methods, demonstrating their optimality in the absence of a priori information.

In this paper, we consider a novel research problem: music-to-text synaesthesia. Different from the classical music tagging problem that classifies a music recording into pre-defined categories, music-to-text synaesthesia aims to generate descriptive texts from music recordings with the same sentiment for further understanding. As existing music-related datasets do not contain the semantic descriptions on music recordings, we collect a new dataset that contains 1,955 aligned pairs of classical music recordings and text descriptions. Based on this, we build a computational model to generate sentences that can describe the content of the music recording. To tackle the highly non-discriminative classical music, we design a group topology-preservation loss, which considers more samples as a group reference and preserves the relative topology among different samples. Extensive experimental results qualitatively and quantitatively demonstrate the effectiveness of our proposed model over five heuristics or pre-trained competitive methods and their variants on our collected dataset.

Inferring music time structures has a broad range of applications in music production, processing and analysis. Scholars have proposed various methods to analyze different aspects of time structures, such as beat, downbeat, tempo and meter. Many state-of-the-art (SOFA) methods, however, are computationally expensive. This makes them inapplicable in real-world industrial settings where the scale of the music collections can be millions. This paper proposes a new state space and a semi-Markov model for music time structure analysis. The proposed approach turns the commonly used 2D state spaces into a 1D model through a jump-back reward strategy. It reduces the state spaces size drastically. We then utilize the proposed method for causal, joint beat, downbeat, tempo, and meter tracking, and compare it against several previous methods. The proposed method delivers similar performance with the SOFA joint causal models with a much smaller state space and a more than 30 times speedup.

We propose Lodge, a network capable of generating extremely long dance sequences conditioned on given music. We design Lodge as a two-stage coarse to fine diffusion architecture, and propose the characteristic dance primitives that possess significant expressiveness as intermediate representations between two diffusion models. The first stage is global diffusion, which focuses on comprehending the coarse-level music-dance correlation and production characteristic dance primitives. In contrast, the second-stage is the local diffusion, which parallelly generates detailed motion sequences under the guidance of the dance primitives and choreographic rules. In addition, we propose a Foot Refine Block to optimize the contact between the feet and the ground, enhancing the physical realism of the motion. Our approach can parallelly generate dance sequences of extremely long length, striking a balance between global choreographic patterns and local motion quality and expressiveness. Extensive experiments validate the efficacy of our method.

Existing work in automatic music generation has primarily focused on end-to-end systems that produce complete compositions or continuations. However, because musical composition is typically an iterative process, such systems make it difficult to engage in the back-and-forth between human and machine that is essential to computer-assisted creativity. In this study, we address the task of personalizable, multi-track, long-context, and controllable symbolic music infilling to enhance the process of computer-assisted composition. We present MIDI-RWKV, a novel model based on the RWKV-7 linear architecture, to enable efficient and coherent musical cocreation on edge devices. We also demonstrate that MIDI-RWKV admits an effective method of finetuning its initial state for personalization in the very-low-sample regime. We evaluate MIDI-RWKV and its state tuning on several quantitative and qualitative metrics, and release model weights and code at https://github.com/christianazinn/MIDI-RWKV.

We apply a complex network approach to analyse the time series of five solar parameters, and propose an strategy to predict the number of sunspots for the next solar maximum, and when will this maximum will occur. The approach is based on the Visibility Graph (VG) algorithm, and a slightly modified version of it, the Horizontal Visibility Graph (HVG), which map a time series into a complex network. Various network metrics exhibit either an exponential or a scale-free behavior, and we find that the evolution of the characteristic decay exponents is consistent with variations of the sunspots number along solar cycles. During solar minimum, the sunspots number and the solar index time series have characteristic decay exponents that correlate well with the next maximum sunspots number, suggesting that they may be good precursors of the intensity of the next solar maximum. Based on this observation, we find that, based on current data, the algorithm predicts a number of 179 sunspots for cycle 25. Combining this with the Hathaway function, adjusted to yield such maximum sunspots number, we find that the maximum for solar cycle 25 will occur in December 2024/January 2025.

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

Recent advances in text-to-music generation models have opened new avenues in musical creativity. However, music generation usually involves iterative refinements, and how to edit the generated music remains a significant challenge. This paper introduces a novel approach to the editing of music generated by such models, enabling the modification of specific attributes, such as genre, mood and instrument, while maintaining other aspects unchanged. Our method transforms text editing to latent space manipulation while adding an extra constraint to enforce consistency. It seamlessly integrates with existing pretrained text-to-music diffusion models without requiring additional training. Experimental results demonstrate superior performance over both zero-shot and certain supervised baselines in style and timbre transfer evaluations. Additionally, we showcase the practical applicability of our approach in real-world music editing scenarios.

Music generation has attracted growing interest with the advancement of deep generative models. However, generating music conditioned on textual descriptions, known as text-to-music, remains challenging due to the complexity of musical structures and high sampling rate requirements. Despite the task's significance, prevailing generative models exhibit limitations in music quality, computational efficiency, and generalization. This paper introduces JEN-1, a universal high-fidelity model for text-to-music generation. JEN-1 is a diffusion model incorporating both autoregressive and non-autoregressive training. Through in-context learning, JEN-1 performs various generation tasks including text-guided music generation, music inpainting, and continuation. Evaluations demonstrate JEN-1's superior performance over state-of-the-art methods in text-music alignment and music quality while maintaining computational efficiency. Our demos are available at http://futureverse.com/research/jen/demos/jen1

In this paper, we present MusPy, an open source Python library for symbolic music generation. MusPy provides easy-to-use tools for essential components in a music generation system, including dataset management, data I/O, data preprocessing and model evaluation. In order to showcase its potential, we present statistical analysis of the eleven datasets currently supported by MusPy. Moreover, we conduct a cross-dataset generalizability experiment by training an autoregressive model on each dataset and measuring held-out likelihood on the others---a process which is made easier by MusPy's dataset management system. The results provide a map of domain overlap between various commonly used datasets and show that some datasets contain more representative cross-genre samples than others. Along with the dataset analysis, these results might serve as a guide for choosing datasets in future research. Source code and documentation are available at https://github.com/salu133445/muspy .

In tandem with the recent advancements in foundation model research, there has been a surge of generative music AI applications within the past few years. As the idea of AI-generated or AI-augmented music becomes more mainstream, many researchers in the music AI community may be wondering what avenues of research are left. With regards to music generative models, we outline the current areas of research with significant room for exploration. Firstly, we pose the question of foundational representation of these generative models and investigate approaches towards explainability. Next, we discuss the current state of music datasets and their limitations. We then overview different generative models, forms of evaluating these models, and their computational constraints/limitations. Subsequently, we highlight applications of these generative models towards extensions to multiple modalities and integration with artists' workflow as well as music education systems. Finally, we survey the potential copyright implications of generative music and discuss strategies for protecting the rights of musicians. While it is not meant to be exhaustive, our survey calls to attention a variety of research directions enabled by music foundation models.

DisCoPy is a Python toolkit for computing with monoidal categories. It comes with two flexible data structures for string diagrams: the first one for planar monoidal categories based on lists of layers, the second one for symmetric monoidal categories based on cospans of hypergraphs. Algorithms for functor application then allow to translate string diagrams into code for numerical computation, be it differentiable, probabilistic or quantum. This report gives an overview of the library and the new developments released in its version 1.0. In particular, we showcase the implementation of diagram equality for a large fragment of the hierarchy of graphical languages for monoidal categories, as well as a new syntax for defining string diagrams as Python functions.

We study the set of networks, which consist of sources, sinks and neutral points, bijective to the permutations. The set of directed edges, which characterizes a network, is constructed from a polyomino or a Rothe diagram of a permutation through a Dyck tiling on a ribbon. We introduce a new combinatorial object similar to a tree-like tableau, which we call a forest. A forest is shown to give a permutation, and be bijective to a network corresponding to the inverse of the permutation. We show that the poset of networks is a finite graded lattice and admits an EL-labeling. By use of this EL-labeling, we show the lattice is supersolvable and compute the M\"obius function of an interval of the poset.

In designing and applying graph neural networks, we often fall into some optimization pitfalls, the most deceptive of which is that we can only build a deep model by solving over-smoothing. The fundamental reason is that we do not understand how graph neural networks work. Stress graph drawing can offer a unique viewpoint to message iteration in the graph, such as the root of the over-smoothing problem lies in the inability of graph models to maintain an ideal distance between nodes. We further elucidate the trigger conditions of over-smoothing and propose Stress Graph Neural Networks. By introducing the attractive and repulsive message passing from stress iteration, we show how to build a deep model without preventing over-smoothing, how to use repulsive information, and how to optimize the current message-passing scheme to approximate the full stress message propagation. By performing different tasks on 23 datasets, we verified the effectiveness of our attractive and repulsive models and the derived relationship between stress iteration and graph neural networks. We believe that stress graph drawing will be a popular resource for understanding and designing graph neural networks.

The {K_{1,1}, K_{1,2},C_m: mgeq3}-factor of a graph is a spanning subgraph whose each component is an element of {K_{1,1}, K_{1,2},C_m: mgeq3}. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a {K_2}-factor. We get a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {K_{1,1}, K_{1,2},C_m: mgeq3}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {K_{1,1}, K_{1,2},C_m: mgeq3}-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible.

With recent advancements in text-to-audio and text-to-music based on latent diffusion models, the quality of generated content has been reaching new heights. The controllability of musical aspects, however, has not been explicitly explored in text-to-music systems yet. In this paper, we present Mustango, a music-domain-knowledge-inspired text-to-music system based on diffusion, that expands the Tango text-to-audio model. Mustango aims to control the generated music, not only with general text captions, but from more rich captions that could include specific instructions related to chords, beats, tempo, and key. As part of Mustango, we propose MuNet, a Music-Domain-Knowledge-Informed UNet sub-module to integrate these music-specific features, which we predict from the text prompt, as well as the general text embedding, into the diffusion denoising process. To overcome the limited availability of open datasets of music with text captions, we propose a novel data augmentation method that includes altering the harmonic, rhythmic, and dynamic aspects of music audio and using state-of-the-art Music Information Retrieval methods to extract the music features which will then be appended to the existing descriptions in text format. We release the resulting MusicBench dataset which contains over 52K instances and includes music-theory-based descriptions in the caption text. Through extensive experiments, we show that the quality of the music generated by Mustango is state-of-the-art, and the controllability through music-specific text prompts greatly outperforms other models in terms of desired chords, beat, key, and tempo, on multiple datasets.

We introduce MusicInfuser, an approach for generating high-quality dance videos that are synchronized to a specified music track. Rather than attempting to design and train a new multimodal audio-video model, we show how existing video diffusion models can be adapted to align with musical inputs by introducing lightweight music-video cross-attention and a low-rank adapter. Unlike prior work requiring motion capture data, our approach fine-tunes only on dance videos. MusicInfuser achieves high-quality music-driven video generation while preserving the flexibility and generative capabilities of the underlying models. We introduce an evaluation framework using Video-LLMs to assess multiple dimensions of dance generation quality. The project page and code are available at https://susunghong.github.io/MusicInfuser.

Semi-transitive graphs, defined in hps98 as examples where ``uniform percolation" holds whenever p>p_c, are a large class of graphs more general than quasi-transitive graphs. Let G be a semi-transitive graph with one end which can be properly embedded into the plane with uniformly bounded face degree for finite faces and minimal vertex degree at least 7. We show that p_u^{site}(G) +p_c^{site}(G_*)=1, where G_* denotes the matching graph of G. This fulfils and extends an observation of Sykes and Essam in 1964 (SE64) to semi-transitive graphs.

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the 1-dimensional Weisfeiler--Leman algorithm (1-WL). Here, the 1-WL is a well-studied heuristic for the graph isomorphism problem, which iteratively colors or partitions a graph's vertex set. While this connection has led to significant advances in understanding and enhancing GNNs' expressive power, it does not provide insights into their generalization performance, i.e., their ability to make meaningful predictions beyond the training set. In this paper, we study GNNs' generalization ability through the lens of Vapnik--Chervonenkis (VC) dimension theory in two settings, focusing on graph-level predictions. First, when no upper bound on the graphs' order is known, we show that the bitlength of GNNs' weights tightly bounds their VC dimension. Further, we derive an upper bound for GNNs' VC dimension using the number of colors produced by the 1-WL. Secondly, when an upper bound on the graphs' order is known, we show a tight connection between the number of graphs distinguishable by the 1-WL and GNNs' VC dimension. Our empirical study confirms the validity of our theoretical findings.

In this paper, we address the challenge of Optical Music Recognition (OMR) for handwritten jazz lead sheets, a widely used musical score type that encodes melody and chords. The task is challenging due to the presence of chords, a score component not handled by existing OMR systems, and the high variability and quality issues associated with handwritten images. Our contribution is two-fold. We present a novel dataset consisting of 293 handwritten jazz lead sheets of 163 unique pieces, amounting to 2021 total staves aligned with Humdrum **kern and MusicXML ground truth scores. We also supply synthetic score images generated from the ground truth. The second contribution is the development of an OMR model for jazz lead sheets. We discuss specific tokenisation choices related to our kind of data, and the advantages of using synthetic scores and pretrained models. We publicly release all code, data, and models.

Fine-tuning large-scale music generation models, such as MusicGen and Mustango, is a computationally expensive process, often requiring updates to billions of parameters and, therefore, significant hardware resources. Parameter-Efficient Fine-Tuning (PEFT) techniques, particularly adapter-based methods, have emerged as a promising alternative, enabling adaptation with minimal trainable parameters while preserving model performance. However, the design choices for adapters, including their architecture, placement, and size, are numerous, and it is unclear which of these combinations would produce optimal adapters and why, for a given case of low-resource music genre. In this paper, we attempt to answer this question by studying various adapter configurations for two AI music models, MusicGen and Mustango, on two genres: Hindustani Classical and Turkish Makam music. Our findings reveal distinct trade-offs: convolution-based adapters excel in capturing fine-grained local musical details such as ornamentations and short melodic phrases, while transformer-based adapters better preserve long-range dependencies crucial for structured improvisation. Additionally, we analyze computational resource requirements across different adapter scales, demonstrating how mid-sized adapters (40M parameters) achieve an optimal balance between expressivity and quality. Furthermore, we find that Mustango, a diffusion-based model, generates more diverse outputs with better adherence to the description in the input prompt while lacking in providing stability in notes, rhythm alignment, and aesthetics. Also, it is computationally intensive and requires significantly more time to train. In contrast, autoregressive models like MusicGen offer faster training and are more efficient, and can produce better quality output in comparison, but have slightly higher redundancy in their generations.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

We study the capabilities of generative autoregressive transformer models trained on large amounts of symbolic solo-piano transcriptions. After first pretraining on approximately 60,000 hours of music, we use a comparatively smaller, high-quality subset, to finetune models to produce musical continuations, perform symbolic classification tasks, and produce general-purpose contrastive MIDI embeddings by adapting the SimCLR framework to symbolic music. When evaluating piano continuation coherence, our generative model outperforms leading symbolic generation techniques and remains competitive with proprietary audio generation models. On MIR classification benchmarks, frozen representations from our contrastive model achieve state-of-the-art results in linear probe experiments, while direct finetuning demonstrates the generalizability of pretrained representations, often requiring only a few hundred labeled examples to specialize to downstream tasks.

Diffusion models have shown promising results in cross-modal generation tasks involving audio and music, such as text-to-sound and text-to-music generation. These text-controlled music generation models typically focus on generating music by capturing global musical attributes like genre and mood. However, music composition is a complex, multilayered task that often involves musical arrangement as an integral part of the process. This process involves composing each instrument to align with existing ones in terms of beat, dynamics, harmony, and melody, requiring greater precision and control over tracks than text prompts usually provide. In this work, we address these challenges by extending the MusicLDM, a latent diffusion model for music, into a multi-track generative model. By learning the joint probability of tracks sharing a context, our model is capable of generating music across several tracks that correspond well to each other, either conditionally or unconditionally. Additionally, our model is capable of arrangement generation, where the model can generate any subset of tracks given the others (e.g., generating a piano track complementing given bass and drum tracks). We compared our model with an existing multi-track generative model and demonstrated that our model achieves considerable improvements across objective metrics for both total and arrangement generation tasks.

Generating the motion of orchestral conductors from a given piece of symphony music is a challenging task since it requires a model to learn semantic music features and capture the underlying distribution of real conducting motion. Prior works have applied Generative Adversarial Networks (GAN) to this task, but the promising diffusion model, which recently showed its advantages in terms of both training stability and output quality, has not been exploited in this context. This paper presents Diffusion-Conductor, a novel DDIM-based approach for music-driven conducting motion generation, which integrates the diffusion model to a two-stage learning framework. We further propose a random masking strategy to improve the feature robustness, and use a pair of geometric loss functions to impose additional regularizations and increase motion diversity. We also design several novel metrics, including Frechet Gesture Distance (FGD) and Beat Consistency Score (BC) for a more comprehensive evaluation of the generated motion. Experimental results demonstrate the advantages of our model.