Daily Papers

Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction and then feed the results thereof into a trainable classifier. The mathematical analysis of deep convolutional neural networks for feature extraction was initiated by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on a wavelet transform followed by the modulus non-linearity in each network layer, and proved translation invariance (asymptotically in the wavelet scale parameter) and deformation stability of the corresponding feature extractor. This paper complements Mallat's results by developing a theory that encompasses general convolutional transforms, or in more technical parlance, general semi-discrete frames (including Weyl-Heisenberg filters, curvelets, shearlets, ridgelets, wavelets, and learned filters), general Lipschitz-continuous non-linearities (e.g., rectified linear units, shifted logistic sigmoids, hyperbolic tangents, and modulus functions), and general Lipschitz-continuous pooling operators emulating, e.g., sub-sampling and averaging. In addition, all of these elements can be different in different network layers. For the resulting feature extractor we prove a translation invariance result of vertical nature in the sense of the features becoming progressively more translation-invariant with increasing network depth, and we establish deformation sensitivity bounds that apply to signal classes such as, e.g., band-limited functions, cartoon functions, and Lipschitz functions.

This research introduces an innovative AI-driven multi-agent framework specifically designed for creating immersive audiobooks. Leveraging neural text-to-speech synthesis with FastSpeech 2 and VALL-E for expressive narration and character-specific voices, the framework employs advanced language models to automatically interpret textual narratives and generate realistic spatial audio effects. These sound effects are dynamically synchronized with the storyline through sophisticated temporal integration methods, including Dynamic Time Warping (DTW) and recurrent neural networks (RNNs). Diffusion-based generative models combined with higher-order ambisonics (HOA) and scattering delay networks (SDN) enable highly realistic 3D soundscapes, substantially enhancing listener immersion and narrative realism. This technology significantly advances audiobook applications, providing richer experiences for educational content, storytelling platforms, and accessibility solutions for visually impaired audiences. Future work will address personalization, ethical management of synthesized voices, and integration with multi-sensory platforms.

Vision transformers have gained significant attention and achieved state-of-the-art performance in various computer vision tasks, including image classification, instance segmentation, and object detection. However, challenges remain in addressing attention complexity and effectively capturing fine-grained information within images. Existing solutions often resort to down-sampling operations, such as pooling, to reduce computational cost. Unfortunately, such operations are non-invertible and can result in information loss. In this paper, we present a novel approach called Scattering Vision Transformer (SVT) to tackle these challenges. SVT incorporates a spectrally scattering network that enables the capture of intricate image details. SVT overcomes the invertibility issue associated with down-sampling operations by separating low-frequency and high-frequency components. Furthermore, SVT introduces a unique spectral gating network utilizing Einstein multiplication for token and channel mixing, effectively reducing complexity. We show that SVT achieves state-of-the-art performance on the ImageNet dataset with a significant reduction in a number of parameters and FLOPS. SVT shows 2\% improvement over LiTv2 and iFormer. SVT-H-S reaches 84.2\% top-1 accuracy, while SVT-H-B reaches 85.2\% (state-of-art for base versions) and SVT-H-L reaches 85.7\% (again state-of-art for large versions). SVT also shows comparable results in other vision tasks such as instance segmentation. SVT also outperforms other transformers in transfer learning on standard datasets such as CIFAR10, CIFAR100, Oxford Flower, and Stanford Car datasets. The project page is available on this webpage.https://badripatro.github.io/svt/.

Graph neural networks (GNNs) have been used extensively for addressing problems in drug design and discovery. Both ligand and target molecules are represented as graphs with node and edge features encoding information about atomic elements and bonds respectively. Although existing deep learning models perform remarkably well at predicting physicochemical properties and binding affinities, the generation of new molecules with optimized properties remains challenging. Inherently, most GNNs perform poorly in whole-graph representation due to the limitations of the message-passing paradigm. Furthermore, step-by-step graph generation frameworks that use reinforcement learning or other sequential processing can be slow and result in a high proportion of invalid molecules with substantial post-processing needed in order to satisfy the principles of stoichiometry. To address these issues, we propose a representation-first approach to molecular graph generation. We guide the latent representation of an autoencoder by capturing graph structure information with the geometric scattering transform and apply penalties that structure the representation also by molecular properties. We show that this highly structured latent space can be directly used for molecular graph generation by the use of a GAN. We demonstrate that our architecture learns meaningful representations of drug datasets and provides a platform for goal-directed drug synthesis.

Image dehazing is a critical challenge in computer vision, essential for enhancing image clarity in hazy conditions. Traditional methods often rely on atmospheric scattering models, while recent deep learning techniques, specifically Convolutional Neural Networks (CNNs) and Transformers, have improved performance by effectively analyzing image features. However, CNNs struggle with long-range dependencies, and Transformers demand significant computational resources. To address these limitations, we propose DehazeSNN, an innovative architecture that integrates a U-Net-like design with Spiking Neural Networks (SNNs). DehazeSNN captures multi-scale image features while efficiently managing local and long-range dependencies. The introduction of the Orthogonal Leaky-Integrate-and-Fire Block (OLIFBlock) enhances cross-channel communication, resulting in superior dehazing performance with reduced computational burden. Our extensive experiments show that DehazeSNN is highly competitive to state-of-the-art methods on benchmark datasets, delivering high-quality haze-free images with a smaller model size and less multiply-accumulate operations. The proposed dehazing method is publicly available at https://github.com/HaoranLiu507/DehazeSNN.

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

Accurate subsurface scattering solutions require the integration of optical material properties along many complicated light paths. We present a method that learns a simple geometric approximation of random paths in a homogeneous volume of translucent material. The generated representation allows determining the absorption along the path as well as a direct lighting contribution, which is representative of all scattering events along the path. A sequence of conditional variational auto-encoders (CVAEs) is trained to model the statistical distribution of the photon paths inside a spherical region in presence of multiple scattering events. A first CVAE learns to sample the number of scattering events, occurring on a ray path inside the sphere, which effectively determines the probability of the ray being absorbed. Conditioned on this, a second model predicts the exit position and direction of the light particle. Finally, a third model generates a representative sample of photon position and direction along the path, which is used to approximate the contribution of direct illumination due to in-scattering. To accelerate the tracing of the light path through the volumetric medium toward the solid boundary, we employ a sphere-tracing strategy that considers the light absorption and is able to perform statistically accurate next-event estimation. We demonstrate efficient learning using shallow networks of only three layers and no more than 16 nodes. In combination with a GPU shader that evaluates the CVAEs' predictions, performance gains can be demonstrated for a variety of different scenarios. A quality evaluation analyzes the approximation error that is introduced by the data-driven scattering simulation and sheds light on the major sources of error in the accelerated path tracing process.

In this paper, we introduce StreakNet-Arch, a novel signal processing architecture designed for Underwater Carrier LiDAR-Radar (UCLR) imaging systems, to address the limitations in scatter suppression and real-time imaging. StreakNet-Arch formulates the signal processing as a real-time, end-to-end binary classification task, enabling real-time image acquisition. To achieve this, we leverage Self-Attention networks and propose a novel Double Branch Cross Attention (DBC-Attention) mechanism that surpasses the performance of traditional methods. Furthermore, we present a method for embedding streak-tube camera images into attention networks, effectively acting as a learned bandpass filter. To facilitate further research, we contribute a publicly available streak-tube camera image dataset. The dataset contains 2,695,168 real-world underwater 3D point cloud data. These advancements significantly improve UCLR capabilities, enhancing its performance and applicability in underwater imaging tasks. The source code and dataset can be found at https://github.com/BestAnHongjun/StreakNet .

Designing front-ends for speech deepfake detectors primarily focuses on two categories. Hand-crafted filterbank features are transparent but are limited in capturing high-level semantic details, often resulting in performance gaps compared to self-supervised (SSL) features. SSL features, in turn, lack interpretability and may overlook fine-grained spectral anomalies. We propose the WST-X series, a novel family of feature extractors that combines the best of both worlds via the wavelet scattering transform (WST), integrating wavelets with nonlinearities analogous to deep convolutional networks. We investigate 1D and 2D WSTs to extract acoustic details and higher-order structural anomalies, respectively. Experimental results on the recent and challenging Deepfake-Eval-2024 dataset indicate that WST-X outperforms existing front-ends by a wide margin. Our analysis reveals that a small averaging scale (J), combined with high-frequency and directional resolutions (Q, L), is critical for capturing subtle artifacts. This underscores the value of translation-invariant and deformation-stable features for robust and interpretable speech deepfake detection.

Recovering the physical attributes of an object's appearance from its images captured under an unknown illumination is challenging yet essential for photo-realistic rendering. Recent approaches adopt the emerging implicit scene representations and have shown impressive results.However, they unanimously adopt a surface-based representation,and hence can not well handle scenes with very complex geometry, translucent object and etc. In this paper, we propose to conduct inverse volume rendering, in contrast to surface-based, by representing a scene using microflake volume, which assumes the space is filled with infinite small flakes and light reflects or scatters at each spatial location according to microflake distributions. We further adopt the coordinate networks to implicitly encode the microflake volume, and develop a differentiable microflake volume renderer to train the network in an end-to-end way in principle.Our NeMF enables effective recovery of appearance attributes for highly complex geometry and scattering object, enables high-quality relighting, material editing, and especially simulates volume rendering effects, such as scattering, which is infeasible for surface-based approaches.

We model and study the processes of excitation, absorption, and transfer in various networks. The model consists of a harmonic oscillator representing a single-mode radiation field, a qubit acting as an antenna, a network through which the excitation propagates, and a qubit at the end serving as a sink. We investigate how off-resonant excitations can be optimally absorbed and transmitted through the network. Three strategies are considered: optimising network energies, adjusting the couplings between the radiation field, the antenna, and the network, or introducing and optimising driving fields at the start and end of the network. These strategies are tested on three different types of network with increasing complexity: nearest-neighbour and star configurations, and one associated with the Fenna-Matthews-Olson complex. The results show that, among the various strategies, the introduction of driving fields is the most effective, leading to a significant increase in the probability of reaching the sink in a given time. This result remains stable across networks of varying dimensionalities and types, and the driving process requires only a few parameters to be effective.

Modeling radio propagation is essential for wireless network design and performance optimization. Traditional methods rely on physics models of radio propagation, which can be inaccurate or inflexible. In this work, we propose using graph neural networks to learn radio propagation behaviors directly from real-world network data. Our approach converts the radio propagation environment into a graph representation, with nodes corresponding to locations and edges representing spatial and ray-tracing relationships between locations. The graph is generated by converting images of the environment into a graph structure, with specific relationships between nodes. The model is trained on this graph representation, using sensor measurements as target data. We demonstrate that the graph neural network, which learns to predict radio propagation directly from data, achieves competitive performance compared to traditional heuristic models. This data-driven approach outperforms classic numerical solvers in terms of both speed and accuracy. To the best of our knowledge, we are the first to apply graph neural networks to real-world radio propagation data to generate coverage maps, enabling generative models of signal propagation with point measurements only.

Graph Neural Networks (GNNs), especially message-passing neural networks (MPNNs), have emerged as powerful architectures for learning on graphs in diverse applications. However, MPNNs face challenges when modeling non-local interactions in graphs such as large conjugated molecules, and social networks due to oversmoothing and oversquashing. Although Spectral GNNs and traditional neural networks such as recurrent neural networks and transformers mitigate these challenges, they often lack generalizability, or fail to capture detailed structural relationships or symmetries in the data. To address these concerns, we introduce Matrix Function Neural Networks (MFNs), a novel architecture that parameterizes non-local interactions through analytic matrix equivariant functions. Employing resolvent expansions offers a straightforward implementation and the potential for linear scaling with system size. The MFN architecture achieves stateof-the-art performance in standard graph benchmarks, such as the ZINC and TU datasets, and is able to capture intricate non-local interactions in quantum systems, paving the way to new state-of-the-art force fields.

Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the tendency of a node to select neighbors with a probability depending on physical distance. Here, we introduce a class of random spatial networks (RSNs) which generalizes many existing random network models but adds spatial structure. In these networks, nodes are placed randomly in space and joined in edges with a probability depending on their distance and their individual expected degrees, in a manner that crucially remains analytically tractable. We use this network class to propose a new generalization of small-world networks, where the average shortest path lengths in the graph are small, as in classical Watts-Strogatz small-world networks, but with close spatial proximity of nodes that are neighbors in the network playing the role of large clustering. Small-world effects are demonstrated on these spatial small-world networks without clustering. We are able to derive partial integro-differential equations governing susceptible-infectious-recovered disease spreading through an RSN, and we demonstrate the existence of traveling wave solutions. If the distance kernel governing edge placement decays slower than exponential, the population-scale dynamics are dominated by long-range hops followed by local spread of traveling waves. This provides a theoretical modeling framework for recent observations of how epidemics like Ebola evolve in modern connected societies, with long-range connections seeding new focal points from which the epidemic locally spreads in a wavelike manner.

We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as quality and quantity of the training dataset, network storage and noise, that is valid in the limit of large network size and structureless datasets: these networks may work in a ultra-storage regime (where they can handle a huge amount of patterns, if compared with shallow neural networks) or in a ultra-detection regime (where they can perform pattern recognition at prohibitive signal-to-noise ratios, if compared with shallow neural networks). Guided by the random theory as a reference framework, we also test numerically learning, storing and retrieval capabilities shown by these networks on structured datasets as MNist and Fashion MNist. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate supervised learning in neural networks, beyond the shallow limit, in general.

Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on discovering these fields, and infer them from the observed dynamics alone, without directly observing them. We theorize the presence of latent force fields, and propose neural fields to learn them. Since the observed dynamics constitute the net effect of local object interactions and global field effects, recently popularized equivariant networks are inapplicable, as they fail to capture global information. To address this, we propose to disentangle local object interactions -- which are SE(n) equivariant and depend on relative states -- from external global field effects -- which depend on absolute states. We model interactions with equivariant graph networks, and combine them with neural fields in a novel graph network that integrates field forces. Our experiments show that we can accurately discover the underlying fields in charged particles settings, traffic scenes, and gravitational n-body problems, and effectively use them to learn the system and forecast future trajectories.

Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions. Recent work has shown that such models can separate generic pairs of non-isomorphic geometric graphs, though they may fail to separate some rare and complicated instances. However, these results assume a fully connected graph, where each node possesses complete knowledge of all other nodes. In contrast, often, in application, every node only possesses knowledge of a small number of nearest neighbors. This paper shows that generic pairs of non-isomorphic geometric graphs can be separated by message-passing networks with rotation equivariant features as long as the underlying graph is connected. When only invariant intermediate features are allowed, generic separation is guaranteed for generically globally rigid graphs. We introduce a simple architecture, EGENNET, which achieves our theoretical guarantees and compares favorably with alternative architecture on synthetic and chemical benchmarks. Our code is available at https://github.com/yonatansverdlov/E-GenNet.

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.

Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in the structure of the graph Laplacian operator, the properties of the associated diffusion equation, and the characteristics of the convolutional models that discretise this equation. In this paper, we use cellular sheaf theory to show that the underlying geometry of the graph is deeply linked with the performance of GNNs in heterophilic settings and their oversmoothing behaviour. By considering a hierarchy of increasingly general sheaves, we study how the ability of the sheaf diffusion process to achieve linear separation of the classes in the infinite time limit expands. At the same time, we prove that when the sheaf is non-trivial, discretised parametric diffusion processes have greater control than GNNs over their asymptotic behaviour. On the practical side, we study how sheaves can be learned from data. The resulting sheaf diffusion models have many desirable properties that address the limitations of classical graph diffusion equations (and corresponding GNN models) and obtain competitive results in heterophilic settings. Overall, our work provides new connections between GNNs and algebraic topology and would be of interest to both fields.

Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. However, those works developed architectures tailored to specific networks such as MLPs and CNNs without normalization layers, and generalizing such architectures to other types of networks can be challenging. In this work, we overcome these challenges by building new metanetworks - neural networks that take weights from other neural networks as input. Put simply, we carefully build graphs representing the input neural networks and process the graphs using graph neural networks. Our approach, Graph Metanetworks (GMNs), generalizes to neural architectures where competing methods struggle, such as multi-head attention layers, normalization layers, convolutional layers, ResNet blocks, and group-equivariant linear layers. We prove that GMNs are expressive and equivariant to parameter permutation symmetries that leave the input neural network functions unchanged. We validate the effectiveness of our method on several metanetwork tasks over diverse neural network architectures.

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.

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental differences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

Message passing neural networks (MPNNs) have been shown to suffer from the phenomenon of over-squashing that causes poor performance for tasks relying on long-range interactions. This can be largely attributed to message passing only occurring locally, over a node's immediate neighbours. Rewiring approaches attempting to make graphs 'more connected', and supposedly better suited to long-range tasks, often lose the inductive bias provided by distance on the graph since they make distant nodes communicate instantly at every layer. In this paper we propose a framework, applicable to any MPNN architecture, that performs a layer-dependent rewiring to ensure gradual densification of the graph. We also propose a delay mechanism that permits skip connections between nodes depending on the layer and their mutual distance. We validate our approach on several long-range tasks and show that it outperforms graph Transformers and multi-hop MPNNs.

We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph including connected components, connectivity, and cycle structures even with no features. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at https://github.com/KrishnaswamyLab/DYMAG.

Graph neural networks have recently achieved great successes in predicting quantum mechanical properties of molecules. These models represent a molecule as a graph using only the distance between atoms (nodes). They do not, however, consider the spatial direction from one atom to another, despite directional information playing a central role in empirical potentials for molecules, e.g. in angular potentials. To alleviate this limitation we propose directional message passing, in which we embed the messages passed between atoms instead of the atoms themselves. Each message is associated with a direction in coordinate space. These directional message embeddings are rotationally equivariant since the associated directions rotate with the molecule. We propose a message passing scheme analogous to belief propagation, which uses the directional information by transforming messages based on the angle between them. Additionally, we use spherical Bessel functions and spherical harmonics to construct theoretically well-founded, orthogonal representations that achieve better performance than the currently prevalent Gaussian radial basis representations while using fewer than 1/4 of the parameters. We leverage these innovations to construct the directional message passing neural network (DimeNet). DimeNet outperforms previous GNNs on average by 76% on MD17 and by 31% on QM9. Our implementation is available online.

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive to information contained at distant nodes. Despite recent methods introduced to mitigate this issue, an understanding of the causes for over-squashing and of possible solutions are lacking. In this theoretical work, we prove that: (i) Neural network width can mitigate over-squashing, but at the cost of making the whole network more sensitive; (ii) Conversely, depth cannot help mitigate over-squashing: increasing the number of layers leads to over-squashing being dominated by vanishing gradients; (iii) The graph topology plays the greatest role, since over-squashing occurs between nodes at high commute (access) time. Our analysis provides a unified framework to study different recent methods introduced to cope with over-squashing and serves as a justification for a class of methods that fall under graph rewiring.

Graph Neural Networks (GNNs) have emerged as powerful tools for learning on graph-structured data, but often struggle to balance local and global information. While graph Transformers aim to address this by enabling long-range interactions, they often overlook the inherent locality and efficiency of Message Passing Neural Networks (MPNNs). We propose a new concept called fractal nodes, inspired by the fractal structure observed in real-world networks. Our approach is based on the intuition that graph partitioning naturally induces fractal structure, where subgraphs often reflect the connectivity patterns of the full graph. Fractal nodes are designed to coexist with the original nodes and adaptively aggregate subgraph-level feature representations, thereby enforcing feature similarity within each subgraph. We show that fractal nodes alleviate the over-squashing problem by providing direct shortcut connections that enable long-range propagation of subgraph-level representations. Experiment results show that our method improves the expressive power of MPNNs and achieves comparable or better performance to graph Transformers while maintaining the computational efficiency of MPNN by improving the long-range dependencies of MPNN.

Artificial Neural Networks are computational network models inspired by signal processing in the brain. These models have dramatically improved the performance of many learning tasks, including speech and object recognition. However, today's computing hardware is inefficient at implementing neural networks, in large part because much of it was designed for von Neumann computing schemes. Significant effort has been made to develop electronic architectures tuned to implement artificial neural networks that improve upon both computational speed and energy efficiency. Here, we propose a new architecture for a fully-optical neural network that, using unique advantages of optics, promises a computational speed enhancement of at least two orders of magnitude over the state-of-the-art and three orders of magnitude in power efficiency for conventional learning tasks. We experimentally demonstrate essential parts of our architecture using a programmable nanophotonic processor.

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance. In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily scaled to higher-dimensional spaces. We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.

The under-display camera (UDC) provides consumers with a full-screen visual experience without any obstruction due to notches or punched holes. However, the semi-transparent nature of the display inevitably introduces the severe degradation into UDC images. In this work, we address the UDC image restoration problem with the specific consideration of the scattering effect caused by the display. We explicitly model the scattering effect by treating the display as a piece of homogeneous scattering medium. With the physical model of the scattering effect, we improve the image formation pipeline for the image synthesis to construct a realistic UDC dataset with ground truths. To suppress the scattering effect for the eventual UDC image recovery, a two-branch restoration network is designed. More specifically, the scattering branch leverages global modeling capabilities of the channel-wise self-attention to estimate parameters of the scattering effect from degraded images. While the image branch exploits the local representation advantage of CNN to recover clear scenes, implicitly guided by the scattering branch. Extensive experiments are conducted on both real-world and synthesized data, demonstrating the superiority of the proposed method over the state-of-the-art UDC restoration techniques. The source code and dataset are available at https://github.com/NamecantbeNULL/SRUDC.

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be SO(3) equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the SO(3) convolutions or tensor products to mathematically equivalent convolutions in SO(2) . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from O(L^6) to O(L^3), where L is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.

Designing nanophotonic structures traditionally grapples with the complexities of discrete parameters, such as real materials, often resorting to costly global optimization methods. This paper introduces an approach that leverages generative deep learning to map discrete parameter sets into a continuous latent space, enabling direct gradient-based optimization. For scenarios with non-differentiable physics evaluation functions, a neural network is employed as a differentiable surrogate model. The efficacy of this methodology is demonstrated by optimizing the directional scattering properties of core-shell nanoparticles composed of a selection of realistic materials. We derive suggestions for core-shell geometries with strong forward scattering and minimized backscattering. Our findings reveal significant improvements in computational efficiency and performance when compared to global optimization techniques. Beyond nanophotonics design problems, this framework holds promise for broad applications across all types of inverse problems constrained by discrete variables.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

Message-passing graph neural networks (MPNNs) emerged as powerful tools for processing graph-structured input. However, they operate on a fixed input graph structure, ignoring potential noise and missing information. Furthermore, their local aggregation mechanism can lead to problems such as over-squashing and limited expressive power in capturing relevant graph structures. Existing solutions to these challenges have primarily relied on heuristic methods, often disregarding the underlying data distribution. Hence, devising principled approaches for learning to infer graph structures relevant to the given prediction task remains an open challenge. In this work, leveraging recent progress in exact and differentiable k-subset sampling, we devise probabilistically rewired MPNNs (PR-MPNNs), which learn to add relevant edges while omitting less beneficial ones. For the first time, our theoretical analysis explores how PR-MPNNs enhance expressive power, and we identify precise conditions under which they outperform purely randomized approaches. Empirically, we demonstrate that our approach effectively mitigates issues like over-squashing and under-reaching. In addition, on established real-world datasets, our method exhibits competitive or superior predictive performance compared to traditional MPNN models and recent graph transformer architectures.

We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a simple expansion rule generates deep networks whose structural layouts are precisely truncated fractals. These networks contain interacting subpaths of different lengths, but do not include any pass-through or residual connections; every internal signal is transformed by a filter and nonlinearity before being seen by subsequent layers. In experiments, fractal networks match the excellent performance of standard residual networks on both CIFAR and ImageNet classification tasks, thereby demonstrating that residual representations may not be fundamental to the success of extremely deep convolutional neural networks. Rather, the key may be the ability to transition, during training, from effectively shallow to deep. We note similarities with student-teacher behavior and develop drop-path, a natural extension of dropout, to regularize co-adaptation of subpaths in fractal architectures. Such regularization allows extraction of high-performance fixed-depth subnetworks. Additionally, fractal networks exhibit an anytime property: shallow subnetworks provide a quick answer, while deeper subnetworks, with higher latency, provide a more accurate answer.

Deep Neural Networks (DNNs) can be represented as graphs whose links and vertices iteratively process data and solve tasks sub-optimally. Complex Network Theory (CNT), merging statistical physics with graph theory, provides a method for interpreting neural networks by analysing their weights and neuron structures. However, classic works adapt CNT metrics that only permit a topological analysis as they do not account for the effect of the input data. In addition, CNT metrics have been applied to a limited range of architectures, mainly including Fully Connected neural networks. In this work, we extend the existing CNT metrics with measures that sample from the DNNs' training distribution, shifting from a purely topological analysis to one that connects with the interpretability of deep learning. For the novel metrics, in addition to the existing ones, we provide a mathematical formalisation for Fully Connected, AutoEncoder, Convolutional and Recurrent neural networks, of which we vary the activation functions and the number of hidden layers. We show that these metrics differentiate DNNs based on the architecture, the number of hidden layers, and the activation function. Our contribution provides a method rooted in physics for interpreting DNNs that offers insights beyond the traditional input-output relationship and the CNT topological analysis.

Mesh-based simulations are central to modeling complex physical systems in many disciplines across science and engineering. Mesh representations support powerful numerical integration methods and their resolution can be adapted to strike favorable trade-offs between accuracy and efficiency. However, high-dimensional scientific simulations are very expensive to run, and solvers and parameters must often be tuned individually to each system studied. Here we introduce MeshGraphNets, a framework for learning mesh-based simulations using graph neural networks. Our model can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation. Our results show it can accurately predict the dynamics of a wide range of physical systems, including aerodynamics, structural mechanics, and cloth. The model's adaptivity supports learning resolution-independent dynamics and can scale to more complex state spaces at test time. Our method is also highly efficient, running 1-2 orders of magnitude faster than the simulation on which it is trained. Our approach broadens the range of problems on which neural network simulators can operate and promises to improve the efficiency of complex, scientific modeling tasks.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). We observe robust improvements in energy mean absolute errors across all models and datasets, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground truth energy.

In this work, we present a new network design paradigm. Our goal is to help advance the understanding of network design and discover design principles that generalize across settings. Instead of focusing on designing individual network instances, we design network design spaces that parametrize populations of networks. The overall process is analogous to classic manual design of networks, but elevated to the design space level. Using our methodology we explore the structure aspect of network design and arrive at a low-dimensional design space consisting of simple, regular networks that we call RegNet. The core insight of the RegNet parametrization is surprisingly simple: widths and depths of good networks can be explained by a quantized linear function. We analyze the RegNet design space and arrive at interesting findings that do not match the current practice of network design. The RegNet design space provides simple and fast networks that work well across a wide range of flop regimes. Under comparable training settings and flops, the RegNet models outperform the popular EfficientNet models while being up to 5x faster on GPUs.

In order to make accurate predictions of material properties, current machine-learning approaches generally require large amounts of data, which are often not available in practice. In this work, an all-round framework is presented which relies on a feedforward neural network, the selection of physically-meaningful features and, when applicable, joint-learning. Next to being faster in terms of training time, this approach is shown to outperform current graph-network models on small datasets. In particular, the vibrational entropy at 305 K of crystals is predicted with a mean absolute test error of 0.009 meV/K/atom (four times lower than previous studies). Furthermore, joint-learning reduces the test error compared to single-target learning and enables the prediction of multiple properties at once, such as temperature functions. Finally, the selection algorithm highlights the most important features and thus helps understanding the underlying physics.

We give an overview of recent developments in the modeling of radiowave propagation, based on machine learning algorithms. We identify the input and output specification and the architecture of the model as the main challenges associated with machine learning-driven propagation models. Relevant papers are discussed and categorized based on their approach to each of these challenges. Emphasis is given on presenting the prospects and open problems in this promising and rapidly evolving area.

Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate change. These calculations are traditionally performed using Density Functional Theory, which is computationally very expensive. Machine learning has the potential to dramatically improve the efficiency of these calculations from days or hours to seconds. We propose the Spherical Channel Network (SCN) to model atomic energies and forces. The SCN is a graph neural network where nodes represent atoms and edges their neighboring atoms. The atom embeddings are a set of spherical functions, called spherical channels, represented using spherical harmonics. We demonstrate, that by rotating the embeddings based on the 3D edge orientation, more information may be utilized while maintaining the rotational equivariance of the messages. While equivariance is a desirable property, we find that by relaxing this constraint in both message passing and aggregation, improved accuracy may be achieved. We demonstrate state-of-the-art results on the large-scale Open Catalyst dataset in both energy and force prediction for numerous tasks and metrics.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

This paper discusses a simple and explicit toy-model example of the categorical Hopfield equations introduced in previous work of Manin and the author. These describe dynamical assignments of resources to networks, where resources are objects in unital symmetric monoidal categories and assignments are realized by summing functors. The special case discussed here is based on computational resources (computational models of neurons) as objects in a category of DNNs, with a simple choice of the endofunctors defining the Hopfield equations that reproduce the usual updating of the weights in DNNs by gradient descent.

Network pruning, aimed at reducing network size while preserving accuracy, has attracted significant research interest. Numerous pruning techniques have been proposed over time. They are becoming increasingly effective, but more complex and harder to interpret as well. Given the inherent complexity of neural networks, we argue that manually designing pruning criteria has reached a bottleneck. To address this, we propose a novel approach in which we "use a neural network to prune neural networks". More specifically, we introduce the newly developed idea of metanetwork from meta-learning into pruning. A metanetwork is a network that takes another network as input and produces a modified network as output. In this paper, we first establish a bijective mapping between neural networks and graphs, and then employ a graph neural network as our metanetwork. We train a metanetwork that learns the pruning strategy automatically which can transform a network that is hard to prune into another network that is much easier to prune. Once the metanetwork is trained, our pruning needs nothing more than a feedforward through the metanetwork and the standard finetuning to prune at state-of-the-art. Our method achieved outstanding results on many popular and representative pruning tasks (including ResNet56 on CIFAR10, VGG19 on CIFAR100, ResNet50 on ImageNet). Our code is available at https://github.com/Yewei-Liu/MetaPruning

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These models extend traditional message-passing GNNs and Transformers by representing node and edge features as spherical tensors that transform under irreducible representations of the rotation group SO(3), ensuring that predictions change in physically meaningful ways under rotations of the input. This guide develops a complete, intuitive foundation for spherical equivariant modeling - from group representations and spherical harmonics, to tensor products, Clebsch-Gordan decomposition, and the construction of SO(3)-equivariant kernels. Building on this foundation, we construct the Tensor Field Network and SE(3)-Transformer architectures and explain how they perform equivariant message-passing and attention on geometric graphs. Through clear mathematical derivations and annotated code excerpts, this guide serves as a self-contained introduction for researchers and learners seeking to understand or implement spherical EGNNs for applications in chemistry, molecular property prediction, protein structure modeling, and generative modeling.

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.

We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as the quality and quantity of the training dataset and the network storage, valid in the limit of large network size and structureless datasets. Moreover, we establish a bridge between macroscopic observables standardly used in statistical mechanics and loss functions typically used in the machine learning. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate neural networks in general.

Sparse neural networks have shown similar or better generalization performance than their dense counterparts while having higher parameter efficiency. This has motivated a number of works to learn or search for high performing sparse networks. While reports of task performance or efficiency gains are impressive, standard baselines are lacking leading to poor comparability and unreliable reproducibility across methods. In this work, we propose Random Search as a baseline algorithm for finding good sparse configurations and study its performance. We apply Random Search on the node space of an overparameterized network with the goal of finding better initialized sparse sub-networks that are positioned more advantageously in the loss landscape. We record the post-training performances of the found sparse networks and at various levels of sparsity, and compare against both their fully connected parent networks and random sparse configurations at the same sparsity levels. First, we demonstrate performance at different levels of sparsity and highlight that a significant level of performance can still be preserved even when the network is highly sparse. Second, we observe that for this sparse architecture search task, initialized sparse networks found by Random Search neither perform better nor converge more efficiently than their random counterparts. Thus we conclude that Random Search may be viewed as a reasonable neutral baseline for sparsity search methods.

It has been shown that a message passing neural networks (MPNNs), a popular family of neural networks for graph-structured data, are at most as expressive as the first-order Weisfeiler-Leman (1-WL) graph isomorphism test, which has motivated the development of more expressive architectures. In this work, we analyze if the limited expressiveness is actually a limiting factor for MPNNs and other WL-based models in standard graph datasets. Interestingly, we find that the expressiveness of WL is sufficient to identify almost all graphs in most datasets. Moreover, we find that the classification accuracy upper bounds are often close to 100\%. Furthermore, we find that simple WL-based neural networks and several MPNNs can be fitted to several datasets. In sum, we conclude that the performance of WL/MPNNs is not limited by their expressiveness in practice.

Statistical channel models are instrumental to design and evaluate wireless communication systems. In the millimeter wave bands, such models become acutely challenging; they must capture the delay, directions, and path gains, for each link and with high resolution. This paper presents a general modeling methodology based on training generative neural networks from data. The proposed generative model consists of a two-stage structure that first predicts the state of each link (line-of-sight, non-line-of-sight, or outage), and subsequently feeds this state into a conditional variational autoencoder that generates the path losses, delays, and angles of arrival and departure for all its propagation paths. Importantly, minimal prior assumptions are made, enabling the model to capture complex relationships within the data. The methodology is demonstrated for 28GHz air-to-ground channels in an urban environment, with training datasets produced by means of ray tracing.

In this work we develop a new method, named Sub-graph Permutation Equivariant Networks (SPEN), which provides a framework for building graph neural networks that operate on sub-graphs, while using a base update function that is permutation equivariant, that are equivariant to a novel choice of automorphism group. Message passing neural networks have been shown to be limited in their expressive power and recent approaches to over come this either lack scalability or require structural information to be encoded into the feature space. The general framework presented here overcomes the scalability issues associated with global permutation equivariance by operating more locally on sub-graphs. In addition, through operating on sub-graphs the expressive power of higher-dimensional global permutation equivariant networks is improved; this is due to fact that two non-distinguishable graphs often contain distinguishable sub-graphs. Furthermore, the proposed framework only requires a choice of k-hops for creating ego-network sub-graphs and a choice of representation space to be used for each layer, which makes the method easily applicable across a range of graph based domains. We experimentally validate the method on a range of graph benchmark classification tasks, demonstrating statistically indistinguishable results from the state-of-the-art on six out of seven benchmarks. Further, we demonstrate that the use of local update functions offers a significant improvement in GPU memory over global methods.

Neural networks have achieved tremendous success in a large variety of applications. However, their memory footprint and computational demand can render them impractical in application settings with limited hardware or energy resources. In this work, we propose a novel algorithm to find efficient low-rank subnetworks. Remarkably, these subnetworks are determined and adapted already during the training phase and the overall time and memory resources required by both training and evaluating them are significantly reduced. The main idea is to restrict the weight matrices to a low-rank manifold and to update the low-rank factors rather than the full matrix during training. To derive training updates that are restricted to the prescribed manifold, we employ techniques from dynamic model order reduction for matrix differential equations. This allows us to provide approximation, stability, and descent guarantees. Moreover, our method automatically and dynamically adapts the ranks during training to achieve the desired approximation accuracy. The efficiency of the proposed method is demonstrated through a variety of numerical experiments on fully-connected and convolutional networks.

We propose the Automatic-differentiated Physics-Informed Echo State Network (API-ESN). The network is constrained by the physical equations through the reservoir's exact time-derivative, which is computed by automatic differentiation. As compared to the original Physics-Informed Echo State Network, the accuracy of the time-derivative is increased by up to seven orders of magnitude. This increased accuracy is key in chaotic dynamical systems, where errors grows exponentially in time. The network is showcased in the reconstruction of unmeasured (hidden) states of a chaotic system. The API-ESN eliminates a source of error, which is present in existing physics-informed echo state networks, in the computation of the time-derivative. This opens up new possibilities for an accurate reconstruction of chaotic dynamical states.

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.

Signed networks allow us to model conflicting relationships and interactions, such as friend/enemy and support/oppose. These signed interactions happen in real-time. Modeling such dynamics of signed networks is crucial to understanding the evolution of polarization in the network and enabling effective prediction of the signed structure (i.e., link signs and signed weights) in the future. However, existing works have modeled either (static) signed networks or dynamic (unsigned) networks but not dynamic signed networks. Since both sign and dynamics inform the graph structure in different ways, it is non-trivial to model how to combine the two features. In this work, we propose a new Graph Neural Network (GNN)-based approach to model dynamic signed networks, named SEMBA: Signed link's Evolution using Memory modules and Balanced Aggregation. Here, the idea is to incorporate the signs of temporal interactions using separate modules guided by balance theory and to evolve the embeddings from a higher-order neighborhood. Experiments on 4 real-world datasets and 4 different tasks demonstrate that SEMBA consistently and significantly outperforms the baselines by up to 80% on the tasks of predicting signs of future links while matching the state-of-the-art performance on predicting the existence of these links in the future. We find that this improvement is due specifically to the superior performance of SEMBA on the minority negative class.

Graph Neural Networks (GNNs) are popular models for machine learning on graphs that typically follow the message-passing paradigm, whereby the feature of a node is updated recursively upon aggregating information over its neighbors. While exchanging messages over the input graph endows GNNs with a strong inductive bias, it can also make GNNs susceptible to over-squashing, thereby preventing them from capturing long-range interactions in the given graph. To rectify this issue, graph rewiring techniques have been proposed as a means of improving information flow by altering the graph connectivity. In this work, we identify three desiderata for graph-rewiring: (i) reduce over-squashing, (ii) respect the locality of the graph, and (iii) preserve the sparsity of the graph. We highlight fundamental trade-offs that occur between spatial and spectral rewiring techniques; while the former often satisfy (i) and (ii) but not (iii), the latter generally satisfy (i) and (iii) at the expense of (ii). We propose a novel rewiring framework that satisfies all of (i)--(iii) through a locality-aware sequence of rewiring operations. We then discuss a specific instance of such rewiring framework and validate its effectiveness on several real-world benchmarks, showing that it either matches or significantly outperforms existing rewiring approaches.

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

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden (or latent) node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.

The parameter space for any fixed architecture of feedforward ReLU neural networks serves as a proxy during training for the associated class of functions - but how faithful is this representation? It is known that many different parameter settings can determine the same function. Moreover, the degree of this redundancy is inhomogeneous: for some networks, the only symmetries are permutation of neurons in a layer and positive scaling of parameters at a neuron, while other networks admit additional hidden symmetries. In this work, we prove that, for any network architecture where no layer is narrower than the input, there exist parameter settings with no hidden symmetries. We also describe a number of mechanisms through which hidden symmetries can arise, and empirically approximate the functional dimension of different network architectures at initialization. These experiments indicate that the probability that a network has no hidden symmetries decreases towards 0 as depth increases, while increasing towards 1 as width and input dimension increase.

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing PINNs are based on point-wise formulation with fully-connected networks to learn continuous functions, which suffer from poor scalability and hard boundary enforcement. Second, the infinite search space over-complicates the non-convex optimization for network training. Third, although the convolutional neural network (CNN)-based discrete learning can significantly improve training efficiency, CNNs struggle to handle irregular geometries with unstructured meshes. To properly address these challenges, we present a novel discrete PINN framework based on graph convolutional network (GCN) and variational structure of PDE to solve forward and inverse partial differential equations (PDEs) in a unified manner. The use of a piecewise polynomial basis can reduce the dimension of search space and facilitate training and convergence. Without the need of tuning penalty parameters in classic PINNs, the proposed method can strictly impose boundary conditions and assimilate sparse data in both forward and inverse settings. The flexibility of GCNs is leveraged for irregular geometries with unstructured meshes. The effectiveness and merit of the proposed method are demonstrated over a variety of forward and inverse computational mechanics problems governed by both linear and nonlinear PDEs.

The utility of a learned neural representation depends on how well its geometry supports performance in downstream tasks. This geometry depends on the structure of the inputs, the structure of the target outputs, and the architecture of the network. By studying the learning dynamics of networks with one hidden layer, we discovered that the network's activation function has an unexpectedly strong impact on the representational geometry: Tanh networks tend to learn representations that reflect the structure of the target outputs, while ReLU networks retain more information about the structure of the raw inputs. This difference is consistently observed across a broad class of parameterized tasks in which we modulated the degree of alignment between the geometry of the task inputs and that of the task labels. We analyzed the learning dynamics in weight space and show how the differences between the networks with Tanh and ReLU nonlinearities arise from the asymmetric asymptotic behavior of ReLU, which leads feature neurons to specialize for different regions of input space. By contrast, feature neurons in Tanh networks tend to inherit the task label structure. Consequently, when the target outputs are low dimensional, Tanh networks generate neural representations that are more disentangled than those obtained with a ReLU nonlinearity. Our findings shed light on the interplay between input-output geometry, nonlinearity, and learned representations in neural networks.

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.

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.

Graph Neural Networks (GNNs) have been widely adopted for drug discovery with molecular graphs. Nevertheless, current GNNs are mainly good at leveraging short-range interactions (SRI) but struggle to capture long-range interactions (LRI), both of which are crucial for determining molecular properties. To tackle this issue, we propose a method that implicitly projects all original atoms into a few Neural Atoms, which abstracts the collective information of atomic groups within a molecule. Specifically, we explicitly exchange the information among neural atoms and project them back to the atoms' representations as an enhancement. With this mechanism, neural atoms establish the communication channels among distant nodes, effectively reducing the interaction scope of arbitrary node pairs into a single hop. To provide an inspection of our method from a physical perspective, we reveal its connection with the traditional LRI calculation method, Ewald Summation. We conduct extensive experiments on three long-range graph benchmarks, covering both graph-level and link-level tasks on molecular graphs. We empirically justify that our method can be equipped with an arbitrary GNN and help to capture LRI.

Human mobility has a significant impact on several layers of society, from infrastructural planning and economics to the spread of diseases and crime. Representing the system as a complex network, in which nodes are assigned to regions (e.g., a city) and links indicate the flow of people between two of them, physics-inspired models have been proposed to quantify the number of people migrating from one city to the other. Despite the advances made by these models, our ability to predict the number of commuters and reconstruct mobility networks remains limited. Here, we propose an alternative approach using machine learning and 22 urban indicators to predict the flow of people and reconstruct the intercity commuters network. Our results reveal that predictions based on machine learning algorithms and urban indicators can reconstruct the commuters network with 90.4% of accuracy and describe 77.6% of the variance observed in the flow of people between cities. We also identify essential features to recover the network structure and the urban indicators mostly related to commuting patterns. As previously reported, distance plays a significant role in commuting, but other indicators, such as Gross Domestic Product (GDP) and unemployment rate, are also driven-forces for people to commute. We believe that our results shed new lights on the modeling of migration and reinforce the role of urban indicators on commuting patterns. Also, because link-prediction and network reconstruction are still open challenges in network science, our results have implications in other areas, like economics, social sciences, and biology, where node attributes can give us information about the existence of links connecting entities in the network.

Graphs are essential data structures for modeling complex interactions in domains such as social networks, molecular structures, and biological systems. Graph-level tasks, which predict properties or classes for the entire graph, are critical for applications, such as molecular property prediction and subgraph counting. Graph Neural Networks (GNNs) have shown promise in these tasks, but their evaluations are often limited to narrow datasets, tasks, and inconsistent experimental setups, restricting their generalizability. To address these limitations, we propose a unified evaluation framework for graph-level GNNs. This framework provides a standardized setting to evaluate GNNs across diverse datasets, various graph tasks (e.g., graph classification and regression), and challenging scenarios, including noisy, imbalanced, and few-shot graphs. Additionally, we propose a novel GNN model with enhanced expressivity and generalization capabilities. Specifically, we enhance the expressivity of GNNs through a k-path rooted subgraph approach, enabling the model to effectively count subgraphs (e.g., paths and cycles). Moreover, we introduce a unified graph contrastive learning algorithm for graphs across diverse domains, which adaptively removes unimportant edges to augment graphs, thereby significantly improving generalization performance. Extensive experiments demonstrate that our model achieves superior performance against fourteen effective baselines across twenty-seven graph datasets, establishing it as a robust and generalizable model for graph-level tasks.

Despite the significant progress made by deep models in various image restoration tasks, existing image restoration networks still face challenges in terms of task generality. An intuitive manifestation is that networks which excel in certain tasks often fail to deliver satisfactory results in others. To illustrate this point, we select five representative networks and conduct a comparative study on five classic image restoration tasks. First, we provide a detailed explanation of the characteristics of different image restoration tasks and backbone networks. Following this, we present the benchmark results and analyze the reasons behind the performance disparity of different models across various tasks. Drawing from this comparative study, we propose that a general image restoration backbone network needs to meet the functional requirements of diverse tasks. Based on this principle, we design a new general image restoration backbone network, X-Restormer. Extensive experiments demonstrate that X-Restormer possesses good task generality and achieves state-of-the-art performance across a variety of tasks.

There has been a recent surge of interest in modeling neural networks (NNs) as Gaussian processes. In the limit of a NN of infinite width the NN becomes equivalent to a Gaussian process. Here we demonstrate that for an ensemble of large, finite, fully connected networks with a single hidden layer the distribution of outputs at initialization is well described by a Gaussian perturbed by the fourth Hermite polynomial for weights drawn from a symmetric distribution. We show that the scale of the perturbation is inversely proportional to the number of units in the NN and that higher order terms decay more rapidly, thereby recovering the Edgeworth expansion. We conclude by observing that understanding how this perturbation changes under training would reveal the regimes in which the Gaussian process framework is valid to model NN behavior.

Recent neural network-based wave functions have achieved state-of-the-art accuracies in modeling ab-initio ground-state potential energy surface. However, these networks can only solve different spatial arrangements of the same set of atoms. To overcome this limitation, we present Graph-learned orbital embeddings (Globe), a neural network-based reparametrization method that can adapt neural wave functions to different molecules. Globe learns representations of local electronic structures that generalize across molecules via spatial message passing by connecting molecular orbitals to covalent bonds. Further, we propose a size-consistent wave function Ansatz, the Molecular orbital network (Moon), tailored to jointly solve Schr\"odinger equations of different molecules. In our experiments, we find Moon converging in 4.5 times fewer steps to similar accuracy as previous methods or to lower energies given the same time. Further, our analysis shows that Moon's energy estimate scales additively with increased system sizes, unlike previous work where we observe divergence. In both computational chemistry and machine learning, we are the first to demonstrate that a single wave function can solve the Schr\"odinger equation of molecules with different atoms jointly.

Graph neural networks (GNNs) have recently become the standard approach for learning with graph-structured data. Prior work has shed light into their potential, but also their limitations. Unfortunately, it was shown that standard GNNs are limited in their expressive power. These models are no more powerful than the 1-dimensional Weisfeiler-Leman (1-WL) algorithm in terms of distinguishing non-isomorphic graphs. In this paper, we propose Path Neural Networks (PathNNs), a model that updates node representations by aggregating paths emanating from nodes. We derive three different variants of the PathNN model that aggregate single shortest paths, all shortest paths and all simple paths of length up to K. We prove that two of these variants are strictly more powerful than the 1-WL algorithm, and we experimentally validate our theoretical results. We find that PathNNs can distinguish pairs of non-isomorphic graphs that are indistinguishable by 1-WL, while our most expressive PathNN variant can even distinguish between 3-WL indistinguishable graphs. The different PathNN variants are also evaluated on graph classification and graph regression datasets, where in most cases, they outperform the baseline methods.

Complex networks can be used for modeling street meshes and urban agglomerates. With such a model, many aspects of a city can be investigated to promote a better quality of life to its citizens. Along these lines, this paper proposes a set of distance-based pattern-discovery algorithmic instruments to improve urban structures modeled as complex networks, detecting nodes that lack access from/to points of interest in a given city. Furthermore, we introduce a greedy algorithm that is able to recommend improvements to the structure of a city by suggesting where points of interest are to be placed. We contribute to a thorough process to deal with complex networks, including mathematical modeling and algorithmic innovation. The set of our contributions introduces a systematic manner to treat a recurrent problem of broad interest in cities.

Modeling and estimating mixed memberships for overlapping unipartite un-weighted networks has been well studied in recent years. However, to our knowledge, there is no model for a more general case, the overlapping bipartite weighted networks. To close this gap, we introduce a novel model, the Bipartite Mixed Membership Distribution-Free (BiMMDF) model. Our model allows an adjacency matrix to follow any distribution as long as its expectation has a block structure related to node membership. In particular, BiMMDF can model overlapping bipartite signed networks and it is an extension of many previous models, including the popular mixed membership stochastic blcokmodels. An efficient algorithm with a theoretical guarantee of consistent estimation is applied to fit BiMMDF. We then obtain the separation conditions of BiMMDF for different distributions. Furthermore, we also consider missing edges for sparse networks. The advantage of BiMMDF is demonstrated in extensive synthetic networks and eight real-world networks.

A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to oversmoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin

This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the slab is extended to a full-space, with a periodic map of mechanical properties and a series of sources located along a periodic pattern. Two types of boundary effects, both on the (small) scale of the wavelength, are observed: one at the boundaries of the slab, and one inside the domain. The former impact the entire energy density (coherent as well as incoherent) and is also observed in half-spaces. The latter, more specific to slabs, corresponds to the constructive interference of waves that have reflected at least twice on the boundaries of the slab and only impacts the coherent part of the energy density.

Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications. Investigation of deep learning for HOIs, thus, has become a valuable agenda for the data mining and machine learning communities. As networks of HOIs are expressed mathematically as hypergraphs, hypergraph neural networks (HNNs) have emerged as a powerful tool for representation learning on hypergraphs. Given the emerging trend, we present the first survey dedicated to HNNs, with an in-depth and step-by-step guide. Broadly, the present survey overviews HNN architectures, training strategies, and applications. First, we break existing HNNs down into four design components: (i) input features, (ii) input structures, (iii) message-passing schemes, and (iv) training strategies. Second, we examine how HNNs address and learn HOIs with each of their components. Third, we overview the recent applications of HNNs in recommendation, bioinformatics and medical science, time series analysis, and computer vision. Lastly, we conclude with a discussion on limitations and future directions.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

Deep learning has been successful in automating the design of features in machine learning pipelines. However, the algorithms optimizing neural network parameters remain largely hand-designed and computationally inefficient. We study if we can use deep learning to directly predict these parameters by exploiting the past knowledge of training other networks. We introduce a large-scale dataset of diverse computational graphs of neural architectures - DeepNets-1M - and use it to explore parameter prediction on CIFAR-10 and ImageNet. By leveraging advances in graph neural networks, we propose a hypernetwork that can predict performant parameters in a single forward pass taking a fraction of a second, even on a CPU. The proposed model achieves surprisingly good performance on unseen and diverse networks. For example, it is able to predict all 24 million parameters of a ResNet-50 achieving a 60% accuracy on CIFAR-10. On ImageNet, top-5 accuracy of some of our networks approaches 50%. Our task along with the model and results can potentially lead to a new, more computationally efficient paradigm of training networks. Our model also learns a strong representation of neural architectures enabling their analysis.

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

We propose a new end-to-end single image dehazing method, called Densely Connected Pyramid Dehazing Network (DCPDN), which can jointly learn the transmission map, atmospheric light and dehazing all together. The end-to-end learning is achieved by directly embedding the atmospheric scattering model into the network, thereby ensuring that the proposed method strictly follows the physics-driven scattering model for dehazing. Inspired by the dense network that can maximize the information flow along features from different levels, we propose a new edge-preserving densely connected encoder-decoder structure with multi-level pyramid pooling module for estimating the transmission map. This network is optimized using a newly introduced edge-preserving loss function. To further incorporate the mutual structural information between the estimated transmission map and the dehazed result, we propose a joint-discriminator based on generative adversarial network framework to decide whether the corresponding dehazed image and the estimated transmission map are real or fake. An ablation study is conducted to demonstrate the effectiveness of each module evaluated at both estimated transmission map and dehazed result. Extensive experiments demonstrate that the proposed method achieves significant improvements over the state-of-the-art methods. Code will be made available at: https://github.com/hezhangsprinter

This paper presents a learning-based method for transparent surface estimation from a single view polarization image. Existing shape from polarization(SfP) methods have the difficulty in estimating transparent shape since the inherent transmission interference heavily reduces the reliability of physics-based prior. To address this challenge, we propose the concept of physics-based prior, which is inspired by the characteristic that the transmission component in the polarization image has more noise than reflection. The confidence is used to determine the contribution of the interfered physics-based prior. Then, we build a network(TransSfP) with multi-branch architecture to avoid the destruction of relationships between different hierarchical inputs. To train and test our method, we construct a dataset for transparent shape from polarization with paired polarization images and ground-truth normal maps. Extensive experiments and comparisons demonstrate the superior accuracy of our method.

We introduce a novel neural network, SkyReconNet, which combines the expanded receptive fields of dilated convolutional layers along with standard convolutions, to capture both the global and local features for reconstructing the missing information in an image. We implement our network to inpaint the masked regions in a full-sky Cosmic Microwave Background (CMB) map. Inpainting CMB maps is a particularly formidable challenge when dealing with extensive and irregular masks, such as galactic masks which can obscure substantial fractions of the sky. The hybrid design of SkyReconNet leverages the strengths of standard and dilated convolutions to accurately predict CMB fluctuations in the masked regions, by effectively utilizing the information from surrounding unmasked areas. During training, the network optimizes its weights by minimizing a composite loss function that combines the Structural Similarity Index Measure (SSIM) and mean squared error (MSE). SSIM preserves the essential structural features of the CMB, ensuring an accurate and coherent reconstruction of the missing CMB fluctuations, while MSE minimizes the pixel-wise deviations, enhancing the overall accuracy of the predictions. The predicted CMB maps and their corresponding angular power spectra align closely with the targets, achieving the performance limited only by the fundamental uncertainty of cosmic variance. The network's generic architecture enables application to other physics-based challenges involving data with missing or defective pixels, systematic artefacts etc. Our results demonstrate its effectiveness in addressing the challenges posed by large irregular masks, offering a significant inpainting tool not only for CMB analyses but also for image-based experiments across disciplines where such data imperfections are prevalent.

Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the purpose of this paper is two-fold: at first we develop rigorous mathematical approaches to address properly a statistical mechanical picture of the phenomenon of {\em replica symmetry breaking} (RSB) in these networks, then -- deepening results stemmed via these routes -- we aim to inspect the {\em glassiness} that they hide. In particular, regarding the methodology, we provide two techniques: the former is an adaptation of the transport PDE to the case, while the latter is an extension of Guerra's interpolation breakthrough. Beyond coherence among the results, either in replica symmetric and in the one-step replica symmetry breaking level of description, we prove the Gardner's picture and we identify the maximal storage capacity by a ground-state analysis in the Baldi-Venkatesh high-storage regime. In the second part of the paper we investigate the glassy structure of these networks: in contrast with the replica symmetric scenario (RS), RSB actually stabilizes the spin-glass phase. We report huge differences w.r.t. the standard pairwise Hopfield limit: in particular, it is known that it is possible to express the free energy of the Hopfield neural network as a linear combination of the free energies of an hard spin glass (i.e. the Sherrington-Kirkpatrick model) and a soft spin glass (the Gaussian or "spherical" model). This is no longer true when interactions are more than pairwise (whatever the level of description, RS or RSB): for dense networks solely the free energy of the hard spin glass survives, proving a huge diversity in the underlying glassiness of associative neural networks.

We show that taking the width and depth to infinity in a deep neural network with skip connections, when branches are scaled by 1/depth (the only nontrivial scaling), result in the same covariance structure no matter how that limit is taken. This explains why the standard infinite-width-then-depth approach provides practical insights even for networks with depth of the same order as width. We also demonstrate that the pre-activations, in this case, have Gaussian distributions which has direct applications in Bayesian deep learning. We conduct extensive simulations that show an excellent match with our theoretical findings.

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Reconstructing and relighting objects and scenes under varying lighting conditions is challenging: existing neural rendering methods often cannot handle the complex interactions between materials and light. Incorporating pre-computed radiance transfer techniques enables global illumination, but still struggles with materials with subsurface scattering effects. We propose a novel framework for learning the radiance transfer field via volume rendering and utilizing various appearance cues to refine geometry end-to-end. This framework extends relighting and reconstruction capabilities to handle a wider range of materials in a data-driven fashion. The resulting models produce plausible rendering results in existing and novel conditions. We will release our code and a novel light stage dataset of objects with subsurface scattering effects publicly available.

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.

Graph Neural Networks (GNNs) that are based on the message passing (MP) paradigm generally exchange information between 1-hop neighbors to build node representations at each layer. In principle, such networks are not able to capture long-range interactions (LRI) that may be desired or necessary for learning a given task on graphs. Recently, there has been an increasing interest in development of Transformer-based methods for graphs that can consider full node connectivity beyond the original sparse structure, thus enabling the modeling of LRI. However, MP-GNNs that simply rely on 1-hop message passing often fare better in several existing graph benchmarks when combined with positional feature representations, among other innovations, hence limiting the perceived utility and ranking of Transformer-like architectures. Here, we present the Long Range Graph Benchmark (LRGB) with 5 graph learning datasets: PascalVOC-SP, COCO-SP, PCQM-Contact, Peptides-func and Peptides-struct that arguably require LRI reasoning to achieve strong performance in a given task. We benchmark both baseline GNNs and Graph Transformer networks to verify that the models which capture long-range dependencies perform significantly better on these tasks. Therefore, these datasets are suitable for benchmarking and exploration of MP-GNNs and Graph Transformer architectures that are intended to capture LRI.

We consider using deep neural networks to solve time-dependent partial differential equations (PDEs), where multi-scale processing is crucial for modeling complex, time-evolving dynamics. While the U-Net architecture with skip connections is commonly used by prior studies to enable multi-scale processing, our analysis shows that the need for features to evolve across layers results in temporally misaligned features in skip connections, which limits the model's performance. To address this limitation, we propose SineNet, consisting of multiple sequentially connected U-shaped network blocks, referred to as waves. In SineNet, high-resolution features are evolved progressively through multiple stages, thereby reducing the amount of misalignment within each stage. We furthermore analyze the role of skip connections in enabling both parallel and sequential processing of multi-scale information. Our method is rigorously tested on multiple PDE datasets, including the Navier-Stokes equations and shallow water equations, showcasing the advantages of our proposed approach over conventional U-Nets with a comparable parameter budget. We further demonstrate that increasing the number of waves in SineNet while maintaining the same number of parameters leads to a monotonically improved performance. The results highlight the effectiveness of SineNet and the potential of our approach in advancing the state-of-the-art in neural PDE solver design. Our code is available as part of AIRS (https://github.com/divelab/AIRS).

Near-field multiple-input multiple-output (MIMO) radar imaging systems have recently gained significant attention. In this paper, we develop novel non-iterative deep learning-based reconstruction methods for real-time near-field MIMO imaging. The goal is to achieve high image quality with low computational cost at compressive settings. The developed approaches have two stages. In the first approach, physics-based initial stage performs adjoint operation to back-project the measurements to the image-space, and deep neural network (DNN)-based second stage converts the 3D backprojected measurements to a magnitude-only reflectivity image. Since scene reflectivities often have random phase, DNN processes directly the magnitude of the adjoint result. As DNN, 3D U-Net is used to jointly exploit range and cross-range correlations. To comparatively evaluate the significance of exploiting physics in a learning-based approach, two additional approaches that replace the physics-based first stage with fully connected layers are also developed as purely learning-based methods. The performance is also analyzed by changing the DNN architecture for the second stage to include complex-valued processing (instead of magnitude-only processing), 2D convolution kernels (instead of 3D), and ResNet architecture (instead of U-Net). Moreover, we develop a synthesizer to generate large-scale dataset for training with 3D extended targets. We illustrate the performance through experimental data and extensive simulations. The results show the effectiveness of the developed physics-based learned reconstruction approach in terms of both run-time and image quality at highly compressive settings. Our source codes and dataset are made available at GitHub.

Designing architectures for deep neural networks requires expert knowledge and substantial computation time. We propose a technique to accelerate architecture selection by learning an auxiliary HyperNet that generates the weights of a main model conditioned on that model's architecture. By comparing the relative validation performance of networks with HyperNet-generated weights, we can effectively search over a wide range of architectures at the cost of a single training run. To facilitate this search, we develop a flexible mechanism based on memory read-writes that allows us to define a wide range of network connectivity patterns, with ResNet, DenseNet, and FractalNet blocks as special cases. We validate our method (SMASH) on CIFAR-10 and CIFAR-100, STL-10, ModelNet10, and Imagenet32x32, achieving competitive performance with similarly-sized hand-designed networks. Our code is available at https://github.com/ajbrock/SMASH

Network pruning techniques, including weight pruning and filter pruning, reveal that most state-of-the-art neural networks can be accelerated without a significant performance drop. This work focuses on filter pruning which enables accelerated inference with any off-the-shelf deep learning library and hardware. We propose the concept of network pruning spaces that parametrize populations of subnetwork architectures. Based on this concept, we explore the structure aspect of subnetworks that result in minimal loss of accuracy in different pruning regimes and arrive at a series of observations by comparing subnetwork distributions. We conjecture through empirical studies that there exists an optimal FLOPs-to-parameter-bucket ratio related to the design of original network in a pruning regime. Statistically, the structure of a winning subnetwork guarantees an approximately optimal ratio in this regime. Upon our conjectures, we further refine the initial pruning space to reduce the cost of searching a good subnetwork architecture. Our experimental results on ImageNet show that the subnetwork we found is superior to those from the state-of-the-art pruning methods under comparable FLOPs.

Neural radiance fields (NeRFs) are a widely accepted standard for synthesizing new 3D object views from a small number of base images. However, NeRFs have limited generalization properties, which means that we need to use significant computational resources to train individual architectures for each item we want to represent. To address this issue, we propose a few-shot learning approach based on the hypernetwork paradigm that does not require gradient optimization during inference. The hypernetwork gathers information from the training data and generates an update for universal weights. As a result, we have developed an efficient method for generating a high-quality 3D object representation from a small number of images in a single step. This has been confirmed by direct comparison with the state-of-the-art solutions and a comprehensive ablation study.

Diffusion models based on permutation-equivariant networks can learn permutation-invariant distributions for graph data. However, in comparison to their non-invariant counterparts, we have found that these invariant models encounter greater learning challenges since 1) their effective target distributions exhibit more modes; 2) their optimal one-step denoising scores are the score functions of Gaussian mixtures with more components. Motivated by this analysis, we propose a non-invariant diffusion model, called SwinGNN, which employs an efficient edge-to-edge 2-WL message passing network and utilizes shifted window based self-attention inspired by SwinTransformers. Further, through systematic ablations, we identify several critical training and sampling techniques that significantly improve the sample quality of graph generation. At last, we introduce a simple post-processing trick, i.e., randomly permuting the generated graphs, which provably converts any graph generative model to a permutation-invariant one. Extensive experiments on synthetic and real-world protein and molecule datasets show that our SwinGNN achieves state-of-the-art performances. Our code is released at https://github.com/qiyan98/SwinGNN.

This paper introduces a novel theoretical simplification of the Diffusion Schr\"odinger Bridge (DSB) that facilitates its unification with Score-based Generative Models (SGMs), addressing the limitations of DSB in complex data generation and enabling faster convergence and enhanced performance. By employing SGMs as an initial solution for DSB, our approach capitalizes on the strengths of both frameworks, ensuring a more efficient training process and improving the performance of SGM. We also propose a reparameterization technique that, despite theoretical approximations, practically improves the network's fitting capabilities. Our extensive experimental evaluations confirm the effectiveness of the simplified DSB, demonstrating its significant improvements. We believe the contributions of this work pave the way for advanced generative modeling. The code is available at https://github.com/checkcrab/SDSB.

We present a simple yet powerful neural network that implicitly represents and renders 3D objects and scenes only from 2D observations. The network models 3D geometries as a general radiance field, which takes a set of 2D images with camera poses and intrinsics as input, constructs an internal representation for each point of the 3D space, and then renders the corresponding appearance and geometry of that point viewed from an arbitrary position. The key to our approach is to learn local features for each pixel in 2D images and to then project these features to 3D points, thus yielding general and rich point representations. We additionally integrate an attention mechanism to aggregate pixel features from multiple 2D views, such that visual occlusions are implicitly taken into account. Extensive experiments demonstrate that our method can generate high-quality and realistic novel views for novel objects, unseen categories and challenging real-world scenes.

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92\%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50\% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

The cost of hyperparameter tuning in deep learning has been rising with model sizes, prompting practitioners to find new tuning methods using a proxy of smaller networks. One such proposal uses muP parameterized networks, where the optimal hyperparameters for small width networks transfer to networks with arbitrarily large width. However, in this scheme, hyperparameters do not transfer across depths. As a remedy, we study residual networks with a residual branch scale of 1/text{depth} in combination with the muP parameterization. We provide experiments demonstrating that residual architectures including convolutional ResNets and Vision Transformers trained with this parameterization exhibit transfer of optimal hyperparameters across width and depth on CIFAR-10 and ImageNet. Furthermore, our empirical findings are supported and motivated by theory. Using recent developments in the dynamical mean field theory (DMFT) description of neural network learning dynamics, we show that this parameterization of ResNets admits a well-defined feature learning joint infinite-width and infinite-depth limit and show convergence of finite-size network dynamics towards this limit.

We propose a novel deep network structure called "Network In Network" (NIN) to enhance model discriminability for local patches within the receptive field. The conventional convolutional layer uses linear filters followed by a nonlinear activation function to scan the input. Instead, we build micro neural networks with more complex structures to abstract the data within the receptive field. We instantiate the micro neural network with a multilayer perceptron, which is a potent function approximator. The feature maps are obtained by sliding the micro networks over the input in a similar manner as CNN; they are then fed into the next layer. Deep NIN can be implemented by stacking mutiple of the above described structure. With enhanced local modeling via the micro network, we are able to utilize global average pooling over feature maps in the classification layer, which is easier to interpret and less prone to overfitting than traditional fully connected layers. We demonstrated the state-of-the-art classification performances with NIN on CIFAR-10 and CIFAR-100, and reasonable performances on SVHN and MNIST datasets.

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.

Neural networks are a powerful class of nonlinear functions that can be trained end-to-end on various applications. While the over-parametrization nature in many neural networks renders the ability to fit complex functions and the strong representation power to handle challenging tasks, it also leads to highly correlated neurons that can hurt the generalization ability and incur unnecessary computation cost. As a result, how to regularize the network to avoid undesired representation redundancy becomes an important issue. To this end, we draw inspiration from a well-known problem in physics -- Thomson problem, where one seeks to find a state that distributes N electrons on a unit sphere as evenly as possible with minimum potential energy. In light of this intuition, we reduce the redundancy regularization problem to generic energy minimization, and propose a minimum hyperspherical energy (MHE) objective as generic regularization for neural networks. We also propose a few novel variants of MHE, and provide some insights from a theoretical point of view. Finally, we apply neural networks with MHE regularization to several challenging tasks. Extensive experiments demonstrate the effectiveness of our intuition, by showing the superior performance with MHE regularization.

In this study, we propose a multi branched network approach to predict the dynamics of a physics attractor characterized by intricate and chaotic behavior. We introduce a unique neural network architecture comprised of Radial Basis Function (RBF) layers combined with an attention mechanism designed to effectively capture nonlinear inter-dependencies inherent in the attractor's temporal evolution. Our results demonstrate successful prediction of the attractor's trajectory across 100 predictions made using a real-world dataset of 36,700 time-series observations encompassing approximately 28 minutes of activity. To further illustrate the performance of our proposed technique, we provide comprehensive visualizations depicting the attractor's original and predicted behaviors alongside quantitative measures comparing observed versus estimated outcomes. Overall, this work showcases the potential of advanced machine learning algorithms in elucidating hidden structures in complex physical systems while offering practical applications in various domains requiring accurate short-term forecasting capabilities.

Can evolving networks be inferred and modeled without directly observing their nodes and edges? In many applications, the edges of a dynamic network might not be observed, but one can observe the dynamics of stochastic cascading processes (e.g., information diffusion, virus propagation) occurring over the unobserved network. While there have been efforts to infer networks based on such data, providing a generative probabilistic model that is able to identify the underlying time-varying network remains an open question. Here we consider the problem of inferring generative dynamic network models based on network cascade diffusion data. We propose a novel framework for providing a non-parametric dynamic network model--based on a mixture of coupled hierarchical Dirichlet processes-- based on data capturing cascade node infection times. Our approach allows us to infer the evolving community structure in networks and to obtain an explicit predictive distribution over the edges of the underlying network--including those that were not involved in transmission of any cascade, or are likely to appear in the future. We show the effectiveness of our approach using extensive experiments on synthetic as well as real-world networks.

Currently, the neural network architecture design is mostly guided by the indirect metric of computation complexity, i.e., FLOPs. However, the direct metric, e.g., speed, also depends on the other factors such as memory access cost and platform characterics. Thus, this work proposes to evaluate the direct metric on the target platform, beyond only considering FLOPs. Based on a series of controlled experiments, this work derives several practical guidelines for efficient network design. Accordingly, a new architecture is presented, called ShuffleNet V2. Comprehensive ablation experiments verify that our model is the state-of-the-art in terms of speed and accuracy tradeoff.

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

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neighborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also demonstrate the performance of our framework on the tasks of network clustering and subgraph classification on the Facebook100 dataset and on Word Adjacency Networks of a set of classic novels.

Recent studies have drawn attention to the untapped potential of the "star operation" (element-wise multiplication) in network design. While intuitive explanations abound, the foundational rationale behind its application remains largely unexplored. Our study attempts to reveal the star operation's ability to map inputs into high-dimensional, non-linear feature spaces -- akin to kernel tricks -- without widening the network. We further introduce StarNet, a simple yet powerful prototype, demonstrating impressive performance and low latency under compact network structure and efficient budget. Like stars in the sky, the star operation appears unremarkable but holds a vast universe of potential. Our work encourages further exploration across tasks, with codes available at https://github.com/ma-xu/Rewrite-the-Stars.

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

Detector simulations are an exciting application of modern generative networks. Their sparse high-dimensional data combined with the required precision poses a serious challenge. We show how combining Conditional Flow Matching with transformer elements allows us to simulate the detector phase space reliably. Namely, we use an autoregressive transformer to simulate the energy of each layer, and a vision transformer for the high-dimensional voxel distributions. We show how dimension reduction via latent diffusion allows us to train more efficiently and how diffusion networks can be evaluated faster with bespoke solvers. We showcase our framework, CaloDREAM, on datasets 2 and 3 of the CaloChallenge.

Massive multiple-input multiple-output (MIMO) communication systems have a huge potential both in terms of data rate and energy efficiency, although channel estimation becomes challenging for a large number of antennas. Using a physical model allows to ease the problem by injecting a priori information based on the physics of propagation. However, such a model rests on simplifying assumptions and requires to know precisely the configuration of the system, which is unrealistic in practice.In this paper we present mpNet, an unfolded neural network specifically designed for massive MIMO channel estimation. It is trained online in an unsupervised way. Moreover, mpNet is computationally efficient and automatically adapts its depth to the signal-to-noise ratio (SNR). The method we propose adds flexibility to physical channel models by allowing a base station (BS) to automatically correct its channel estimation algorithm based on incoming data, without the need for a separate offline training phase.It is applied to realistic millimeter wave channels and shows great performance, achieving a channel estimation error almost as low as one would get with a perfectly calibrated system. It also allows incident detection and automatic correction, making the BS resilient and able to automatically adapt to changes in its environment.

We present a generalization of graph convolutional networks by generalizing the diffusion operation underlying this class of graph neural networks. These sheaf neural networks are based on the sheaf Laplacian, a generalization of the graph Laplacian that encodes additional relational structure parameterized by the underlying graph. The sheaf Laplacian and associated matrices provide an extended version of the diffusion operation in graph convolutional networks, providing a proper generalization for domains where relations between nodes are non-constant, asymmetric, and varying in dimension. We show that the resulting sheaf neural networks can outperform graph convolutional networks in domains where relations between nodes are asymmetric and signed.

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.

Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research, serving as a vital bridge between theoretical foundations and practical applications. Nevertheless, the intrinsic complexity and structural heterogeneity characterizing real-world networks, with particular emphasis on dynamic and higher-order networks, present substantial obstacles to the development of universal frameworks for critical node identification. This paper provides a comprehensive review of critical node identification techniques, categorizing them into seven main classes: centrality, critical nodes deletion problem, influence maximization, network control, artificial intelligence, higher-order and dynamic methods. Our review bridges the gaps in existing surveys by systematically classifying methods based on their methodological foundations and practical implications, and by highlighting their strengths, limitations, and applicability across different network types. Our work enhances the understanding of critical node research by identifying key challenges, such as algorithmic universality, real-time evaluation in dynamic networks, analysis of higher-order structures, and computational efficiency in large-scale networks. The structured synthesis consolidates current progress and highlights open questions, particularly in modeling temporal dynamics, advancing efficient algorithms, integrating machine learning approaches, and developing scalable and interpretable metrics for complex systems.

Topological deep learning has emerged for modeling higher-order relational structures beyond pairwise interactions that standard graph neural networks fail to capture. Although combinatorial complexes offer a unified topological framework, most existing topological deep learning methods rely on local message passing via attention mechanisms, which incur quadratic complexity and remain low-dimensional, limiting scalability and rank-aware information aggregation in higher-order complexes.We propose Combinatorial Complex Mamba (CCMamba), the first unified mamba-based neural framework for learning on combinatorial complexes. CCMamba reformulates message passing as a selective state-space modeling problem by organizing multi-rank incidence relations into structured sequences processed by rank-aware state-space models. This enables adaptive, directional, and long range information propagation in linear time without self attention. We further establish the theoretical analysis that the expressive power upper-bound of CCMamba message passing is the 1-Weisfeiler-Lehman test. Experiments on graph, hypergraph, and simplicial benchmarks demonstrate that CCMamba consistently outperforms existing methods while exhibiting improved scalability and robustness to depth.

Machine learning frameworks such as graph neural networks typically rely on a given, fixed graph to exploit relational inductive biases and thus effectively learn from network data. However, when said graphs are (partially) unobserved, noisy, or dynamic, the problem of inferring graph structure from data becomes relevant. In this paper, we postulate a graph convolutional relationship between the observed and latent graphs, and formulate the graph learning task as a network inverse (deconvolution) problem. In lieu of eigendecomposition-based spectral methods or iterative optimization solutions, we unroll and truncate proximal gradient iterations to arrive at a parameterized neural network architecture that we call a Graph Deconvolution Network (GDN). GDNs can learn a distribution of graphs in a supervised fashion, perform link prediction or edge-weight regression tasks by adapting the loss function, and they are inherently inductive. We corroborate GDN's superior graph recovery performance and its generalization to larger graphs using synthetic data in supervised settings. Furthermore, we demonstrate the robustness and representation power of GDNs on real world neuroimaging and social network datasets.

The Wilson-Cowan model for metapopulation, a Neural Mass Network Model, treats different subcortical regions of the brain as connected nodes, with connections representing various types of structural, functional, or effective neuronal connectivity between these regions. Each region comprises interacting populations of excitatory and inhibitory cells, consistent with the standard Wilson-Cowan model. By incorporating stable attractors into such a metapopulation model's dynamics, we transform it into a learning algorithm capable of achieving high image and text classification accuracy. We test it on MNIST and Fashion MNIST, in combination with convolutional neural networks, on CIFAR-10 and TF-FLOWERS, and, in combination with a transformer architecture (BERT), on IMDB, always showing high classification accuracy. These numerical evaluations illustrate that minimal modifications to the Wilson-Cowan model for metapopulation can reveal unique and previously unobserved dynamics.

Tensor networks are efficient representations of high-dimensional tensors which have been very successful for physics and mathematics applications. We demonstrate how algorithms for optimizing such networks can be adapted to supervised learning tasks by using matrix product states (tensor trains) to parameterize models for classifying images. For the MNIST data set we obtain less than 1% test set classification error. We discuss how the tensor network form imparts additional structure to the learned model and suggest a possible generative interpretation.