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78 papers in the last four weeks, up 179% on the four weeks before. 0.8% of all new papers.

Jul 13Week of Sep 28

Latest papers 692

Jul 14, 2025cs.LG

Effects of relational graph modularity and depth on the learning performance of neural networks

In recent years, graph-based machine learning techniques, such as reinforcement learning and graph neural networks, have garnered significant attention. While some recent studies have started to explore the relationship between the graph structure of neural networks and their predictive performance, they often limit themselves to a narrow range of model networks, particularly lacking mesoscale structures such as communities. Our work advances this area by conducting a more comprehensive investigation, incorporating realistic network structures characterized by heterogeneous degree distributions and community structures, which are typical characteristics of many real networks. These community structures offer a nuanced perspective on network architecture. Our analysis employs model networks such as random and scale-free networks, alongside a comparison with a biological neural network and its subsets for more detailed analysis. We examine the impact of these structural attributes on the performance of image classification tasks. Our findings reveal that structural properties do affect performance to some extent. Specifically, within moderate-depth architectures, networks featuring coherent, densely interconnected communities demonstrate enhanced learning capabilities. Crucially, we find that this advantage is strictly depth-dependent: extending the architecture to eight layers reverses the effect entirely. This comparison with the biological neural network emphasizes the relevance of our findings to real-world structures, suggesting an intriguing connection worth further exploration. This study contributes meaningfully to network science and machine learning, providing insights that could inspire the design of more biologically informed neural networks.

Yash Arya, Sang Hoon Lee

Department of Physics, Gyeongsang National University, Jinju, 52828, Korea

Network Science Neural Network

Jul 11, 2025cs.LG

Understanding Two-Layer Neural Networks with Smooth Activation Functions

This paper aims to understand the training solution, which is obtained by the back-propagation algorithm, of two-layer neural networks whose hidden layer is composed of the units with smooth activation functions, including the usual sigmoid type most commonly used before the advent of ReLUs. The mechanism contains four main principles: construction of Taylor series expansions, strict partial order of knots, smooth-spline implementation and smooth-continuity restriction. The universal approximation for arbitrary input dimensionality is proved and the explanation of training solutions is given. Through the principles proposed, the mystery of ``black box'' of the solution space is largely revealed. The new proofs employed also enrich approximation theory.

Changcun Huang

Shuitu Institute of Applied Mathematics, Chongqing 400700, P.R.C

Two-Layer Neural Networks Activation Functions Neural Network Backpropagation Intrinsic Dimensionality

Jul 2, 2025cs.LG

PERTINENCE: Input-based Opportunistic Neural Network Dynamic Execution

Deep neural networks (DNNs) are widely used for their ability to model complex patterns across domains such as computer vision, speech recognition, and robotics. However, larger models, while often more accurate, are computationally expensive and energy-intensive. Since such a cost is typically needed only for challenging inputs, dynamically selecting lighter models for simpler inputs can improve efficiency with minimal impact on accuracy. We introduce PERTINENCE, a runtime method that selects, from a set of pre-trained models, the lightest model likely to process each input correctly. An ML-based dispatcher performs this selection, and a genetic algorithm explores dispatcher training strategies to identify Pareto-optimal trade-offs between accuracy and computational cost. We evaluate PERTINENCE on CNNs trained on CIFAR-10 and CIFAR-100, ViTs trained on TinyImageNet, and a YOLO-based road occupancy estimation application using real-time intersection camera feeds. Results show that PERTINENCE matches or improves the accuracy of state-of-the-art pre-trained models while reducing operations by up to 36%, with equivalent or lower end-to-end inference time through tunable invocation intervals.

Omkar Shende, Gayathri Ananthanarayanan, Marcello Traiola

Department of Computer Science and Engineering, Indian Institute of Technology Dharwad, Karnataka, India · University of Rennes, CNRS, Inria, IRISA, Rennes, France

Neural Network Inference Neural Network Neural Dynamics

Jun 26, 2025cs.NE

Stochastic Quantum Spiking Neural Networks with Quantum Memory and Local Learning

Neuromorphic and quantum computing have recently emerged as promising paradigms for advancing artificial intelligence, each offering complementary strengths. Neuromorphic systems built on spiking neurons excel at processing time series data efficiently through sparse, event-driven computation, consuming energy only upon input events. Quantum computing, on the other hand, operates on state spaces that grow exponentially in dimension with the number of qubits -- as a consequence of tensor-product composition -- with quantum states admitting superposition across basis states and entanglement between subsystems. Hybrid approaches combining these paradigms have begun to show potential, but existing quantum spiking models have important limitations. Notably, they implement classical memory mechanisms on single qubits, requiring repeated measurements to estimate firing probabilities, while relying on conventional backpropagation for training. In this paper, we propose a novel stochastic quantum spiking (SQS) neuron model that addresses these challenges. The SQS neuron uses multi-qubit quantum circuits to realize a spiking unit with internal quantum memory, enabling event-driven probabilistic spike generation in a single shot during inference. Furthermore, we study networks of SQS neurons, dubbed SQS neural networks (SQSNN), and demonstrate that they can be trained via a hardware-friendly local learning rule, eliminating the need for global classical backpropagation. The proposed SQSNN model is shown via experiments with both conventional and neuromorphic datasets to improve over previous quantum spiking neural networks, as well as over classical counterparts, when fixing the overall number of trainable parameters, highlighting its potential for event-driven applications such as neuromorphic integrated sensing and communications (N-ISAC).

Jiechen Chen, Bipin Rajendran, Osvaldo Simeone

Department of Engineering, King’s College London, London, WC2R 2LS, UK · Institute for Intelligent Networked Systems, Northeastern University London, One Portsoken Street, London, E1 8PH, UK

Quantum Neural Networks Spiking Neural Networks Neuromorphic Computing Time-To-First-Spike Neural Network

Jun 23, 2025math.NA

DPG loss functions for learning parameter-to-solution maps by neural networks

We develop, analyze, and experimentally explore residual-based loss functions for machine learning of parameter-to-solution maps in the context of parameter-dependent families of partial differential equations (PDEs). Our primary concern is on rigorous accuracy certification to enhance the prediction capability of the resulting deep neural network reduced models. This is achieved by the use of variationally correct loss functions. Through one specific example of an elliptic PDE, details for establishing the variational correctness of a loss function from an ultraweak Discontinuous Petrov Galerkin (DPG) discretization are worked out. Despite the focus on the example, the proposed concepts apply to a much wider scope of problems, namely problems for which stable DPG formulations are available. The issue of high-contrast diffusion fields and ensuing difficulties with degrading ellipticity are discussed. Both numerical results and theoretical arguments illustrate that for high-contrast diffusion parameters the proposed DPG loss functions deliver much more robust performance than simpler least-squares losses.

Pablo Cortés Castillo, Wolfgang Dahmen, Jay Gopalakrishnan

Variational Formulation Neural Network

Jun 2, 2025cs.CV

OD3: Optimization-free Dataset Distillation for Object Detection

Training large neural networks on large-scale datasets requires substantial computational resources, particularly for dense prediction tasks such as object detection. Although dataset distillation (DD) has been proposed to alleviate these demands by synthesizing compact datasets from larger ones, most existing work focuses solely on image classification, leaving the more complex detection setting largely unexplored. In this paper, we introduce OD3, a novel optimization-free data distillation framework specifically designed for object detection. Our approach involves two stages: first, a candidate selection process in which object instances are iteratively placed in synthesized images based on their suitable locations, and second, a candidate screening process using a pre-trained observer model to remove low-confidence objects. We perform our data synthesis framework on MS COCO and PASCAL VOC, two popular detection datasets, with compression ratios ranging from 0.25% to 5%. Compared to the prior solely existing dataset distillation method on detection and conventional core set selection methods, OD3 delivers superior accuracy, establishes new state-of-the-art results, surpassing prior best method by more than 14% on COCO mAP50 at a compression ratio of 1.0%. Code is available at: https://github.com/VILA-Lab/OD3.

Salwa K. Al Khatib, Ahmed ElHagry, Shitong Shao +1

Mohamed bin Zayed University of Artificial Intelligence · Hong Kong University of Science and Technology (Guangzhou)

Object Detection Diffusion-Based Dataset Distillation Dataset Distillation Neural Network

May 26, 2025cs.LG

Tensorization is a powerful but underexplored tool for compression and interpretability of neural networks

Tensorizing a neural network involves reshaping some or all of its dense weight matrices into higher-order tensors and approximating them using low-rank tensor network decompositions. This technique has shown promise as a model compression strategy for large-scale neural networks. However, despite encouraging empirical results, tensorized neural networks (TNNs) remain underutilized in mainstream deep learning. In this position paper, we offer a perspective on both the potential and current limitations of TNNs. We argue that TNNs represent a powerful yet underexplored framework for deep learning--one that deserves greater attention from both engineering and theoretical communities. Beyond compression, we highlight the value of TNNs as a flexible class of architectures with distinctive scaling properties and increased interpretability. A central feature of TNNs is the presence of bond indices, which introduce new latent spaces not found in conventional networks. These internal representations may provide deeper insight into the evolution of features across layers, potentially advancing the goals of mechanistic interpretability. We conclude by outlining several key research directions aimed at overcoming the practical barriers to scaling and adopting TNNs in modern deep learning workflows.

Safa Hamreras, Sukhbinder Singh, Román Orús

Donostia International Physics Center, Paseo Manuel de Lardizabal 4, E-20018 San Sebastián, Spain · Multiverse Computing, Spadina Ave., Toronto, ON M5T 2C2, Canada · Multiverse Computing, Paseo de Miramón 170, E-20014 San Sebastián, Spain

Tensor Networks Neural Network Compressed Model Mechanistic Interpretability Interpretability Deep Learning+3

May 9, 2025cs.NE

Sigma-Delta Neural Network Conversion on Loihi 2

Neuromorphic computing aims to improve the efficiency of artificial neural networks by taking inspiration from biological neurons and leveraging temporal sparsity, spatial sparsity, and compute near/in memory. Although these approaches have shown efficiency gains, training these spiking neural networks (SNN) remains difficult. The original attempts at converting trained conventional analog neural networks (ANN) to SNNs used the rate of binary spikes to represent neuron activations. This required many simulation time steps per inference, which degraded efficiency. Intel's Loihi 2 is a neuromorphic platform that supports graded spikes which can be used to represent changes in neuron activation. In this work, we use Loihi 2's graded spikes to develop a method for converting ANN networks to spiking networks, which exploits temporal and spatial sparsity. We evaluated the performance of this network on Loihi 2 and compared it to NVIDIA's Jetson Xavier edge AI platform. The results show that neuromorphic approaches achieve significant improvements in efficiency and latency (energy-delay product) over existing solutions.

Matthew Brehove, Sadia Anjum Tumpa, Espoir Kyubwa +2

ChromoLogic LLC Monrovia, California, USA · Pennsylvania State University University Park, Pennsylvania, USA

Neuromorphic Computing Time-To-First-Spike Neural Network

May 5, 2025cs.LG

A Theoretical Analysis of Provable Compositional Generalization in Neural Networks: A Necessary and Sufficient Condition

Compositional generalization

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the ability to systematically process novel combinations of known components

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is a hallmark of human intelligence; however, its theoretical foundation in neural networks is not yet well understood. This paper establishes a necessary and sufficient condition for provable compositional generalization, precisely characterizing its boundary. Conceptually, the condition consists of two principles: (i) structural alignment, where a model's computational graph aligns with a task's true compositional hierarchy, and (ii) unambiguous minimized representations, where each component encodes adequate but not redundant information on the training data. The result is fully proved and machine-verified in Lean 4 and holds even in few-shot and one-shot regimes. The necessity direction establishes that provable compositional generalization cannot circumvent these requirements, while the sufficiency direction yields a unified inductive bias that jointly governs architectural design, training data properties, and regularization strategies. Building on this condition, we develop an example algorithmic approach, illustrate it through a controlled minimal example, and further demonstrate the condition on the SCAN jump task. All conclusions are derived mathematically without reliance on empirical validation. Our work provides a theoretical characterization of provable compositional generalization.

Yuanpeng Li

Compositional Generalization Neural Network Inductive Bias Theory Sufficiency

Apr 21, 2025stat.ME

Deep learning with missing data

In the context of multivariate nonparametric regression with missing covariates, we propose Pattern Embedded Neural Networks (PENNs), which can be applied in conjunction with any existing imputation technique. In addition to a neural network trained on the imputed data, PENNs pass the vectors of observation indicators through a second neural network to provide a compact representation. The outputs are then combined in a third neural network to produce final predictions. Our main theoretical result exploits an assumption that the observation patterns can be partitioned into cells on which the Bayes regression function behaves similarly, and belongs to a compositional Hölder class. It provides a finite-sample excess risk bound that holds for an arbitrary missingness mechanism, and in combination with a complementary minimax lower bound, demonstrates that our PENN estimator attains in typical cases the minimax rate of convergence as if the cells of the partition were known in advance, up to a poly-logarithmic factor in the sample size. Numerical experiments on simulated, semi-synthetic and real data confirm that the PENN estimator consistently improves, often dramatically, on standard neural networks without pattern embedding. Code to reproduce our experiments, as well as a tutorial on how to apply our method, is publicly available.

Tianyi Ma, Tengyao Wang, Richard J. Samworth

Statistical Laboratory, University of Cambridge · Department of Statistics, London School of Economics

Imputation Exponential Family Neural Network Deep Learning Covariates

Apr 18, 2025cs.NE

Causal pieces: analysing and improving spiking neural networks piece by piece

We introduce "causal pieces", a novel concept for analysing spiking neural networks (SNNs), inspired by "linear pieces" used to study expressivity and trainability in artificial neural networks (ANNs). Causal pieces partition the input and parameter space of a feedforward SNN with single-spike coding into distinct regions where the same subnetwork causes the output spikes. For networks of current-based leaky integrate-and-fire (LIF) neurons with large membrane time constants, we show that within each causal piece, output spike times are locally Lipschitz continuous with respect to inputs and network parameters. We further prove a lower bound on the approximation error that depends on the number of causal pieces. Thus, the number of causal pieces is a measure of the approximation capabilities of SNNs, which is valid despite spike-time discontinuities and applies to networks with both excitatory and inhibitory synapses. Empirically, we find that parameter initialisations yielding more causal pieces on the training set strongly correlate with SNN training success across multiple benchmarks, including Yin-Yang, Fashion-MNIST, and EuroSAT. Moreover, simulations with standard single-spike LIF neurons indicate that our findings extend beyond the theoretically analysed regime. These results establish causal pieces as a powerful and principled tool for analysing and improving the computational capabilities of SNNs.

Dominik Dold, Philipp Christian Petersen

Spiking Neural Networks Lfsr-Based Stochastic Leaky Integrate-And-Fire Neuron Time-To-First-Spike Neural Network Single Excitation Time History Causal

Apr 9, 2025cs.LG

FLASH: Flexible Learning of Adaptive Sampling from History in Temporal Graph Neural Networks

Aggregating temporal signals from historic interactions is a key step in future link prediction on dynamic graphs. However, incorporating long histories is resource-intensive. Hence, temporal graph neural networks (TGNNs) often rely on historical neighbors sampling heuristics such as uniform sampling or recent neighbors selection. These heuristics are static and fail to adapt to the underlying graph structure. We introduce FLASH, a learnable and graph-adaptive neighborhood selection mechanism that generalizes existing heuristics. FLASH integrates seamlessly into TGNNs and is trained end-to-end using a self-supervised ranking loss. We provide theoretical evidence that commonly used heuristics hinder TGNNs performance, motivating our design. Extensive experiments across multiple benchmarks demonstrate consistent and significant performance improvements for TGNNs equipped with FLASH.

Or Feldman, Krishna Sri Ipsit Mantri, Carola-Bibiane Schönlieb +2

Ben-Gurion University of the Negev, Israel · Purdue University, USA · University of Cambridge, UK

Temporal Graph Neural Networks Zero-Shot Link Prediction Flash Adaptive Sampling Neural Network Learn

Apr 6, 2025stat.ML

Hyperflux: Pruning Reveals Importance

Network pruning is used to reduce inference latency and power consumption in large neural networks. However, most methods focus on empirical results at the expense of understanding the pruning process. We introduce Hyperflux, a novel

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method which models pruning as a continuously evolving system determined by flux, the gradient response to a weight's removal, and pressure, a global regularization driving weights toward pruning. By exploiting this model, Hyperflux's pruning behavior becomes understandable at both microscopic (weight regrowth/pruning) and macroscopic (sparsity convergence, etc.) levels. We also introduce a novel pressure scheduler that reliably targets desired sparsities. Hyperflux achieves competitive results with ResNet-50, VGG-19 and DeiT-T/S on CIFAR-10, CIFAR-100 and ImageNet datasets.

Eugen Barbulescu, Antonio Alexoaie, Lucian Busoniu

Department of Computer Science Technical University of Cluj-Napoca · Department of Automation Technical University of Cluj-Napoca

Unstructured Pruning Structured Pruning Sparsity Neural Network Importance

Apr 2, 2025cs.LG

AYLA: Architecting a loss landscape in shallow neural networks to accelerate feature recovery

Feature learning in shallow neural networks exhibits rich yet fragile dynamics, including prolonged plateaus, abrupt phase transitions, and sensitivity to optimization hyperparameters. While recent theoretical work has characterized these behaviors through the geometry of loss landscapes, saddle escape mechanisms, and emergent scaling laws, practical methods for actively shaping these dynamics remain limited. In this paper, we introduce AYLA, a principled loss reparameterization framework that dynamically modulates gradient magnitudes during training without altering the location of stationary points or optimal solutions. AYLA applies a smooth, sigmoid-controlled power-law transformation to empirical loss, yielding a state-dependent effective learning rate that accelerates descent in flat or saddle-dominated regions while stabilizing late-stage optimization. Crucially, AYLA preserves all critical points of the original objective, acting solely as a monotone transformation that reshapes optimization trajectories rather than objectives. We evaluate AYLA in controlled teacher student settings using two-layer tanh networks trained on synthetic Gaussian data. Across stochastic gradient descent and multiple loss-exponent schedules, AYLA consistently improves feature recovery. This evidence is observed in terms of weight alignment, per-neuron cosine similarity, hidden-activation correlation, and spectral properties of learned representations, while AYLA maintains competitive or faster loss convergence. Spectral analyses further demonstrate that AYLA mitigates rank collapse and promotes richer internal representations, signaling a transition from lazy to active feature-learning regimes. AYLA offers a lightweight, theoretically grounded way to improve shallow-network optimization, especially in resource-limited or noise-sensitive settings.

Behnam Gheshlaghi, Shahin Atakishiyev

Anisotropic Loss Landscapes Feature Learning Neural Network Pool-Based Active Learning Escape Mitigation

Mar 31, 2025cs.NI

Traffic Engineering in Large-scale Networks with Generalizable Graph Neural Networks

Traffic Engineering (TE) in large-scale networks like cloud Wide Area Networks (WANs) and Low Earth Orbit (LEO) satellite constellations is a critical challenge. Although learning-based approaches have been proposed to address the scalability of traditional TE algorithms, their practical application is often hindered by a lack of generalization, high training overhead, and a failure to respect link capacities. This paper proposes TELGEN, a novel TE algorithm that learns to solve TE problems efficiently in large-scale network scenarios, while achieving superior generalizability across diverse network conditions. TELGEN is based on the novel idea of transforming the problem of "predicting the optimal TE solution" into "predicting the optimal TE algorithm", which enables TELGEN to learn and efficiently approximate the end-to-end solving process of classical optimal TE algorithms. The learned algorithm is agnostic to the exact underlying network topology or traffic patterns, and is able to very efficiently solve TE problems given arbitrary inputs and generalize well to unseen topologies and demands. We train and evaluate TELGEN with random and real-world topologies, with networks of up to 5000 nodes and 3.6x10^6 links in testing. TELGEN shows less than 3% optimality gap while ensuring feasibility in all testing scenarios, even when the test network has 2-20x more nodes than the largest training network. It also saves up to 84% TE solving time than traditional interior-point method, and reduces up to 79.6% training time per epoch than the state-of-the-art learning-based algorithm.

Fangtong Zhou, Xiaorui Liu, Ruozhou Yu +1

Department of Computer Science, North Carolina State University, Raleigh, NC, 27606, USA · School of Computing and Augmented Intelligence, Arizona State University, Tempe, AZ, 85287, USA

Bringing Network Coding Accurate Traffic Forecasting Traffic Signal Control Temporal Graph Neural Networks Network Science Graph Neural Networks+1

Mar 15, 2025cs.LO

PICID: Proof-Driven Clause Learning in Neural Network Verification

Current Deep Neural Network (DNN) verifiers are typically designed to prioritize scalability over reliability. Reliability can be reinforced through the generation of proofs that are checkable by trusted, external proof checkers. To date, only a handful of verifiers support proof production; and these rely on verifier-specific formats, and balance between scalability, proof detail, and the trustworthiness of their proof checker. In this tool paper, we introduce PICID, a DNN verifier that produces proofs in the standard Alethe format for SMT solving, checkable by an independent checker. PICID implements a parallel CDCL(T) architecture that integrates the state-of-the-art, proof-producing CaDiCaL SAT solver with the Marabou DNN verifier. Furthermore, PICID leverages UNSAT proofs to derive conflict clauses. Our evaluation shows that PICID generates valid proofs in the vast majority of cases and significantly outperforms existing tools that produce comparable proofs.

Omri Isac, Idan Refaeli, Haoze Wu +2

The Hebrew University of Jerusalem · Amherst College · Stanford University

Neural Network Verification Theorem Proving Satisfiability Neural Network

Mar 13, 2025cs.LG

Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problems

The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making traditional approaches such as exact mathematical models or heuristic methods prone to high computational overhead or reliant on the design of complex heuristic operators to achieve optimal or near optimal solutions. Meanwhile, although some recent learning-based methods can produce good performance for VRP with straightforward constraint scenarios, they often fail to effectively handle hard constraints that are common in practice. This study introduces a novel end-to-end framework that combines constraint-oriented hypergraphs with reinforcement learning to address vehicle routing problems. A central innovation of this work is the development of a constraint-oriented dynamic hyperedge reconstruction strategy within an encoder, which significantly enhances hypergraph representation learning. Additionally, the decoder leverages a double-pointer attention mechanism to iteratively generate solutions. The proposed model is trained by incorporating asynchronous parameter updates informed by hypergraph constraints and optimizing a dual loss function comprising constraint loss and policy gradient loss. The experiment results on benchmark datasets demonstrate that the proposed approach not only eliminates the need for sophisticated heuristic operators but also achieves substantial improvements in solution quality.

Zhenwei Wang, Tiehua Zhang, Jing Liu +3

University of Nottingham Ningbo China, 199 East Taikang Road, Ningbo, 315100, Zhejiang, China · Tongji University, 1239,Siping Road, Shanghai, 200092, Shanghai, China · State Key Laboratory for Novel Software Technology, Nanjing University, 163,Xianlin Road, Nanjing, 210023, Jiangsu, China +1

Vehicle Routing Problem Combinatorial Optimization Hypergraphs Graph Neural Networks Neural Network

Feb 26, 2025cs.LG

Fourier Multi-Component and Multi-Layer Neural Networks: Unlocking High-Frequency Potential

The architecture of a neural network and the choice of its activation function are both fundamental to its performance. Equally important is ensuring that these two elements are well matched, as their alignment is key to effective representation and learning. In this paper, we introduce the Fourier Multi-Component and Multi-Layer Neural Network (FMMNN), a model that combines sine-type activations with the multi-component and multi-layer structure of MMNNs. In an FMMNN, each component is represented as a trainable linear combination of fixed random sine-type basis functions, while multi-layer composition generates more complex and adaptive high-frequency features. We establish that FMMNNs retain exponential expressive power for function approximation even under a low-rank architectural structure. We also analyze the optimization landscape of FMMNNs and find it to be substantially more favorable than that of standard fully connected neural networks, especially for high-frequency targets. In addition, we propose a scaled random initialization method for the first-layer weights in FMMNNs, which accelerates training and improves final performance when sufficient samples are available. Extensive numerical experiments support our theoretical insights, showing that FMMNNs achieve strong accuracy and favorable convergence behavior on oscillatory function-approximation benchmarks.

Shijun Zhang, Hongkai Zhao, Yimin Zhong +1

Department of Applied Mathematics Hong Kong Polytechnic University · Department of Mathematics Duke University · Department of Mathematics and Statistics Auburn University +1

Two-Layer Neural Networks Neural Network Activation Functions Basis Functions Fourier High-Frequency Reconstruction

Feb 21, 2025cs.LG

Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networks

Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying space is transformed with the same group element, as opposed to a local ``gauge'' symmetry, where each point is transformed with a different group element, exponentially enlarging the size of the symmetry group. Gauge equivariant networks have so far mainly been applied to problems in quantum chromodynamics. Here, we introduce a novel application domain for gauge-equivariant networks in the theory of topological condensed matter physics. We use gauge equivariant networks to predict topological invariants (Chern numbers) of multiband topological insulators. The gauge symmetry of the network guarantees that the predicted quantity is a topological invariant. We introduce a novel gauge equivariant normalization layer to stabilize the training and prove a universal approximation theorem for our setup. We train on samples with trivial Chern number only but show that our models generalize to samples with non-trivial Chern number. We provide various ablations of our setup. Our code is available at https://github.com/sitronsea/GENet/tree/main.

Longde Huang, Oleksandr Balabanov, Hampus Linander +3

Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, SE-412 96 Gothenburg, Sweden. · Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden · VERSES AI Research Lab, Los Angeles, USA +1

Equivariant Neural Networks Quantum Phases Equivariance Topology Neural Network Symmetry+1

Jan 29, 2025cs.NE

Perforated Backpropagation: A Neuroscience Inspired Extension to Artificial Neural Networks

The neurons of artificial neural networks were originally invented when much less was known about biological neurons than is known today. Our work explores a modification to the core neuron unit to make it more parallel to a biological neuron. The modification is made with the knowledge that biological dendrites are not simply passive activation funnels, but also compute complex non-linear functions as they transmit activation to the cell body. The paper explores a novel system of

perforated'' backpropagation empowering the artificial neurons of deep neural networks to achieve better performance coding for the same features they coded for in the original architecture. After an initial network training phase, additional

dendrite'' nodes are added to the network and separately trained with a different objective: to correlate their output with the remaining error of the original neurons. The trained dendrites are then frozen, and the original neurons are further trained, now taking into account the additional error signals provided by the dendrites. The cycle of training the original neurons and then adding and training dendrites can be repeated several times until satisfactory performance is achieved. Our algorithm was successfully added to modern state-of-the-art PyTorch networks across multiple domains, improving upon original accuracies and allowing for significant model compression without a loss in accuracy.

Rorry Brenner, Laurent Itti

Perforated AI Inc. · Computer Science and Neuroscience, University of Southern California

Neurons Backpropagation Neural Network Neuroscience Extended Version

Jan 28, 2025cs.IT

Bridging Neural Networks and Wireless Systems with MIMO-OFDM Semantic Communications

Semantic communications aim to enhance transmission efficiency by jointly optimizing source coding, channel coding, and modulation. While prior research has demonstrated promising performance in simulations, real-world implementations often face significant challenges, including noise variability and nonlinear distortions, leading to performance gaps. This article investigates these challenges in a multiple-input multiple-output (MIMO) and orthogonal frequency-division multiplexing (OFDM)-based semantic communication system, focusing on the practical impacts of power amplifier (PA) nonlinearity and peak-to-average power ratio (PAPR) variations. Our analysis identifies frequency selectivity of the actual channel as a critical factor in performance degradation and demonstrates that targeted mitigation strategies can enable semantic systems to approach theoretical performance. By addressing key limitations in existing designs, we provide actionable insights for advancing semantic communications in practical wireless environments. This work establishes a foundation for bridging the gap between theoretical models and real-world deployment, highlighting essential considerations for system design and optimization.

Hanju Yoo, Dongha Choi, Yonghwi Kim +4

School of Integrated Technology, Yonsei University, Seoul 03722, South Korea · Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA

Orthogonal Frequency-Division Multiplexing Semantic Communications Wireless Communications Multiple-Input Multiple-Output Nonlinearity Neural Network

Jan 12, 2025q-bio.NC

Improving the adaptive and continuous learning capabilities of artificial neural networks: Lessons from multi-neuromodulatory dynamics

Continuous adaptive learning, the ability to adapt to the environment and keep improving performance, is a hallmark of natural intelligence. Biological organisms excel in acquiring, transferring, and retaining knowledge while adapting to volatile environments, making them a source of inspiration for artificial neural networks (ANNs). This study explores how neuromodulation, a building block of learning in biological systems, can help address catastrophic forgetting and enhance the robustness of ANNs in continual learning. Driven by neuromodulators including dopamine (DA), acetylcholine (ACh), serotonin (5-HT) and noradrenaline (NA), neuromodulatory processes in the brain operate at multiple scales, facilitating dynamic responses to environmental changes through mechanisms ranging from local synaptic plasticity to global network-wide adaptability. Importantly, the relationship between neuromodulators and their interplay in modulating sensory and cognitive processes is more complex than previously expected, demonstrating a "many-to-many" neuromodulator-to-task mapping. To inspire neuromodulation-aware learning rules, we highlight (i) how multi-neuromodulatory interactions enrich single-neuromodulator-driven learning, (ii) the impact of neuromodulators across multiple spatio-temporal scales, and correspondingly, (iii) strategies for approximating and integrating neuromodulated learning processes in ANNs, and (iv) an architectural-general formulation of multi-neuromodulatory dynamics. We also present a conceptual study to showcase how neuromodulation-inspired mechanisms, such as DA-driven reward processing and NA-based cognitive flexibility, can enhance ANN performance in a Go/No-Go task. Though multi-scale neuromodulation, we aim to bridge the gap between biological and artificial learning, paving the way for ANNs with greater flexibility, robustness, and adaptability.

Jie Mei, Alejandro Rodriguez-Garcia, Daigo Takeuchi +4

IT:U Interdisciplinary Transformation University Austria, Linz, Austria · International Research Center for Neurointelligence, The University of Tokyo, Tokyo, Japan · Department of Anatomy, University of Quebec in Trois-Rivieres, Trois-Rivieres, QC, Canada +8

Adaptive Deep Brain Stimulation Neural Network Catastrophic Forgetting

Jan 5, 2025cs.LG

Network Dynamics-Based Framework for Understanding Deep Neural Networks

Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical systems theory. We redefine the notions of linearity and nonlinearity in neural networks by introducing two fundamental transformation units at the neuron level: order-preserving transformations and non-order-preserving transformations. Different transformation modes lead to distinct collective behaviors in weight vector organization, different modes of information extraction, and the emergence of qualitatively different learning phases. Transitions between these phases may occur during training, accounting for key phenomena such as grokking. To further characterize generalization and structural stability, we introduce the concept of attraction basins in both sample and weight spaces. The distribution of neurons with different transformation modes across layers, along with the structural characteristics of the two types of attraction basins, forms a set of core metrics for analyzing the performance of learning models. Hyperparameters such as depth, width, learning rate, and batch size act as control variables for fine-tuning these metrics. Our framework not only sheds light on the intrinsic advantages of deep learning, but also provides a novel perspective for optimizing network architectures and training strategies.

Yuchen Lin, Yong Zhang, Sihan Feng +1

Department of Physics, Xiamen University, Xiamen 361005, China · 2Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, China · 3Shenzhen Angel FOF Management Co., Ltd., Shenzhen 518000, China

Neural Network Deep Learning Dynamical Systems Nonlinearity Collective Behaviors

Nov 24, 2024cs.CV

A Tunable Despeckling Neural Network Stabilized via Diffusion Equation

The removal of multiplicative Gamma noise is a critical research area in the application of synthetic aperture radar (SAR) imaging, where neural networks serve as a potent tool. However, real-world data often diverges from theoretical models, exhibiting various disturbances, which makes the neural network less effective. Adversarial attacks can be used as a criterion for judging the adaptability of neural networks to real data, since they can find the most extreme perturbations that make neural networks ineffective. In this work, we propose a tunable, regularized neural network framework that unrolls a shallow neural denoising block and a diffusion regularization block into a single network for end-to-end training. The linear heat equation, known for its inherent smoothness and low-pass filtering properties, is adopted as the diffusion regularization block. The smoothness of our outputs is controlled by a single time step hyperparameter that can be adjusted dynamically. The stability and convergence of our model are theoretically proven. Experimental results demonstrate that the proposed model effectively eliminates high-frequency oscillations induced by adversarial attacks. Finally, the proposed model is benchmarked against several state-of-the-art denoising methods on simulated images, adversarial samples, and real SAR images, achieving superior performance in both quantitative and visual evaluations.

Yi Ran, Zhichang Guo, Jia Li +3

School of Mathematics, Harbin Institute of Technology, 150001 Harbin, China · Helmholtz Imaging, Deutsches Elektronen-Synchrotron DESY, 22607 Hamburg, Germany · Fachbereich Mathematik, Universität Hamburg, 20146 Hamburg, Germany

Iterative Denoising Methods Synthetic Aperture Radar Regularization Multiplicative Gamma Noise Neural Network Tuning

Oct 30, 2024cs.LG

Koopman-informed recurrent neural networks

Recurrent neural networks are a successful neural architecture for many time-dependent problems, including time series analysis, forecasting, and modeling of dynamical systems. In the context of dynamical systems, training with backpropagation through time can lead to challenges arising from exploding or vanishing gradients. In this contribution, we introduce Koopman-informed recurrent neural networks, a computational approach to construct all weights and biases of a recurrent neural network without using gradient-based methods. The approach is based on a combination of random feature networks and Koopman operator theory for dynamical systems. The hidden parameters of a single recurrent block are sampled at random, while the outer weights are constructed using extended dynamic mode decomposition. This approach alleviates some problems with backpropagation commonly related to recurrent networks. The connection to Koopman operator theory also allows us to start using results in this area to analyze recurrent neural networks. In computational experiments on time series, forecasting for chaotic dynamical systems, control problems, and on real-world data, we observe that with comparable forecasting accuracy, the training time of the Koopman-informed recurrent neural networks is significantly improved when compared to models trained with commonly used gradient-based methods.

Erik Lien Bolager, Ana Čukarska, Iryna Burak +2

Munich Data Science Institute · School of Computation, Information and Technology, Technical University of Munich, Germany · Interdisciplinary Center for Scientific Computing (IWR) +1

Recurrent Neural Networks Koopman Operator Recurrent Model Neural Network Chaos Gradient-Based Optimization

Oct 14, 2024stat.ML

Statistical Properties of Deep Neural Networks with Dependent Data

This paper develops theory for deep neural network (DNN) estimators under dependent data. To provide theory applicable to a variety of DNN-based estimators, I first establish nonasymptotic probability bounds on the theoretical and empirical

\mathcal{L}^{2}

-errors of nonparametric sieve estimators for a general class of estimation problems under possibly nonstationary

β

-mixing data taking values in unbounded sets. I then apply the theory to fully connected and convolutional DNN estimators without bounds or sparsity restrictions on the DNN weights. For both DNN classes, I derive general results when the function to be estimated is Hölder smooth and the data are nonstationary, subgaussian, and

β

-mixing with either exponential or polynomial decay. I then specialize these to nonparametric regression, logistic regression, and quantile regression settings. Under exponential

β

-mixing, the resulting estimators attain the nonparametric minimax rate of Stone (1982) up to logarithmic factors.

Chad Brown

Department of Economics, University of Colorado Boulder, 80309, USA.

Exponential Family Minimax Rate Neural Network High-Dimensional

Sep 18, 2024cs.RO

Generation of Uncertainty-Aware High-Level Spatial Concepts in Factorized 3D Scene Graphs via Graph Neural Networks

Enabling robots to autonomously discover high-level spatial concepts (e.g., rooms and walls) from primitive geometric observations (e.g., planar surfaces) within 3D Scene Graphs is essential for robust indoor navigation and mapping. These graphs provide a hierarchical metric-semantic representation in which such concepts are organized. To further enhance graph-SLAM performance, Factorized 3D Scene Graphs incorporate these concepts as optimization factors that constrain relative geometry and enforce global consistency. However, both stages of this process remain largely manual: concepts are typically derived using hand-crafted, concept-specific heuristics, while factors and their covariances are likewise manually designed. This reliance on manual specification limits generalization across diverse environments and scalability to new concept classes. This paper presents a novel learning-based method that infers spatial concepts online from observed vertical planes and introduces them as optimizable factors within a SLAM backend, eliminating the need to handcraft concept generation, factor design, and covariance specification. We evaluate our approach in simulated environments with complex layouts, improving room detection by 20.7% and trajectory estimation by 19.2%. Validated on real construction sites, room detection improves by 5.3% and map matching accuracy by 3.8%.

Jose Andres Millan-Romera, Muhammad Shaheer, Miguel Fernandez-Cortizas +3

Automation and Robotics Research Group, Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg · University of Amsterdam

3D Scene Graphs Orb-Slam2 Spatial Grounding Robot Navigation Stable Spatial Understanding Robot Systems+1

Jul 9, 2024cs.LG

A Generalization Bound for Nearly-Linear Networks

We consider nonlinear networks as perturbations of linear ones. Based on this approach, we present novel generalization bounds that become non-vacuous for networks that are close to being linear. The main advantage over the previous works which propose non-vacuous generalization bounds is that our bounds are a-priori: performing the actual training is not required for evaluating the bounds. To the best of our knowledge, they are the first non-vacuous generalization bounds for neural nets possessing this property.

Eugene Golikov

Chair of Statistical Field Theory École Polytechnique Fédérale de Lausanne (EPFL)

Generalization Bounds Nonlinearity Neural Network

Jun 14, 2024cs.LG

Over-parameterization and Adversarial Robustness in Neural Networks: An Overview and Empirical Analysis

Thanks to their extensive capacity, over-parameterized neural networks exhibit superior predictive capabilities and generalization. However, having a large parameter space is considered one of the main suspects of the neural networks' vulnerability to adversarial example -- input samples crafted ad-hoc to induce a desired misclassification. Relevant literature has claimed contradictory remarks in support of and against the robustness of over-parameterized networks. These contradictory findings might be due to the failure of the attack employed to evaluate the networks' robustness. Previous research has demonstrated that depending on the considered model, the algorithm employed to generate adversarial examples may not function properly, leading to overestimating the model's robustness. In this work, we empirically study the robustness of over-parameterized networks against adversarial examples. However, unlike the previous works, we also evaluate the considered attack's reliability to support the results' veracity. Our results show that over-parameterized networks are robust against adversarial attacks as opposed to their under-parameterized counterparts.

Srishti Gupta, Zhang Chen, Luca Demetrio +9

Sapienza University of Rome, Rome, Italy. · University of Cagliari, Cagliari, Italy. · Northwestern Polytechnical University, Xi’An, China. +1

Overparameterization Neural Network

May 30, 2024cs.LG

A Computational Tropical Geometry Framework for Neural Networks

We propose a computational tropical geometry framework for the symbolic analysis of neural networks with tropical activations. The number of linear regions of a neural network has been actively studied as a measure of the expressivity of a given architecture. To study these, we work in the setting of tropical geometry---a combinatorial and polyhedral variant of algebraic geometry---where there are known connections between tropical rational maps and feedforward neural networks. We expand this connection by developing concrete computational tools for studying the linear regions of neural networks. We present an algorithm, together with a proof of correctness, which computes the linear regions of a neural network as explicit unions of polyhedra. We further relate the computation of the number of linear regions of a tropical expression to the number of monomials that appear in it, and show how tropical expressions can often be pruned to remove redundant monomials. We introduce the Hoffman constant of a neural network's tropical expression, a geometric quantity that controls the distance from any point in the input space to the farthest linear region. We provide the open source Julia library TropicalNN.jl, which is built on top of the OSCAR computer algebra system and implements the algorithms mentioned above to analyze neural networks symbolically using their tropical representations. We present a set of proof-of-concept computational examples to demonstrate how our tropical geometric theory can be applied to reveal insights on the expressivity of a network architecture.

Paul Lezeau, Thomas Walker, Yueqi Cao +2

Department of Mathematics, Imperial College London, UK · London School of Geometry and Number Theory, UK · Department of Electrical and Computer Engineering, Rice University, USA +2

Neural Network Polytopes Representation Space Symbol-

Nov 27, 2022cs.LG

Adversarial Rademacher Complexity of Deep Neural Networks

Deep neural networks (DNNs) are highly vulnerable to adversarial attacks. Ideally, a robust model should perform well on both perturbed training data and unseen perturbed test data. While DNNs can fit perturbed training data, generalizing to perturbed test data remains a significant challenge. This motivates the study of generalization guarantees from a learning theory perspective. This paper focuses on adversarial Rademacher complexity (ARC), first introduced by Khim and Loh (2018) and Yin et al. (2019). Their work primarily addressed linear functions and highlighted the open question of how to bound ARC for neural networks. Since then, several attempts have been made, with the latest results applying ARC only to two-layer neural networks. The main challenge arises from the dynamic nature and unknown closed-form solution of adversarial examples. In this paper, we resolve this issue and provide the first bound on ARC for deep neural networks. Our bound is qualitatively comparable to Rademacher complexity bounds in similar settings. The key ingredient is a new concept we introduce, termed intermediate adversarial examples, along with a framework for calculating the covering number that is compatible with them. Finally, we present experiments to analyze poor robust generalization, demonstrating that the weight norm is a crucial factor influencing the robust generalization gap.

Jiancong Xiao, Yanbo Fan, Ruoyu Sun +1

The Chinese University of Hong Kong, Shenzhen Shenzhen, China · Nanjing University Suzhou, China

Adversarial Training Generalization Bounds Adversarial Examples Neural Network Maximum Independent Set

Jun 21, 2019cs.LG

Theory of the Frequency Principle for General Deep Neural Networks

Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training. The F-Principle has been very useful in providing both qualitative and quantitative understandings of DNNs. In this paper, we rigorously investigate the F-Principle for the training dynamics of a general DNN at three stages: initial stage, intermediate stage, and final stage. For each stage, a theorem is provided in terms of proper quantities characterizing the F-Principle. Our results are general in the sense that they work for multilayer networks with general activation functions, population densities of data, and a large class of loss functions. Our work lays a theoretical foundation of the F-Principle for a better understanding of the training process of DNNs.

Tao Luo, Zheng Ma, Zhi-Qin John Xu +1

Department of Mathematics, Zheng Ma Purdue University · Department of Mathematics, Purdue University · New York University Abu Dhabi and Courant Institute

Modern Deep Networks Neural Network Activation Functions Frequency Theory