Introduces TT-NF for more compact neural field representations.
problem Finding more compact and easy-to-fit neural field representations.
method Tensor Train parameterization trained with backpropagation.
result Low-rank compression improves downstream task quality metrics.
New neural networks learn mappings between probability measures and functions.
problem Learning mappings between Wasserstein space of probability measures and function spaces.
method Two types of neural networks: bin density and cylindrical approximation, are proposed and supported by universal approximation theorems.
result Accuracy and efficiency of mean-field neural networks in generalization error with various test distributions.
Renormalization in neural networks linked to quantum field theory.
problem Implementing renormalization in neural networks.
method Mapping neural networks to quantum field theory, applying renormalization techniques.
result Changing weight standard deviation corresponds to a renormalization flow.
Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how probabilistic inference can be implemented by a network of spiking neurons in th…
Neural networks learn vector fields constrained by linear operators.
problem Learning vector fields from physical systems with linear operator constraints.
method Model the target function as a linear transformation of a potential field, which is a neural network.
result Predictions of the target function satisfy the linear operator constraints.
Simplified neural network EFTs reveal a single critical condition.
problem Understanding neuron statistics in neural networks at initialization.
method Diagrammatic approach to effective field theories (EFTs).
result A single condition governs criticality of all neuron preactivations.
New model improves field learning with improved equivariance.
problem Learning equivariant stochastic fields.
method Equivariant Gaussian processes and Steerable Conditional Neural Processes.
result SteerCNPs significantly improve performance in transfer learning tasks.
This work discovers latent field effects governing interacting dynamical systems.
problem Discovering field effects governing interacting dynamical systems.
method Proposes neural fields to learn latent force fields from observed dynamics, disentangling local object interactions and global field effects.
result Accurately discovers latent field effects in various dynamical systems.
Global convergence proved for three-layer neural networks in mean field regime.
problem Optimization efficiency of multilayer neural networks in the mean field regime.
method Developed a rigorous framework for mean field limit of three-layer networks using stochastic gradient descent and neuronal embedding.
result Global convergence guarantee for unregularized feedforward three-layer networks in the mean field regime.
Develops a new theory for neural systems stability and width effects.
problem Stability and finite-width effects in deep neural systems.
method Gauge-covariant stochastic effective field theory using classical commuting fields.
result Predicts the edge of chaos and low-frequency spectral deformation.
This work shows linear convergence for two-layer neural networks in mean-field regime.
problem Optimizing two-layer neural networks in the mean-field regime.
method Mean-field analysis and continuous-time noisy gradient descent.
result Establishes linear convergence rate for two-layer neural networks.
Neural nets solve electric field in non-convex microfluidic devices.
problem Solving differential equations in non-convex geometries.
method Neural network approximation of electric potential and field.
result Deep neural networks outperform shallow networks in accuracy.
New method learns vector fields from noisy time series data.
problem Learning vector fields from noisy time series data.
method Neural network architecture with tensor products of one-dimensional neural shape functions for vector field approximation, alternating minimization for noise handling.
result Neural shape function architecture robust to noise, learning accurate vector fields from data with up to 10% Gaussian noise.
The abstract proposes a neural network theory using quantum field theory.
problem Understanding the behavior of neural networks in the asymptotic and non-asymptotic limits.
method Mapping neural networks to Wilsonian effective field theory, using Gaussian processes and Feynman diagrams.
result Established a direct connection between overparameterization and simplicity of neural network likelihoods.
New algorithm solves mean-field control problems using actor-critic learning with moment neural networks.
problem Solving mean-field control problems in continuous time reinforcement learning.
method Gradient-based policy and value function learning with moment neural networks on the Wasserstein space.
result Effective solution for diverse mean-field control problems, including multi-dimensional and nonlinear settings.
Two-layer neural networks learn efficiently using kernel methods in mean-field analysis.
problem Feature learning ability of two-layer neural networks in the mean-field regime.
method Mean-field analysis through kernel methods, focusing on dynamics of the first layer's kernel.
result Two-layer neural networks can learn a union of multiple reproducing kernel Hilbert spaces more efficiently than kernel methods.
New framework models neural systems with random architecture on manifolds.
problem Complex, uncertain systems with non-Gaussian outputs.
method Latent random field on compact manifold generates neural architecture and weights.
result Synthetic neural systems can produce stochastic outputs for deterministic inputs.
LFIS uses a time-dependent velocity field to sample from complex distributions.
problem Sampling from unnormalized density functions.
method LFIS learns a time-dependent velocity field to transport samples from a simple initial distribution to a complex target distribution.
result LFIS achieves state-of-the-art performance on various benchmark problems.
NAS helps find best neural network designs.
problem Designing optimal neural network architectures.
method Optimization algorithms and search spaces.
result Introduction to major advances in NAS for CNNs.
NON model improves tabular data classification accuracy.
problem Tabular data classification in real-world applications.
method Field-wise network, across field network, operation fusion network.
result NON significantly outperforms state-of-the-art models.
A novel Neural Network architecture is proposed using the mathematically and physically rich idea of vector fields as hidden layers to perform nonlinear transformations in the data. The data points are interpreted as particles moving along a flow defined by the vector field which intuitively represents the desired move…
PICN learns physical fields from shallow neural networks, improving AI in multi-physical systems.
problem Challenges in modeling and forecasting multi-physical systems due to data scarcity and noise.
method Physics-informed convolutional network (PICN) combining CNN and physical laws, using deconvolution and convolution layers.
result PICN effectively solves and estimates nonlinear physical operator equations and recovers physical information from noisy observations.
Neural network models colloidal particle dynamics in non-equilibrium systems.
problem Analyzing non-equilibrium dynamics of many-body colloidal systems.
method Combining power functional theory and machine learning, training a neural network to predict internal force fields.
result The neural network accurately predicts dynamics in non-equilibrium systems, in good agreement with simulations.
Method generates dense fields from sparse measurements without needing spatial statistics or examples.
problem Generating dense physical fields from sparse measurements.
method Introduces a differentiable numerical simulator into neural network training.
result Superior results on fluid mechanics problems compared to statistical and neural network methods.
Improved particle approximation for mean-field neural networks.
problem Particle approximation error for mean-field neural networks.
method Improved particle approximation error by leveraging the problem structure in risk minimization.
result Established an LSI-constant-free particle approximation error concerning the objective gap.
E-LMC improves spatial field prediction accuracy by linearizing complex fields.
problem Predicting complex spatial fields with high accuracy and efficiency.
method Introducing an invertible neural network to linearize nonlinear spatial fields, enabling the use of LMC for nonlinear problems.
result Maximum improvement of about 40% over original LMC, outperforming other models.
The paper explores a new method for landmark matching using sub-Riemannian geometry and neural networks.
problem Finding a time-dependent vector field to warp points from an initial set to a target set.
method Sub-Riemannian geometry and residual neural networks.
result Demonstrates the importance of regularization in landmark matching.
Paper adds Fisher Information to mean field optimization for faster convergence.
problem Mean field optimization in neural networks training.
method Developed energy-dissipation method and gradient flow on probability space.
result Marginal distributions converge exponentially to minimizer.
NN-Turb generates turbulent velocity statistics using neural networks.
problem Creating a 1D field with turbulent velocity statistics.
method Fully-convolutional neural network (NN-Turb) to generate the field.
result NN-Turb generates a 1D field that satisfies Kolmogorov's 2/3 and 4/5 laws, exhibiting intermittency.
Recommendation systems and computing advertisements have gradually entered the field of academic research from the field of commercial applications. Click-through rate prediction is one of the core research issues because the prediction accuracy affects the user experience and the revenue of merchants and platforms. Fe…
GPU-accelerated particle methods outperform neural samplers in LFT benchmarks.
problem High-dimensional multimodal sampling problems in lattice field theory.
method GPU-accelerated particle Monte Carlo methods (Sequential Monte Carlo and nested sampling).
result These methods match or outperform neural samplers in sample quality and wall-clock time.
The paper extends mean field results to three-layer neural networks using SGD.
problem Understanding the dynamics of training three-layer neural networks with SGD.
method Extending mean field results from two-layer networks to three-layer networks with two hidden layers, using non-linear partial differential equations.
result The distributions of weights in the two hidden layers are independent.
A neural network model minimizes region-based free energy for faster inference in MRFs.
problem Efficient inference in complex Markov random fields (MRFs).
method Region-based Energy Neural Network (RENN) that directly minimizes region-based free energy.
result RENN outperforms other methods in marginal distribution estimation, partition function estimation, and MRF learning.
New approach to deeper graph neural networks to avoid performance degradation.
problem Performance degradation of graph neural networks when going deeper.
method Decoupling representation transformation and propagation in graph convolution operations.
result Deeper graph neural networks can be used to learn graph node representations from larger receptive fields.
Deep learning enhances Hamiltonian Monte Carlo for sampling gauge field configurations.
problem Sampling from complex gauge field topologies efficiently.
method Stacked neural networks to generalize Hamiltonian Monte Carlo.
result Significantly reduces computational cost for generating gauge field configurations.
Neural solver computes Wasserstein geodesics and velocity fields efficiently.
problem Computing Wasserstein geodesics and velocity fields efficiently.
method Sample-based neural network approach to solve the minimax problem.
result Directly samples from target distribution and estimates velocity field.
New framework analyzes deep neural networks using feature probabilities.
problem Degenerate situation in over-parameterized DNNs.
method Mean-field framework representing DNNs by feature probabilities and functions.
result Global convergence proof for over-parameterized Res-Net training.
This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of implicit vector fields moving data as particles in a flow. A new architecture, Vec…
Study bounds graph neural networks' over-parameterized error.
problem Understanding graph neural networks' performance in over-parameterized regimes.
method Developed mean-field regime bounds for graph convolutional and message passing neural networks.
result Established upper bounds with a convergence rate of O(1/n) for generalization error. Machine learning explores symmetries in field theory and algebra.
problem Understanding symmetries in field theory and algebra.
method Using neural networks to analyze conformal field theory and Lie algebra representation theory.
result Recent advances in machine learning have uncovered new symmetries.
Proposes new convex relaxations for certifying spatial robustness of neural networks.
problem Lack of provable guarantees for robustness against vector field transformations.
method Novel convex relaxations for certifying robustness against vector field transformations.
result First time providing a certificate of robustness against vector field transformations.
Deep Bayesian neural nets can use simpler weight approximations without sacrificing performance.
problem The need for complex weight posterior approximations in deep Bayesian neural networks.
method Theoretical and empirical analysis of mean-field variational inference in deep networks.
result Mean-field variational weight posteriors in deep networks can induce similar function-space distributions as complex approximations in shallower networks.
The paper proposes a method to sample quantum field configurations using neural operators and flows.
problem Sampling lattice field configurations from Boltzmann distributions in quantum field theories.
method Approximating a time-dependent neural operator to map between free and target theories, discretizing to a normalizing flow, and training to diffeomorphism.
result The method can generalize to larger lattice sizes when pre-trained on smaller ones, improving efficiency.
Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from a theoretical point of view. The mathematical description of learning problems i…
The paper solves complex control problems using neural networks.
problem Solving McKean-Vlasov control problems.
method Mean-field neural networks and algorithms based on dynamic programming and stochastic maximum principle.
result Extensive numerical results show the accuracy of the proposed algorithms.
Softmax policy gradient achieves global optimality in wide neural networks with entropy regularization.
problem Optimizing softmax policies with neural networks in the mean-field regime.
method Modeling neural networks as Wasserstein gradient flows and proving global optimality of fixed points.
result Global optimality of softmax policy gradient in wide single hidden layer neural networks with entropy regularization.
Conservative SPDEs emerge from fluctuating SGD dynamics in neural networks.
problem Understanding the convergence of stochastic gradient descent to SPDEs.
method Mean-field analysis and central limit theorem for SPDEs.
result Optimal convergence rates for SPDEs derived from SGD.
Neural net reconstructs dark matter density from halo velocities.
problem Reconstructing local dark matter density from halo velocities.
method Hybrid architecture combining U-Net and DeepSets.
result Hybrid network recovers density amplitudes and phases better than U-Net.