Network embedding helps predict speed limits on incomplete Danish road network.
problem Incomplete speed limit data on Danish roads limits machine learning applications.
method Applied node2vec network embedding to Danish road network.
result Network embedding can derive useful features for predicting speed limits.
Wide neural networks can benefit from multi-task learning in their infinite-width limit.
problem The generalization behavior of wide neural networks in multi-task learning settings.
method Optimizing wide ReLU neural networks with L2-regularization promotes multi-task learning in the infinite-width limit.
result An exact quantitative characterization of multi-task learning in the infinite-width limit of wide ReLU neural networks.
We analyze multi-layer neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations. We rigorously establish the limiting behavior of the multi-layer neural network output. The limit procedure is valid for any number of hidde…
New framework for understanding infinite-width neural networks.
problem Understanding the infinite-width limit behavior of neural networks.
method General framework to study limit behavior of neural models based on hyperparameter scaling.
result Derives scaling for existing mean-field and neural tangent kernel limits and introduces new dynamically stable limits.
We analyze single-layer neural networks with the Xavier initialization in the asymptotic regime of large numbers of hidden units and large numbers of stochastic gradient descent training steps. The evolution of the neural network during training can be viewed as a stochastic system and, using techniques from stochastic…
Study infinite-depth limits of neural networks with fixed width.
problem Understanding the behavior of neural networks as depth increases with fixed width.
method Analyzing finite-width residual networks with random Gaussian weights, focusing on the infinite-depth limit.
result The pre-activations converge to a zero-drift diffusion process, differing from the infinite-width limit.
Infinite CNNs lose spatial correlations, but can be restored by correlated weights.
problem Infinite CNNs lose spatial correlations, which are crucial for their performance.
method Introduced correlated weights to restore spatial correlations in infinite CNNs.
result Optimal performance is achieved with a moderate level of weight correlation.
New method for Bayesian neural networks with unbounded weights.
problem Posterior inference for Bayesian neural networks with unbounded weights.
method Conditionally Gaussian representation for efficient posterior inference.
result Interpretable and computationally efficient procedure for posterior inference.
Survey on GNNs' power and limitations.
problem Theoretical limitations of GNNs.
method Comprehensive overview of GNNs and their variants.
result Provably powerful variants of GNNs.
This work studies fluctuation in multilayer neural networks using mean field theory.
problem Understanding fluctuation in multilayer neural networks with mean field training.
method Developed a second-order mean field limit to capture fluctuation, demonstrating stability of gradient descent training.
result Gradient descent training in multilayer networks biases towards minimal fluctuation, even after convergence.
Study Gaussian-process limits of neural networks using tensor programs.
problem Understanding the behavior of neural networks as they approach infinite width.
method Quantitative analysis through tensor programs and Wasserstein distance.
result Explicit finite-width error bounds, showing convergence to Gaussian-process limits.
The paper analyzes SGD in high-dimensional networks, revealing new scaling limits.
problem Understanding SGD dynamics in high-dimensional networks.
method Analyzing the effective dynamics of SGD using recent work on the subject.
result A new correction term emerges at the critical scaling regime, changing the phase diagram.
ResNets approximate log-Gaussian at initialization, improving network performance.
problem Understanding the initialization behavior of deep neural networks like ResNets.
method Analyzing ReLU ResNets in the infinite-depth-and-width limit, showing log-Gaussian behavior.
result ResNets at initialization exhibit hypoactivation and interlayer correlations, which are not captured by Gaussian limits.
Novel framework explains generalization in deep neural networks.
problem Understanding and improving generalization in deep neural networks.
method Topological Quantum Neural Networks as the semi-classical limit of Deep Neural Networks.
result Demonstrates that the perceptron, viewed as the semi-classical limit, achieves similar results to standard neural networks without training.
This paper develops a new neural network architecture for modeling spatial distributions (i.e., distributions on R^d) which is computationally efficient and specifically designed to take advantage of the spatial structure of limit order books. The new architecture yields a low-dimensional model of price movements deep …
This work characterizes the fundamental limit of network pruning using statistical dimension and convex geometry.
problem The fundamental limit of network pruning is still lacking, especially for deep neural networks.
method Directly imposing sparsity constraint on the loss function and using statistical dimension in convex geometry.
result Characterizes the sharp phase transition point as the fundamental limit of pruning ratio.
Wide neural networks with narrow bottlenecks behave like deep Gaussian processes.
problem Understanding the behavior of neural networks with narrow layers in the wide limit.
method Analyzing the wide limit of BNNs with narrow bottlenecks, showing they behave like a composition of GPs.
result Wide neural networks with narrow bottlenecks form a composition of GPs, termed a bottleneck NNGP.
Study reveals three limiting regimes for neural network functionals.
problem Understanding the behavior of functionals of random neural networks.
method Central and non-central limit theorems, Hermite expansions, Diagram Formula, Stein-Malliavin techniques.
result Three distinct limiting regimes based on fixed points of covariance function.
The paper connects neural networks to physics using probability theory.
problem Creating neural networks that follow physical laws.
method Applying the central limit theorem and Gaussian process theory to neural networks.
result Neural networks can be designed to obey physical laws by choosing appropriate activation functions.
Study of deep linear neural networks with proportional width and depth.
problem Lack of descriptive power in Gaussian limit of deep linear neural networks.
method Proportional infinite-width infinite-depth limit for deep linear neural networks.
result Characterization of limiting distribution as a nontrivial mixture of Gaussians.
We rigorously prove a central limit theorem for neural network models with a single hidden layer. The central limit theorem is proven in the asymptotic regime of simultaneously (A) large numbers of hidden units and (B) large numbers of stochastic gradient descent training iterations. Our result describes the neural net…
Band-limited training reduces resource usage without sacrificing accuracy.
problem Resource constraints in training Convolutional Neural Networks (CNNs).
method Artificially constraining the frequency spectra of convolutional filters during training.
result CNNs can leverage lower-frequency components effectively, reducing resource usage.
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.
Transformers predict price movements from limit order books.
problem Predicting price movements from limit order books.
method Causal convolutional network with masked self-attention.
result Significantly outperforms existing architectures on FI-2010 dataset.
Paper derives CLT for Bayesian neural networks trained with variational inference.
problem Analyzing the fluctuation behavior of Bayesian neural networks trained with different variational inference schemes.
method Rigorous derivation of CLT for three variational inference schemes: idealized, Bayes-by-Backprop, and Minimal VI.
result Minimal VI scheme has larger variances but is more computationally efficient.
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.
Finite-precision learning of anh networks is limited by the Monte Carlo rate.
problem Learning anh neural networks under finite precision method Using iterated anh activations to construct localized bump functions result No adaptive randomized algorithm can achieve higher convergence rate than Monte Carlo rate in finite precision
New framework connects two neural network theories, improving finite-width approximations.
problem Theoretical guarantees for neural network training in general cases.
method Developed a general framework linking mean-field and constant kernel theories.
result Discrete-time MF limit provides better approximation for finite-width nets.
Stable processes emerge as limits of deep neural networks with symmetric stable distributions.
problem Understanding the behavior of deep neural networks as they become infinitely wide.
method Analyzing fully connected feed-forward deep neural networks with symmetric stable distributions and showing the limit as a stable process.
result The infinite wide limit of the network is a stable process with multivariate stable distributions.
In network embedding, random walks play a fundamental role in preserving network structures. However, random walk based embedding methods have two limitations. First, random walk methods are fragile when the sampling frequency or the number of node sequences changes. Second, in disequilibrium networks such as highly bi…
Stabilizes GAN training with limited data.
problem Overfitting in GANs with scarce data.
method Adaptive discriminator augmentation.
result Good results possible with few thousand images.
Bayesian neural networks approximate Student-t processes in the infinite-width limit.
problem Modeling uncertainty in neural networks with greater flexibility.
method Extending asymptotic properties of Gaussian processes to Student-t processes in the infinite-width limit of BNNs.
result Posterior BNNs converge to Student-t processes in the infinite-width limit.
Gradient descent dynamics in wide neural networks are analyzed using a dynamical CLT.
problem Understanding the fluctuations in wide shallow neural networks trained via gradient descent.
method Dynamical Central Limit Theorem (CLT) applied to neural network dynamics.
result Asymptotic fluctuations remain bounded in mean square throughout training.
Study of deep neural networks with dependent weights leading to new model limits and properties.
problem Characterizing deep neural networks with dependent weights in the infinite-width limit.
method Modeling weights as a mixture of Gaussian distributions and analyzing the infinite-width limit.
result Characterization of neural network layers by scalar parameters and Lévy measures, leading to new model limits.
Bayesian neural networks with dependent weights converge to Gaussian mixtures.
problem Limitations of standard Gaussian priors in neural networks.
method Posterior analysis with Gaussian likelihood for networks with dependent weights.
result Posterior distribution identified in the wide-width limit, ensuring invertibility of random covariance matrix.
Tensor programs prove neural network limits for any architecture.
problem Understanding the limits of neural networks of any architecture.
method Prove convergence of neural network's Tangent Kernel (NTK) to a deterministic limit as network widths increase.
result Identify conditions for correct NTK limit calculation based on gradient independence assumption.
Wide stochastic networks show Gaussian behavior and improve training with PAC-Bayesian methods.
problem Analyzing and training over-parameterised neural networks with large width.
method Establishing Gaussian behavior for a stochastic architecture, applying PAC-Bayesian training.
result PAC-Bayesian training on large but finite-width networks outperforms standard methods.
Adaptive kernels from neural networks improve model performance.
problem Improving neural network performance through adaptive kernels.
method Deriving adaptive kernels from infinite-width neural networks using feature learning and gradient flow training.
result Adaptive kernels achieve lower test loss compared to traditional kernels.
Framework captures neural network learning in large-width limit.
problem Understanding learning dynamics in large neural networks.
method Developed a rigorous framework for multilayer neural networks in mean field limit.
result Global convergence guarantees for various network architectures and initializations.
Study on limits and cut-off phenomena in deep neural networks.
problem Understanding the behavior of deep neural networks as the number of layers increases.
method Analysis of semi-invariant metrics and application of non-commutative ergodic theorems.
result Observation of a cut-off phenomenon in the number of layers for random network initialization.
Learning three data points can generate all types of periodic orbits in a neural network.
problem Can learning three data points generate all types of periodic orbits in a neural network?
method Investigated a continuous one-dimensional map with period three in a random neural network in its thermodynamic limit.
result Almost all learned periods are unstable, and each network has its own characteristic attractors.
In this paper, we study the information-theoretic limits of learning the structure of Bayesian networks (BNs), on discrete as well as continuous random variables, from a finite number of samples. We show that the minimum number of samples required by any procedure to recover the correct structure grows as Ω(m) and $Ω…
Deep QMC ansatzes improve variational QMC accuracy.
problem Improving variational QMC accuracy with neural network ansatzes.
method Analysis of deep neural network ansatzes PauliNet and FermiNet convergence to fixed-node limit.
result Deep QMC ansatzes can reach fixed-node limit with large network sizes.
Theoretical limits of deep residual networks show consistent covariance structures.
problem Understanding the limits of deep residual networks.
method Analyzing the behavior of deep residual networks with skip connections as width and depth approach infinity.
result Theoretical analysis confirms that the covariance structure remains consistent regardless of the order of width and depth.
The evolution of a deep neural network trained by the gradient descent can be described by its neural tangent kernel (NTK) as introduced in [20], where it was proven that in the infinite width limit the NTK converges to an explicit limiting kernel and it stays constant during training. The NTK was also implicit in some…
The study proves a quantitative functional CLT for neural networks with smooth activation functions.
problem Understanding the convergence rates of neural networks with different activation functions.
method Functional versions of the Stein-Malliavin approach and a quantitative functional central limit theorem.
result Rates of convergence depend on the smoothness of the activation function, ranging from logarithmic to sqrt(n).
Embedded ensembles improve neural network performance efficiently.
problem Improving neural network performance with fewer resources.
method Analyzing the wide network limit of gradient descent dynamics using Neural-Tangent-Kernel.
result Embedded ensembles exhibit two regimes: independent and collective, affecting performance.
The paper examines how deep linear neural networks behave as they become infinitely wide.
problem Understanding the behavior of deep linear neural networks as they approach infinite width.
method Analyzes the infinite-width limit of deep linear neural networks, proving convergence to deterministic models and providing precise laws for random weights.
result The training dynamics of deep linear neural networks converge to those of a deterministic model, and the weights' behavior is precisely described.