Stochastic neural networks with infinite width become deterministic, reducing training variance.
problem Understanding how stochasticity in neural networks affects learning and regularization.
method Theoretical analysis of stochastic neural networks with infinite width.
result As the width of an optimized stochastic neural network increases, its predictive variance on the training set decreases to zero.
Neural networks can approximate complex stochastic equations well.
problem Approximating general stochastic differential equations.
method Identified neural network classes approximating continuous functions.
result Neural stochastic differential equations can approximate general stochastic differential equations arbitrarily well.
Bayesian neural networks can be partially stochastic without losing predictive power.
problem The necessity of fully stochastic parameters in Bayesian neural networks.
method Theoretical and empirical investigation of partially stochastic networks compared to fully stochastic ones.
result Expressive predictive distributions require only small amounts of stochasticity, and partially stochastic networks can match or outperform fully stochastic networks.
Langevin algorithms enhance training of deep neural networks for stochastic control problems.
problem Training acceleration for deep neural networks in stochastic control problems.
method Application of Langevin algorithms to minimize the loss of deep neural networks in stochastic control problems.
result Langevin algorithms improve training on various stochastic control problems.
Stochastic Bayesian Neural Network improves scalability and performance.
problem Challenges in calculating posterior distribution in Bayesian Neural Networks.
method Maximizes Evidence Lower Bound using Stochastic Evidence Lower Bound objective function.
result Demonstrates improved performance and scalability over previous algorithms.
SMGD trains low-bit neural networks with memory constraints.
problem Training large neural networks with limited memory.
method Stochastic Markov Gradient Descent (SMGD).
result Encouraging numerical results and theoretical guarantees.
New method uses backward SDEs for deep learning uncertainty.
problem Uncertainty quantification in deep learning models.
method Probabilistic machine learning with stochastic neural networks and stochastic optimal control.
result Effectiveness validated through numerical experiments.
Paper introduces multitask neural networks for efficient stochastic control problems.
problem Infeasibility of simulating state variables in some stochastic control problems.
method Multitask neural networks with dynamic task balancing.
result Multitask neural networks outperform state-of-the-art approaches in derivatives pricing problems.
Deep neural networks solve stochastic control problems with delay.
problem Challenges in stochastic control problems with delay due to path-dependence and high dimensions.
method Employing recurrent neural networks (RNNs) to parameterize policies and optimize objectives.
result RNNs, especially LSTMs, efficiently capture path-dependence and outperform feedforward networks in training and performance.
VSDN models sporadic time series with neural SDEs.
problem Modeling irregular and sparse time series data.
method Variational Bayesian method and neural SDEs.
result VSDNs outperform state-of-the-art models in prediction and interpolation.
We develop a scalable method for Bayesian neural networks with stochastic differential equations.
problem Uncertainty quantification in deep neural networks.
method Gradient-based stochastic variational inference in continuous-depth Bayesian neural networks.
result Gradient estimator with zero variance as the approximation improves.
Stochastic RNNs classify biological neural network paths with robust error bounds.
problem Classifying biological neural network paths.
method Modelled as a continuous-time stochastic recurrent neural network (RNN) with identity activation function, analysed in the robust regime.
result Generalisation error bound holds with high probability, showing the empirical risk minimiser is the best-in-class hypothesis.
Study on deep neural networks using concentration inequalities and optimal stopping.
problem Understanding the performance and structure of stochastic deep neural networks.
method Introduced concentration inequalities for SDNN outputs and an EC classifier. Determined the optimal number of layers via an optimal stopping procedure.
result Optimal number of layers for SDNNs determined via an optimal stopping procedure.
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The c…
Stochastic gradient methods converge for training wide PINNs.
problem Convergence of stochastic gradient descent in training over-parameterized PINNs.
method Established linear convergence of stochastic gradient descent/flow in training over-parameterized two-layer PINNs.
result Linear convergence with high probability for general activation functions.
We symmetrise neural networks for groups using Markov categories.
problem Convert H-equivariant networks to G-equivariant networks. method Formulate in Markov categories, abstracting measure-theoretic details.
result Flexible and compositional framework for symmetrisation.
Neural networks solve SPDEs using Wiener chaos expansion.
problem Solving stochastic partial differential equations (SPDEs) numerically.
method Using neural networks in the truncated Wiener chaos expansion.
result Approximation rates for learning SPDE solutions with noise.
New method improves training stochastic neural networks with tighter guarantees.
problem Training stochastic neural networks with provable guarantees.
method Developed partially-aggregated estimators and reformulated PAC-Bayesian bounds.
result Derives a differentiable objective leading to tighter generalisation guarantees.
Neural networks model financial data with Lévy processes.
problem Forecasting chaotic financial time series with big jumps.
method Lévy-induced stochastic differential equation network approximated by neural networks.
result The method improves prediction accuracy using non-Gaussian Lévy processes.
Law derived for neural networks with sparse connections.
problem Understanding the behavior of neural networks with sparse connections.
method Law of large numbers for empirical distribution of parameters derived.
result Law for neural networks with sparse connections derived.
We propose a generic framework to calibrate accuracy and confidence of a prediction in deep neural networks through stochastic inferences. We interpret stochastic regularization using a Bayesian model, and analyze the relation between predictive uncertainty of networks and variance of the prediction scores obtained by …
Paper develops SINNOs for approximating stochastic processes.
problem Approximating stochastic processes with neural networks.
method Developed stochastic interpolation neural network operators (SINNOs) with random coefficients.
result Established boundedness, interpolation accuracy, and approximation capabilities of SINNOs.
SGD fails to converge for deep ReLU networks with limited random initializations.
problem SGD convergence in deep neural networks with limited random initializations.
method Analysis of four discretization parameters: network architecture, training data, gradient steps, and random initializations.
result SGD fails to converge for ReLU networks with depth much larger than width.
Stochastic approach improves neural network training for kinetic simulations.
problem Training neural networks under physical constraints in kinetic fusion simulations.
method Stochastic augmented Lagrangian approach using pyTorch.
result Higher model prediction accuracy achieved compared to fixed penalty method.
Proposes scale mixture of NNGPs for more flexible stochastic processes.
problem Limited focus on broadening the class of stochastic processes from NNGPs.
method Scale mixture of NNGPs with scale priors on last-layer parameters.
result Turns neural networks into a richer class of stochastic processes.
Bayesian inference using stochastic neural networks ensembles.
problem Approximating Bayesian posterior distributions.
method Formulate stochastic ensembles of neural networks, train with variational inference, and evaluate using Monte Carlo dropout.
result Stochastic ensembles provide more accurate posterior estimates than other methods.
Embeds sparsity in deep neural networks, allowing exact zero parameters.
problem Learning sparse structures in deep networks.
method Embeds sparsity into neural network structure, allowing exact zero parameters during training.
result Can learn both structured and unstructured sparsity.
Paper proposes a fast stochastic algorithm for neural network quantization with error bounds.
problem Error analysis for quantized neural networks with non-convex loss functions and nonlinear activations.
method Greedy path-following mechanism combined with stochastic quantizer.
result Established full-network error bounds for quantized neural networks.
A neural network method estimates entropy production from system trajectories.
problem Estimating entropy production from system trajectories without detailed dynamics.
method Developed a neural estimator (NEEP) for entropy production (EP).
result NEEP rigorously proves to provide stochastic EP by optimizing an objective function.
This paper describes and discusses Bayesian Neural Network (BNN). The paper showcases a few different applications of them for classification and regression problems. BNNs are comprised of a Probabilistic Model and a Neural Network. The intent of such a design is to combine the strengths of Neural Networks and Stochast…
Deep learning model approximates stochastic responses.
problem Approximating stochastic responses using neural networks.
method Generative neural network with conditional maximum mean discrepancy (CMMD) loss.
result Excellent performance on benchmark problems.
Improved Bayesian neural network inference by selectively removing redundant modes.
problem Redundant modes in Bayesian neural network posteriors complicate approximate inference.
method Structured partial stochasticity and deterministic subset selection of weights.
result Improved performance of approximate inference schemes with simplified posterior distribution.
New neural network method simplifies high-dimensional data.
problem Scalability issues in nonlinear sufficient dimension reduction.
method Stochastic neural network with adaptive gradient algorithm.
result Proposed method outperforms existing methods on large-scale data.
We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian processes. The proposed method can also achieve high generalization performance fo…
SPEQ improves quantized neural networks by stochastic precision sharing and cosine similarity loss.
problem Improving quantized deep neural networks for edge devices.
method SPEQ combines stochastic precision sharing and cosine similarity loss for knowledge distillation.
result SPEQ outperforms existing methods in various tasks.
Dropout and similar stochastic neural network regularization methods are often interpreted as implicitly averaging over a large ensemble of models. We propose STE (stochastically trained ensemble) layers, which enhance the averaging properties of such methods by training an ensemble of weight matrices with stochastic r…
Deep learning solves barrier options with stochastic volatility.
problem Solving barrier options with stochastic volatility.
method Unsupervised deep learning neural networks trained to satisfy PDE and boundary conditions.
result Neural networks accurately price barrier options in a single framework.
In this paper, we show that the recent integration of statistical models with deep recurrent neural networks provides a new way of formulating volatility (the degree of variation of time series) models that have been widely used in time series analysis and prediction in finance. The model comprises a pair of complement…
Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.
problem Training neural networks with ReLU activation.
method Non-asymptotic convergence analysis of SGHMC with discontinuous gradients.
result Explicit upper bounds for expected excess risk in non-convex optimization.
Leveraging advances in variational inference, we propose to enhance recurrent neural networks with latent variables, resulting in Stochastic Recurrent Networks (STORNs). The model i) can be trained with stochastic gradient methods, ii) allows structured and multi-modal conditionals at each time step, iii) features a re…
Averaged SGD achieves optimal convergence rate for neural networks in the NTK regime.
problem Convergence analysis of averaged stochastic gradient descent for neural networks.
method Analyzed convergence of averaged stochastic gradient descent for overparameterized two-layer neural networks.
result Achieved minimax optimal convergence rate with global convergence guarantee.
Deep neural networks estimate long memory parameters efficiently.
problem Estimating long memory parameters in stochastic processes.
method Scale-invariant 1D Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) models trained with synthetic data.
result Neural models outperform conventional methods in precision, speed, consistency, and robustness.
This work explains GANs as Bayesian neural networks with partial stochasticity.
problem Challenges in optimizing GANs and understanding their limitations.
method Interpreting GANs as Bayesian neural networks with partial stochasticity, establishing conditions, and proposing strategies to smooth the loss landscape and find solutions with minimum description length.
result Proposed strategies lead to performance improvements and deeper understanding of GANs.
Efficiently quantifies uncertainty in subsurface flow using neural networks guided by theory.
problem Uncertainty in dynamic subsurface flow predictions.
method Theory-guided Neural Network (TgNN) for efficient uncertainty quantification.
result TgNN surrogate improves efficiency of uncertainty quantification compared to MC method.
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.
Neural Ordinary Differential Equation (Neural ODE) has been proposed as a continuous approximation to the ResNet architecture. Some commonly used regularization mechanisms in discrete neural networks (e.g. dropout, Gaussian noise) are missing in current Neural ODE networks. In this paper, we propose a new continuous ne…
This work learns effective dynamics from short-term data of stochastic systems.
problem Learning effective dynamics from short-term data of stochastic systems.
method Proposes a novel algorithm using a neural network (Auto-SDE) to learn invariant slow manifold from data.
result Validated through numerical experiments to be accurate, stable, and effective.
Continuous-time SGD converges under certain conditions, useful for deep learning.
problem Minimizing population expected loss in learning problems.
method Continuous-time approximation of stochastic gradient descent.
result Establishes sufficient conditions for convergence, applicable to overparametrized neural networks.