arXiv research

New method learns population dynamics from snapshots, outperforming existing models.

New framework for online control in evolving populations.

Infinitesimal boosting converges to a deterministic process in large sample limit.

Polyak step size GD reaches final radius of convergence after log iterations.

A new method for learning gradient flows from population dynamics.

New method improves NN performance across various settings.

We propose a population-based Evolutionary Stochastic Gradient Descent (ESGD) framework for optimizing deep neural networks. ESGD combines SGD and gradient-free evolutionary algorithms as complementary algorithms in one framework in which the optimization alternates between the SGD step and evolution step to improve th…

Continuous-time SGD converges under certain conditions, useful for deep learning.

Gradient descent learns over-param neural nets better than NTK.

Training activation quantized neural networks involves minimizing a piecewise constant function whose gradient vanishes almost everywhere, which is undesirable for the standard back-propagation or chain rule. An empirical way around this issue is to use a straight-through estimator (STE) (Bengio et al., 2013) in the ba…

Gradient descent learns a single neuron without knowing the relationship between inputs and labels.

Gradient descent struggles with high-dimensional data fitting.

A new method simulates large, diverse populations of learning agents evolving in games.

Uncertainty sampling, a popular active learning algorithm, is used to reduce the amount of data required to learn a classifier, but it has been observed in practice to converge to different parameters depending on the initialization and sometimes to even better parameters than standard training on all the data. In this…

New approach uses 'growth' and 'harvesting' concepts to improve deep learning models.

This work learns models for population dynamics using variational methods and higher-order quadrature.

We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in the limit of infinite data), followed by results that apply to updates based on a …

Gradient descent methods for deep ReLU networks achieve optimal generalization rates.

Paper analyzes SVGD algorithm for non-asymptotic convergence.

The curse of dimensionality affects neural network optimization, especially with smooth functions.

We study the Stochastic Gradient Langevin Dynamics (SGLD) algorithm for non-convex optimization. The algorithm performs stochastic gradient descent, where in each step it injects appropriately scaled Gaussian noise to the update. We analyze the algorithm's hitting time to an arbitrary subset of the parameter space. Two…

Aims to describe neural network training dynamics using two-time-scale models.

Boost-R uses gradient boosted trees for analyzing recurrence data.

Despite recent innovations in network architectures and loss functions, training RNNs to learn long-term dependencies remains difficult due to challenges with gradient-based optimisation methods. Inspired by the success of Deep Neuroevolution in reinforcement learning (Such et al. 2017), we explore the use of gradient-…

The paper develops statistical inference for gradient flows in optimization.

The paper analyzes the maximum margin algorithm's performance on noisy data.

Improved DP algorithms for non-convex optimization with tighter generalization bounds.

Estimating the log-likelihood gradient with respect to the parameters of a Restricted Boltzmann Machine (RBM) typically requires sampling using Markov Chain Monte Carlo (MCMC) techniques. To save computation time, the Markov chains are only run for a small number of steps, which leads to a biased estimate. This bias ca…

D2SRM solves complex PDEs using deep learning.

In order to interact intelligently with objects in the world, animals must first transform neural population responses into estimates of the dynamic, unknown stimuli which caused them. The Bayesian solution to this problem is known as a Bayes filter, which applies Bayes' rule to combine population responses with the pr…

Deep Reinforcement Learning (DRL) algorithms have been successfully applied to a range of challenging control tasks. However, these methods typically suffer from three core difficulties: temporal credit assignment with sparse rewards, lack of effective exploration, and brittle convergence properties that are extremely …

New method identifies drift and diffusivity from SDE marginals.

New bounds for KANs trained with DP-SGD, addressing correlated noise.

A powerful approach for understanding neural population dynamics is to extract low-dimensional trajectories from population recordings using dimensionality reduction methods. Current approaches for dimensionality reduction on neural data are limited to single population recordings, and can not identify dynamics embedde…

The paper improves QD policy ensembles using distribution ratio estimators.

We propose novel first-order stochastic approximation algorithms for canonical correlation analysis (CCA). Algorithms presented are instances of inexact matrix stochastic gradient (MSG) and inexact matrix exponentiated gradient (MEG), and achieve $ε$-suboptimality in the population objective in $\operatorname{poly}(\fr…

To understand how rich dynamics emerge in neural populations, we require models exhibiting a wide range of activity patterns while remaining interpretable in terms of connectivity and single-neuron dynamics. However, it has been challenging to fit such mechanistic spiking networks at the single neuron scale to empirica…

Resampling outperforms reweighting for correcting biased data in machine learning models.

Improves exploration in reinforcement learning with diverse population.

Optimal private ERM and SCO with subquadratic gradient complexity.

Analyzes how bias evolves in SGD training across different data sub-populations.

This paper studies the landscape of empirical risk of deep neural networks by theoretically analyzing its convergence behavior to the population risk as well as its stationary points and properties. For an $l$-layer linear neural network, we prove its empirical risk uniformly converges to its population risk at the rat…

Gradient descent converges to a small neighborhood of the true parameter in logistic regression with Gaussian design.

New method reduces bias in incomplete data using deliberate missingness.

This work aims to provide understandings on the remarkable success of deep convolutional neural networks (CNNs) by theoretically analyzing their generalization performance and establishing optimization guarantees for gradient descent based training algorithms. Specifically, for a CNN model consisting of $l$ convolution…

Stochastic Gradient Descent can overfit after just a few passes, contrary to initial expectations.

Improved algorithm finds second-order stationary points in non-convex optimization.

The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and Lojasiewicz inequality), tight bounds on the asymptotic bias of the iterates generated b…