Gradient descent biases towards stable rank networks for nearly-orthogonal data.
problem Understanding implicit bias in non-smooth neural networks trained by gradient descent.
method Analysis of two-layer ReLU and leaky ReLU networks trained by gradient descent on nearly-orthogonal data.
result Gradient descent biases towards networks with stable rank and uniform margin for nearly-orthogonal data.
Gradient descent learns ReLU functions with non-zero bias efficiently.
problem Learning ReLU functions with non-zero bias under Gaussian distributions.
method Gradient descent starting from random initialization.
result Gradient descent achieves near-optimal error with high probability.
New method reduces bias in incomplete data using deliberate missingness.
problem Systematic gradient biases in incomplete data for stochastic learning.
method Richardson-SGD debiasing procedure with deliberate missingness.
result Reduces gradient bias from O ( ∥ p ∥ ) O(\|p\|) O ( ∥ p ∥ ) to O ( ∥ p ∥ 2 ) O(\|p\|^2) O ( ∥ p ∥ 2 ) . Gradient clipping helps private SGD converge despite potential bias.
problem Gradient clipping in private SGD can bias convergence.
method Theoretical analysis and empirical evaluation of gradient clipping effects.
result Gradient clipping can prevent convergence to stationary points and introduces bias.
This study investigates how gradient-based methods bias neural networks trained on high-dimensional data.
problem The implicit biases of gradient-based optimization algorithms in neural networks trained on high-dimensional data.
method Investigation of gradient flow and gradient descent in two-layer fully-connected neural networks with leaky ReLU activations.
result Gradient flow and gradient descent lead to neural networks with low-rank solutions and linear decision boundaries.
Gradient descent stagnates in low-precision, but unbiased rounding schemes improve convergence.
problem Stagnation of gradient descent in low-precision computation.
method Proposed unbiased stochastic rounding schemes that trade zero bias for larger probability of preserving small gradients.
result Unbiased rounding methods typically improve convergence rate of gradient descent for convex problems.
Gradient descent struggles with learning a single neuron with bias.
problem Learning a single neuron with a bias term in the realizable setting with ReLU activation.
method Theoretical study using gradient descent, characterizing critical points, and providing convergence guarantees.
result Gradient descent faces significant challenges in learning a single neuron with bias, unlike the bias-less case.
Gradient flow in ReLU networks biases towards generalization but makes them vulnerable to adversarial attacks.
problem Generalization vs. Adversarial Robustness in ReLU Networks
method Analysis of gradient flow in two-layer ReLU networks with clustered data.
result Gradient flow biases towards generalization but also makes networks vulnerable to adversarial attacks.
This work overcomes bias in concave multi-objective reinforcement learning.
problem Gradient bias in policy gradient methods for concave scalarized multi-objective reinforcement learning.
method Developed a Natural Policy Gradient (NPG) algorithm with a multi-level Monte Carlo (MLMC) estimator.
result Achieved optimal O ~ ( ε − 2 ) \widetilde{\mathcal{O}}(ε^{-2}) O ( ε − 2 ) sample complexity for computing an ε ε ε -optimal policy. New minibatching strategy reduces stochastic gradient bias in optimisation.
problem Reducing bias in stochastic gradient descent.
method Symmetric Minibatching Strategy combined with momentum.
result Reduced stochastic gradient bias from O ( h 2 ) \mathcal{O}(h^2) O ( h 2 ) to O ( h 4 ) \mathcal{O}(h^4) O ( h 4 ) . A bias classifier is introduced to resist adversarial attacks.
problem Resisting adversarial attacks on deep neural networks (DNNs).
method Introducing the bias part of a DNN with Relu as the activation function as a classifier, and adding a random first-degree part to make it information-theoretically safe.
result The bias classifier is more robust than DNNs of similar size against adversarial attacks.
Semiparametric method removes bias in functional bilevel gradient estimation.
problem First-order bias in plug-in hypergradient when lower-level problem is nonparametric.
method Semiparametric debiasing theory based on efficient influence function leads to cross-fitted orthogonal hypergradient estimator.
result Asymptotic normality and uniform control over outer parameter established for the estimator.
Bias correction improves language model training performance.
problem Stochastic update bias in preconditioned optimizers.
method Cross-fitted preconditioning and variance-corrected inversion.
result Reduces held-out pretraining loss by 0.15 nats.
New bounds show SGD can match deterministic gradient descent's convergence rate.
problem Optimizing SGD convergence rate under strong convexity and smoothness.
method Computer-aided Lyapunov analysis, focusing on bias-optimal bounds.
result SGD achieves optimal convergence rate in bias terms for a wide range of step-sizes.
Paper proposes a new method to stabilize noisy gradient algorithms.
problem Stochastic-gradient Langevin algorithms can introduce bias when taming denominators depend on stochastic-gradient realizations.
method Proposes a structure-preserving framework for designing tamed denominators that avoid unnecessary taming and maintain the stabilizing effect of taming.
result The method avoids stationary bias and explains the stationary error split into bias and remaining error.
Gradient-trained shallow networks can generalize well but are vulnerable to small-radius adversarial attacks.
problem Adversarial robustness of gradient-trained shallow networks.
method Analysis of neuron alignment and polynomial ReLU activation.
result Gradient-trained shallow networks with polynomial ReLU activation are robust to small-radius adversarial attacks.
U-Clip clips gradients to reduce bias without discarding them.
problem Reduces bias in stochastic gradient descent.
method Maintains a buffer of clipped gradients to add to next iteration.
result U-Clip updates are unbiased on average.
Study reveals biases in gradient descent for GLNs, improving neural network performance.
problem Understanding and improving the inductive biases of deep neural networks.
method Derive infinite-time training limit of gated linear networks and generalize to other networks.
result Theoretical framework captures key inductive biases of ReLU networks.
A new Q-learning variant reduces underestimation bias in deep reinforcement learning.
problem Underestimation bias in deep reinforcement learning policies.
method Introducing a novel, parameter-free Deep Q-learning variant.
result Significantly outperforms existing approaches and improves state-of-the-art performance.
New algorithm corrects bias in LDP-released data for better analysis.
problem Bias in data released under Local Differential Privacy (LDP).
method Inverse Weierstrass Private Stochastic Gradient Descent (IWP-SGD).
result Converges to true population risk minimizer at O ( 1 / n ) \mathcal{O}(1/n) O ( 1/ n ) rate. There exist a number of reinforcement learning algorithms which learnby climbing the gradient of expected reward. Their long-runconvergence has been proved, even in partially observableenvironments with non-deterministic actions, and without the need fora system model. However, the variance of the gradient estimator ha…
This paper analyzes implicit bias in Deep Linear Discriminant Analysis.
problem The implicit bias of Deep Linear Discriminant Analysis.
method Analyzing gradient flow on a L-layer diagonal linear network.
result Under balanced initialization, the network transforms additive updates into multiplicative updates, conserving the (2/L) quasi-norm.
Study reveals how initialization scale affects training accuracy in linear networks.
problem Understanding implicit bias in linear classification models.
method Asymptotic analysis of gradient flow trajectories and training loss minimization.
result Implicit bias is more complex at reasonable initialization scales and training accuracies.
Truncated backpropagation through time (TBPTT) is a popular method for learning in recurrent neural networks (RNNs) that saves computation and memory at the cost of bias by truncating backpropagation after a fixed number of lags. In practice, choosing the optimal truncation length is difficult: TBPTT will not converge …
Improved sampling efficiency with Random Reshuffling for Langevin dynamics.
problem Sampling efficiency in stochastic gradient algorithms.
method Random Reshuffling for Stochastic Gradient Langevin Dynamics (SGLD).
result Random Reshuffling leads to improved performance in sampling.
New tensor formulation reveals gradient flow's bias in linear neural networks.
problem Understanding implicit bias in linear neural network training.
method Tensor formulation of neural networks, including fully-connected, diagonal, and convolutional networks.
result Gradient flow on linear tensor networks converges to solutions of specific optimization problems.
With the purpose of examining biased updates in variance-reduced stochastic gradient methods, we introduce SVAG, a SAG/SAGA-like method with adjustable bias. SVAG is analyzed in a cocoercive root-finding setting, a setting which yields the same results as in the usual smooth convex optimization setting for the ordinary…
Resampling outperforms reweighting for correcting biased data in machine learning models.
problem Correcting sampling bias in machine learning models trained on biased data sets.
method Compared resampling and reweighting techniques, focusing on their performance with stochastic gradient algorithms.
result Resampling outperforms reweighting when combined with stochastic gradient algorithms.
SkMM selects data for finetuning by balancing bias and variance.
problem Balancing bias and variance in high-dimensional finetuning.
method Gradient sketching for bias reduction and moment matching for variance reduction.
result Gradient sketching selects samples efficiently and accurately.
Adversarial domain adaptation reduces sample bias in high energy physics classifier.
problem Sample bias in high energy physics classifier training.
method Adversarial domain adaptation using neural networks with gradient reversal layer.
result Successful bias removal on simulated events at the LHC.
This study reveals efficient finite-difference computation for gradient regularization in deep learning.
problem Improving generalization performance in deep learning through gradient regularization.
method Analyzes and reveals a specific finite-difference computation that reduces computational cost and improves generalization performance.
result Finite-difference computation strengthens the implicit bias towards rich regimes and enhances generalization performance.
New method improves online covariance estimation for SGD.
problem Improving online covariance estimation for SGD.
method Proposes a de-biased covariance estimator that eliminates second-order derivatives.
result Achieves a convergence rate of n ( α − 1 ) / 2 log n n^{(α-1)/2} \sqrt{\log n} n ( α − 1 ) /2 log n , outperforming existing methods. This paper studies how gradient descent in control systems can perform well on unseen data.
problem The extent of a learned controller's ability to extrapolate to unseen initial states.
method Theoretical study of policy gradient in Linear Quadratic Regulator (LQR) problems, focusing on the role of exploration.
result The performance of a learned controller on unseen initial states depends on the degree of exploration induced by the system.
Stochastic Gradient Descent shows directional bias with moderate learning rates, impacting optimization outcomes.
problem Understanding the bias of SGD with moderate learning rates in practical scenarios.
method Analyzing SGD and GD on an overparameterized linear regression problem.
result SGD converges along large eigenvalue directions, GD along small ones, affecting early stopping outcomes.
SGD noise has no bias advantage in online learning, contrary to offline learning.
problem The role of SGD noise in online learning.
method Extensive empirical analysis of image and language data.
result Small batch sizes do not confer any implicit bias advantages in online learning.
PES method reduces bias in gradient estimation for unrolled graphs.
problem High variance and bias in gradient estimation for unrolled computation graphs.
method Divide graph into unrolls, apply ES update, accumulate correction terms.
result PES provides unbiased, low-variance gradient estimates.
This work analyzes the maximum-margin bias in quasi-homogeneous neural networks.
problem Analyzing the maximum-margin bias in quasi-homogeneous neural networks.
method Geometric analysis of gradient dynamics for quasi-homogeneous models.
result Gradient flow implicitly favors a subset of parameters, leading to asymmetric norm minimization.
We study the problem of learning-to-learn: inferring a learning algorithm that works well on tasks sampled from an unknown distribution. As class of algorithms we consider Stochastic Gradient Descent on the true risk regularized by the square euclidean distance to a bias vector. We present an average excess risk bound …
Our paper characterizes how ReLU affects GD's implicit bias in high-dimensional neural networks.
problem Understanding the implicit bias of gradient descent on neural networks.
method Novel primal-dual analysis tracking predictions and coefficients.
result The implicit bias approximates the minimum- ℓ 2 \ell_2 ℓ 2 -norm solution with high probability. This paper analyzes SGD with biased gradients for deep learning models.
problem Analyzing SGD with biased gradients for deep learning models.
method Non-asymptotic analysis of SGD with adaptive steps for non-convex smooth functions.
result Adagrad, RMSProp, and AMSGRAD converge to critical points at a similar rate to unbiased case.
SGD benefits from a directional bias in kernel regression models.
problem Improving generalization in kernel regression models.
method Generalized directional bias property of SGD in kernel regression.
result SGD converges along the eigenvector of the largest eigenvalue of the Gram matrix.
Gradient descent training of neural networks leads to solutions close to natural cubic splines.
problem Understanding the implicit bias of gradient descent in neural networks.
method Analysis of gradient descent training for wide neural networks, focusing on the curvature penalty and initialization schemes.
result The solutions of gradient descent training are polyharmonic splines for certain initialization schemes.
A new algorithm reduces bias and variance in distributionally robust optimization.
problem Distributionally robust optimization with bias and variance issues.
method Prospect, a stochastic gradient-based algorithm that reduces hyperparameter tuning.
result Prospect achieves linear convergence and 2-3x faster convergence on various benchmarks.
We study sampling as optimization in the space of measures. We focus on gradient flow-based optimization with the Langevin dynamics as a case study. We investigate the source of the bias of the unadjusted Langevin algorithm (ULA) in discrete time, and consider how to remove or reduce the bias. We point out the difficul…
The study reveals simplicity bias in neural networks leading to better compositional mappings.
problem Understanding when and how to encourage neural networks to learn compositional mappings.
method Examined compositional mappings through coding length and gradient descent dynamics.
result Neural networks tend to learn the simplest bijections, explaining their good generalization.
Gradient boosting method enforced with individual fairness.
problem Enforcing fairness in machine learning models.
method Functional gradient descent on robust loss function.
result Algorithm converges globally and generalizes.
Mirror flow in shallow neural networks shows similar implicit bias to gradient flow, with key differences in curvature penalties.
problem Analyzing implicit bias in shallow neural networks with mirror flow.
method Characterization through variational problems and scaled potentials.
result Mirror flow with scaled potentials induces a rich class of biases not captured by RKHS norms.
New model reduces matrix factorization bias, yielding truly low-rank solutions.
problem Gradient descent's implicit bias in matrix factorization.
method Introducing a new factorization model with constrained factors and diagonal components.
result The new model consistently exhibits a strong implicit bias, yielding truly low-rank solutions.