Inherent Noise in Gradient Based Methods
Previous work has examined the ability of larger capacity neural networks to generalize better than smaller ones, even without explicit regularizers, by analyzing gradient based algorithms such as GD and SGD. The presence of noise and its effect on robustness to parameter perturbations has been linked to generalization. We examine a property of GD and SGD, namely that instead of iterating through all scalar weights in the network and updating them one by one, GD (and SGD) updates all the parameters at the same time. As a result, each parameter $w^i$ calculates its partial derivative at the stale parameter $\mathbf{w_t}$, but then suffers loss $\hat{L}(\mathbf{w_{t+1}})$. We show that this causes noise to be introduced into the optimization. We find that this noise penalizes models that are sensitive to perturbations in the weights. We find that penalties are most pronounced for batches that are currently being used to update, and are higher for larger models.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
On the Inherent Privacy of Zeroth Order Projected Gradient Descent
Differentially private zeroth-order optimization methods have recently gained popularity in private fine tuning of machine learning models due to their reduced memory requirements. Current approaches for privatizing zero…
Asynchronous stochastic convex optimization: the noise is in the noise and SGD don't care
We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same cond…
Stochastic OptimizationAsynchronous stochastic convex optimization
We show that asymptotically, completely asynchronous stochastic gradient procedures achieve optimal (even to constant factors) convergence rates for the solution of convex optimization problems under nearly the same cond…
Stochastic OptimizationAxiomatization of Gradient Smoothing in Neural Networks
Gradients play a pivotal role in neural networks explanation. The inherent high dimensionality and structural complexity of neural networks result in the original gradients containing a significant amount of noise. While…
Securing Distributed SGD against Gradient Leakage Threats
This paper presents a holistic approach to gradient leakage resilient distributed Stochastic Gradient Descent (SGD). First, we analyze two types of strategies for privacy-enhanced federated learning: (i) gradient pruning…
Federated Learning