A Granger-Causal Perspective on Gradient Descent with Application to Pruning

• URL: http://arxiv.org/abs/2412.03035v1
• Date: Wed, 04 Dec 2024 05:16:48 GMT
• Title: A Granger-Causal Perspective on Gradient Descent with Application to Pruning
• Authors: Aditya Shah, Aditya Challa, Sravan Danda, Archana Mathur, Snehanshu Saha,
• Abstract summary: This article explores the causality aspect of gradient descent. We show that the gradient descent procedure has an implicit granger-causal relationship between the reduction in loss and a change in parameters. We illustrate the significance of the causal approach using the application of Pruning.
• Score: 2.8602509244926413
• License:
• Abstract: Stochastic Gradient Descent (SGD) is the main approach to optimizing neural networks. Several generalization properties of deep networks, such as convergence to a flatter minima, are believed to arise from SGD. This article explores the causality aspect of gradient descent. Specifically, we show that the gradient descent procedure has an implicit granger-causal relationship between the reduction in loss and a change in parameters. By suitable modifications, we make this causal relationship explicit. A causal approach to gradient descent has many significant applications which allow greater control. In this article, we illustrate the significance of the causal approach using the application of Pruning. The causal approach to pruning has several interesting properties - (i) We observe a phase shift as the percentage of pruned parameters increase. Such phase shift is indicative of an optimal pruning strategy. (ii) After pruning, we see that minima becomes "flatter", explaining the increase in accuracy after pruning weights.

Related papers

• Gradient Normalization Provably Benefits Nonconvex SGD under Heavy-Tailed Noise [60.92029979853314]
  We investigate the roles of gradient normalization and clipping in ensuring the convergence of Gradient Descent (SGD) under heavy-tailed noise. Our work provides the first theoretical evidence demonstrating the benefits of gradient normalization in SGD under heavy-tailed noise. We introduce an accelerated SGD variant incorporating gradient normalization and clipping, further enhancing convergence rates under heavy-tailed noise.
  arXiv  Detail & Related papers  (2024-10-21T22:40:42Z)
• Emergence of heavy tails in homogenized stochastic gradient descent [1.450405446885067]
  Loss by gradient descent (SGD) leads to heavy-tailed network parameters. We analyze a continuous diffusion approximation of SGD, called homogenized gradient descent. We quantify the interplay between optimization parameters and the tail-index.
  arXiv  Detail & Related papers  (2024-02-02T13:06:33Z)
• Inference and Interference: The Role of Clipping, Pruning and Loss Landscapes in Differentially Private Stochastic Gradient Descent [13.27004430044574]
  Differentially private gradient descent (DP-SGD) is known to have poorer training and test performance on large neural networks. We compare the behavior of the two processes separately in early and late epochs. We find that while DP-SGD makes slower progress in early stages, it is the behavior in the later stages that determines the end result.
  arXiv  Detail & Related papers  (2023-11-12T13:31:35Z)
• Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms [88.74308282658133]
  Reization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. Recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes. We propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls.
  arXiv  Detail & Related papers  (2023-10-30T18:43:21Z)
• Towards Training Without Depth Limits: Batch Normalization Without Gradient Explosion [83.90492831583997]
  We show that a batch-normalized network can keep the optimal signal propagation properties, but avoid exploding gradients in depth. We use a Multi-Layer Perceptron (MLP) with linear activations and batch-normalization that provably has bounded depth. We also design an activation shaping scheme that empirically achieves the same properties for certain non-linear activations.
  arXiv  Detail & Related papers  (2023-10-03T12:35:02Z)
• Improving Differentially Private SGD via Randomly Sparsified Gradients [31.295035726077366]
  Differentially private gradient observation (DP-SGD) has been widely adopted in deep learning to provide rigorously defined privacy bound compression. We propose an and utilize RS to strengthen communication cost and strengthen privacy bound compression.
  arXiv  Detail & Related papers  (2021-12-01T21:43:34Z)
• Differentiable Annealed Importance Sampling and the Perils of Gradient Noise [68.44523807580438]
  Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective. We propose a differentiable algorithm by abandoning Metropolis-Hastings steps, which further unlocks mini-batch computation.
  arXiv  Detail & Related papers  (2021-07-21T17:10:14Z)
• Learning High-Precision Bounding Box for Rotated Object Detection via Kullback-Leibler Divergence [100.6913091147422]
  Existing rotated object detectors are mostly inherited from the horizontal detection paradigm. In this paper, we are motivated to change the design of rotation regression loss from induction paradigm to deduction methodology.
  arXiv  Detail & Related papers  (2021-06-03T14:29:19Z)
• Implicit Gradient Regularization [18.391141066502644]
  gradient descent can be surprisingly good at optimizing deep neural networks without overfitting and without explicit regularization. We call this Implicit Gradient Regularization (IGR) and we use backward error analysis to calculate the size of this regularization.
  arXiv  Detail & Related papers  (2020-09-23T14:17:53Z)
• The Break-Even Point on Optimization Trajectories of Deep Neural Networks [64.7563588124004]
  We argue for the existence of the "break-even" point on this trajectory. We show that using a large learning rate in the initial phase of training reduces the variance of the gradient. We also show that using a low learning rate results in bad conditioning of the loss surface even for a neural network with batch normalization layers.
  arXiv  Detail & Related papers  (2020-02-21T22:55:51Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.