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

arXiv: https://arxiv.org/abs/2412.03035 · HTML: https://mlsanity.com/paper/2412.03035/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 32 references that are in the map.
- First posted on arXiv 4 Dec 2024.

## Builds on (most cited first, 12 of 12)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Fantastic Generalization Measures and Where to Find Them](https://mlsanity.com/paper/1912.02178/) (2019)
- [Efficient Neural Audio Synthesis](https://mlsanity.com/paper/1802.08435/) (2018)
- [Fast as CHITA: Neural Network Pruning with Combinatorial Optimization](https://mlsanity.com/paper/2302.14623/) (2023)
- [WoodFisher: Efficient Second-Order Approximation for Neural Network Compression](https://mlsanity.com/paper/2004.14340/) (2020)
- [Why is the State of Neural Network Pruning so Confusing? On the Fairness, Comparison Setup, and Trainability in Network Pruning](https://mlsanity.com/paper/2301.05219/) (2023)

## Built on by (most cited first, 1 of 1)

- [Sparsity-Driven Plasticity in Multi-Task Reinforcement Learning](https://mlsanity.com/paper/2508.06871/) (2025)

## Abstract (arXiv)

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.