Summary of Gd Doesn’t Make the Cut: Three Ways That Non-differentiability Affects Neural Network Training, by Siddharth Krishna Kumar
GD doesn’t make the cut: Three ways that non-differentiability affects neural network training
by Siddharth Krishna Kumar
First submitted to arxiv on: 16 Jan 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computer Vision and Pattern Recognition (cs.CV)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper investigates fundamental differences between gradient methods applied to non-differentiable functions (NGDMs) and classical gradient descents (GDs) for differentiable functions. The authors reveal significant gaps in current deep learning optimization theory, showing that NGDMs exhibit distinct convergence properties compared to GDs. The study challenges the applicability of existing neural network convergence literature based on L-smoothness to non-smooth neural networks. Moreover, the analysis reveals paradoxical behavior of NDGM solutions for L1-regularized problems, questioning widely adopted L1 penalization techniques for network pruning. Additionally, the authors challenge the assumption that optimization algorithms like RMSProp behave similarly in differentiable and non-differentiable contexts. The study expands on the Edge of Stability phenomenon, demonstrating its occurrence in a broader class of functions, including Lipschitz continuous convex differentiable functions. This finding raises questions about its relevance and interpretation in non-convex, non-differentiable neural networks using ReLU activations. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper looks at how computer programs learn from data. It compares two ways that machine learning algorithms work: one for smooth (easy to understand) problems and another for non-smooth (harder to understand) problems. The study finds that these two methods behave differently than previously thought, which means we need to rethink how we optimize neural networks. This is important because it affects how we design and train artificial intelligence models. |
Keywords
* Artificial intelligence * Deep learning * Machine learning * Neural network * Optimization * Pruning * Relu
