Summary of A Generalized Neural Tangent Kernel For Surrogate Gradient Learning, by Luke Eilers et al.
A generalized neural tangent kernel for surrogate gradient learning
by Luke Eilers, Raoul-Martin Memmesheimer, Sven Goedeke
First submitted to arxiv on: 24 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Disordered Systems and Neural Networks (cond-mat.dis-nn); Machine Learning (cs.LG); Probability (math.PR); Neurons and Cognition (q-bio.NC)
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| 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 addresses the limitation of state-of-the-art neural network training methods, which rely on the derivative of the network’s activation function. Binary and discrete-time spiking neural networks, for instance, lack useful derivatives, making traditional methods inapplicable. To overcome this challenge, researchers often employ surrogate gradient learning (SGL), substituting the activation function’s derivative with a surrogate derivative. While SGL performs well in practice, it lacks theoretical foundation. The authors leverage the neural tangent kernel (NTK) to provide a generalization, dubbed the surrogate gradient NTK, which enables the analysis of SGL. They demonstrate that SGL is ill-posed in the infinite-width limit and generalize the NTK for gradient descent with surrogate derivatives. Numerical experiments confirm the effectiveness of the surrogate gradient NTK in characterizing SGL. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us understand how to train neural networks better. Right now, we have methods that work well but are based on an assumption that might not always be true. For example, some types of artificial neurons don’t have a derivative (a measure of how they change). To get around this problem, researchers use something called surrogate gradient learning. This method works okay, but we don’t fully understand why it works or what it means for the way our networks learn. The authors of this paper take a step towards solving this problem by creating a new tool called the surrogate gradient NTK. They show that it can help us analyze how well our networks learn and make predictions. |
Keywords
» Artificial intelligence » Generalization » Gradient descent » Neural network
