Deep Networks Are Kernel Machines (Paper Explained)

#deeplearning #kernels #neuralnetworks

Full Title: Every Model Learned by Gradient Descent Is Approximately a Kernel Machine

Deep Neural Networks are often said to discover useful representations of the data. However, this paper challenges this prevailing view and suggest that rather than representing the data, deep neural networks store superpositions of the training data in their weights and act as kernel machines at inference time. This is a theoretical paper with a main theorem and an understandable proof and the result leads to many interesting implications for the field.

OUTLINE:
0:00 - Intro & Outline
4:50 - What is a Kernel Machine?
10:25 - Kernel Machines vs Gradient Descent
12:40 - Tangent Kernels
22:45 - Path Kernels
25:00 - Main Theorem
28:50 - Proof of the Main Theorem
39:10 - Implications & My Comments

Paper: https://arxiv.org/abs/2012.00152
Street Talk about Kernels: https://youtu.be/y_RjsDHl5Y4

ERRATA: I simplify a bit too much when I pit kernel methods against gradient descent. Of course, you can even learn kernel machines using GD, they're not mutually exclusive. And it's also not true that you "don't need a model" in kernel machines, as it usually still contains learned parameters.

Abstract:
Deep learning's successes are often attributed to its ability to automatically discover new representations of the data, rather than relying on handcrafted features like other learning methods. We show, however, that deep networks learned by the standard gradient descent algorithm are in fact mathematically approximately equivalent to kernel machines, a learning method that simply memorizes the data and uses it directly for prediction via a similarity function (the kernel). This greatly enhances the interpretability of deep network weights, by elucidating that they are effectively a superposition of the training examples. The network architecture incorporates knowledge of the target function into the kernel. This improved understanding should lead to better learning algorithms.

Authors: Pedro Domingos

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