Deep Networks Are Kernel Machines (Paper Explained)

Deep Networks Are Kernel Machines (Paper Explained)

Feb 05, 2021
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#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 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 Links: TabNine Code Completion (Referral): http://bit.ly/tabnine-yannick YouTube: https://www.youtube.com/c/yannickilcher Twitter: https://twitter.com/ykilcher Discord: https://discord.gg/4H8xxDF BitChute: https://www.bitchute.com/channel/yannic-kilcher Minds: https://www.minds.com/ykilcher Parler: https://parler.com/profile/YannicKilcher LinkedIn: https://www.linkedin.com/in/yannic-kilcher-488534136/ BiliBili: https://space.bilibili.com/1824646584 If you want to support me, the best thing to do is to share out the content :) If you want to support me financially (completely optional and voluntary, but a lot of people have asked for this): SubscribeStar: https://www.subscribestar.com/yannickilcher Patreon: https://www.patreon.com/yannickilcher Bitcoin (BTC): bc1q49lsw3q325tr58ygf8sudx2dqfguclvngvy2cq Ethereum (ETH): 0x7ad3513E3B8f66799f507Aa7874b1B0eBC7F85e2 Litecoin (LTC): LQW2TRyKYetVC8WjFkhpPhtpbDM4Vw7r9m Monero (XMR): 4ACL8AGrEo5hAir8A9CeVrW8pEauWvnp1WnSDZxW7tziCDLhZAGsgzhRQABDnFy8yuM9fWJDviJPHKRjV4FWt19CJZN9D4n

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
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