Hopfield Networks is All You Need (Paper Explained)

Hopfield Networks are one of the classic models of biological memory networks. This paper generalizes modern Hopfield Networks to continuous states and shows that the corresponding update rule is equal to the attention mechanism used in modern Transformers. It further analyzes a pre-trained BERT model through the lens of Hopfield Networks and uses a Hopfield Attention Layer to perform Immune Repertoire Classification. OUTLINE: 0:00 - Intro & Overview 1:35 - Binary Hopfield Networks 5:55 - Continuous Hopfield Networks 8:15 - Update Rules & Energy Functions 13:30 - Connection to Transformers 14:35 - Hopfield Attention Layers 26:45 - Theoretical Analysis 48:10 - Investigating BERT 1:02:30 - Immune Repertoire Classification Paper: https://ift.tt/33v47N1 Code: https://ift.tt/3kfo4xh Immune Repertoire Classification Paper: https://ift.tt/33GPGFC My Video on Attention: https://youtu.be/iDulhoQ2pro My Video on BERT: https://youtu.be/-9evrZnBorM Abstract: We show that the transformer attention mechanism is the update rule of a modern Hopfield network with continuous states. This new Hopfield network can store exponentially (with the dimension) many patterns, converges with one update, and has exponentially small retrieval errors. The number of stored patterns is traded off against convergence speed and retrieval error. The new Hopfield network has three types of energy minima (fixed points of the update): (1) global fixed point averaging over all patterns, (2) metastable states averaging over a subset of patterns, and (3) fixed points which store a single pattern. Transformer and BERT models operate in their first layers preferably in the global averaging regime, while they operate in higher layers in metastable states. The gradient in transformers is maximal for metastable states, is uniformly distributed for global averaging, and vanishes for a fixed point near a stored pattern. Using the Hopfield network interpretation, we analyzed learning of transformer and BERT models. Learning starts with attention heads that average and then most of them switch to metastable states. However, the majority of heads in the first layers still averages and can be replaced by averaging, e.g. our proposed Gaussian weighting. In contrast, heads in the last layers steadily learn and seem to use metastable states to collect information created in lower layers. These heads seem to be a promising target for improving transformers. Neural networks with Hopfield networks outperform other methods on immune repertoire classification, where the Hopfield net stores several hundreds of thousands of patterns. We provide a new PyTorch layer called "Hopfield", which allows to equip deep learning architectures with modern Hopfield networks as a new powerful concept comprising pooling, memory, and attention. GitHub: this https URL Authors: Hubert Ramsauer, Bernhard Schäfl, Johannes Lehner, Philipp Seidl, Michael Widrich, Lukas Gruber, Markus Holzleitner, Milena Pavlović, Geir Kjetil Sandve, Victor Greiff, David Kreil, Michael Kopp, Günter Klambauer, Johannes Brandstetter, Sepp Hochreiter Links: YouTube: https://www.youtube.com/c/yannickilcher Twitter: https://twitter.com/ykilcher Discord: https://ift.tt/3dJpBrR BitChute: https://ift.tt/38iX6OV Minds: https://ift.tt/37igBpB Parler: https://ift.tt/38tQU7C LinkedIn: https://ift.tt/2Zo6XRA 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://ift.tt/2DuKOZ3 Patreon: https://ift.tt/390ewRH Bitcoin (BTC): bc1q49lsw3q325tr58ygf8sudx2dqfguclvngvy2cq Ethereum (ETH): 0x7ad3513E3B8f66799f507Aa7874b1B0eBC7F85e2 Litecoin (LTC): LQW2TRyKYetVC8WjFkhpPhtpbDM4Vw7r9m Monero (XMR): 4ACL8AGrEo5hAir8A9CeVrW8pEauWvnp1WnSDZxW7tziCDLhZAGsgzhRQABDnFy8yuM9fWJDviJPHKRjV4FWt19CJZN9D4n