Hopfield Networks is All You Need (Paper Explained)

#ai #transformer #attention

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://arxiv.org/abs/2008.02217
Code: https://github.com/ml-jku/hopfield-la...
Immune Repertoire Classification Paper: https://arxiv.org/abs/2007.13505

My Video on Attention:    • Attention Is All You Need  
My Video on BERT:    • BERT: Pre-training of Deep Bidirectio...  

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

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