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Linear Transformers Are Secretly Fast Weight Programmers

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arxiv 2102.11174 v3 pith:OQXHYGWX submitted 2021-02-22 cs.LG

Linear Transformers Are Secretly Fast Weight Programmers

classification cs.LG
keywords fastweightadditiveattentiondynamicallykeyslearnlearns
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We show the formal equivalence of linearised self-attention mechanisms and fast weight controllers from the early '90s, where a ``slow" neural net learns by gradient descent to program the ``fast weights" of another net through sequences of elementary programming instructions which are additive outer products of self-invented activation patterns (today called keys and values). Such Fast Weight Programmers (FWPs) learn to manipulate the contents of a finite memory and dynamically interact with it. We infer a memory capacity limitation of recent linearised softmax attention variants, and replace the purely additive outer products by a delta rule-like programming instruction, such that the FWP can more easily learn to correct the current mapping from keys to values. The FWP also learns to compute dynamically changing learning rates. We also propose a new kernel function to linearise attention which balances simplicity and effectiveness. We conduct experiments on synthetic retrieval problems as well as standard machine translation and language modelling tasks which demonstrate the benefits of our methods.

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