Linear Transformers Are Secretly Fast Weight Programmers
This work addresses memory and efficiency issues in linear transformers for researchers and practitioners in natural language processing, offering incremental improvements over existing methods.
The paper demonstrates that linear transformers are equivalent to fast weight programmers from the 1990s, revealing a memory capacity limitation in existing methods and proposing a new kernel and delta rule-like programming to improve performance, with experiments showing benefits in tasks like machine translation and language modeling.
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.