Convexifying Transformers: Improving optimization and understanding of
transformer networks
- URL: http://arxiv.org/abs/2211.11052v1
- Date: Sun, 20 Nov 2022 18:17:47 GMT
- Title: Convexifying Transformers: Improving optimization and understanding of
transformer networks
- Authors: Tolga Ergen, Behnam Neyshabur, Harsh Mehta
- Abstract summary: We study the training problem of attention/transformer networks and introduce a novel convex analytic approach.
We first introduce a convex alternative to the self-attention mechanism and reformulate the regularized training problem of transformer networks.
As a byproduct of our convex analysis, we reveal an implicit regularization mechanism, which promotes sparsity across tokens.
- Score: 56.69983975369641
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Understanding the fundamental mechanism behind the success of transformer
networks is still an open problem in the deep learning literature. Although
their remarkable performance has been mostly attributed to the self-attention
mechanism, the literature still lacks a solid analysis of these networks and
interpretation of the functions learned by them. To this end, we study the
training problem of attention/transformer networks and introduce a novel convex
analytic approach to improve the understanding and optimization of these
networks. Particularly, we first introduce a convex alternative to the
self-attention mechanism and reformulate the regularized training problem of
transformer networks with our alternative convex attention. Then, we cast the
reformulation as a convex optimization problem that is interpretable and easier
to optimize. Moreover, as a byproduct of our convex analysis, we reveal an
implicit regularization mechanism, which promotes sparsity across tokens.
Therefore, we not only improve the optimization of attention/transformer
networks but also provide a solid theoretical understanding of the functions
learned by them. We also demonstrate the effectiveness of our theory through
several numerical experiments.
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