Rethinking Softmax: Self-Attention with Polynomial Activations
Keywords: polynomial activations, softmax, theory of transformers.
TL;DR: We theoretically show softmax implicitly regularizes the Frobenius norm of the attention matrix and then show certain polynomial activations can achieve a similar effect, giving new insights into activations for attention matrices.
Abstract: This paper challenges the conventional belief that softmax attention in transformers is effective primarily because it generates a probability distribution for attention allocation. Instead, we theoretically show that its success lies in its ability to implicitly regularize the Frobenius norm of the attention matrix during training. We then explore alternative activations that regularize the Froebnius norm of the attention matrix, demonstrating that certain polynomial activations can achieve this effect, making them suitable for attention-based architectures. Empirical results indicate these activations perform comparably or better than softmax across various computer vision and language tasks, suggesting new possibilities for attention mechanisms beyond softmax.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 6398
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