Rethinking Attention: Polynomial Alternatives to Softmax in Transformers
This provides a new theoretical understanding of attention mechanisms that could simplify transformer architectures, though it appears incremental as it substitutes rather than replaces the overall attention framework.
This paper challenges the necessity of softmax's probability distribution properties in transformer attention mechanisms, arguing that its effectiveness comes from Frobenius norm regularization instead, and demonstrates that polynomial alternatives can achieve comparable performance across applications.
This paper questions whether the strong performance of softmax attention in transformers stems from producing a probability distribution over inputs. Instead, we argue that softmax's effectiveness lies in its implicit regularization of the Frobenius norm of the attention matrix, which stabilizes training. Motivated by this, we explore alternative activations, specifically polynomials, that achieve a similar regularization effect. Our theoretical analysis shows that certain polynomials can serve as effective substitutes for softmax, achieving strong performance across transformer applications despite violating softmax's typical properties of positivity, normalization, and sparsity. Extensive experiments support these findings, offering a new perspective on attention mechanisms.