Key Points
1. The paper proves that transformers with sigmoid attention are universal function approximators, retaining the desirable property of being able to approximate any continuous sequence-to-sequence function to arbitrary precision.
2. The paper analyzes the regularity of sigmoid attention and provides a Lipschitz bound on its Jacobian, showing that it has better regularity properties compared to softmax attention.
3. The paper introduces F LASH S IGMOID, a hardware-aware and memory-efficient implementation of sigmoid attention that provides a 17% inference kernel speed-up over F LASH ATTENTION 2 on H100 GPUs.
4. Experiments across language, vision, and speech tasks show that properly normalized sigmoid attention matches the performance of softmax attention, overcoming limitations of prior attempts.
5. The paper highlights the importance of stabilizing the large initial attention norms during the early stages of training for successful training of models with sigmoid attention.
6. Techniques like using relative positional embeddings like ALiBi or a bias term proportional to the log of sequence length are crucial for stabilizing sigmoid attention.
7. LayerScale is found to be important for the performance of sigmoid attention in vision tasks, but less critical for language modeling.
8. The paper demonstrates that sigmoid attention with one attention head can match the performance of multi-head attention, reducing model complexity.
9. Overall, the paper establishes sigmoid attention as a viable alternative to softmax attention, providing theoretical guarantees, practical techniques for stabilization, and performance matching across diverse domains and scales."
Summary
Sigmoid Attention as an Alternative to Softmax Attention
The paper explores the use of sigmoid attention as a replacement for the standard softmax attention mechanism in transformer models. It provides a theoretical and empirical analysis of sigmoid attention, highlighting its properties as a universal function approximator and its improved regularity compared to softmax attention.
Theoretical Analysis
Theoretically, the paper proves that transformers with sigmoid attention are universal function approximators, able to approximate any continuous, permutation-equivariant sequence-to-sequence function to arbitrary precision. This maintains the strong representational capabilities of transformers even when replacing the softmax attention mechanism.
Regularity Analysis
The paper also provides an analysis of the regularity of sigmoid attention, computing its Lipschitz constant and showing that it has a much lower worst-case Jacobian bound compared to softmax attention. This implies sigmoid attention has better stability and robustness properties.
Empirical Challenges and Solutions
Empirically, the paper identifies a key challenge with sigmoid attention - the tendency for the initial attention norms to be large, which can lead to training instability. To address this, the paper proposes two solutions: 1) using a relative positional embedding like ALiBi to shift attention logit mass to the zero regime under sigmoid, and 2) initializing the attention logit bias b to a negative offset proportional to the sequence length. These techniques allow sigmoid attention to match the strong performance of softmax attention across language, vision, and speech domains. The paper also introduces F LASH S IGMOID, a hardware-aware and memory-efficient implementation of sigmoid attention that provides a 17% inference speed-up over the F LASH ATTENTION 2 softmax attention implementation on H100 GPUs. This highlights the computational benefits of sigmoid attention.
Overall, the paper provides a comprehensive analysis demonstrating that sigmoid attention is a viable alternative to softmax attention in transformers, matching performance while offering improved regularity and computational efficiency. It establishes best practices for successfully training models with sigmoid attention.
Reference: https://arxiv.org/abs/2409.044...