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On the Role of Attention Masks and LayerNorm in Transformers (2405.18781v2)

Published 29 May 2024 in cs.LG and stat.ML

Abstract: Self-attention is the key mechanism of transformers, which are the essential building blocks of modern foundation models. Recent studies have shown that pure self-attention suffers from an increasing degree of rank collapse as depth increases, limiting model expressivity and further utilization of model depth. The existing literature on rank collapse, however, has mostly overlooked other critical components in transformers that may alleviate the rank collapse issue. In this paper, we provide a general analysis of rank collapse under self-attention, taking into account the effects of attention masks and layer normalization (LayerNorm). In particular, we find that although pure masked attention still suffers from exponential collapse to a rank one subspace, sparse or local masked attention can provably slow down the collapse rate. In the case of self-attention with LayerNorm, we first show that for certain classes of value matrices, collapse to a rank one subspace still happens exponentially. However, through construction of nontrivial counterexamples, we then establish that with proper choice of value matrices, a general class of sequences may not converge to a rank one subspace, and the self-attention dynamics with LayerNorm can simultaneously possess a rich set of equilibria with any possible rank between one and full. Our result refutes the previous hypothesis that LayerNorm plays no role in the rank collapse of self-attention and suggests that self-attention with LayerNorm constitutes a much more expressive, versatile nonlinear dynamical system than what was originally thought.

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Authors (5)
  1. Xinyi Wu (47 papers)
  2. Amir Ajorlou (11 papers)
  3. Yifei Wang (141 papers)
  4. Stefanie Jegelka (122 papers)
  5. Ali Jadbabaie (143 papers)
Citations (7)
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Summary

Analysis of Rank Collapse in Self-Attention Mechanisms with Attention Masks and LayerNorm

This academic paper investigates the phenomenon of rank collapse within transformer models, specifically focusing on the self-attention mechanism and the mitigating roles of attention masks and LayerNorm. The authors provide a thorough theoretical analysis supported by numerical experiments, which enriches the existing understanding of token dynamics in transformers.

Summary of Findings

The paper addresses two pivotal questions related to the rank collapse issue in self-attention layers. The central findings can be summarized as follows:

  1. Rank Collapse in Pure Self-Attention:
    • The analysis reveals that pure self-attention mechanisms inevitably lead to an exponential collapse into a rank one subspace, irrespective of various attention masks. This implies that as the depth of the transformer model increases, token representations become increasingly homogeneous.
    • This phenomenon is termed as rank collapse and is consistent across different attention schemes, such as causal masks, sliding windows, and sparse attention patterns.
  2. Effect of Attention Masks:
    • The paper shows that while all quasi-strongly connected attention masks lead to rank collapse, local or sparse attention mechanisms (like sliding windows) exhibit a slower rate of collapse compared to global attention mechanisms.
    • The authors suggest that this slower rate of collapse in local attention may have advantages in terms of model expressivity and practical applications.
  3. Role of LayerNorm:
    • The paper refutes the previously held hypothesis that LayerNorm does not affect rank collapse. Instead, it demonstrates that LayerNorm, combined with appropriately chosen value matrices, can prevent tokens from collapsing into a rank one subspace.
    • It is shown through nontrivial counterexamples that the self-attention dynamics with LayerNorm can possess a range of equilibria with ranks between one and full. This suggests a more expressive and versatile behavior of the system.
    • The presence of LayerNorm leads to configurations where token representations are anisotropic, aligning with empirical observations and enhancing the model's capacity to prevent rank collapse.

Implications

The theoretical results have several important implications for the design and utilization of transformer models:

  1. Practical Design of Transformer Models:
    • The insights regarding the effect of attention masks suggest that using local or sparse attention could be beneficial not only for computational efficiency but also for maintaining model expressivity.
    • The understanding that LayerNorm can prevent rank collapse emphasizes its critical role in the architecture, impacting how transformers should be constructed and optimized.
  2. Expressivity and Model Dynamics:
    • The finding that LayerNorm can maintain full-rank token representations without collapse shows the importance of normalization techniques in preserving model complexity and functionality, even as the depth increases.
  3. Future Research Directions:
    • The paper opens up new avenues for exploring how different types of attention masks and normalization strategies can be systematically designed to balance rank preservation and model expressivity.
    • Further empirical research is needed to fully understand how these findings translate to improvements in specific downstream tasks, such as language understanding and generation.

Concluding Remarks

This paper makes a significant contribution to the theoretical understanding of self-attention dynamics in transformers. By addressing the rank collapse issue through the lenses of attention masks and LayerNorm, it provides a more nuanced understanding of the mechanisms underlying token dynamics. The results highlight the importance of architectural components that are often taken for granted, suggesting that careful consideration of these elements is crucial for the development of more effective and expressive transformer-based models. Future research can build upon these findings to further enhance the performance and interpretability of AI models.

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