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About this paper
Petar Veličković, Christos Perivolaropoulos, Federico Barbero, Razvan Pascanu
Researchers at Google DeepMind and the University of Oxford formally prove that the softmax function, a core component of Transformer attention, inherently disperses its attention coefficients as the number of input items increases, which explains why these models struggle with "sharp" reasoning on larger, out-of-distribution inputs. They also propose an adaptive temperature mechanism that dynamically adjusts softmax behavior, demonstrating improved generalization on algorithmic reasoning tasks.
Key insights
- Softmax attention coefficients inherently disperse and decay as "Theta(1/n)" as the number of input items (n) increases, leading to an inability to maintain sharp focus.
- This inherent dispersion directly causes "reasoning failures" in tasks requiring sharp decisions (e.g., identifying specific high-valued items) when input size grows beyond the training distribution.
- Achieving sharpness in softmax-based attention requires large singular values of query/key matrices and large input vector norms, posing a tension with model stability and generalizability.
Summary by alphaXiv.
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