Towards Analyzing Self-attention via Linear Neural Network
Primary Area: learning theory
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Keywords: transformers, linear neural networks, gradient flow analysis
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Abstract: Self-attention is a key component of the transformer architecture which has driven much of recent advances in AI. Theoretical analysis of self-attention has received significant attention and remains a work in progress. In this paper, we analyze gradient flow training of a simplified transformer model consisting of a single linear self-attention layer (thus it lacks softmax, MLP, and layer-normalization) with a single head on a histogram-like problem: the input is a sequence of characters from an alphabet and the output is the vector of counts of each letter in the input sequence. Our analysis goes via a reduction to 2-layer linear neural networks in which the input layer matrix is a diagonal matrix. We provide a complete analysis of gradient flow on these networks. Our reduction to linear neural networks involves one assumption which we empirically verify. Our analysis extends to various extensions of the histogram problem.
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Submission Number: 9108
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