Positional LSH: Binary Block Matrix Approximation for Attention with Linear Biases
Positional encoding in transformers is commonly implemented through positional embeddings, attention masks, or bias terms, but formal connections between these mechanisms remain limited. We study attention with positional bias through the lens of locality-sensitive hashing (LSH), focusing on Attention with Linear Biases (ALiBi). We show that the ALiBi bias matrix is the expectation of contiguous block-diagonal binary masks induced by a ``positional LSH'' scheme. The empirical mean of masks sampled from this scheme yields spectral norm and max-norm approximation guarantees with bounded block sizes with high probability. This structural theorem implies a uniform approximation theorem for AL...
| Authors | Daniel Wolfson, Tal Wagner |
|---|---|
| Primary category | cs.LG |
| Published | 10 May 2026 |
| Last updated at source | 10 May 2026 |
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