VC-pattern attention compression

Integrate this into a Transformer attention block immediately after computing query-key scores and before value aggregation. Start with one head, one threshold τ, and a random or uniformly spaced sample Y of m cached keys, such as m=32 or 64. Compute S_Y=QK_Y^T/√d, choose τ_q as the sampled r-th-largest score for each query or use a fixed percentile, and form b_q=1[S_Y(q,:)≥τ_q]. Hash each binary vector b_q and group equal hashes into buckets. For every bucket p, choose a representative query q_p, compute its full top-r or thresholded KV aggregation, then broadcast the result to all bucket members. In pseudocode: compute sampled scores; construct threshold masks; hash masks; build buckets; compute G_p for each representative; scatter G_p back to every query in bucket. Estimate the effective dimension from the observed number R of patterns using the smallest integer d_eff satisfying R≤1+m^d_eff; also transpose the sampled incidence matrix and compare query-side and key-side grouping costs using the paper's dual-family relation. A two-threshold version can encode coarse and high-confidence neighborhoods, while a learned gate mixes the bucket output with a cheap per-query local correction. The first experiment should use a 125M-parameter decoder-only Transformer on WikiText-103 or a small C4 subset, comparing dense attention and standard top-r sparse attention. Record unique bucket count, attention FLOPs, wall-clock latency, KV-cache memory, and perplexity. A positive result is at least 2x fewer expensive aggregations with less than 0.2 perplexity degradation, or lower memory at equal perplexity.