popcountmem

the question

Are Log-Linear Attention's addressable memory slots at query t exactly log(t) as the paper implies, and is its recency bias absolute?

what came out

Slots at t are exactly popcount(t), not the floor(log2 t)+1 bound. Each slot is a rank-d state resolving tokens only up to bucket size d, and the newest token's fidelity collapses to the linear-attention floor at every multiple of the smallest power of two above d. Within-query recency ordering holds; the absolute claim fails.

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