Adaptive Memory Decay for Log-Linear Attention

• URL: http://arxiv.org/abs/2605.06946v1
• Date: Thu, 07 May 2026 21:05:28 GMT
• Title: Adaptive Memory Decay for Log-Linear Attention
• Abstract summary: Sequence models face a fundamental tradeoff between memory capacity and computational efficiency.<n>Log-linear attention navigates this tradeoff by organizing memory across a Fenwick tree hierarchy.<n>We propose learning directly from the input via a lightweight two-layer, producing per-token, per-level decay that adapts to content rather than position.
• Score: 1.0099625992507715
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Sequence models face a fundamental tradeoff between memory capacity and computational efficiency. Transformers achieve expressive context modeling at quadratic cost, while linear attention and state-space models run in linear time by compressing context into a fixed-size hidden state, inherently limiting recall. Log-linear attention navigates this tradeoff by organizing memory across a Fenwick tree hierarchy, growing its hidden state logarithmically with sequence length at log-linear compute cost. However, its memory decay parameter λ is fixed and independent of the input, assigning uniform weights across all hierarchy levels regardless of the content, which introduces unnecessary rigidity. We propose learning λ directly from the input via a lightweight two-layer MLP, producing per-token, per-level decay that adapts to content rather than position. A softplus activation lets each Fenwick tree level scale independently, avoiding the inter-level competition that softmax introduces. This modification preserves log-linear complexity exactly and adds negligible parameter overhead. We evaluate on associative recall, selective copying, and language modeling, finding that input-dependent decay consistently outperforms the baseline, with the largest gains in long-range memory settings where baseline λ degrades or collapses entirely.

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