Adaptive Memory Decay for Log-Linear Attention
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866909025457668096 |
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| author | Amin, Yaxita Li, Helen Zichen Zhang, Mengfan Ayhan, Samet |
| author_facet | Amin, Yaxita Li, Helen Zichen Zhang, Mengfan Ayhan, Samet |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_06946 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Memory Decay for Log-Linear Attention Amin, Yaxita Li, Helen Zichen Zhang, Mengfan Ayhan, Samet Machine Learning Artificial Intelligence 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. |
| title | Adaptive Memory Decay for Log-Linear Attention |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.06946 |