Quantifying Memory Use in Reinforcement Learning with Temporal Range
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917129315418112 |
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| author | Lafuente-Mercado, Rodney Rus, Daniela Rusch, T. Konstantin |
| author_facet | Lafuente-Mercado, Rodney Rus, Daniela Rusch, T. Konstantin |
| contents | How much does a trained RL policy actually use its past observations? We propose \emph{Temporal Range}, a model-agnostic metric that treats first-order sensitivities of multiple vector outputs across a temporal window to the input sequence as a temporal influence profile and summarizes it by the magnitude-weighted average lag. Temporal Range is computed via reverse-mode automatic differentiation from the Jacobian blocks $\partial y_s/\partial x_t\in\mathbb{R}^{c\times d}$ averaged over final timesteps $s\in\{t+1,\dots,T\}$ and is well-characterized in the linear setting by a small set of natural axioms. Across diagnostic and control tasks (POPGym; flicker/occlusion; Copy-$k$) and architectures (MLPs, RNNs, SSMs), Temporal Range (i) remains small in fully observed control, (ii) scales with the task's ground-truth lag in Copy-$k$, and (iii) aligns with the minimum history window required for near-optimal return as confirmed by window ablations. We also report Temporal Range for a compact Long Expressive Memory (LEM) policy trained on the task, using it as a proxy readout of task-level memory. Our axiomatic treatment draws on recent work on range measures, specialized here to temporal lag and extended to vector-valued outputs in the RL setting. Temporal Range thus offers a practical per-sequence readout of memory dependence for comparing agents and environments and for selecting the shortest sufficient context. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_06204 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantifying Memory Use in Reinforcement Learning with Temporal Range Lafuente-Mercado, Rodney Rus, Daniela Rusch, T. Konstantin Machine Learning Artificial Intelligence How much does a trained RL policy actually use its past observations? We propose \emph{Temporal Range}, a model-agnostic metric that treats first-order sensitivities of multiple vector outputs across a temporal window to the input sequence as a temporal influence profile and summarizes it by the magnitude-weighted average lag. Temporal Range is computed via reverse-mode automatic differentiation from the Jacobian blocks $\partial y_s/\partial x_t\in\mathbb{R}^{c\times d}$ averaged over final timesteps $s\in\{t+1,\dots,T\}$ and is well-characterized in the linear setting by a small set of natural axioms. Across diagnostic and control tasks (POPGym; flicker/occlusion; Copy-$k$) and architectures (MLPs, RNNs, SSMs), Temporal Range (i) remains small in fully observed control, (ii) scales with the task's ground-truth lag in Copy-$k$, and (iii) aligns with the minimum history window required for near-optimal return as confirmed by window ablations. We also report Temporal Range for a compact Long Expressive Memory (LEM) policy trained on the task, using it as a proxy readout of task-level memory. Our axiomatic treatment draws on recent work on range measures, specialized here to temporal lag and extended to vector-valued outputs in the RL setting. Temporal Range thus offers a practical per-sequence readout of memory dependence for comparing agents and environments and for selecting the shortest sufficient context. |
| title | Quantifying Memory Use in Reinforcement Learning with Temporal Range |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2512.06204 |