Physical Time as a Missing Dimension of Robot Policy Memory Dynamics

Memory-dependent robotic manipulation requires policies to use information that is no longer available in the current observation. Retaining history alone is insufficient: memory must preserve information that supports future actions. One challenge is whether a memory-free foundation model can learn to retain and use historical information from action demonstrations alone, without external memory support. We introduce T$^2$Mem, a framework that develops this capability within a pretrained vision-language-action policy, without external reasoning models or memory-specific annotations. T$^2$Mem uses test-time training to encode observation history into compact fast weights through online self-supervised updates, avoiding repeated processing of the full history. An observation-grounded interface extracts vision-language information for memory formation and supplies retrieved context to the action expert. Action supervision shapes what the memory learns to retain and use, while alternating memory-policy learning gives each component a fixed counterpart during optimization. Across 16 RoboMME tasks, T$^2$Mem improves average success from 17.93% to 56.83% over the memory-free base policy and outperforms the recurrent-memory methods reported in the benchmark, while controlled profiling indicates at least 3x inference speedup over explicit methods. Project website: https://yzliu84.github.io/T2MEM-project/

Memory is essential for long-horizon robotic manipulation, where successful actions may depend on past events that are no longer recoverable from the current observation. As episodes grow longer, however, retaining the full history becomes increasingly costly, creating a fundamental scalability challenge for memory-augmented policies. Existing approaches address this challenge by either storing selected past observations in a bounded memory bank or compressing interaction history into a fixed-size parametric state through Test-Time Training (TTT). Yet these formulations do not explicitly distinguish between historical information that can already be recovered from the policy's current context and information that must persist beyond it. We introduce TTT-RM, which repurposes TTT as Residual Memory, using fast weights not to generically compress history but to complement a bounded memory bank by preserving task-relevant historical information that cannot be recovered from the policy's current context. Concretely, TTT-RM learns a history decoder that reconstructs historical representations from the current observation and retrieved memory. The resulting reconstruction residual captures what this context fails to explain and serves as the learning target for TTT. The TTT slow weights are optimized against this residual target so that online fast-weight updates learn to encode complementary historical information over time. The fast-weight state is then queried to produce a residual memory representation that conditions action generation. Extensive experiments on memory-intensive simulation benchmarks and real-world tasks show that TTT-RM consistently improves across multiple memory designs, outperforms diverse baselines, and supports sustained execution on a three-minute, eight-stage stowing task.

Robot policies often convert sensing and control into fixed-rate observation-action sequences, leaving physical time implicit in sequence position. This assumption breaks when observation rates or delays vary, or when inference latency changes. We introduce Chronos Policy, which makes physical time explicit by conditioning on observation capture times and desired action execution times. We study two ways to incorporate time into a diffusion transformer: adding timestamp embeddings to token features, or encoding physical time in positional encoding through time-aware rotary positional encodings (time-aware RoPE). We find that time-aware RoPE is more robust, allowing attention to depend directly on physical time while keeping token content unchanged. During training, we temporally randomize which observations are sampled and when the action chunk begins, exposing the policy to a wider range of sensing and execution schedules that may occur during deployments. This also enables learning from asynchronous, multi-rate data without forcing all measurements onto a fixed temporal grid. Across simulation and real-world experiments, Chronos Policy improves performance on dynamic tasks, where observation-to-action timing is critical, and on multisensory tasks, where the relative timing between observations matters. On standard quasi-static tasks, it preserves nominal performance while improving robustness to changes in sensing and inference timing.