Where is Physical RSI capability from? An Observational Scaling Law of LLM-as-policy
Zekai Li, Jiayi Yu, Jinlu Zhang, Luyang Niu, Zekun Qi, Jun Zheng, Xuchuan Chen, Dairu Liu, Yintianrun Zhang, He Wang, Li Yi
cs.RO, cs.AI, cs.CV
2026-10-20
Six VLMs revise frozen-weight workspaces on 18 arm tasks. Astra solves 15 and leads all five axes; code-stronger GPT-5.6 Sol solves 1.
Frontier VLMs already write robot actions and, across trials, edit skills, code, and tools while the weights stay frozen. Galbot calls that loop physical RSI: recursive self-improvement from physical feedback, stored in a workspace rather than in new parameters.
An endpoint score does not say whether a strong first try and a recovery after failure draw on the same capabilities. It also hides when the gain arrives and how much physical interaction it spends. A rising score cannot separate notes glued to the practice table from a procedure that still works on a new layout or a new task.
Most embodied coding evals report one success rate per episode or inside a time budget. Extra attempts raise the chance of stumbling into a win. A previously reported Astra trace made the gap concrete: a self-written fix worked once and failed on the next run. Similar public averages can still hide very different improvement curves.
PhysRSI-eval freezes the weights and allows edits only inside a persistent workspace. Each of the six main systems is a model plus its runtime setup: GPT-6 Astra, GPT-6.1 Sol, GPT-6 Sol, GPT-5.6 Sol, Claude Opus 5.5, and Claude Sonnet 5.5. Gemini 4 is a side run on 10 tasks and stays out of the main table.
The suite is 18 RoboDojo dual-arm tasks: arrangement, stacking, container placement, insertion, pouring, pushing, and dynamic picking, covering the official Precision, Long-Horizon, Memory, Open, and Generalization categories. Difficulty strata were locked before the study from official success rates, three tasks each, from D1 (60–68.7%) to D6 (0–0.4%). The main run uses layout 0 and seed 0. Native scores lie in [0, 1], with step limits of 300 to 1300 at 25 Hz.
K0 has no persistent workspace: three tries per task, averaged, as the starting point. Rounds K1 through K17 are the self-improvement segment. The Harness workspace starts nearly empty, with only the host's read-only tools. Each round is one judged physical attempt; the agent then revises with robot actions disabled, and stops at the first native success or at round 17. Reasoning is capped at 4200 seconds a round. Revision time is up to 1800 seconds for GPT systems and 600 seconds for Claude systems. The step from K0 to K1 also changes the interface, so the improvement curve is read on the Harness rounds.
Five axes pull the endpoint apart. A1 is the K0 mean. A2 divides the average lift from K1 to K16, relative to the start, by the net gain at the end. Curves are not replaced by their running best. A3 averages the scores from τ90 onward, the first round at or above the start plus 90% of peak gain. A4, only on solved tasks, measures physical budget saved. A5 is the share of tasks failed at K1 that later succeed inside the budget.
Seventeen public benchmarks collapse into Spatial, Perception, Coding, and Harness ranks. Observational scaling asks two predictive questions: whether the other systems' capability profiles rank a held-out system on both how far it improves and how early, and whether a reference curve, calibrated on the first few rounds, forecasts the rest. Clearing history, freezing the workspace on unseen layouts, and moving it onto another task ask what the saved files are still worth off the practice scene.
On the 18 tasks the six systems solve 15, 12, 7, 1, 13, and 11, in the order Astra, GPT-6.1 Sol, GPT-6 Sol, GPT-5.6 Sol, Opus, and Sonnet.
| System | A1 start | A2 timing | A3 late score | A4 budget saved | A5 recovery | Solved |
| GPT-6 Astra | 0.3676 | 0.8594 | 0.8509 | 0.8429 | 0.7500 | 15/18 |
| GPT-6.1 Sol | 0.2843 | 0.8224 | 0.7028 | 0.8081 | 0.5714 | 12/18 |
| Claude Opus 5.5 | 0.1769 | 0.6091 | 0.7444 | 0.5794 | 0.6875 | 13/18 |
| Claude Sonnet 5.5 | 0.1241 | 0.6946 | 0.7006 | 0.6984 | 0.5625 | 11/18 |
| GPT-6 Sol | 0.0306 | 0.4658 | 0.4722 | 0.3718 | 0.3889 | 7/18 |
| GPT-5.6 Sol | 0.0120 | 0.2247 | 0.1037 | 0.3013 | 0.0556 | 1/18 |
Opus posts an A3 of 0.744 against 0.703 for GPT-6.1 Sol, with A2 at 0.609 versus 0.822 and A4 at 0.579 versus 0.808. The higher late score shows up later and saves less of the physical budget.
Rank correlations on the six systems split by axis. Spatial reasoning tracks A1 at ρ = 0.94 and A2/A4 at 0.83. Perception tracks A3 and A5 at ρ = 0.94. Coding stays at or below 0.37 on every axis. GPT-5.6 Sol beats Astra on LiveBench code generation and completion and still solves 1 task against Astra's 15. Across the four GPT systems, the mean of 17 public benchmarks spans 54.1 to 78.1, while the equal-weight five-axis mean spans 13.9 to 73.4, ranges of 24 points and 59.5 points. GPT-5.6 Sol stays near zero cumulative success for about 16 rounds.
Ranking systems by the equal-weight average of the four capability profiles reproduces the observed order of the best mean score by K17. T50 is the first round at which that best mean reaches half the gain from K1 to K17. A kernel regressor fit on the other four systems gets every pairwise T50 order right. τ90, the round where gain first hits 90% of its peak, is K9 for Astra, K7 for GPT-6.1 Sol, K15 for Opus, K13 for Sonnet, and K17 for both GPT-6 Sol and GPT-5.6 Sol.
A Weibull template fit to Astra's K1–K17 mean, with start, plateau, and speed set only from GPT-6.1 Sol's first five rounds, forecasts the rest of the way to K17 at a mean absolute error of 0.019. Holding the last observed score yields 0.112.
The history ablation is Astra only: six tasks, two chains each, a new layout every round, and runs that continue after success. Over K4–K6, success is 15/36 (41.7%) with the full loop, 3/36 (8.3%) with no history, 5/36 (13.9%) without grader feedback, and 12/36 (33.3%) without earlier images. Workspace plus grader feedback alone reaches 17/36 (47.2%), slightly above the full loop. Images and action logs add little once those two channels remain.
Workspaces frozen after K6, with revision turned off, go to unseen layouts. Files alone succeed in 25 of 60 trials (41.7%) across 12 sources. Adding the raw records gives 23/60 (38.3%). Workspaces trained on a fixed layout reach 27/60 (45.0%) on held-out layouts, against a reported 14/16 (88%) on their own layout. The denominators differ, so this is not a paired comparison. Three cross-task initializations move first success earlier: Sonnet on Cover Blocks from K9 to K1, Opus on Organize Table from K14 to K7, and Opus on Deposit Coin from K15 to K8.
Choosing a robot policy from a public average, or from a coding leaderboard, mis-orders physical self-improvement. GPT-5.6 Sol leads Astra on LiveBench code and solves 1 of 18 tasks. Astra solves 15 and leads every axis. When the physical interaction budget is the scarce resource, Opus is the case a solved-count misses: a higher late score than GPT-6.1 Sol, later gains, and less budget saved.
Inside a model family, five early rounds plus a borrowed curve cut later error from 0.112 to 0.019, so every candidate does not need the full 17 rounds. Removing history drops late-round success from 41.7% to 8.3%. More tries at the same task do not explain the rise. Frozen files still succeed on 41.7% of trials in new layouts, so scene-specific gains and transferable files show up together.
This is a measurement result, further along than any new training recipe. Against a single final success rate, the five axes and the interventions are a real step. They do not show how to turn one success into a policy that repeats.
The main comparison is six model-plus-config systems, one improvement chain per task. Three K0 repeats do not estimate the variance of a full chain. Stopping at the first success records a single success. Reliable re-execution needs another test. A4 and A5 average over task sets that change with the system, so cross-model comparisons do not share a denominator. Without the supplementary hints Astra solves 13 tasks; the main run solves 15.
A ρ of 0.94 is a rank correlation on six points. The barrel claim is a candidate bottleneck, not a causal finding. The public benchmarks were also collected under different protocols. Revision limits are unequal, 1800 seconds for GPT systems and 600 for Claude, so model skill and scaffold travel together inside each system.
The ablation and the frozen-workspace tests cover Astra and six tasks. The cross-task speedups are three first-run cases, not repeats. Gemini 4 uses another 10 tasks through K20, solves 6, and posts means of 0.050 at K0 and 0.48 at K10, so it does not line up with the 18-task table. The barrel hypothesis and the perfect T50 ordering are still observations waiting on a direct test.