Robot Wiki

RL Fine-Tuning of Policies

DPPO, ConRFT, Recap, pi_RL, residual RL, and HIL-SERL: closing the reliability gap with on-policy experience.

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Imitation learning gets a policy that is good on the demonstration distribution and brittle off it, because small per-step errors compound into states the demonstrator never visited Ross 2011. Physical Intelligence states the operational version of the same problem: it is relatively easy to get a VLA to succeed at a task some of the time, and quite hard to make it succeed reliably Amin 2025. Reinforcement learning is the only mechanism in the toolbox that learns from failure rather than only from success. The obstacle is cost: naive online RL on a multi-billion-parameter VLA, on real hardware, at control rates, is infeasible. Everything in this module is a way around that constraint, and by 2026 the field has converged on a small set of recipes that demonstrably work.

The scrubber below uses a fictional espresso episode to illustrate conditioning. Its timings, values and stage tags are toy choices, not measurements from Recap. Drag the slider to compare keeping high- and low-tag examples during training with asking for the high-conditioned policy at execution.

espresso episode, one failed attempt

Teaching toy, not a measured Recap episode: the 40 s timeline, 20 s arc, positive arbitrary values and stage-difference tags are illustrative. Real Recap uses reward-inclusive estimates, a task-dependent threshold and a failure penalty. Conditioning does not guarantee that low-tag behavior is eliminated.

failure blamed on the grasp, 20 s earlierReachGraspDose and tampInsert and lockOutcomeV(s)0 s10 s20 s30 s40 s

solid outline: value rises, high advantage. dashed outline: value falls, low advantage. the elapsed value trace is the heavier line from the left. trace shape is illustrative, after the Recap portafilter example.

Current segment: Reach: high advantage (+8.0)

  • Reach0-8 s+8.0high advantage

    The arm approaches the portafilter and pre-shapes the hand.

  • Grasp8-16 s-12.0low advantage

    In this toy, the portafilter is grasped at a bad angle and the arbitrary score falls. This is not evidence that a value function is the only possible signal.

  • Dose and tamp16-26 s+7.0high advantage

    Grounds are dosed and tamped. Locally competent, but the grasp angle has not been corrected.

  • Insert and lock26-36 s-21.0low advantage

    The misaligned portafilter will not seat. The failure is observed here, 20 s after the grasp that caused it.

  • Outcome36-40 s-2.0low advantage

    No extraction. The episode ends in failure and every transition keeps its advantage tag.

At t = 0.0 s this teaching toy shows an arbitrary value score of 30.0 in the Reach segment, tagged high advantage because its score changes by +8.0. The dashed arc links a fictional insertion failure at 32 s to a grasp 20 s earlier. The tinted stage blocks show these fictional stage tags. Its timings, values and stage-difference tags are illustrative, not a measured Recap episode or its reward-inclusive, task-thresholded advantage estimator.

Toy value along the fictional espresso episode
time (s)valuesegmentplayhead
030.0Reachplayhead
838.0Graspoff
1626.0Dose and tampoff
2633.0Insert and lockoff
3218.0Insert and lockoff
4010.0Outcomeoff
>2x
espresso throughput
Double espresso: on-robot RL vs offline RL + SFT; lab-reported
1-2.5 h
reported RL training
Nearly all HIL-SERL tasks; timing-belt assembly: 6 h
15-90 min
online fine-tune
ConRFT Table I; prose says 45-90. 96.3% mean, 8 tasks, 20 trials/task.
2026
pi_RL revision
v3, January 29; path/transition likelihoods

The flow-matching log-likelihood problem

Modern policies emit actions through diffusion or flow-matching heads, and that choice breaks the standard policy-gradient machinery. PPO-style updates need the log-likelihood of the action the policy actually took; for a flow-matching head the "action" is the endpoint of an ODE integration, and its likelihood under the model is intractable. For two years this was the standard argument for why RL could not touch the frontier VLAs directly. Three methods dissolve it in different ways Ren 2024 Chen 2025 Chen 2026.

DPPO (Ren et al., 2024) embeds the diffusion denoising process inside the environment MDP. Each policy action in this combined MDP is a denoising transition with an analytically evaluable Gaussian likelihood; the environment advances and supplies reward only after the final denoising step. PPO updates the denoising policy, not the environment dynamics. Environment-discounted advantages are multiplied by a separate denoising discount that downweights earlier, noisier steps. The value function depends on the environment state. The paper also fine-tunes only the last selected denoising steps, using a frozen original network for earlier steps and a trainable copy for the selected steps Ren 2024.

The v3 comparisons are specific to their benchmarks and protocols. DPPO is the strongest performer among the compared diffusion-based RL methods on the paper's state-input Robomimic tasks; the PPO comparisons also cover Gaussian and Gaussian-mixture policies with different network architectures. This is not a universal efficiency ranking: some Gym baselines are competitive, off-policy methods are more sample-efficient on HalfCheetah, and Appendix D reports slower wall-clock iterations than several baselines. The Gaussian baseline also slightly outperforms DPPO on the low-randomness Lamp task Ren 2024.

Its physical demonstration is zero-shot transfer of a simulation-trained One-leg assembly policy to a Franka Emika Panda, not on-robot RL fine-tuning. At 10 Hz, DPPO succeeds in 16 of 20 hardware trials. The simulation comparisons, this small physical evaluation, and wall-clock time per training iteration measure different things Ren 2024.

ConRFT (Chen et al., 2025) fine-tunes a consistency-policy action head while keeping the visual encoders and transformer backbone frozen. The main eight-task study uses Octo-small on a 7-DoF Franka Emika arm at 10 Hz. Offline Cal-ConRFT combines a consistency-based behavior cloning loss and a negative-Q actor loss with a Cal-QL critic, starting from 20-30 demonstrations per task. Online HIL-ConRFT keeps both actor losses, changes their weights, and uses a standard temporal-difference critic loss. Training batches sample equally from the demonstration and online replay buffers; human takeover transitions enter the demonstration buffer Chen 2025.

Do not confuse training noise levels with inference steps. Appendix B specifies 40 sub-intervals for the consistency policy's training noise grid. Its separate five-step setting describes the diffusion-policy baseline, not a measured ConRFT inference-call count Chen 2025.

In v2, Table I reports 96.3% mean success rate across eight tasks, with 20 trials per task. The listed online training times range from 15 to 90 minutes, with a reported mean of 48.8 minutes; the abstract and results prose instead state 45-90 minutes. Training time includes scripted motions, policy rollouts and onboard computation on an NVIDIA RTX A6000. The table's 144% is a rounded relative gain over the corresponding offline Cal-ConRFT mean of 39.4%, not a percentage-point gain. The separate SFT baseline happens to have the same reported mean Chen 2025.

Keep the intervention caveats with that comparison. The online learning curves can include successes produced by human takeovers, so they are not autonomous-policy success measurements. Table I's caption says all methods use human interventions, but Figure 3 and the PA-RL discussion explicitly describe PA-RL without them. These are the authors' task-specific results, not independent replication; the paper also warns about reward-classifier hacking and limited generalization Chen 2025.

pi_RL (Chen et al., 2026; v3) fine-tunes flow-based policies with online PPO. Flow-Noise learns Gaussian noise for denoising transitions jointly with the velocity network, then uses the joint likelihood of the denoising path. This is not an exact marginal likelihood for the final executed action. The noise network is discarded for deterministic inference. Flow-SDE uses Gaussian transition likelihoods in a two-layer denoising/environment MDP; its hybrid sampler makes one randomly chosen denoising step stochastic and leaves the others as deterministic ODE updates. The PPO objective is distinct from the conditional flow-matching regression used in supervised training Chen 2026.

The main experiments use pi0 and pi0.5. Appendix B.2 reports full-model supervised fine-tuning followed by a frozen VLM and a trainable 300M-parameter action expert, on eight NVIDIA H100 80GB GPUs. Appendix F separately compares PPO with GRPO and studies VLM LoRA; Appendix H evaluates PPO with Flow-SDE on GR00T N1.5. These are different evaluated configurations, not a universal best recipe Chen 2026.

The ID comparisons cover LIBERO, ManiSkill, MetaWorld and CALVIN. LIBERO reports 500 initial states per task suite; the CALVIN Scene D evaluation uses 1,000 five-subtask episodes. ManiSkill tests visual, semantic and execution shifts. Gains under distribution shifts do not consistently extend to the five unseen tasks in MetaWorld ML45, which trains on 45 tasks Chen 2026.

Two setup descriptions disagree within v3. Section 4.3.2 puts pi0.5's proprioceptive state into the VLM, whereas Appendix B.2 says its pi0.5 setting omits state. Appendix D.2 describes CALVIN ABC-to-D evaluation, but its results also say D-to-D training. Neither conflict establishes one unambiguous input or OOD training protocol Chen 2026.

RL training is simulated. A separate Real2Sim2Real case uses 20 motion-planner trajectories for supervised fine-tuning and 100 RL iterations, then transfers zero-shot to a physical Franka Panda with a RealSense D435 camera. Section E.2 reports 40% real-world success without stating an evaluation-trial denominator. This is a separate transfer test, not on-robot RL training or a general reliability guarantee Chen 2026.

Recap: advantage-conditioned policy learning

Amin 2025 Recap, the method behind π*0.6, combines demonstrations, expert teleoperation corrections during rollouts, and autonomous experience. The training sequence is offline-RL pre-training, demonstration fine-tuning for a task, then batch collection and retraining; it is not a continuously updated online policy.

The language-conditioned distributional value function predicts negative remaining steps for successful episodes and a large negative value for failures, with per-task normalization. For post-training, Appendix F estimates advantage using rewards over the next N = 50 steps plus the later value minus the current value. Pre-training uses a separate episode-return estimator. A task-dependent threshold turns the estimate into a binary indicator, and human corrections are explicitly assigned the positive indicator Amin 2025.

The text input “Advantage: positive” or “Advantage: negative” appears after the predicted subtask and before the actions. Both good and bad data can train the policy. The default evaluation uses the positive-conditioned policy; indicator dropout during training also permits conditional/unconditional classifier-free guidance. A raw increase in value is not the complete advantage estimator or its threshold rule Amin 2025.

Section III first recalls the exponential solution for a KL-regularized objective:

π^(ao)πref(ao)exp ⁣(Aπref(o,a)/βKL).\hat{\pi}(a \mid o) \propto \pi_{\mathrm{ref}}(a \mid o)\,\exp\!\left(A^{\pi_{\mathrm{ref}}}(o,a)/\beta_{\mathrm{KL}}\right).

Recap's practical binary-conditioning method is motivated by a related improvement-indicator construction, not by asserting that binarization exactly implements that exponential weighting. Equation 2 instead writes the improved policy as

π^(ao,)πref(ao,)(πref(aI,o,)πref(ao,))βCFG.\hat{\pi}(a \mid o,\ell) \propto \pi_{\mathrm{ref}}(a \mid o,\ell) \left(\frac{\pi_{\mathrm{ref}}(a \mid I,o,\ell)} {\pi_{\mathrm{ref}}(a \mid o,\ell)}\right)^{\beta_{\mathrm{CFG}}}.

At βCFG=1\beta_{\mathrm{CFG}}=1, this reduces to the indicator-conditioned policy. The distinct subscripts here separate the paper's two uses of β; they do not claim the two constructions are identical Amin 2025.

This avoids a PPO-style policy-extraction objective, not training gradients through the action expert. The actual objective combines discrete next-token prediction with a continuous flow-matching loss. Knowledge Insulation stops the action expert's gradient at the VLM-backbone interface; the action expert itself is trained Amin 2025 Physical Intelligence 2025.

The scrubber is a deterministic teaching example, not a recorded Recap episode or an implementation of its estimator. Its forty-second timeline, twenty-second credit-assignment arc, arbitrary positive values and stage-difference tags are chosen for illustration. Real Recap uses reward-inclusive estimates, task-dependent thresholds and a failure penalty. The execution view illustrates the requested conditioning, not a guarantee that every low-tag behavior disappears.

Recap's on-robot experience more than doubles successful completions per hour for double-shot espresso and the diverse-laundry evaluation, relative to offline RL plus task-specific demonstration fine-tuning. These are results on the report's static bimanual setup, with a button-up-shirt test rather than the full 11-item-type laundry training set Amin 2025. The pi-line evaluation details give the hardware, task protocols and time limits.

The paper qualifies its reliability claims: Section VI-C describes failure reduction as “about a factor of two,” while Figure 8 says “more than 2×.” Its “90%+” success summary excludes diverse laundry, and the box chart reports separate stages. This does not establish strictly greater than 90% end-to-end success for every application Amin 2025. See the task-by-task qualifications.

The companion blog separately says that espresso throughput and success rate more than doubled after adding on-robot experience. Its demonstration-video caption gives 5:30am to 11:30pm for making various espresso drinks, while the report's introduction says “13 hours straight.” These are different duration accounts; neither supplies a denominator for the quantitative double-espresso result, and they should not be merged into one continuous-run success statistic Amin 2025 Amin 2025.

These are Physical Intelligence's own reported results, not independent replication. The report describes human reward labeling, interventions and episode resets, and batch offline updates. Intervention use varies by task: the T-shirt/shorts improvement experiment uses autonomous evaluation data without expert corrections Amin 2025.

HIL-SERL: a human in the loop, RL on the robot

HIL-SERL (Luo et al., 2024) combines vision-based off-policy RL built on RLPD with demonstrations and human corrections. The learner samples equally from demonstration and online replay buffers. Intervention transitions enter both buffers; autonomous policy transitions enter only the RL buffer. Training typically starts with 20 to 30 demonstrations. Jenga whipping is an exception to online correction: it starts with 30 demonstrations and does not use real-time human takeovers Luo 2024.

Table 1a reports 100% observed success in 100 evaluation trials per task, except IKEA whole assembly, which uses 10 trials and allows at most two attempts per sub-policy. Training takes 1 to 2.5 hours for nearly all tasks, but timing-belt assembly takes 6 hours. The reported time includes scripted motion, policy rollouts, intended stops and onboard computation on one RTX 4090. Table 1a reports average success of 49.7% for the imitation baseline and 100% for HIL-SERL, about twice the success rate, and average cycle times of 9.6 versus 5.4 seconds, described as 1.8× faster. These averages compare against HG-DAgger with matched episodes and interventions, except for flat BC on Jenga whipping and object flipping, trained on 50 and 200 demonstrations respectively. The separate Table 1b comparison uses 200 demonstrations for DP, BC, IBRL, Residual RL and DAPG; that is not HIL-SERL's universal initialization Luo 2024.

The online learning curves can include human-assisted successes and are not the same measurement as Table 1a evaluation. A separate baseline inconsistency also remains: Table 1b gives DP 18% on dashboard assembly, while the prose says 28%; neither value is silently chosen as definitive Luo 2024.

Luo and colleagues did not test generalization in unstructured environments or perform extensive randomization, and they leave substantially longer-horizon tasks uncertain. The paper reports code availability, not a field-wide ranking or a fleet-scale staffing result. The RL for Robotics module covers the off-policy context Luo 2024.

Residual RL and distillation back into the generalist

PLD (Probe, Learn, Distill; Xiao et al., 2025) freezes a VLA while training task-specific residual actors with off-policy RL. A hybrid collection stage first rolls out the base policy, then lets a residual specialist recover from the states it reaches. The resulting trajectories fine-tune the generalist through SFT. Freezing the base during specialist training does not mean it stays frozen during distillation, or that residual exploration guarantees safety Xiao 2025.

Table 1 reports 99.2% average success for the model labelled OpenVLA, versus 91.8% for its baseline; pi0 reaches 97.2% versus 93.4%. These results cover LIBERO-Spatial, Object and Goal, ten tasks per suite, with 50 evaluation episodes per task, not every LIBERO task. On a separate four-task SimplerEnv suite, Table 2 reports Octo-SFT improving from 71.8% to 96.6% on average. The WidowX carrot task rises from 43.3% to 93.9%, a 50.6-percentage-point gain. The table's printed average delta is +24.9, although its displayed means differ by 24.8 points; neither is a benchmark-wide relative gain above 50% Xiao 2025.

The Franka experiment starts with 200 teleoperated trajectories. After RL data generation and distillation, PLD records 30/30 randomized trials each for cube pick-up and peg insertion; peg insertion also reaches 30/30 with the comparison data sources. Under changed clutter and object conditions, PLD records 28/30 for a blue cube and 20/30 for a red cube. These finite trial results do not imply perfect reliability across tasks Xiao 2025.

The abstract's 100% real-robot headline needs a further qualification for YAM. The detailed experiment describes four GPU insertion/removal stages, at most eight hours of training per subtask, and distillation into one BC policy. It reports at least one hour of continuous operation with recovery, while explicitly stating that per-stage one-shot success is not 100%. Human setup is not absent: the Franka peg experiment uses human hole repositioning. These results support a bounded data-generation recipe, not universal self-improvement or a safety guarantee Xiao 2025.

RLDG (Xu et al., 2024) uses task-specific RL policies to generate data for fine-tuning generalists, rather than applying RL updates directly to the generalist. The paper implements its specialists with HIL-SERL and evaluates fine-tuned OpenVLA and Octo. Its comparisons match the task setup, training configuration, observation and action spaces, and number of successful training episodes, changing the data source. In the FMB single-object assembly experiment, RL supplies the insertion-stage data while human demonstrations still supply grasping and transport. OpenVLA succeeds in 20/20 trials with this mixed dataset versus 12/20 with human demonstrations: 100% versus 60%, a 40-percentage-point gain, not a 40% relative increase Xu 2024.

Xu and colleagues' FMB-insertion ablation relabels human-data actions with an RL policy. Its results suggest that both action quality and state distribution contribute, with action quality accounting for most of the benefit; they do not establish that recovery-state coverage is always the cause. The method still requires task rewards, and the authors report that speed-optimized RL data can produce premature object drops after distillation Xu 2024.

The paper's OpenVLA setup commands actions at 4 Hz; data collection, RL and Octo use 10 Hz. The separate low-level impedance controller runs at 1 kHz. These are setup-specific rates, not a cross-model throughput ranking Xu 2024.

The six methods side by side

Six RL fine-tuning methods, with results reported by their own sources under different protocols, not a leaderboard. Evidence labels describe the inspected publication type, not independent replication. Code marks a source's code-release statement, not verified weights or licensing; not disclosed is limited to the named sources in that row.
MechanismHeadline resultOpenness
DPPO2024PPO over Gaussian denoising transitions in a two-layer MDP; separate environment and denoising discounts; selected final denoising steps can be fine-tunedPaper-specific Robomimic comparisons; zero-shot One-leg hardware transfer: 16/20 trials at 10 Hz. Not a universal sample-efficiency or wall-clock winnerpreprint
codeDPPO v3 announces a website with code; repository contents, weights and license terms were not inspected.
HIL-SERL2024RLPD with demonstration and online buffers plus human corrections; Jenga whipping uses demonstrations without online correctionsTable 1a: 100% observed success (100 trials/task; IKEA whole assembly 10 trials); 1-2.5 h for nearly all tasks, 6 h for timing belt. Imitation comparison: 49.7% vs 100%, 9.6 s vs 5.4 spreprint
codeThe retained HIL-SERL body points to accompanying videos and code; its body revision, repository contents, weights and license terms are not independently established here.
ConRFT2025Frozen Octo-small encoders/backbone; consistency action head with BC and Q objectives offline and online, plus human takeoversTable I: 96.3% mean on 8 Franka tasks, 20 trials/task; 15-90 min online (prose says 45-90); rounded 144% relative gain over offline Cal-ConRFTpreprint
codeConRFT v2 states that videos and code are available on its project site; weights and license terms are not established by the inspected paper.
Recap (pi*0.6)2025Negative remaining-step values with a failure penalty; reward-inclusive advantage is thresholded into a conditioning token. Supervised-style extraction still trains the action expertDouble-espresso throughput >2x versus offline RL + SFT; the paper’s 90%+ summary excludes diverse laundry, and its box chart reports subtask successvendor-reported
not disclosedInspected Physical Intelligence report, companion blog and model card: checkpoint availability and model-specific license terms are not established. This is not a claim that the model is closed.
Residual RL (PLD)2025Frozen VLA prior, off-policy residual specialists, hybrid recovery-data collection, then SFT of the generalistOpenVLA-labelled model: 99.2% across 3 LIBERO suites, 50 trials/task; Octo: 96.6% across 4 Simpler tasks; Franka: 30/30 on each of 2 tasks; YAM: at least 1 h with recovery, not 100% one-shot successpreprint
not disclosedThe inspected PLD v1 preprint does not establish a PLD code or weight release; mentions of open-source code refer to baseline models, not PLD release terms.
pi_RL2026Online PPO: Flow-Noise uses learned Gaussian transition noise and joint denoising-path likelihood; Flow-SDE uses transition likelihoods in a two-layer MDPID gains for pi0/pi0.5 across four simulation benchmarks; OOD gains do not consistently extend to unseen MetaWorld tasks. Separate Franka transfer test; paper-reported code release, not a weight/license claimpreprint
codeThe printed pi_RL v3 paper states a code release; a particular downloadable weight checkpoint and its license are not established.

Read these as source-specific reports, not a cross-paper ranking. Recap's results are the lab's own reports on its own hardware, not independent replication. Publication type alone does not establish independent verification.

DPPO, ConRFT, HIL-SERL and pi_RL state that code is available. Those statements do not verify repository contents, particular downloadable weight checkpoints or license terms. The inspected PLD preprint does not establish a code or weight release. Recap's inspected report, blog and model card do not establish model-specific checkpoint availability or licensing; this is not a claim that the model is closed. The openness notes keep those source scopes with each row Ren 2024 Chen 2025 Luo 2024 Chen 2026 Amin 2025 Amin 2025 Physical Intelligence 2025 Xiao 2025.

What RL actually buys, and the caveats

Liu et al.'s NeurIPS 2025 study reports that PPO beat the tested DPO/TPO and GRPO implementations in its OpenVLA pick-and-place setup, where preferences and returns came from sparse task rewards. The authors summarize the main OOD comparison with supervised fine-tuning as stronger semantic and execution generalization, with comparable visual robustness; this is not a test of arbitrary new-task generalization. The inspected January 2026 v4 appendix also includes a preliminary sim-to-real trial and an articulated-object task, despite the main text's narrower limitation statement. Its results are not uniform: SFT wins on the articulated-task visual average and rephrased instructions, and on the action-chunking multi-receptacle test Liu 2025.

Peng et al.'s PAIR-VLA study addresses a related limitation rather than showing that RL newly creates visual fragility. In simulated ManiSkill3 pick-and-place experiments with OpenVLA and π0.5, it adds paired-view invariance and sensitivity objectives to PPO: preserve action distributions for task-preserving changes and separate them for target-pose changes. The authors argue that task rewards alone give limited guidance about this distinction and report improved OOD success over standard PPO under the tested visual shifts. The sensitivity-only ablation loses to PPO on target-pose success; the separate camera-view experiment, using a different task-preserving view construction, also trails PPO slightly in-distribution despite its OOD gains. That comparison does not isolate reward design as the cause of a pre-to-post-RL loss of robustness; its task-preserving views also rely on simulator object masks, and real-world transfer remains untested Peng 2026.

How to read these numbers

Most RL fine-tuning results live on simulated benchmarks (LIBERO, SimplerEnv) or a handful of real tasks, so cross-paper comparisons are unreliable. Reward specification is unsolved: nearly every method uses a hand-written success detector or a VLM-based one, which is itself a reward-hacking surface. Recap's results are vendor-reported; the inspected report, blog and model card do not establish model-specific weight-release or license terms. Treat the table above as a map of mechanisms, not a leaderboard.

See also

  • The Pi Line

    pi0 to pi0.7: flow-matching action experts, FAST tokenization, open-world generalization, and source-scoped checkpoint availability.

  • Behavior Cloning Foundations

    Covariate shift and compounding error: why naive imitation breaks in closed loop, with DAgger as the standard fix.

  • The Evaluation Crisis

    Why N-of-10 trials and unreported variance mislead: 95% per-step success is unusable at 30 steps.

  • RL for Robotics

    Sample efficiency decides which reinforcement learning algorithms a robot can actually be trained with, from PPO in simulation to offline learning on a fixed dataset.

Linked from

  • Behavior Cloning Foundations

    Covariate shift and compounding error: why naive imitation breaks in closed loop, with DAgger as the standard fix.

  • RL for Robotics

    Sample efficiency decides which reinforcement learning algorithms a robot can actually be trained with, from PPO in simulation to offline learning on a fixed dataset.

  • Offline Reinforcement Learning for Robotics

    CQL, IQL, TD3+BC and Q-Transformer under the support constraint, with a decision rule for when behavior cloning is the stronger baseline.

  • The Evaluation Crisis

    Why N-of-10 trials and unreported variance mislead: 95% per-step success is unusable at 30 steps.

  • The Reliability Gap

    80% is a demo, 99.9% is a product: what deployment numbers actually show.

  • Competing Theses

    End-to-end scaling versus hierarchy versus world models versus RL fine-tuning, with falsification criteria.

References

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    https://arxiv.org/abs/1011.0686

  2. Allen Z. Ren, Justin Lidard, Lars L. Ankile, Anthony Simeonov, Pulkit Agrawal, Anirudha Majumdar, Benjamin Burchfiel, Hongkai Dai, and 1 more, 2024.

    https://arxiv.org/abs/2409.00588

  3. Yuhui Chen, Shuai Tian, Shugao Liu, Yingting Zhou, Haoran Li, Dongbin Zhao, 2025.

    https://arxiv.org/abs/2502.05450

  4. Kang Chen, Zhihao Liu, Tonghe Zhang, Zhen Guo, Si Xu, Hao Lin, Hongzhi Zang, Xiang Li, and 8 more, 2026.

    https://arxiv.org/abs/2510.25889

  5. Ali Amin, Raichelle Aniceto, Ashwin Balakrishna, Kevin Black, Ken Conley, Grace Connors, James Darpinian, Karan Dhabalia, and 47 more, 2025.

    https://www.pi.website/download/pistar06.pdf

  6. Ali Amin, Raichelle Aniceto, Ashwin Balakrishna, Kevin Black, Ken Conley, Grace Connors, James Darpinian, Karan Dhabalia, and 47 more, 2025.

    https://www.pi.website/blog/pistar06

  7. Physical Intelligence, 2025.

    https://website.pi-asset.com/pi06star/PI06_model_card.pdf

  8. Jianlan Luo, Charles Xu, Jeffrey Wu, Sergey Levine, 2024.

    https://arxiv.org/abs/2410.21845

  9. Wenli Xiao, Haotian Lin, Andy Peng, Haoru Xue, Tairan He, Yuqi Xie, Fengyuan Hu, Jimmy Wu, and 4 more, 2025.

    https://arxiv.org/abs/2511.00091

  10. Charles Xu, Qiyang Li, Jianlan Luo, Sergey Levine, 2024.

    https://arxiv.org/abs/2412.09858

  11. Jijia Liu, Feng Gao, Bingwen Wei, Xinlei Chen, Qingmin Liao, Yi Wu, Chao Yu, Yu Wang, NeurIPS 2025.

    https://arxiv.org/abs/2505.19789

  12. Yuanfang Peng, Jingjing Fu, Chuheng Zhang, Li Zhao, Jiang Bian, Mingyu Liu, Ling Zhang, Jun Zhang, and 1 more, 2026.

    https://arxiv.org/abs/2605.13105

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