{"id":"fd3eac59-425a-4b0b-b111-233c80a00e4c","arxiv_id":"2504.16738","paper_version":3,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"MOSAIC is a multi-directional skill-centric planner that seeds feasible local trajectories with generator skills, links them with connector skills, and uses a statistical oracle and physics simulation to guide the search.","lead":"This paper introduces MOSAIC, a planner that composes robot skills by generating local motion snippets and linking them with connector motions, guided by skill-success estimates from physics simulation. It offers a route for robots to solve long, multi-step manipulation tasks by chaining imperfect pre-trained skills rather than retraining end-to-end policies.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section IV-C's probabilistic-completeness proof does not follow from the oracle's random sampling: continuous parameter spaces and nearest-neighbor-only node-pair selection preclude exhaustive coverage.","rationale":"The reader's weakest assumption was simulator fidelity for real-world transfer. That is a genuine risk, but the more load-bearing gap is the probabilistic-completeness proof in Section IV-C: the paper presents PC as a formal contribution, and the supplied argument does not establish it even under the paper's own deterministic-trajectory assumption. The issue is not merely a missing epsilon-delta detail; the oracle's nearest-neighbor connection strategy can systematically avoid the exact node pair needed for a feasible solution, and continuous parameter sampling cannot hit exact parameter values. This means the claimed theoretical foundation is not currently supported. The reader already flagged the PC claim as 'only sketched' in the rationale, which is why I mark agreement as partial rather than full. The empirical central claim may still hold, and the reader's conditional verdict is appropriate: the paper should either provide a rigorous PC proof with explicit coverage assumptions and all-pair connection attempts, or explicitly weaken the theoretical claim. Since the verdict already conditions on such unresolved issues, I do not recommend changing it. If the PC claim is later removed or proven under restrictive assumptions, the practical contribution could still be valuable, but 'outperforms' claims rest on the limited experimental reporting and the qualitative real-world validation noted by the reader.","tokens_in":15143,"tokens_out":5800,"duration_ms":59201,"concrete_test":"Construct a minimal counterexample with a one-dimensional state space: two generator nodes A and B whose trajectories are valid, and a connector skill that succeeds only for the pair (A,B) but fails on all nearest-neighbor pairs. Instrument Algorithm 1 with the described oracle modes and run it for a large number of iterations, recording which node pairs are attempted. If the pair (A,B) is never selected, PC as stated is false. In parallel, attempt to re-derive PC under explicit assumptions: compact parameter spaces with absolutely continuous distributions, a positive-clearance condition on feasible solutions, and an oracle that eventually attempts every node pair. If the proof cannot be completed without all-pair connector attempts, the completeness claim should be downgraded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central theoretical claim is probabilistic completeness (PC) in Section IV-C. The proof argues that because the oracle assigns non-zero probability to selecting any skill and samples parameters randomly, 'given infinite time, all possible skill combinations and parameter configurations will be explored.' This does not hold as stated. First, skill parameter spaces are continuous: object poses, seeds in ranges, and diffusion-policy inputs are drawn from continuous distributions. A random sample from a continuous distribution has probability zero of hitting a specified exact parameter value, so 'all parameter configurations' cannot be enumerated by random sampling. Standard PC arguments in continuous spaces require explicit dense-sampling and clearance assumptions; none are given. Second, even ignoring parameter coverage, condition (2) requires attempting to connect every disconnected node with every connector skill and parameter. The oracle's node-pair selection (Appendix S-A2) selects a random node and its nearest neighbor, or start/goal-biased nearest neighbors, and it penalizes pairs with failed attempts. It never systematically attempts arbitrary node pairs. A feasible solution that requires connecting two nodes that are not nearest neighbors can therefore be missed forever, directly contradicting Definition 4. The proof conflates 'non-zero probability of selecting a skill' with 'coverage of all skill-parameter and node-pair configurations.' In uncountable spaces and under a nearest-neighbor graph, those are different. The PC claim is accordingly unsupported; if the intended statement is heuristic or practical completeness, the paper should say so explicitly.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes MOSAIC, a multi-directional, skill-centric planning algorithm for long-horizon manipulation. It constructs a graph whose nodes are generated skill trajectories and whose edges are connector-skill trajectories, using an oracle to choose skills, sample parameters, and select node pairs to connect, with physics simulation used to evaluate skill outcomes. The paper claims probabilistic completeness for the framework and reports experiments on three tabletop manipulation scenarios in simulation and on a real UR10e, claiming superior performance over skill-chaining, CEM, and roadmap-based baselines.","tokens_in":15378,"tokens_out":4283,"duration_ms":42817,"significance":"The core idea of focusing planning on 'islands of competence' and using physics simulation to prune infeasible skill compositions is a plausible and practically useful contribution to skill-based manipulation planning. If the claims are substantiated, the framework would offer a way to plan with imperfect learned skills without hand-coded symbolic preconditions and effects. The paper also provides detailed descriptions of the oracle, skill library, and experimental setups. However, the formal probabilistic-completeness proof is not valid as written, and the real-world validation is only qualitative, so the strongest theoretical and empirical claims outrun the evidence.","major_comments":[{"comment":"The proof that MOSAIC is probabilistically complete is not correct. Condition (1) requires invoking every generator with 'every parameter configuration' and condition (2) requires attempting to connect 'every disconnected node' with every connector and parameter. The oracle samples parameters from continuous distributions (e.g., object poses and diffusion seeds), so any particular exact parameter configuration has probability zero of being sampled; 'all parameter configurations' cannot be covered by random sampling without additional dense-sampling and clearance assumptions, which are not stated. More importantly, the oracle's node-pair selection in Appendix S-A2 only connects a node to its nearest neighbor (or to start/goal-biased nearest neighbors) and never systematically attempts arbitrary disconnected node pairs. A feasible solution whose intermediate trajectory segments correspond to two nodes that are not nearest neighbors can therefore be missed forever, directly contradicting condition (2). The assertion that nonzero selection probabilities guarantee eventual exploration of all skill/parameter and node-pair configurations conflates 'nonzero probability of selecting a skill' with 'coverage of uncountable configuration spaces and arbitrary node pairs.' I recommend either providing a rigorous proof under explicit dense-sampling and node-pair coverage assumptions or replacing the probabilistic-completeness claim with a weaker, precisely stated completeness or consistency guarantee that actually follows from the algorithm.","section":"IV-C (Definition 4 and proof sketch)"},{"comment":"The abstract and contributions state that MOSAIC demonstrates efficacy 'in both simulation and the real world,' but the real-world evidence in Section V-D consists solely of the sentence 'Our hardware validation tests (Fig. 2) trended similarly; View videos in our supplementary materials.' No quantitative hardware results are reported: no number of trials, success/failure counts, execution times, or failure analysis. Because real-world performance is explicitly claimed as part of the contribution, either report the hardware results in a quantitative form or revise the claim to a qualitative validation.","section":"V-D (real-world validation)"}],"minor_comments":[{"comment":"The contribution statement claims that MOSAIC 'outperforms existing methods in performance, generalization, and scalability,' but the experiments do not directly measure generalization (e.g., novel object poses or unseen clutter configurations) or scalability (e.g., increasing number of objects or skills). Consider adding explicit tests or qualifying the claim.","section":"V-D / Fig. 3"},{"comment":"The informal description says the oracle 'restricts the available skills to be only the connector skills if there are fewer nodes than vertices in the mosaic graph.' Since the text defines V(E) as the number of edges, this likely should read 'fewer edges than nodes'; as written the sentence is confusing.","section":"Appendix S-A2 (Oracle node-pair selection)"},{"comment":"The Cross-Entropy Method baseline is described as evaluating skill-parameter sequences 'based on task progress' and selecting top candidates, but the precise progress/score function used for ranking is not specified. This makes the comparison difficult to reproduce and interpret.","section":"V-C (CEM baseline)"},{"comment":"The definition of Π* as 'the set of all feasible solutions' is informal; in a rigorous probabilistic-completeness statement the solution set should be defined precisely, particularly whether it is finite or infinite and how 'discovered' trajectories at iteration k are measured.","section":"IV-C (Definition 4)"},{"comment":"The values and initialization of the oracle parameters α, p_lb, p_up, p_s, p_g, and p_{s-g} are not reported. Please state whether these were fixed across all scenarios and how they were chosen, especially given the claim that the oracle 'requires no task-specific tuning.'","section":"V / Appendix S-B"}],"recommendation":"major_revision","confidential_remarks":"The probabilistic-completeness proof is the main obstacle. If the authors cannot supply a rigorous proof under explicit assumptions, they should remove or explicitly downgrade the PC claim, since the version in Section IV-C is unsupported and could be misleading. The real-world validation also needs quantitative support before the paper's central empirical claims can be accepted. The simulation experiments and the competence-island idea are valuable, so I see this as a major-revision issue rather than a rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know two things about this paper. The first: the algorithmic core is genuinely decent. The generator/connector split plus an oracle that uses the graph's structure and each skill's rollout success rate to decide what to expand next is a practical way to compose imperfect manipulation skills without symbolic task definitions. The experiments, though compressed, show it solving tasks that sequential skill chaining and CEM struggle with, and the real-world validation, while qualitative, is a plus. The second: the theoretical claim in Section IV-C does not hold as written.\n\nWhat is actually new is the feasibility-driven, multi-directional exploration and the competence-guided oracle. The idea of letting skills 'vote' where to plan by running them in simulation is sensible, and the paper correctly identifies that most chaining methods are goal-directed in a way that misses non-obvious intermediate steps. The MOSAIC-Roadmap baselines are a nice ablation showing the oracle matters.\n\nThe soft spots. The PC proof is the biggest one. It says the oracle's random sampling guarantees all skill-parameter configurations and all node pairs will be explored. But the parameter spaces are continuous—object poses, diffusion seeds—and random sampling from a continuous distribution has probability zero of hitting a specific configuration. And the oracle's node-pair selection (Appendix S-A2) picks a random node and its nearest neighbor, or start/goal-biased nearest neighbors, with penalties for failed pairs. It never systematically attempts arbitrary pairs. So the proof conflates 'non-zero probability of selecting a skill' with 'coverage of all configurations.' If the intended statement is practical or heuristic completeness, the paper should say so. As written, the claim is unsupported.\n\nThe evaluation is a second soft spot, though not as severe. Success rates come without error bars or trial counts, planning-time plots are medians/IQR but without numbers, and the real-world 'trended similarly' tells us little. The simulator-fidelity assumption is the main risk for hardware claims, but that is true of any sim-to-real planning paper.\n\nBottom line: the framework is a plausible advance, and the oracle is the real contribution. The PC proof needs a rewrite or a downgrade to a heuristic argument. With that fixed, and with a few numeric details added, this is a solid paper for a robotics venue. I would send it to serious reviewers rather than desk-reject; a good referee will push on the theory but should find the empirical story worth engaging.\n\nRecommendation: engage, but expect revision on the theory.","headline":"MOSAIC's oracle and generator/connector split are a real step for composing imperfect skills, but the probabilistic completeness proof is a sketch that does not survive contact with continuous parameter spaces and the algorithm's own nearest-neighbor node selection.","tokens_in":15929,"tokens_out":2281,"would_cite":true,"duration_ms":21531,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"MOSAIC plans long-horizon manipulation by focusing search on regions where skills are demonstrably effective, composing imperfect skills without symbolic task specifications.","keywords":["skill-centric planning","long-horizon manipulation","physics simulation","generator and connector skills","mosaic graph","probabilistic completeness","task and motion planning","diffusion policy"],"falsifier":"Run MOSAIC's planned skill sequences for the three tabletop scenarios on the physical robot and compare per-skill success rates with the same sequences executed in the simulator. If the real-world success rate for pushes or grasps in the discovered islands falls far below the simulated rate, or if the planner must re-plan after contact failures on hardware, the competence-island transfer premise is falsified.","tokens_in":14910,"feed_emoji":"🧩","tokens_out":5023,"duration_ms":42729,"temperature":0.7,"pith_summary":"MOSAIC is a planning framework for long-horizon robot manipulation that composes a library of imperfect, generic skills—such as pushing, grasping, and transporting—without requiring a symbolic task specification. Its central claim is that planning should be anchored in 'islands of competence': regions of the state space where a skill is demonstrably likely to succeed, discovered by rolling skills out in a physics simulator during search. A multi-directional search builds a graph of skill trajectories, with generator skills producing local trajectories and connector skills linking them by solving boundary value problems. The paper argues this feasibility-driven approach solves tasks whose solutions require non-obvious intermediate steps, and that it outperforms sequential skill chaining and roadmap baselines in success rate, generalization, and scalability. If true, it would let robots handle novel tabletop tasks by composing existing skills rather than learning new policies or manually engineering symbolic planners.","feed_headline":"MOSAIC plans long tasks by focusing on where skills succeed","feed_subtitle":"Uses physics simulation to chain imperfect pushes and grasps, beating goal-directed planning in complex tabletop setups.","key_machinery":"The central mechanism is the mosaic graph together with the two skill families. Generators are parameterized skills that produce trajectories without specified start or goal states, creating new nodes; connectors are conditional skills that produce trajectories between specified boundary conditions, creating edges. A third component, the oracle, orchestrates search: it decides whether to invoke a generator or connector based on the node-to-edge ratio, selects skills by a score balancing past success rate with an exploration bonus, and chooses node pairs to connect via random, goal-bias, start-bias, or unification modes. Physics simulation is used to evaluate every skill rollout, so only valid, collision-free trajectories enter the graph, and the fraction of invalid rollouts in a batch is reflected in the trajectory's cost. This machinery shifts the search from goal-directed to multi-directional and feasibility-anchored.","core_discovery":"On its own terms, the paper establishes that long-horizon manipulation planning can be recast as graph construction over skill trajectories, where the graph is grown not from the start or goal but from wherever the skills themselves are reliable. The core discovery is that imperfect skills can be made into reliable building blocks by using physics simulation as an in-the-loop oracle: each candidate trajectory is rolled out to verify contacts and prune infeasible plans, and the success statistics guide further exploration. The paper calls the resulting object a mosaic graph—nodes are generator-produced trajectories, edges are connector trajectories that satisfy boundary conditions—and shows that a domain-independent statistical oracle that balances exploitation of successful skills with exploration of underused ones can build this graph efficiently. It also proves probabilistic completeness for the skill-centric setting under deterministic skill-trajectory generation: given infinite iterations, every skill and parameter combination is eventually invoked, so any feasible solution decomposable into library skills is found.","pith_inferences":["A testable extension is to swap the statistical oracle for a large language model or learned affordance model; the paper notes the oracle can be any module, so an LLM that proposes connector boundary conditions could reduce search on tasks with strong semantic structure.","If competence islands are task-independent, the same generator-generated nodes could be cached and reused across planning queries, turning MOSAIC into an anytime roadmap that amortizes simulation cost over repeated tasks.","The sim-to-real dependence suggests MOSAIC's practical ceiling tracks simulator fidelity; using a learned world model or real-to-sim calibration in place of the physics engine would change the competence estimates and is a direct way to test the framework's robustness.","The probabilistic-completeness argument assumes deterministic skill-trajectory generation; extending it to stochastic policies would require a different convergence notion, since batch rollouts only provide empirical success probabilities."],"forward_implications":["Long-horizon manipulation problems can be solved without hand-written symbolic preconditions and effects, since the simulator supplies feasibility checks and boundary conditions are defined by world states.","Skill libraries with imperfect components, such as a push policy with roughly 70% success, can be composed into reliable plans by concentrating effort on regions where the skills succeed.","The framework's multi-directional search finds solutions involving non-obvious intermediate steps, such as clearing a movable obstacle before grasping, which directed forward or backward search tends to miss.","Probabilistic completeness guarantees that if a feasible decomposition into the given skill library exists, MOSAIC will find it asymptotically.","Because the oracle is domain-independent, the same algorithm and skill library can be reused across tasks without task-specific tuning."],"supporting_citations":[{"why":"Supplies the physics engine used to roll out skills and verify contact outcomes during planning.","marker":"[3]"},{"why":"Provides the diffusion policy used as the push skill, both as generator and connector.","marker":"[28]"},{"why":"Defines the skill-chaining baseline (Skills as Options) that MOSAIC is compared against.","marker":"[32]"},{"why":"Defines the cross-entropy method baseline using receding-horizon skill-parameter sequences.","marker":"[47]"},{"why":"Supplies the PRM-inspired roadmap baseline that MOSAIC-Roadmap builds on.","marker":"[48]"},{"why":"Provides RRT-Connect, used as a motion-planning subroutine inside skills and connectors.","marker":"[44]"},{"why":"Provides the Open Motion Planning Library routines used by skills to compute collision-free motions.","marker":"[45]"},{"why":"Defines the options framework to which the paper's parameterized-skill definition is related.","marker":"[33]"}],"fun_headline_variants":["MOSAIC: physics sim finds skill islands for long tasks","Skill islands guide long-horizon planning in MOSAIC","Plan long tasks by testing skills in simulation first","MOSAIC chains imperfect skills via physics-sim oracle"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole approach rests on the physics simulator predicting real contact outcomes well enough that the competence islands found in simulation remain competent on the real robot.","fun_headline_variants_meta":{"raw":{"variants":["MOSAIC: physics sim finds skill islands for long tasks","Skill islands guide long-horizon planning in MOSAIC","Plan long tasks by testing skills in simulation first","MOSAIC chains imperfect skills via physics-sim oracle"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00027,"raw_usage":{"total_tokens":1637,"prompt_tokens":967,"completion_tokens":670,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":583,"completion_tokens_details":{"reasoning_tokens":603}},"tokens_in":583,"tokens_out":670,"duration_ms":5882,"temperature":1.0,"reasoning_tokens":603,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:56:35.139999+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run MOSAIC's planned skill sequences for the three tabletop scenarios on the physical robot and compare per-skill success rates with the same sequences executed in the simulator. If the real-world success rate for pushes or grasps in the discovered islands falls far below the simulated rate, or if the planner must re-plan after contact failures on hardware, the competence-island transfer premise is falsified.","supporting_citations":[{"cited_title":"SAPIEN: A simulated part-based interactive environment,","cited_arxiv_id":null,"evidence_quote":"Supplies the physics engine used to roll out skills and verify contact outcomes during planning."},{"cited_title":"Diffusion policy: Vi- suomotor policy learning via action diffusion,","cited_arxiv_id":null,"evidence_quote":"Provides the diffusion policy used as the push skill, both as generator and connector."},{"cited_title":"Skill discovery in con- tinuous reinforcement learning domains using skill chaining,","cited_arxiv_id":null,"evidence_quote":"Defines the skill-chaining baseline (Skills as Options) that MOSAIC is compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the cross-entropy method baseline using receding-horizon skill-parameter sequences."},{"cited_title":"Probabilistic roadmaps for path planning in high-dimensional configuration spaces,","cited_arxiv_id":null,"evidence_quote":"Supplies the PRM-inspired roadmap baseline that MOSAIC-Roadmap builds on."},{"cited_title":"Rrt-connect: An efficient approach to single-query path planning,","cited_arxiv_id":null,"evidence_quote":"Provides RRT-Connect, used as a motion-planning subroutine inside skills and connectors."},{"cited_title":"The open motion planning library,","cited_arxiv_id":null,"evidence_quote":"Provides the Open Motion Planning Library routines used by skills to compute collision-free motions."},{"cited_title":"between mdps and semi-mdps: A framework for temporal abstraction in reinforcement learning,","cited_arxiv_id":null,"evidence_quote":"Defines the options framework to which the paper's parameterized-skill definition is related."}],"review_version":1}