mlsanityData to 14 Oct 2026

Terminal Symmetry as a Carrier of Asymmetric Process Knowledge: Statewise Refinement for Anytime Verified Construction

arXiv 2608.11318 ↗First posted 11 Aug 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

Many sequential construction tasks have exact terminal symmetries even though execution is directed and depends on history. Process evidence supplies order. Terminal correspondence transports it between equivalent outcomes; the realized state updates relevance. These roles define a carrier framework: transport what the outcome preserves; refine what history changes. SymBuild combines transported process and state residual ranks by ordinal rank meet. Its rank threshold sets equal the corresponding unions, yielding a tight worst-case verifier query bound under prefix information. We evaluate SymBuild in three construction domains: computer-aided design (CAD) assembly, Mini-Programs, and exact-fill packing, and its ordinal adaptation in target removal. SymBuild improves the area under the anytime verified success curve by up to 6.77, 21.75, and 8.68 points over Static in the three construction domains. Refresh gains recur beyond SymBuild under alternative aggregation, planning, and learned scoring methods; on Geometric Reasoning Network (GRN) target removal, direct Combined refresh has the lowest mean verifier query score at all three scales and reduces distinct scored states by factors of 6.48-12.22 relative to refreshed population-based search. Together, these results support the carrier framework and demonstrate that SymBuild is an effective, analyzable method for anytime verified construction.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 34 of its 57 references that are in the map. First posted on arXiv 11 Aug 2026.

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34 of 57 references.

References · 34

  1. 2022Do As I Can, Not As I Say: Grounding Language in Robotic Affordancescited by 2,348
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  11. 2023EDGI: Equivariant Diffusion for Planning with Embodied Agentscited by 36
  12. 2024Symmetry Considerations for Learning Task Symmetric Robot Policiescited by 28
22 more
  1. 2024Differentiable Task Graph Learning: Procedural Activity Representation and Online Mistake Detection from Egocentric Videoscited by 26
  2. 2024ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policycited by 26
  3. 2024Pard: Permutation-Invariant Autoregressive Diffusion for Graph Generationcited by 25
  4. 2023Discovering Symmetry Breaking in Physical Systems with Relaxed Group Convolutioncited by 20
  5. 2025Act2Goal: From World Model To General Goal-conditioned Policycited by 20
  6. 2018Robustness via Retrying: Closed-Loop Robotic Manipulation with Self-Supervised Learningcited by 19
  7. 2023ASAP: Automated Sequence Planning for Complex Robotic Assembly with Physical Feasibilitycited by 18
  8. 2024Equivariant Reinforcement Learning under Partial Observabilitycited by 18
  9. 2025Improving Equivariant Networks with Probabilistic Symmetry Breakingcited by 16
  10. 2024IKEA Manuals at Work: 4D Grounding of Assembly Instructions on Internet Videoscited by 12
  11. 2016A Unifying Formalism for Shortest Path Problems with Expensive Edge Evaluations via Lazy Best-First Search over Paths with Edge Selectorscited by 9
  12. 2024Equivariant Symmetry Breaking Setscited by 9
  13. 2025Compositional Diffusion with Guided Search for Long-Horizon Planningcited by 8
  14. 2024Generalizable Motion Planning via Operator Learningcited by 7
  15. 2024VeriGraph: Scene Graphs for Execution Verifiable Robot Planningcited by 7
  16. 2025Symmetry-Aware GFlowNetscited by 7
  17. 2026Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generationcited by 7
  18. 2024Equivariant Action Sampling for Reinforcement Learning and Planningcited by 4
  19. 2025Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networkscited by 3
  20. 2025Partially Equivariant Reinforcement Learning in Symmetry-Breaking Environmentscited by 3
  21. 2025Extracting Visual Plans from Unlabeled Videos via Symbolic Guidancecited by 1
  22. 2026Symmetries Here and There, Combined Everywhere: Cross-space Symmetry Compositions in Roboticscited by 1

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