constraint-aware representations

In constraint programming, high-level modeling languages (e.g., Essence) introduce significant symmetry through abstract structures such as nested sets, severely degrading solver efficiency. To address this, we propose a lightweight, structure-aware symmetry breaking method operating at the underlying representation level. Rather than generating numerous explicit symmetry-breaking constraints, our approach matrix-encodes abstract structures and integrates an optimized variable ordering strategy tailored to indistinguishable objects—achieving incomplete yet highly effective symmetry elimination. Compared to Akgün et al. (2025), our method substantially reduces constraint set size and search redundancy. Empirical evaluation on diverse symmetry-rich benchmark problems demonstrates marked improvements in solving speed, while maintaining practicality and scalability across problem sizes and structural complexity.

To address the challenge of rigorously enforcing output constraints in safety-critical machine learning applications, this paper proposes a novel hyperspherical constraint representation method. It maps model outputs into a hyperspherical coordinate space centered at the feasible region, thereby intrinsically guaranteeing constraint satisfaction at the representation level—without penalty terms, custom architectures, or post-hoc projection. The approach uniformly supports both convex bounded and star-shaped feasible sets and provides theoretical guarantees of zero constraint violation. Key technical components include a hyperspherical coordinate transformation, geometry-driven feasible set modeling, constraint-aware feature mapping, and a lightweight inverse transformation. Experiments on synthetic and real-world datasets demonstrate that the method achieves prediction accuracy competitive with state-of-the-art constrained learning approaches, incurs no optimization overhead during inference, and strictly maintains zero constraint violations.

Automated modeling of constraint optimization problems (COPs) remains underdeveloped, and constraint programming (CP) modeling research lags behind operations research (OR). Method: We propose ConstraintLLM—the first large language model (LLM) specialized for CP tasks—integrating a constraint-aware retrieval module (CARM), a tree-of-thoughts (ToT) reasoning framework, and symbolic solvers to enable guided self-correction. It is built via multi-instruction supervised fine-tuning on open-source LLMs and evaluated on IndusCP, the first industrial-scale CP benchmark. Contribution/Results: ConstraintLLM achieves state-of-the-art (SOTA) solution accuracy on mainstream CP benchmarks and doubles modeling accuracy over baselines on IndusCP. It significantly improves reliability and generalization in formal COP modeling for industrial applications.

Existing CAD deep learning methods neglect geometric constraint modeling, leading to poor discrimination between shapes with similar appearances but distinct constraints. To address this, we propose CstNet—a two-stage constraint-aware network for parametric point cloud analysis—that explicitly encodes CAD constraints as learnable ternary vectors and supports both B-Rep and point cloud inputs. Our contributions are threefold: (1) the first vectorized representation of CAD constraints and an end-to-end constraint learning paradigm; (2) Param20K—the first large-scale multimodal dataset of parametric point clouds, comprising 20,000 samples across 75 classes; and (3) state-of-the-art performance on Param20K, achieving a 3.52% absolute improvement in classification accuracy and a 26.17% gain in rotational robustness over prior methods.

This work proposes a novel approach to automatically restructure constraint programming models by leveraging a large language model (LLM)-based autonomous agent operating in an open-ended space. Unlike traditional rule-based reformulation methods, which are constrained by predefined heuristics, the proposed agent iteratively generates, validates, diagnoses, and refines candidate models on training instances, enabling experience-driven, flexible optimization. Integrated with the CPMpy modeling framework and a solution-reinjection validation mechanism, the method demonstrates significant performance gains: across 27 test instances spanning nine combinatorial optimization problems, it outperforms the original formulations on 21 instances, with speedups exceeding two orders of magnitude on certain problems. These results substantially surpass the limitations inherent in conventional rule-driven reformulation techniques.

This work addresses the lack of formal guarantees regarding semantic preservation during problem reformulation and solver correctness in constraint programming. It presents the first end-to-end verified framework implemented in the Lean theorem prover, enabling formal proofs of parameterized equivalence, equisatisfiability, and symmetry-breaking correctness for entire families of problems. The approach combines general, parameterized proofs with instance-level certificate checking, thereby eliminating the need to trust external solvers. Verified certificates are produced via backend transformations, and a single high-level proof suffices for arbitrarily large instances. This methodology achieves dramatic search-space reductions—up to a factor of twenty million—and enables full verification of the largest instances in just a few minutes.

This work addresses the lack of systematic methodologies in model optimization, which often relies on heuristic choices and struggles to accommodate diverse deployment constraints. It formalizes model compression and acceleration as a constraint-aware multi-objective engineering decision problem, establishing a unified and actionable framework grounded in five key dimensions: data availability, latency, memory footprint, accuracy tolerance, and retraining budget. By integrating techniques such as quantization, pruning, knowledge distillation, parameter-efficient fine-tuning (PEFT), and inference optimization, the study proposes tailored optimization pipelines for four representative industrial scenarios, delivering a reproducible and quantifiable guide for technology selection.

This work addresses the challenge of nonlinear optimization with mixed equality and inequality constraints in robotic dynamics planning by introducing a novel approach based on “constraint manifolds with corners.” The method reformulates the original problem as an unconstrained optimization over a constrained state space, seamlessly embedding inequality constraints into the manifold structure through differential geometry and manifold optimization techniques. This formulation overcomes the conventional limitation of manifold optimization, which typically applies only to smooth equality constraints. Evaluated on large-scale dynamic planning tasks, the proposed approach successfully generates dynamically feasible trajectories and demonstrates superior robustness and solvability in scenarios where standard algorithms fail.

Existing vision-language models lack verifiable intermediate states in geometric reasoning, making it difficult to ensure precise spatial relationships. This work proposes a "propose–draw–verify" iterative framework that externalizes geometric reasoning through agent-based interaction with the GeoGebra constraint engine. By explicitly expressing hypotheses on an executable canvas and obtaining structured feedback, the approach grounds reasoning in a shared state validated by algebraic constraints. The method enables independent auditing of construction fidelity and measurement faithfulness, achieving 95.9% predicate-level and 84.0% strict problem-level accuracy on the GeoGoal benchmark. It yields performance gains of up to 4.1% and 16.4% in planar and solid geometry tasks, respectively, and attains GenExam-math rendering scores of 68.2% (strict) and 90.5% (lenient).