Structural Constraints

The Antibandwidth and Cyclic Antibandwidth problems are NP-hard graph labeling problems that aim to maximize the minimum (cyclic) distance between labels assigned to adjacent vertices. Extensive research on these problems has resulted in a variety of mathematical formulations and computational approaches. However, their minimum span perspective, in which a prescribed minimum (cyclic) distance is fixed and the objective is to minimize the label span, has received comparatively little attention. In this paper, we consider this complementary perspective by introducing the Minimum Span Antibandwidth/Cyclic Antibandwidth Labeling (MSABL/MSCABL) problems and developing a unified Boolean Satisfiability (SAT)-based framework for solving them. The SAT-based framework formulates MSABL/MSCABL as a sequence of decision problems and exploits their monotonicity to accelerate the search process. We also consider two SAT solving strategies, parallel and incremental SAT solving: the former examines multiple candidate spans concurrently, while the latter reuses a single SAT instance while progressively restricting the label domain. The proposed approaches are evaluated on benchmark instances from the Harwell-Boeing Sparse Matrix Collection and compared with CPLEXCP, CPLEXMIP, and Gurobi. The results show that SAT-based approaches are highly competitive in solution quality, with the parallel approach performing best overall for MSCABL and the incremental approach for MSABL. With the no-hole constraint, they remain competitive with CPLEXCP and significantly outperform CPLEXMIP and Gurobi, particularly for MSCABL. These results demonstrate the effectiveness of SAT solving as an exact approach for MSABL and MSCABL.

Because of its collaborative nature, Wikidata suffers from errors, in- consistencies, and excessive complexity, such as redundant classes, ambiguity between instances and classes, wrong taxonomic paths, and type constraint violations. The manual curation of these issues is infeasible at scale. To address these challenges, we introduce WiCleanData, a refined version of Wikidata with a consistent tax- onomy and free from type constraint violations. Specifically, we have designed an automated pipeline that first cleans the taxonomy with language model assistance, then simplifies type constraints by hierarchical aggregation, and finally filters facts accordingly. The resulting knowledge graph, free from any type violation, is made publicly available via a Web interface, enabling easy exploration and downstream applications.

Time series forecasting has seen signicant advancements with the emergence of new deep learning models. However, forecasting time series in applications involving physical processes remains a major challenge. Despite the apparition of Physics Informed Neural Networks (PINN), recent models do not estimate unobservable intermediate physical variables, which are important for domain experts to understand the target behavior. To this end, we propose a Physics Informed Recurrent Neural Network (PIRNN) which predicts, along the target, unobservable variables on both historic data and forecast target. This approach enhances the model robustness and results interpretation using domain knowledge. Our method is easily adaptable to any physical model using several equations, each having its own set of unobservable variables, to describe it-self. As a case study, we incorporate physical equations used for groundwater levels predictions by the physical model called Gardenia. This model uses transfers equations between reservoirs, optimized with data assimilation, to simulate the evolution of groundwater levels. Evaluation includes several well known neural network models and the Gardenia model compared on twelve real world datasets. In addition, we study the impact of each component through an ablation study. Our model outperforms other models on ve out of the twelve datasets and our ablation study underlines the importance of having a physical background in our time series forecasting task. Finally, the coherence of the physical variables predicted by our neural network is assessed by a domain expert.

Simultaneous localization and mapping (SLAM) is one of the services running on an autonomous robot. It is typically run to assist other tasks such as planning, manipulation, etc. All these tasks are run on edge hardware and are subject to severe resource constraints. However, most SLAM systems are built and tested in isolation, and their performance is reported as if they are the only task running on a system. We observe that existing benchmarks lack a common mechanism for comparing SLAM systems under realistic resource constraints. To address this limitation, we have developed SLAMSqueezeBench, a framework that allows testing of SLAM systems under realistic workloads on edge hardware. It does so by imposing constraints on compute and memory resources available for the SLAM system during execution. It also simulates realistic camera frame acquisition with frame drops when a finite buffer is full. Using SLAMSqueezeBench, we compare nine SLAM systems spanning classical systems, learning-based systems, and approaches for Gaussian splatting. Our testing framework will be available for use by the community upon publication.

Figured-bass realization can be described as a sequence of choices constrained both within each sonority and between successive sonorities. This paper gives an explicit mathematical model of a restricted, examination-style four-part realization problem. Pitch spelling, range, chord membership, doubling, omission, spacing, crossing, overlap, melodic motion, consecutive perfect intervals, and selected resolution requirements are expressed as predicates. We distinguish hard constraints from optional preference costs. Four labeled notes are represented visually as the vertices of a quadrilateral and computationally as one ordered voicing state. Legal progressions become paths through a layered graph. We prove that feasibility and minimum-cost realization are polynomial-time problems for a fixed number of voices with explicit finite note domains and fixed local rules. For fixed ranges, a fixed note alphabet, and adjacent-event rules, the number of graph operations is linear in the number of events. Worked two-, four-, and eight-beat examples illustrate legality, optimization, and the failure of a greedy choice. The result concerns the stated formal model; it is not a claim that every musical judgment is captured by local predicates.

Deep Reinforcement Learning has demonstrated remarkable capability in quadrotor control, yet learned policies offer no guarantee of respecting safety constraints during training or deployment. We present CALOS (Control-Affine Lyapunov On-manifold Safety), a runtime safety layer that enforces attitude constraints on a quadrotor without modifying the underlying learning algorithm. CALOS formulates four tilt-angle inequalities and a Lyapunov descent condition as a single quadratic program whose solution is the minimum-norm correction to the nominal torque output of the policy. The quadratic program is solved exactly via active-set enumeration over the three-dimensional torque space, with a computational cost low enough to enforce constraints in real time across thousands of parallel simulation environments, as required by modern massively parallel Deep Reinforcement Learning training. Evaluated on trajectory-tracking tasks in NVIDIA Isaac Lab, CALOS reduces lateral tracking error by 55-60% relative to an unconstrained Proximal Policy Optimization baseline while achieving zero attitude-constraint violations on the training trajectory. By restricting exploration to safe regions of the state space, the safety layer also accelerates training convergence and improves data efficiency without producing suboptimal policies.

Some of the sharpest challenges in sampling from the energy functions of physical systems arise at phase transitions, where the density of states changes abruptly and many sampling algorithms stall. Nested sampling is a particle method that traverses the density of states under a hard energy constraint and is known to be robust to such transitions, but its application in high dimension is limited by the difficulty of sampling under that constraint. In this work we introduce Quenched Ensemble Sampling, which generalises the hard constraint to a family of repulsive potentials at the energy boundary. This preserves the quenched path of monotonically decreasing energy while making the constrained target amenable to scalable gradient-based kernels. We demonstrate on synthetic models of phase transitions that our method estimates the marginal likelihood and draws posterior samples across a first-order transition where popular alternatives such as tempering fail. We apply the procedure to marginal likelihood estimation in Bayesian neural networks, enabling model comparison between network architectures. Finally, in a high-dimensional continuous lattice field theory, we show that this method traverses a first-order transition and estimates the partition function.

Regularization-based methods have become a standard approach for training Deep Reinforcement Learning policies against adversarial input perturbations. In this paper, we unify these methods by deriving new upper bounds on the performance gap between the nominal and worst-case policies. Each upper bound is expressed as an existing regularization objective plus a KL-divergence penalty between the nominal and worst-case policies, which further explains why adding a KL penalty improves robustness in practice. Building on these bounds, we formulate robust training as a constrained optimization problem, showing that existing methods correspond to the special case of a fixed Lagrange multiplier. We instead update the multiplier jointly with the policy to automatically tune the regularization weight. Finally, we conduct extensive adversarial evaluations across several continuous control tasks to validate our theoretical analysis.

Cryptocurrency forecasting presents a distinctive combination of extreme cross-asset scale heterogeneity, non-stationary dynamics, and structural dependencies among Open, High, Low, and Close (OHLC) variables. We present CryptoL, a unified framework designed to address these challenges within multivariate time-series forecasting. CryptoL evaluates forecasting error in context-normalized coordinates within the RevIN pipeline, preventing inverse normalization from introducing an additional squared-scale weighting into the MSE objective. We formally characterize this effect through the empirical risk and parameter-gradient geometry, establishing the conditions under which large-scale assets can disproportionately influence shared-model optimization. Beyond loss-space normalization, CryptoL examines channel-independent and channel-dependent normalization for OHLC data, showing that a shared channel-dependent affine transformation preserves candle-order relations that independent channel transformations need not preserve. The framework further incorporates scale-adaptive numerical stabilization to reduce distortions caused by a fixed normalization constant across assets spanning many orders of magnitude, together with a soft feasibility loss that penalizes violations of the defining OHLC inequalities. Experiments across heterogeneous cryptocurrency assets evaluate these components through controlled ablations and demonstrate improvements in forecasting accuracy, training stability, and the frequency of financially valid OHLC predictions relative to the considered baselines. CryptoL therefore provides an integrated approach to scale-balanced optimization, structure-preserving normalization, numerical stabilization, and constraint-aware cryptocurrency forecasting.

Quantifier instantiation is currently the main approach to non-ground SMT solving: solvers generate ground instances and solve the resulting ground SMT problems with CDCL(T)-style reasoning. When a conflict is found, conflict analysis learns only a ground clause, even though the conflict comes from instances of non-ground clauses. Yet non-ground reasoning can give exponentially shorter proofs than purely ground reasoning. We propose a calculus that consists of ground instantiations, CDCL(T)-style rules, and non-ground conflict analysis. The solver reasons on ground instances, but the resolution steps of conflict analysis are performed on their original non-ground clauses. This produces learned clauses that are typically more general than the ground conflict. With a suitable strategy, the learned clauses are even non-redundant. We also show how chronological backtracking can be included in SMT solving. Our calculus gives a common setting for CDCL(T)-style SMT solving, a range of instantiation-based procedures, and non-ground clause learning, and we prove that it simulates CDCL, SCL(FOL), SCL(T), and even Resolution.

Vision-Language-Action (VLA) and World-Action Models (WAMs) have demonstrated strong capabilities in general-purpose robotic manipulation, yet their generated actions may violate hard physical constraints and therefore be unsafe or infeasible for deployment. Existing safety approaches either optimize statistical safety objectives without deterministic per-step guarantees or correct unsafe actions only during inference, creating a mismatch between policy training and execution. We introduce ActSafeGuard, a differentiable and training-aligned safeguard layer for flow-matching based policies. ActSafeGuard integrates hard action feasibility into policy learning, not merely treating safety as an inference-time external component. Through an analytical ray-scaling operator design, ActSafeGuard enables boundary-aware gradients to guide the model to naturally learn constrained manifolds. Extensive experiments on multiple standard foundation backbones ($π_{0.5}$ and Fast-WAM) across various tasks demonstrate that ActSafeGuard consistently achieves a $100\%$ step safety rate while fully preserving or even boosting task success rates, providing a scalable and minimally invasive solution for safe embodied AI deployment.

We construct counterexamples to Rockafellar's sum conjecture in which two maximally monotone operators satisfy the interior-domain condition but their sum is not maximally monotone, thereby providing the complete disproof of the conjecture. We establish a general construction theorem that computes the entire monotone polar of a class of graphs, gives a necessary and sufficient condition for their maximal monotonicity, and shows how a positive rank-one perturbation yields a nonmaximal sum under this condition. We verify the theorem's hypotheses and its maximality criterion on $c_0$, thereby obtaining a counterexample to the conjecture. Furthermore, we construct a bounded linear surjection from $\ell^1$ onto $c_0$ and use it to obtain the counterexample on $\ell^1$. Lean formalizations of the $c_0$ counterexample and the pullback lemma are also provided.

Ensuring the satisfaction of Signal Temporal Logic (STL) specifications under uncertainty is challenging, as reachability-based monitoring provides guarantees but does not indicate how to restore satisfaction when it becomes indeterminate. A key difficulty is identifying which uncertain components actually affect global satisfaction, especially for nested formulas. This paper introduces a logical dependency tracking framework that propagates uncertainty through the STL structure and captures the causal contribution of reachable sets to satisfaction. By associating markers to uncertain predicates and propagating them via three-valued semantics, we extract in milliseconds a compact Disjunctive Normal Form (DNF) of sufficient constraints, avoiding combinatorial enumeration. As an application, we formulate control correction as a minimum-effort optimization problem. Using zonotopic reachability, the derived constraints are enforced via linear programming, yielding corrections that guarantee STL satisfaction under bounded uncertainty and provide certified probabilistic bounds in the stochastic case. We demonstrate the approach on a nonlinear system with nested STL specifications, showing that dependency tracking enables efficient and formally guaranteed correction. The tracking implementation is available at https://github.com/Antoine-Bst/STL-Three-Valued-Clause-Filtering/.

Input devices for robotic microsurgery are frequently described as preserving the surgeon's trained technique, but the claim is rarely measured. We compared manual and teleoperated intraocular instrument motion with the trocar constraint, the instrument, the eye model and the tracking source common to both conditions, so that the control interface was the only factor varied. Prior comparisons cannot hold the instrument fixed, because a robotic instrument is not the tool used manually. Sixteen participants performed a navigation task on a commercial ophthalmic simulator by hand and through a three-degree-of-freedom input device commanding a five-joint robot. Task outcome was equal but at ceiling: every participant acquired all five targets under both interfaces with no retinal or lens injury. Execution differed on every measure. Teleoperated trials took three times as long at a quarter of the median speed, covered less than half the angular working range, and were broken into 3.5 times as many separate movements. Completion time and movement fragmentation improved substantially across four trials of practice and had not plateaued; the measures set by the configured rate ceiling and joint limit changed the least. Finger activity doubled and pinch variability tripled, so reducing instrument degrees of freedom redistributed manual effort rather than reducing it. The interface preserves the outcome and reshapes the execution.

We study certificates of positivity and optimality for learning problems whose objectives and constraints need not be polynomial. We isolate an axiomatic core of Fischer's constructive strict and weak Positivstellensätze and prove the resulting theorems for abstract function algebras over ordered fields. The framework separates two roles that can otherwise be conflated: objective and constraint functions may be built from broad classes of continuous or definable operations, while the auxiliary primitives used to construct a certificate satisfy explicit scalar and closure axioms. We give instances over continuous and definable function algebras, including ordered fields not closed under square roots, derive lower-bound and global-optimality certificates, and analyze both expanded term length and shared computation-graph complexity.

Ensuring safety in reinforcement learning under nonstationarity requires anticipating changes in risk before they lead to unsafe behavior. Existing approaches typically rely on safety constraints defined at design time or updated reactively during execution, assuming that such constraints remain valid over time. However, in nonstationary environments with evolving contexts and changing driving layouts, these assumptions may fail. We propose a framework for proactive safety constraint generation based on context forecasting. The approach infers latent environmental context from observations, predicts its future evolution, and constructs safety constraints adapted to anticipated conditions. This enables the agent to proactively avoid unsafe regions instead of reacting only after safety violations occur. We evaluate the method in driving environments with structured context variation. The experiments include a sweep over nonstationarity intensities and additional held-out driving layouts, including highway, intersection, and racetrack scenarios. Results show that proactive constraint generation substantially reduces collisions under both seen and out-of-training nonstationarity intensities and generally remains effective across held-out driving layouts while maintaining usable task performance. These findings suggest that context-based constraint generation is a promising approach for safe reinforcement learning under nonstationarity.

Natural-language Computer-Aided Design (CAD) code generation aims to turn design intent into executable and editable parametric programs. Large language models (LLMs) make this goal increasingly practical, but useful systems must preserve the construction process behind the rendered geometry. Existing benchmarks and methods mostly focus on how closely the generated CAD model matches the reference geometry, often using metrics such as Intersection over Union (IoU). Such metrics can miss errors in part decomposition, construction hierarchy, Boolean operations, sketch structure, and geometric relations. This gap calls for a representation that makes design intent explicit and lets a system check generated code against that intent. We propose CIT-CAD, a framework that infers a Constraint Intent Tree (CIT) from the input description to represent the intended entities, hierarchy, operations, and relations. The tree has two roles: it guides CAD code generation and defines expected constraints for verification. The framework extracts actual constraints from the generated program, compares them with the expected constraints, and uses mismatches to localize and repair design violations. Experiments show that the framework improves CAD generation performance, with larger gains on more complex multi-entity designs. By turning design intent into an explicit and checkable object, this work is the first attempt to move text-to-CAD generation beyond rendered-geometry matching toward construction-aware synthesis, verification, and repair.

Diffusion Large Language Models (dLLMs) generate text via bidirectional iterative denoising, naturally supporting user-specified constraints anchored at arbitrary output positions, a paradigm known as In-place Prompting (IPP). We formalize this as the In-place Instruction Following (IIF) task and construct IIF-Bench, a hierarchical benchmark spanning literal, style, and discourse-function constraints, paired with a rubric-based local-global evaluation protocol. An inference-time attention-bias probe suggests that vanilla dLLMs often under-prioritize constraint spans during denoising. We then propose GRAFT, an IPP-oriented post-training framework combining constraint-aware SFT and preference optimization. On four representative dLLMs, GRAFT raises the average IIF score from 57.75 to 73.10 (+15.35 points), with absolute gains of 15.91 and 15.57 points on literal and discourse-function constraints, while preserving general generation ability.

We study constrained online convex optimization with adversarial constraints and conditionally unbiased, finite-variance observations of constraint values and gradients. Under common feasibility, our \LEDGER\ algorithm attains $O(\sqrt T)$ expected regret and $O(\sqrt{T\log(eT)})$ expected budget violation, the largest cumulative overspend over any window. It uses a reflected exponential potential, clipped signed observations, and predictable adaptive regularization, with one feedback triple and one projection per round. Neither a Slater condition, independence between feedback channels, nor an absolute constraint-value bound is needed. A Gaussian testing lower bound proves that the budget rate has optimal horizon dependence under square-root regret at fixed positive noise, including the logarithm. The same obstruction holds for terminal violation, so the logarithm is not a cost of maximizing over windows; an $O(\sqrt T)$ budget bound instead forces linear regret. In contrast, fixed positive Gaussian value noise yields a joint regret--hard-violation lower bound of $Ω(\min\{σ,1\}T/\log^2 T)$, even with exact gradients in one dimension. The hard-violation construction matches arbitrarily many moments while preserving a feasible-endpoint gap and constant endpoint probabilities. Together, the bounds separate uncertainty about hard feasibility from learnable signed budgets. Deterministic restarts remove the horizon input without changing either upper rate.

Large language models (LLMs) are increasingly used to formulate optimization models from natural-language problem descriptions, yet realistic operations research (OR) requests are often incomplete: missing objectives, constraints, or business rules can change the resulting mathematical program. Existing evaluations largely assume a complete specification and therefore overlook whether an agent knows when clarification is needed before modeling. We introduce OR-Clarify, a benchmark for pre-formulation clarification. Each task presents a partial public problem description, withholds structured hidden slots, and evaluates agents through bounded interaction with a simulated user. The benchmark supports both openended and choice-based clarification, and measures slot recovery, stopping behavior, silent assumptions, and interaction cost. We further propose Interactive Optimization (InterOPT), a two-stage framework that identifies unresolved formulation-critical gaps and uses them to guide whether to ask the next question or to stop. In our choice-based experiments, InterOPT substantially outperforms all baselines in exact slot recovery; in the open-ended setting, it remains competitive with strong prior methods. Together, OR-Clarify and InterOPT reframe OR assistance as a selective completeness decision: clarify when needed, stop when ready, and quantify what remains missing.

While HTN planning has received significant attention in recent years, support for numerical reasoning remains very limited. In this paper, we investigate numerical Totally-Ordered HTN (TOHTN) planning and show how standard SAT-based encodings can be naturally extended with SMT to handle numeric fluents. In addition, we introduce a benchmark suite for numerical TOHTN planning, providing a first common basis for evaluation in this setting. Experimental results show that this simple encoding already constitutes a competitive baseline. This work opens the way to more expressive approaches to HTN planning.

Learning-based schedulers have been proposed to provide real-time user, target, and access point (AP) association in distributed cell-free integrated sensing and communication systems. In a typical approach, a graph neural network (GNN), trained on labels from a mixed-integer linear program, maps lightweight per-AP statistics to decisions on AP clustering, user and target scheduling, and mode selection in one forward pass. Such solutions assume that hard constraints, enforced only as soft training penalties, hold at inference, and that the self-reported statistics are truthful. Using our ASSENT algorithm as an example, we find that despite high $F_1$ scores, many solutions violate at least one hard constraint, demonstrating that high prediction accuracy does not ensure joint feasibility. Projecting the GNN output onto a feasible solution restores constraint satisfaction with low utility loss, even with a simple greedy repair procedure. We further show that feasibility alone does not guarantee robustness to false data injection attacks. A single malicious AP that reports false information cannot substantially increase its user associations, but can greatly increase the rate of infeasible solutions. The effect of such attacks depends on the type of information being falsified. Misreporting information that affects the objective can largely be mitigated through feasibility projection, whereas falsifying information that affects the constraints cannot. The latter can, however, be detected using a low-complexity cross-AP consistency check. These results show that learned ISAC schedulers should be evaluated using constraint-aware feasibility metrics in addition to conventional accuracy measures.

Long-horizon tool-use agents need not only to search and plan, but also to decide when to finalize. We study late-stage pressure states, in which an agent is biased toward submitting a final answer that appears complete and polished while key constraints remain unresolved. We first train a linear probe to show that this pressure state is identifiable from the agent's hidden states. Then, we use activation interventions along this pressure direction and find that shifting the hidden states changes both the pressure score and whether the agent continues tool use or submits early. Through controlled context manipulations, we further see that the pressure is mitigated by constraint clarity and action mapping. Based on these findings, we propose Probe-Sensed Pressure Relief (PSPR), a plugin that applies lightweight pressure relief direction under moderate pressure and moves to structured organization under high pressure risk. Experiments on multiple long-horizon benchmarks show that our method consistently strengthens existing agent methods.

Large Language Models (LLMs) have shown remarkable promise in translating and reformulating complex mathematical optimization problems across modeling languages. However, validating such transformations through empirical solver executions alone is unreliable, as solver outcomes may be affected by local minima, structural timeouts, numerical artifacts, and subtle semantic divergence between formulations. We introduce SOVER, an LLM-assisted SMT framework that separates semantic mapping from formal certification: Z3 checks domain cross-feasibility and global objective-order preservation for mixed-integer linear formulations, while dReal provides tolerance-aware feasibility/range and $ε$-argmin checks for continuous nonlinear formulations. We also introduce NLEquiv-150, a public benchmark of 100 equivalent and 50 deliberately hard non-equivalent nonlinear reformulation pairs. With LLM-extracted mappings, SOVER classifies 149/150 pairs (99.33%) correctly, including all 50 hard negatives; the sole error is an incomplete mapping extraction.

Let $r\geq3$ be fixed, and let $\mathbf{G}_n$ be the set of all simple graphs with vertex set $[n]=\{1,\ldots,n\}$. We consider an exponential random graph model which gives higher probability to $G \in \mathbf{G}_n$ than to $H \in \mathbf{G}_n$ if $G$ has fewer $r$-cliques than $H$. But all graphs in $\mathbf{G}_n$ have positive probability. The degree to which graphs with fewer $r$-cliques are given higher probability is determined by a positive weight $w$. We prove that, asymptotically almost surely as $n \to \infty$, a random graph from $\mathbf{G}_n$ has a vertex partition into $r-1$ parts of roughly equal size, the density of edges between the parts is close to $1/2$, and for every $\varepsilon > 0$ the density of edges within any part is less than $\varepsilon$. The asymptotic structural properties are independent of the weight $w$ as long as it is positive. We also extend the result to the context of several clique sizes, each one with its own weight.

Healthcare workforce scheduling is an NP-hard optimization problem requiring simultaneous satisfaction of labor regulations, coverage requirements, employee preferences and cost objectives. Existing approaches (genetic algorithms, integer programming, constraint programming) model 6-12 constraints at shift-level granularity and cannot guarantee regulatory compliance. They also lack support for multi-role, multi-skill heterogeneity, mandatory break scheduling with midpoint control, acuity-weighted workload equity, sub-shift granularity, inter-week stability, and cross-midnight shifts. This paper presents CP-SAT: a Constraint Programming formulation for multi-role, multi-skill healthcare scheduling. CP-SAT enforces 14 hard constraints guaranteeing zero regulatory violations, while optimizing 15 soft objectives via a unified weighted penalty function. Contributions include a shift-window decomposition enabling break scheduling with centrality control, acuity-weighted workload equity, multi-granularity resolution from 15 minutes to 1 day, inter-week stability, and grid-offset preprocessing mapping cross-midnight shifts into a single scheduling day without solver changes. CP-SAT is evaluated on 18 instances: five synthetic hospital units (10-33 nurses), 10 INRC-II benchmarks (5-80 nurses, up to 8-week horizons) and 3 NRP-23 compatible instances (10-25 nurses) with cross-midnight Night shifts. Results: zero hard-constraint violations across all 18 instances by construction; proven optimality on INRC-II n005w4 (objective 118, gap 0.0%, 104s); feasible schedules scaling to 179,800 variables and 351,425 constraints (80 nurses); service quality improved 50-67% over MOGA; and model size scaling near-linearly at approximately 4,400 variables per employee. The formulation enforces 29 total constraints (14 hard, 15 soft), nearly three times the industry average.

Logical reasoning with large language models (LLMs) is a critical capability, as it reflects a system's ability to correctly deduce hypotheses from a given context using faithful deductive processes. However, LLM reasoning has often been shown to be sensitive to small surface-level variations in problem formulation, raising questions about whether models truly follow the underlying logical structure. Studying this behavior is challenging because the symbolic components of logical problems, such as operators and predicates, are difficult to systematically manipulate in natural language. We introduce a tool-driven framework for generating controlled, label-preserving edits to logical reasoning problems. Our method operates on symbolic representations of first-order logic and constraint satisfaction problem tasks, enabling targeted modifications to logical operators and other structural components before translating them back into natural language. Using this framework, we evaluate various LLMs under cumulative and individual operator edits and analyze their behavior in response to these changes. Our quantitative and qualitative analyses show that LLM reasoning behavior under controlled operator edits is inconsistent, regardless of model size or family: models sometimes adapt correctly to structural changes but often fail to track their logical consequences. The results from this automated stress test enable an evaluation of language models across different dimensions and help measure the reliability of their reasoning.

The total scaled-gradient variation (TSGV) regularizer, derived from sparse modeling of piecewise-linear structures, has been shown to preserve edges and corners in image restoration. However, its highly nonconvex and nonlinear nature poses severe computational challenges, as existing methods often suffer from parameter sensitivity or lack convergence guarantees. To overcome this, we propose a tailored bilinear decomposition that decouples the nonlinear weighted gradient in the TSGV regularizer. This approach yields an equivalent optimization problem governed by cone or sphere constraints, depending on the chosen scaling function. In particular, the cone constraint plays a central role in characterizing edge- and corner-preserving behavior. We solve this reformulation using the alternating minimization method (AMM) equipped with a majorization--minimization strategy, ensuring a monotonic decrease in energy without step-size tuning. Furthermore, we provide a geometric interpretation of the edge-preserving properties of these constraints by analyzing their asymptotic behavior near image singularities. We establish the global convergence of the proposed method to a critical point within the Kurdyka--Łojasiewicz framework. Extensive numerical experiments on Gaussian denoising and non-line-of-sight (NLOS) imaging show that the proposed method achieves PSNR and SSIM competitive with or superior to representative variational methods, especially at high noise levels, and improves the structural reconstruction under dense and sparse scanning.

Global sharpness of a sampling bound does not determine whether the bound is attainable on a particular fixed design. We study ordinary fixed-size volume sampling followed by selected unweighted least squares, with the feature pool and response fixed; subset selection is the only randomness. We first prove a globally sharp all-budget Loewner envelope for centered, full-Gram-whitened coefficient covariance. We then characterize the fixed-design question left open by global sharpness. On the positive-loss, no-coloop strict-interior domain, a feature-only geometric margin is positive if and only if every compatible residual has strict covariance slack at every strict-interior budget, whereas zero margin holds if and only if one compatible residual reaches the Loewner ceiling in at least one coefficient direction at every strict-interior budget. For real whitened designs without coloops, the phase sign is equivalently determined by a pairwise Naimark-complement minor test, which also yields an explicit lower slack certificate. Residual augmentation exposes the response-aware contraction, and a critical equal-leverage specialization identifies an explicit geometric boundary. Any verified positive lower bound on the margin therefore yields a conservative certificate for strictness and for the subset-refit variance term in fixed-query squared loss. Together, these results give a design-specific phase characterization for this finite-pool randomized linear-readout primitive.

Agent harnesses combine retrieval, routing, state, provenance, and verification, but locally successful components may disagree on shared state. We model this failure with a finite \emph{capability sheaf}: stalks encode typed behavior signatures, restriction maps retain shared fields, and accepted runs are useful global sections. An exact finite constraint-satisfaction problem (CSP) defines acceptance, while a linearized relative cohomology class provides a diagnostic and search feature. A controlled experiment over 20 task clusters introduces hidden interior mediators whose raw states are nuisance variables. Quotienting their coboundaries reduces the candidate budget from 2,000 to 1,000 per cluster; aligning the hidden state removes the gap. Exact CSP matches the quotient, so the result demonstrates invariance to stale representatives, not superiority over exact reasoning. We then test the method on a discovery split from the SWE-bench Multilingual pool of PatchFuseBench: 160 issues from 20 repositories, 875 real candidate patches, 2,579 source-aware edit atoms, and 153 newly executed patches. A first pool-level construction is constant because $[b-Dx]=[b]$ in $\operatorname{coker}D$ and therefore cannot rank configurations. A candidate-indexed repair is nontrivial on 848/875 candidates and varies within 120/160 issues. It resolves 118 issues versus 116 for a matched noncohomological selector, but the difference is not supported across repositories (exact sign-flip $p=0.75$). A leave-one-repository-out abstention gate reaches 127/160, tying the strong anchor and exceeding its matched gate by one issue ($p=1.0$). The discovery gate therefore fails and the confirmatory split remains sealed. The study supports the controlled invariance mechanism and an identifiability correction, but not a real-world cohomological advantage.

Multi-turn dialogues let users revoke constraints as easily as impose them, but revocation does not reliably take effect: models keep enacting withdrawn requirements (occasionally beneath comments asserting their removal), a failure we call \emph{behavioral relapse}, or revocation inertia. No existing instrument measures this influence per clause, predicts it before delivery, or repairs it under matched budgets. \sysname{} closes the three gaps through the model API alone: a contract ledger pairs every constraint with an executable checker, records revocations as tombstones, and compiles the net constraint state ahead of time into a single specification; a sequential ablation probe measures per-clause adherence and incremental behavioral effect; a repair ladder operates under token- and attempt-matched budgets. On \dataname{} (\NTasks{} HumanEval tasks, \NClauses{} verified checkers), relapse at an 8B operating point climbs from \ScaleDelayedMTwo{} to \ScaleDelayedMEight{} as constraint load grows, while stronger models sit at floor. Under matched checkers, model, and budget, ahead-of-time compilation significantly reduces relapse against a no-ledger verifier-retry baseline (\RestoreDiff{}, 95% CI \RestoreDiffCI{}, $p$ \RestoreDiffP{}); adaptive ladder interventions stacked on top add no detectable gain (95% confidence excludes gains $\geq$ \LadderExcludedGain{}). The probe predicts relapse before delivery (AUROC \AurocPrimary{}); a one-sentence tombstone note recovers about a third of the compilation effect and survives a placebo control. At \CostDeliveryFactor{} delivery overhead and \CostTotalHedged{} of API compute for every result, revocation failure becomes a measurable, predictable, and repairable property of dialogue state rather than an invisible one.

Large language models are increasingly deployed in settings that require simultaneous adherence to multiple explicit constraints - reasoning structure, safety boundaries, output schemas. Individual constraints are handled proficiently, but the compositional regime, where many must hold jointly, remains poorly characterized: how rapidly does performance degrade, what governs the degradation, and can the collapse be mitigated? We introduce Constraint Saturation Evaluation (CSE), a procedurally generated benchmark that systematically varies the number of simultaneous constraints (k), with every constraint scored by a deterministic, rule-based verifier and zero LLM-judge involvement: 15 models, 36 constraint types, 369,753 checks at k=1-12. Three findings emerge. First, per-constraint pass rate decays gradually and predictably, while the chance of satisfying all k constraints collapses - a model passing individual constraints at ~41% at k=8 succeeds on all eight just 5.7% of the time. Second, constraints do not degrade equally: structural constraints lose 2x more baseline capability per added constraint than lexical ones, ordered by a comprehension-maintenance gap that separates constraints requiring sustained tracking from binary decisions immune to composition. Third, failures are nearly independent, which is what makes the accumulation multiplicative; the residual coupling that does exist tracks shared output features rather than pairwise interference - a wrong sentence count fails every constraint that reads it. Reliable instruction following breaks down beyond 5-6 simultaneous constraints: probe-level success falls below 50% at 7 constraints for the strongest model, and at 3 or fewer for 12 of 15.

The Traveling Salesperson Problem (TSP) is one of the best-known problems in computer science and arises in many engineering applications, such as smart vehicles and intelligent transportation systems. In the "Euclidean" case, each node is defined by its coordinates in the plane and distances are computed using the Euclidean metric. In the Constraint Programming (CP) literature, the Euclidean TSP is typically addressed by computing the full distance matrix and treating it as a general case; however this approach ignores the geometric information carried by the points' coordinates. In this work, we propose new filtering algorithms, implemented in Constraint Logic Programming (CLP), that exploit such geometric information to achieve stronger constraint propagation than existing approaches. Moreover, we show how this methodology can be extended to other Euclidean variants of the TSP, including the Euclidean Generalized Traveling Salesperson Problem (EGTSP), which is relevant in practical routing and logistics applications. Experimental results demonstrate the computational advantages of the proposed approach.

A common problem in social choice is to determine whether there is a social choice procedure, such as a voting method, satisfying some desired criteria. Computer-aided methods such as SAT solving can sometimes answer these questions. However, under typical encodings, a SAT solver may only synthesize a voting method on a finite domain, while we may want one on an infinite domain, such as the domain of all preference profiles for a fixed number of candidates but any finite number of voters. In this paper, we use an approach based on reasoning with constrained Horn clauses and computation with polyhedra to synthesize a voting method on an infinite domain. We then use SMT and Lean to verify its properties. Our main result is a possibility theorem about four well-known criteria from voting theory: the Condorcet winner and loser criteria, positive involvement, and resolvability. Previous work has shown that for five or more candidates, there is no voting method satisfying these axioms, and that for four candidates, there is no method satisfying these core axioms plus one more invariance axiom. Here we show that for four candidates, there does exist a method satisfying the core axioms and more.

Recommendation systems thrive on personalization, where ''correctness'' is rarely a binary truth but a matter of subjective human preference. As Large Language Models (LLMs) are deployed as autonomous verifiers of safety and quality guidelines, they face a distinctive challenge: context-aware preference alignment. Recent gains in Reinforcement Learning with Verifiable Rewards (RLVR) are indexed mostly on objective, mathematical tasks. Through a large-scale study spanning both proprietary and open-source models on four real-world verification tasks from a production recommender platform, we ask whether explicit reasoning generalizes to subjective, human-centric industry rubrics. We expose a fundamental vulnerability: rigid, math-centric reasoning traces actively degrade verification, and applying standard RLVR triggers a phenomenon we term reasoning collapse, in which the policy abandons deliberation in favor of rapid heuristic guessing. We introduce a conditional length-penalized post-training algorithm that intertwines verification accuracy with bounded reasoning length, halting collapse and recovering performance. Finally, we show that a reasoning trace's efficacy is tightly coupled with its socio-linguistic framing: across 1500 synthesized personas, verification accuracy swings by nearly 0.38 macro-F1 depending solely on the adopted reasoning persona---evidence that much subjective-verification error is really reasoning-style mismatch. This observation motivates a mid-training architecture that routes reasoning through contextually aligned personas. This work offers both a scalable algorithmic patch and a long-term architectural blueprint for aligning reasoning models with real-world subjective constraints.

Robotic neural-thread placement requires regulating the insertion-tool tip relative to tissue that moves with cardiac and respiratory pulsation. This paper develops a preview-based relative-motion controller that estimates latency-delayed periodic surface motion, predicts it over a short horizon, and uses offset-free model predictive control to regulate relative placement while limiting actuator effort and lateral relative velocity. In MuJoCo, the 1-DOF controller achieves 12.0\um\ free-space and 1.9\um\ contact RMS relative-placement error, versus 18.3/176.8\um\ for delayed-feedback impedance and 286.1/275.5\um\ for lab-frame PD, at the cost of higher peak contact force (3.43 versus 2.00mN) since offset-free tracking drives the tip fully to the commanded depth rather than yielding against the tissue. In 3 DOF, coupled preview reduces contact lateral shear from 1.34 to 0.50mm/s with 2.1\um\ lateral RMS error. A feasibility-restored octagonal shear formulation keeps the QP solvable under degraded sensing by adding a bounded shared slack: at 10\um\ RMS per-axis sensing noise, where a matched cost-only controller violates the 0.80mm/s budget in all 10 seeds (mean/maximum 0.988/1.175mm/s), the soft-octagon controller completes all 10 seeds with no fallback and no measured violation (0.653/0.712~mm/s), with its operating envelope characterized up to 15\um\ RMS. A two-vertex Lyapunov certificate for the controller's actual finite-horizon error-feedback gain holds over $-40\%/{+}50\%$ reflected-mass mismatch. The modeled tip is a rigid contact point, and the study is simulation-only: flexible-thread and carrier-needle mechanics, a validated transient-force constraint, biological damage thresholds, and hardware-realistic sensing and timing remain required before deployment.

The runtime of Constraint Programming (CP) solvers is highly sensitive to modeling choices, such as symmetry breaking, implied constraints, global constraints, constraint reformulation, and variable representation. Improving these constraint models has traditionally required human expertise, and existing automated reformulation systems are restricted to a predefined library of hand-crafted transformation rules. We introduce an agentic framework that instead reformulates a constraint model from an open-ended space and establishes correctness empirically rather than by construction: a Large Language Model (LLM) agent, given a model and three training instances, proposes alternative formulations, validates each by injecting its solution back into the original model, and diagnoses and repairs failures, returning the best variant it finds in a median of about fifteen minutes. The models are expressed in the CPMpy modeling library, and each proposed model is evaluated on three larger test instances. Across nine combinatorial optimization problems, the generated models outperform the originals on 21 of 27 test instances, and on some problems solve more than two orders of magnitude faster. A comparison against non-agentic baselines that reuse the same validation and selection tools indicates that the gains stem from the agent's iterative diagnosis and repair, not merely from sampling several candidates. These results demonstrate that autonomous agentic methods can support the improvement of constraint models.

There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators. These methods return the result as raw data: an adjacency matrix or a string encoding. The raw data certifies that the graph exists, but it does not reveal any structural properties of the graph. We ask whether one can automatically discover a short algebraic description if only this raw data is provided. We look for a description such as a Cayley graph $\mathrm{Cay}(Γ, S)$ or a lexicographic product $C_5[K_3]$. We address this question with a neurosymbolic approach. We propose an agent that runs on a general-purpose large language model with no fine-tuning or per-target training. The model interleaves reasoning with calls to the computer algebra system SageMath: it analyzes the target graph, proposes and tests candidate constructions, and revises them until the output matches the target. The agent communicates with SageMath through a Model Context Protocol (MCP) server, which we release as a general-purpose bridge. Whether a construction matches the target is checked by a single exact isomorphism test, and therefore rests on the symbolic side and not on the model. We test the approach on a benchmark of 100 highly symmetric graphs, namely two-orbit graphs on up to 25 vertices; the benchmark was fixed in advance. Our agent could find verified algebraic constructions for all of them, without falling back to raw encodings. A strong template-enumeration baseline reaches only about $20\%$, and a catalog lookup could not identify any of these graphs. However, construction quality declines when symmetry is removed. As a concrete application, we identify the smallest known counterexample to the Bernhart-Kainen dispersability conjecture, a $16$-vertex graph that enumeration found as raw data. For this graph, our agent found an explicit algebraic construction.

In this work, viscous fluid flow governed by the Stokes equations in highly perforated domains is studied using physics-informed neural networks (PINNs). Perforated microstructures induce complex boundary conditions and fine-scale flow features that are difficult for standard neural networks to resolve. Conventional PINNs, even when combined with advanced training techniques, can suffer from a loss of accuracy and efficiency as the number of perforations increases. One important source of this difficulty is the soft enforcement of boundary conditions through penalty terms, which can lead to stiffness, gradient conflicts, and poor resolution of near-boundary flow structures. Hard constraints provide an alternative by encoding boundary conditions exactly into the network ansatz, but may introduce undesirable non-local effects due to the global nature of the approximation. To address these challenges, finite basis PINNs (FBPINNs), which are based on domain decomposition and localisation principles, are used together with hard boundary constraints that efficiently encode perforation-related boundary conditions. This approach helps mitigate spectral bias, improves overall accuracy, and exhibits convergence that is only weakly affected by the number of perforations, thereby providing an efficient and highly parallelisable neural network framework. The proposed approach is further supported with theoretical arguments, specifically focusing on the localisation and approximation properties of FBPINNs.

Concept Bottleneck Models (CBMs) provide an interpretable framework by grounding predictions in human-understandable concepts, enabling semantic inspection and test-time intervention. Recent variants have improved CBMs through richer concept representations, uncertainty estimation, and dependency modeling. However, robust reasoning under unreliable concept states remains underexplored. Without such reasoning, misleading semantic evidence can propagate through the bottleneck, compromising both explanations and downstream predictions. To address this issue, we propose ReCBM, an uncertainty-gated relational reasoning framework for CBMs. ReCBM introduces semantically defined concept relations into the bottleneck and uses uncertainty to guide their refinement. By modeling co-occurrence, implication, and exclusion, ReCBM specifies how evidence is exchanged across concepts, while uncertainty modulates the contribution of each concept during this process. Experiments across diverse datasets showed that ReCBM improved concept and task recovery under missing and flipped concepts, supported uncertainty-aware intervention, and extracted compact task-relevant concept subsets without degrading downstream performance.

Code generated by LLMs can violate a developer's implicit intentions when given an ambiguous prompt, yet standard benchmarks measure only whether code passes its stated test. We introduce the Intent Violation Rate (IVR) and a 49-problem pilot benchmark derived from HumanEval+. Each problem strips implicit constraints from a clarified prompt and encodes them as hidden constraint tests. IVR measures the fraction of LLM-generated solutions that pass the stated (visible) tests yet fail hidden constraint tests that capture unstated intent. Evaluating Claude Sonnet 4.6 and OpenAI GPT 4.1, we find both pass over 92% of stated tests yet violate intent in over half of problems (54.5% and 63.5%), following a systematic, bimodal pattern consistent across both models. Out findings indicate that pass rates overstate how well generated code reflects developer intent.

Planning a degree from official university sources requires solving two problems in order. The institution's curriculum must first be reconstructed from catalogs, departmental pages, JSON endpoints, and PDFs that share no schema, and only then can a student-specific path be optimized under prerequisite logic and overlapping requirement constraints. Coupling the two lets each failure mode hide the other, because a planner that drives its own crawling never learns facts its current plan does not need. We present KnowPlan, which enforces an extraction-first boundary and measures the interface between the stages rather than assuming it. CatalogBrowse explores with no access to any user profile. It scores legal actions by lower-confidence expected marginal gain over a finite set of atomic catalog obligations per unit of source access, parses deterministically through platform adapters with a span-constrained clause-to-AST model fallback, and terminates on a closure certificate over index, schema, provenance, and reference completeness instead of a reward threshold. Its output contract is three provenance-linked JSON documents. DegreeMap consumes only those documents. It compiles them into a typed requirement hypergraph and optimizes lexicographically with CP-SAT over hard feasibility, completion horizon, load and risk, personalized utility, and option value, so that each stage optimizes inside the previous stage's proven optimum and stays certifiable within the solver budget. Across a 100-university broad track and a six-school dense track, CatalogBrowse reaches 96.2% inventory recall and 88.7% masked-source recovery at 47% less source access than an exhaustive crawler, DegreeMap holds 100.0% hard feasibility while improving personalized utility by +0.066 over the strongest baseline, and the full pipeline certifies 99.5% of requests with a utility gap to the privileged gold graph of 0.015.

Large language models can derive a plausible mathematical object yet still violate explicit requirements--for example, by omitting a modular reduction, returning a non-integer, or using the wrong encoded answer form. We introduce Constraint-First Reasoning (CFR), a training-free two-stage prompting protocol: Stage 1 extracts and summarizes constraints entailed by the problem, and Stage 2 solves while checking intermediate and final results against that summary. Routed-CFR activates the two-stage protocol only when a text-only regex router detects restrictive cues; otherwise it uses direct chain-of-thought (CoT). Across AIME, CMIMC, BRUMO, and AIMO_AMC, the method improves direct CoT on multiple backbones. We further report convention-controlled routing experiments, matched prompting baselines, problem-level paired tests, decoding robustness, constraint-quality audits, total-token accounting, and an OlympiadBench evaluation. These analyses position CFR as a targeted test-time intervention whose benefit depends on recoverable constraints and reliable Stage 1 extraction, rather than as a general-purpose replacement for mathematical reasoning.

We present a unified theoretical framework connecting classical universal approximation theory, Fourier-feature approximation, and diffractive optical processors. We show that phase-encoded diffractive processors implement finite Fourier-feature expansions whose mathematical completeness follows from Fourier/Stone-Weierstrass arguments, while their physical realizability is governed by finite coefficient synthesis through optimized spatially varying coherent point-spread functions (PSFs). Our analyses derive approximation-error bounds that separate Fourier truncation, PSF-synthesis, input phase error, optical hardware, readout, and noise contributions; establish scaling relationships linking approximation complexity to optical degrees of freedom and input/output space-bandwidth products; derive photon-budget and throughput limits imposed by photon statistics; formulate finite-class statistical learnability bounds for phase-quantized diffractive function approximators; and analyze the impact of spatially incoherent illumination. We further analyze coherent optical cascadability and show that quadratic feature expansion through coherent mixing and optical readout provides a mechanism for enhanced representation while remaining fundamentally distinct from the depth-separation results established for digital neural networks. Our analyses provide a rigorous theoretical foundation for diffractive nonlinear function approximation and establish quantitative relationships among mathematical expressivity, optical hardware resources, statistical learning, and physical performance limits, thereby offering general design principles for large-scale analog optical computing systems.

Recent large language models (LLMs) have demonstrated remarkable progress in constraint-aware navigation, maze reasoning, and graph reasoning. However, their ability to reason about complex routing problems under strict geometric, topological, and electrical constraints remains largely unexplored, despite routing being one of the most challenging and critical stages of electronic design automation (EDA). To bridge this gap, we introduce OmniRouting, the first large-scale benchmark designed to evaluate LLMs on printed-circuit-board (PCB) routing reasoning under real-world industrial design-rule, manufacturability, and connectivity constraints. OmniRouting contains 1,681 industrial-grade schematic-coupled PCB designs, including board geometries, routable component placements by human engineers, footprints, pad locations, netlists, stackup information, and routing constraints. The benchmark comprises four tasks: (1) geometric routing reasoning, generating physically valid copper traces, vias, and layer assignments to connect circuit nets within constrained board regions; (2) design-rule-aware routing reasoning, producing routable layouts that satisfy clearance, trace-width, via, obstacle-avoidance, and board-boundary constraints; (3) electrical functionality reasoning, preserving schematic-specified connectivity while reasoning over net names and functional roles to produce electrically correct routing; and (4) tool-augmented agentic routing, leveraging external tools for tasks (1)-(3). Our results reveal substantial limitations of current LMMs in PCB routing, including weak path-planning capabilities, poor adherence to design-rule constraints, and inconsistent preservation of electrical functionality. We will open-source all benchmark data, evaluation code, and tool interfaces to facilitate future research.

Chain-of-thought (CoT) reasoning improves large language model (LLM) performance while also providing an observable interface to the model's reasoning process. Existing approaches that leverage verbalized CoTs to monitor reasoning correctness, however, largely evaluate the semantic correctness or consistency of individual intermediate steps, rather than how the reasoning process evolves across the trace. As a result, failures distributed across the reasoning trajectory, rather than those localized to a single incorrect step, remain comparatively underexplored. Furthermore, verbalized CoTs need not faithfully reflect the model's internal reasoning, motivating analyses that do not treat individual statements as literal accounts of internal computation. In this work, we therefore ask whether the dynamics of visible CoT can be leveraged to systematically distinguish successful from failed reasoning without assuming such semantic faithfulness. We study a range of LLMs on verifiable Boolean satisfiability tasks with variable complexity, enabling controlled comparisons near each model's capability frontier. Tagging CoT sentences by reasoning function reveals premature verification collapse on SAT problems: incorrect traces enter clause checking earlier, repeat similar operations, and finalize sooner. On UNSAT problems, models presumptuously move towards incorrect SAT conclusions, checking candidate assignments rather than deriving contradictions across constructed cases. Subsequently, a targeted proof-search prompt intervention raises Llama3-70B accuracy from 13.3% to 85%, correcting 84.6% of these errors. These results show that capability failures can manifest as distributed, task-dependent changes in the structure of visible reasoning, and that CoT dynamics agnostic to whether the verbalized trace reflects the model's internal computations can help diagnose and correct failures.

In robot-assisted surgery, Forbidden Region Active Constraints (FRAC) represent a control strategy that helps maintain task safety by generating anisotropic haptic guidance to surgeons. However, several challenges need to be overcome before FRAC can benefit teleoperative surgery in a clinical setting. These challenges include the ability to allow for dynamic tissue deformation, maintain energetic passivity, and speed of implementation, among others. In this study, we propose the pipeline design for an energy dissipative FRAC strategy, which accommodates the dynamic tissue deformation caused by respiratory movements, by utilizing a depth sensing camera. The proposed FRAC strategy adopts a fine mesh representation, with a total number of 122,806 polygons in the case study presented, while running at 43.48Hz. We designed in vitro trajectory tracking experiments conducted by a "virtual" surgeon to aid quantitative assessment of the method, including its effectiveness in maintaining task safety, which was confirmed by successfully maintaining a pre-defined safety distance across all trials. We also conducted comparative studies to investigate the robustness and time-efficiency of our method against other FRAC methods that rely on simple geometry AC representations. We demonstrate that our method provides a more robust and effective guidance overall, while maintaining comparable, if not lower, time costs.

Many operational problems are constrained sequential decision processes with large, combinatorial action spaces and interdependent feasibility constraints. Mixed-integer linear programs (MILPs) handle such constraints flexibly but scale poorly in stochastic environments. Deep reinforcement learning (DRL) promises scalable decision rules, but existing methods either penalize constraints rather than enforce them, or rely on feasibility mechanisms that break down once constraints interact. We bridge this gap by embedding a differentiable convex optimization module inside the policy: a neural network proposes continuous action targets, a quadratic program projects them onto the relaxed feasible set, and a dual-informed integer mapping restores integrality while preserving feasibility. Given a differentiable simulator, the policy trains end to end from sampled trajectories using pathwise gradients, while handling hard constraints with similar flexibility to MILPs. We show that our feasibility enforcement has bounded error relative to an exact integer projection and ensures the entire feasible action space is reachable. We apply the method to multi-echelon production-inventory planning under shared resource and material constraints. Our policy attains an average optimality gap below 1% on small instances. It further outperforms state-of-the-art echelon base-stock policies by up to 9.75% and a rolling-horizon multi-stage stochastic program by at least 7.7% in larger networks. On an industry-scale case study from ASML, it reduces average cost by up to 3.22% relative to the best-known benchmark policy. The savings are largest where planning is hardest: in tightly capacitated systems with high demand variability. More broadly, our work shows that DRL can deliver economically significant savings in sequential decision problems with interdependent hard constraints, which are widespread in practice.

We propose an instantiation of flow matching that relies on a time-independent velocity field (an \emph{autonomous flow}) to exactly map between two distributions, so long as the target is singular, i.e.\ supported on a lower-dimensional data manifold. We also show that the one-step generative map associated with this flow is the unique solution of a simple conservation equation, which can be used to learn the map directly from samples. These autonomous flows and maps give a dynamical meaning to the flux constraint of Beckmann's transportation problem. Their construction provides a unifying framework that recovers, for instance, the closed-form Poisson-flow generative model and equilibrium matching with a quadratic flow-matching regression loss. We illustrate how this theory corrects inconsistencies in existing methods and demonstrate the effectiveness of the autonomous flow and the one-step map on ImageNet 256x256.

This paper introduces SCHEDBench, a natural-language benchmark for evaluating combinatorial scheduling constraint faithfulness under surface-form variation. Grounded in canonical scheduling instances and solver-derived feasibility and optimality, SCHEDBench assesses whether large language models (LLMs) generate schedules with the same constraint-feasible behavior across varied natural-language (NL) surface forms. SCHEDBench spans 1,132 instances across job-shop scheduling problems (JSP), single and multi-mode resource-constrained project scheduling problems (RCPSP), nurse rostering/scheduling, and curriculum timetabling problems of varying difficulty. Instances are templated into natural language problems using domain-specific templates, themed entities, lexical-syntactic template rephrasing, and constraint-level surface-form variation, with reference solutions verified for feasibility and objective optimality. Across thirteen frontier and open-weight LLMs, we find that models are not reliably invariant to semantically equivalent renderings of the same scheduling problem. Surface-form variation reduces feasibility and induces above-noise shifts in per-instance hard-constraint violations on matched instances. Among the tested isolated axes, constraint reordering yields the clearest above-noise sensitivity.

Maintaining consistency between natural language documentation of business rules and their evolving internal implementations is a significant challenge in large-scale systems. We present SIRNA, a tool and framework for checking such consistency using SMT solvers. Using the case study of cost calculations in tax domains, we demonstrate a three-part system that combines large language models (LLMs) with formal verification methods. SIRNA translates natural language documentation into candidate SMT formulas using LLMs, followed by checks to validate the translations. Then, corresponding business rules are converted into equivalent SMT representations and validated against the natural language formalizations. Our method is generalizable to domains where business logic exists in both natural language documentation and programmatic implementation. Compared to baseline evaluations, SIRNA significantly reduces the number of false positives and false negatives while offering explainability for its findings.

When the context window is under pressure, LLM systems compact prior context to continue ongoing tasks. We identify a class of user-issued instructions, Session Constraints (SCs), such as "do not delete any emails until I confirm," that are meant to constrain LLM's behavior for the remainder of a session but are silently dropped during compaction. To quantify this loss, we introduce COMPINT, an evaluation suite that evaluates compactors across three long-context scenarios: multi-turn chat, agentic trajectory, and long-horizon research. Current compactors retain only 17% of injected SCs on average, and most perform worse than running the same task without compaction. Retention varies sharply with compactor, prompt, context length, SC phrasing, and injection location, showing that the loss is systematic rather than tied to any single setting. We propose an SC-aware extractor that runs alongside the compactor as a plug-and-play module, achieving over 90% retention across all three scenarios without modifying the compactor or LLM. The COMPINT evaluation suite and accompanying implementation are available at https://github.com/ZhiqiEliWang/compaction-integrity.

Large language models (LLMs) can translate natural-language optimization problems into solver-ready formulations, but direct code generation is brittle: schema, indexing, and semantic errors can cause compilation failures, infeasible models, or incorrect objectives, while iterative repair, search, and multi-agent workflows increase inference cost. We present IR2Solve, an intermediate-representation-first autoformulation pipeline that uses a single semantic LLM call to produce a schema-constrained ModelIR, followed by two deterministic stages: verification and IR-to-solver compilation. ModelIR explicitly represents sets, parameters, variables, objectives, and constraints using restricted Python-like expression strings. A concrete scalar-constraint convention represents finite per-index constraint families as individual entries, reducing free-index and implicit-quantification errors while simplifying downstream verification and compilation. Across six cleaned optimization benchmarks, IR2Solve achieves strong objective correctness and remains competitive with recent optimization-modeling systems. A controlled ablation on 153 IndustryOR and ComplexLP instances shows sequential gains from the structured IR interface, the scalar-constraint instruction, and deterministic verification. On a matched ten-instance cost panel, IR2Solve uses one semantic call per instance, whereas Chain-of-Experts and SAC-Opt use 8 and 39 calls per instance and consume 3.3 and 22.9 times the token volume of IR2Solve, respectively. These results show that structured intermediate representations, combined with deterministic post-generation processing, provide a practical accuracy-cost trade-off for LLM-based optimization autoformulation.

Professional-document review is a constraint-checking problem in which decisions depend on relations among text, geometry, pages, and document revisions. We present an evidence-grounded pipeline that normalizes extracted facts, executes four-state rules deterministically, retains source spans, and escalates unresolved cases. We evaluate its PDF evidence allocator on 160 reference-based tasks from 29 construction projects using a repeated four-system test and a disjoint two-system breadth extension. In the repeated test, reallocating a four-image budget from retrieved page overviews to one overview and three overlapping tiles improves project-family standardized decision accuracy by 10.6 percentage points (95% project-cluster bootstrap CI: 4.3 to 18.0; exact p = 0.031). This effect does not persist in the broader block: Region-RAG changes accuracy by -4.1 points (95% CI: -10.2 to 1.9; exact p = 0.209), while an equal-image sensitivity favors page breadth. Exact finding-set recovery remains low, false passes remain common, and repeated-run agreement is poorly calibrated. The results identify a resolution-breadth trade-off rather than a universal advantage for region-focused evidence, motivating rule-aware evidence routing and expert review.

Traversing crests, ledges, and ditches at high speed often launches vehicles into the air, and a mishandled landing presents a substantial crash hazard. We show that the airborne phase is barely controllable: on a 1383 kg platform the wheel angular-momentum budget caps the recoverable pitch-rate change at roughly $9$-$13^\circ$/s in the tighter nose-up direction under drive at typical takeoff wheel speeds, and at about twice that in the reverse-inclusive braking direction; driving the wheels to their drivetrain hard limit raises the measured nose-up ceiling to only $16$-$18^\circ$/s. Takeoff pitch-rate disturbances beyond this directional budget are physically unrecoverable in flight, so the decisive leverage lies before takeoff. DART (Dual-Axis Airborne Reachability-Gated Torque-Reaction) back-propagates the landing constraint into a closed-form certified feasible-takeoff set, which supplies a conservative go/no-go condition and a pre-takeoff speed-shaping law. In flight, DART regulates pitch and roll via steer-resolved wheel-reaction torque, governed by a per-flight roll latch derived from the yaw-coupling analysis. In deterministic full-scale simulation in BeamNG.tech, a calibrated pre-takeoff speed regulator reduces touchdown speed by 36% and raises on-target landings from 0/30 to 30/30. Under the same steep-lip approach the airborne law completes 29/30 safe landings under crash-avoidance bounds versus 0/30 for reaction-wheel-style PD (RW-PD) and time-optimal bang-bang (TOBB). On banked run-ups DART holds the median pitch error at or below $2^\circ$ at every cross-slope, with the largest baseline separation at $γ=12^\circ$. Across disturbance regimes, the latch preserves pitch-only allocation on low-disturbance entries and enables dual-axis control when roll becomes binding. All results are from simulation; hardware validation remains open.

Constraint programming is a core technology for solving complex combinatorial problems in scheduling, planning, configuration, and verification. Trusting its results therefore demands guarantees at two levels: that reformulations applied beforehand are semantics-preserving, and that solvers produce correct answers. In this work, we introduce a framework that addresses both verification levels in the Lean theorem prover: it can be used to prove formulation-level properties, such as equivalence, equisatisfiability, and the correctness of symmetry-breaking constraints, parametrically for entire problem families; and to check solver-produced certificates for individual instances via translation backends to external formats such as MiniZinc, SMT-LIB, and OPB. Combining both levels yields an end-to-end workflow that establishes the satisfiability or unsatisfiability of a constraint problem without trusting the external solver. Experimental results show that our framework's verified symmetry breaking also pays off in practice: a single parametric proof per problem family, reused across all instance sizes, reduces solver search effort by a factor of up to 2x10^7, while the entire in-Lean certification stays affordable, taking at most a few minutes for our largest instances.

Combinatorial problems appear in numerous industrial applications. A common approach is to formulate these problems as declarative constraint models that can subsequently be compiled to and solved by a range of back-end solvers. Recent work shows that Large Language Models (LLMs) can produce correct models from natural language, but even a correct model can be expensive to solve because performance remains sensitive to modelling choices. In this work, we investigate whether LLMs can automate performance-oriented model reformulation. Inspired by Automatic Heuristic Design (AHD), we use an evolutionary framework in which an LLM proposes candidate reformulations that are verified and benchmarked against the user-defined baseline model. We compare AHD-adapted search strategies that control which prior attempts, instructions, and measured feedback enter each prompt. Existing retention strategies prioritize recency or performance, but do not explicitly diversify the context. To cover this gap, we introduce Profile-Diverse Retention (PDR), which applies Maximal Marginal Relevance (MMR) to instance-level runtime vectors to retain behaviourally diverse attempts. We systematically evaluate the strategies on eight CSPLib problems using validation-based final model selection. The results show that: (i) iterative reformulation can produce substantial held-out speedups; (ii) strategies that keep the retained context diverse outperform those that retain only recent or the fastest attempts; and (iii) validation-based selection improves the held-out speedup of every strategy.

Writing Answer Set Programming (ASP) theories from scratch is a difficult and time-consuming task. We take a neurosymbolic approach to study whether a model can distill complete and correct theories, given a fixed agent harness with the solver in the loop. The protocol is dataset-agnostic: with a single prompt and an empty file as the starting point the model is given a 1-hour time limit to derive a complete theory. We chose VQA as the application domain, three benchmarks (CLEVR, GQA, CLEVRER), as these are publicly available and non-trivial. In order to study the model scale required for solving this task we nine different models: four frontier (Claude Sonnet 4.6, Claude Opus 4.7, GPT-5, DeepSeek V4 Pro), two mid-tier (DeepSeek V4 Flash, gpt-oss-120b), and three open-weights (qwen3.6-27b, gpt-oss-20b, qwen3.5-9b). Three of four frontier models reach 100% on CLEVR and 92.8%-98.8% on GQA; on CLEVRER, Sonnet, Opus, DeepSeek V4 Pro score 92.7%-95.3%. GPT-5 reaches 98.7% on CLEVR but drops to 41.8% on GQA and to 86.7% on CLEVRER. Adding handwritten reference theories from other datasets moves the other three frontier models by at most +/-3.4 pp but reduces GPT-5's accuracy by 3-19 pp. We release the code, prompts, and theories distilled.

SHACL shapes enable data graph validation, making automatic shape learning essential for knowledge graph applications. We investigate the well-known fitting approach to this task: given sets P and N of positive and negative example nodes from an input graph, compute a shape expression C, possibly using shape names defined in a recursive shape catalogue, that validates at every node in P and none in N. We focus on the case where C is written in a core fragment of SHACL corresponding to the Description Logic ELI. For the catalogue, we consider the well-founded, stable, and supported semantics. We address fitting existence and most specific fitting computation, establish tight exponential-time upper bounds for both problems, and obtain polynomial bounds for relevant special cases.

Instruction-following ability is critical for deploying large language models in real-world applications, where downstream components depend on the output satisfying specific constraints. Modern deployments increasingly handle the full task in a single LLM call, with one prompt specifying a layered output whose overall artifact, structural sections, and nested fields must each satisfy concrete constraints. Existing instruction-following benchmarks treat the constraint set as a flat list applied uniformly to the response, so they cannot scope a check to a particular section of the output. We introduce IFHierBench, a hierarchical instruction-following benchmark of 600 prompts stratified across four constraint-tree depths and 35 distinct constraints, each prompt paired with a deterministic checker that verifies satisfaction at every scope. Evaluating seven leading proprietary and open-weight models, we find that even the strongest model only marginally exceeds 50% prompt-level accuracy and that accuracy degrades sharply as constraint depth grows. Reliably following nested constraints remains a substantial gap for current LLMs, motivating future training methods that consider constraint adherence at finer granularity to achieve better instruction-following ability.