Feasible but Not Safe: Constraint Violations and Report-Channel Attacks in Learned Cell-Free ISAC Association

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.

frb100-40 After Two Decades: An Optimality Certificate and a Preregistered Search Study

For more than 20 years, the Model-RB benchmark frb100-40 remained an open challenge; since 2014, its public record had stood at 99 of 100 variables. We give a directly checkable 100-vertex independent set for its 4,000-vertex graph. Together with a verified partition into 100 cliques of size 40, the witness proves that the maximum independent-set size is 100 and the minimum vertex-cover size is 3,900. The stochastic run that found the witness is kept separate from this proof. We evaluated its added pair and triple repair operators in a preregistered campaign comprising 8,668 valid runs. The primary comparison found no detectable acceleration over base ULSA (hazard ratio 0.967, 95% confidence interval 0.915-1.023; p=0.248), and the factorial ablation reached the same conclusion. On a smaller FRB suite, the group-aware CSP pipeline solved 2,500/2,500 runs, compared with 2,391/2,500 for LibMVC-NuMVC. On frb100-40, full ULSA, base ULSA, and NuMVC each produced 0/56 new certificates. With no events, the planned cross-solver hazard ratios remain unidentified. NuMVC ended with cover size 3,902 in 40 runs and 3,903 in 16. Exhaustive enumeration showed that none of the 108 unique recorded conflict-two states had a strictly improving group-aware CSP neighbor within Hamming radius three. The certificate settles the instance. The experiments characterize the search barrier, and the preregistered comparisons show no heuristic advantage.

Beyond Surface Forms: Symbolic Edits as a Test for Logical Reasoning with LLMs

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.

Constrained Entity Selection under Partial Knowledge for LLM-Based Knowledge Graph QA

Large language models are increasingly used for knowledge graph question answering (KGQA), but can fail to correctly ground answers in the underlying graph. Current approaches to LLM-based KGQA either rely on full semantic parsing into executable queries such as SPARQL, which is brittle in practice due to complex schemas or incompleteness of real-world KGs, or on LLM-reasoning and answer generation over KGs, which can be more robust but lacks formal guarantees. In this work, we study a complementary setting in which \emph{candidate} answers are generated by an LLM-based system and subsequently verified using lightweight symbolic constraints derived from the question. We introduce \emph{Constrained Entity Selection under Partial Knowledge (CES-PK)}, a problem formulation that focuses on eliminating invalid answers and providing symbolic support for valid ones without requiring construction of executable logical forms. To account for incomplete KGs, we employ a three-valued constraint semantics (\emph{satisfied, violated, unknown}) that avoids incorrect rejections under open-world assumptions. To demonstrate the effects of our method, we instantiate this framework over the Hetionet biomedical knowledge graph and evaluate the impact of type, relation, and exclusion constraints. Experiments show that precision improves by filtering invalid candidates, while recall is preserved due to retaining candidates whose constraints are not explicitly violated. Satisfied constraints provide additional positive symbolic evidence to rank remaining candidates.

Evaluating SAT Solver Metrics as Predictors of Human-Perceived Nonogram Difficulty

Algorithmic solver effort is often assumed to align with perceived puzzle difficulty, but this assumption is rarely tested against human solving data. We evaluate this assumption for Nonograms, a popular logic puzzle similar to Sudoku in which numeric clues along each row and column determine a unique solution grid. We formulate Nonograms as a constraint satisfaction problem and solve them using existing SAT solvers. We then conduct a user study in which we collect data on both participant interactions and reported difficulty. We find that neither participants' reported difficulty nor their behavioural signals correlate meaningfully with SAT solver metrics; however, we find evidence that expertise moderates the relationship between solver metrics and reported difficulty. In this process, we uncover distinct, recurring solving strategies that indicate human preference for complex propagation, diverging from solver-measured complexity.

Generate in the Chart, Not on the Boundary: Function-Symbol Grounding for Hard Constraints in LTN-GANs

Logic Tensor Network-Enhanced Generative Adversarial Networks (LTN-GANs) inject background knowledge by grounding each logical axiom as a predicate and training the generator to raise its satisfaction, a fuzzy truth value in $[0,1]$. Previous LTN-GAN work grounded every constraint this way, at the predicate level, and improved constraint satisfaction. A predicate, however, only scores a sample, so it cannot embed hard structural constraints, rules such as orderings, positivity, and definitional identities that must hold in every generated sample. In this work, we investigate grounding each axiom as a function symbol inside the LTN framework. We compare against the state-of-the-art alternative, a constraint layer that clamps each violating sample onto the feasible boundary and so produces outputs that are always valid. Our investigation shows that a valid sample is not always a realistic one. An inequality is not merely satisfied or violated. It holds by a margin, and a faithful generator should also reproduce the margin's real distribution. We find that the resolution ratio $R$, the data's scale over the margin's spread, is a diagnostic, computable before training, of which constraints a chosen grounding can learn. When $R$ is large, the predicate receives no learning signal, the clamp pushes every sample onto the boundary, and the margin distribution is lost while every standard metric still looks fine. A function symbol avoids both failures, computing the constrained variable rather than scoring it. Together the function symbols form a chart, a coordinate system inside the feasible region, where every sample is valid by construction and the margin is learned like any other quantity.

Synthesizing Feature Extractors: An Agentic Approach for Algorithm Selection

Algorithm selection for constraint satisfaction problems requires extracting features that capture problem structure. Manually designing feature extractors demands deep domain expertise and quickly becomes a bottleneck when new problem classes appear. We present an automated approach that uses Large Language Models (LLMs) in an agentic check--fix--verify loop to synthesize executable Python scripts that act as interpretable, problem-specific feature extractors. Given a high-level MiniZinc model and an instance, the LLM agent generates code that constructs a typed graph representation and computes structural properties such as graph density, variable clustering, and constraint tightness. We evaluate our approach on three combinatorial problems (vehicle routing, car sequencing, fixed-length error-correcting codes) with a portfolio of five state-of-the-art solvers. The synthesized extractors yield algorithm selectors that consistently outperform both expert-curated mzn2feat features (up to $8.3$ percentage points (pp) test-set accuracy on FLECC) and the best transformer-based trans2feat variants. In the meanwhile, the synthesized feature extractors remain inspectable.

MACS: A Hybrid Multi-Agent Framework for Reliable Conversational E-Commerce Recommendation

Conversational recommendation for e-commerce is increasingly mediated by large language models (LLMs), yet many real-world deployments operate under a stricter requirement: recommendations must be drawn only from a merchant's fixed catalog, without web search or unsupported product claims. In this setting, the main challenge is reliability under hard constraints: the system must satisfy user requirements, remain grounded in available inventory, and preserve preferences across multiple conversational turns. We present MACS (Multi-Agent Commerce System), a hybrid multi-agent framework for reliable conversational recommendation in fixed-catalog settings. MACS uses LLMs for language-facing tasks such as interpreting user requests, eliciting preferences, and generating responses, while correctness-critical operations, including product retrieval, hard-constraint filtering, brand exclusion, and progressive relaxation, are executed deterministically by the merchant agent. A session-persistent preference layer tracks constraints across turns, enabling consistent handling of budget overwrites and exclusion reversals. On a 140-query single-turn benchmark, MACS achieves the highest pass rate (87.1%) and perfect brand compliance (1.000). On a 10-scenario multi-turn benchmark, MACS achieves the strongest macro Pass@5 (72% vs. 56% GPT+Catalog / 52% Gemini+Catalog) with zero constraint drift. The advantage is sharpest on exclusion reversal (100% vs. 20% / 0%) and constraint accumulation (100% vs. 60% / 40%). Mean judged response quality is similar across systems (0.751 vs. 0.736). These results suggest that hybrid architectures combining deterministic constraint enforcement with session-persistent preference tracking provide stronger reliability-oriented performance than catalog-bound prompt-only baselines in the fixed-catalog merchant setting.

Large Language Models Can Follow Instructions, But Not Many at Once: Phase Transitions in Compositional Constraint Satisfaction

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.

TRACE: Trustworthy Retrieval-Augmented Conversational Engine

Public service chatbots are expected to deliver recommendations from an underlying public service directory, while also making sure that the recommendations respect explicit user constraints. In practice, public service directories are noisy and inconsistent, and general-purpose large language model (LLM) or AI-based chatbots frequently generate unreliable recommendations, citing unverified sources from the web. We investigate the impact of retrieval quality on constraint-aware recommendation in public service conversational systems built over noisy and heterogeneous service directories. We propose TRACE (Trustworthy Retrieval-Augmented Conversational Engine), a retrieval-based, constraint-aware framework that parses input user queries into structural and semantic constraints for downstream retrieval, with the help of a dual data representation schema. Using a curated statewide pantry directory and a synthetic query benchmark, we evaluate multiple knowledge-representation variants with and without knowledge graphs (KGs). We experiment with several open-source LLMs and a proprietary model, showing that strengthening retrieval substantially improves user constraint satisfaction while reducing hallucinated recommendations. Performance differences across LLMs narrowed in our experiments as retrieval quality improved, making results less sensitive to model size. These findings suggest that the quality of retrieval is key for robust public service conversational systems.

ComboShoppingBench: Evaluating LLM Agents for Budget-Constrained Basket Shopping with Coupons

Real-world shopping often requires constructing a basket of complementary items rather than retrieving a single product. Such combo-shopping tasks arise in device setup, meal preparation, event planning, and group takeout ordering, requiring joint reasoning about item compatibility, availability, store-level requirements, delivery fees, coupons, and budgets. Evaluation is challenging because multiple baskets may satisfy the same request, making exact-match metrics unsuitable, whereas semantic evaluation alone cannot detect infeasible orders, invalid coupon combinations, or incorrect payments. We introduce ComboShoppingBench, an agentic shopping benchmark for open-ended yet verifiable basket construction in a simulated commerce and takeout environment. During task synthesis, an exploration agent constructs a feasible and semantically coherent basket of purchasable products; this witness guides the generation of coupons, budget constraints, user queries, and aligned evaluation rubrics. During evaluation, LLM judges assess semantic satisfaction, response quality, and claim faithfulness, while deterministic validation checks product-ID validity, budget compliance, and coupon optimality. Experiments with diverse LLM agents demonstrate that even strong agents struggle on ComboShoppingBench, highlighting substantial room for improvement in reliable, constraint-aware combo shopping.

Commitment Before Realization: When Classifier-Free Guidance Becomes Unnecessary in Masked Diffusion Language Models

Classifier-free guidance (CFG) is usually kept on throughout masked diffusion language model decoding, although its benefit varies across prompts and over time. We study when CFG is actually needed by comparing, from any partial output, the probability of eventual constraint satisfaction under continued CFG and under base-only continuation. Their difference defines the remaining value of guidance. Guidance dependence is highly prompt-specific. Many prompts already succeed without CFG, while for others it provides no measurable benefit or can be harmful. For prompts that do benefit, the gain is often concentrated early. We define the commitment horizon $\astar$ as the earliest point from which switching all remaining decoding to the base model reduces final success by no more than a chosen tolerance. Under the base model, the corresponding success probability, or committor, is a martingale. To first order, CFG's per-step effect is governed by the covariance between the guidance logit direction and the successor committor. This gives a local account of when guidance can help, but it does not by itself locate the horizon. Among prompts with an observed preterminal horizon, $\astar$ is usually early and varies more within constraint families than between them. Freezing each prompt at its own cross-fitted horizon is noninferior to full CFG on all 13 subtasks at the prespecified margin, even while many tokens remain masked. This separates commitment from realization. The boundary also identifies a later region in which higher parallelism adds only a small cost in constraint success, although fluency still degrades with parallel width. For failed trajectories, reopening committed positions improves recovery in both failure modes.

SCHEDBench: A Benchmark for Evaluating LLM Constraint Faithfulness in Natural-Language Combinatorial Scheduling

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.

Maximum Satisfiability of Simple Temporal Problems

The Simple Temporal Problem (STP) is a core framework for quantitative temporal constraints. As STP data can be inconsistent, we study MAXSTP: compute a maximum-cardinality consistent subset of constraints. This extension is NP-hard, and we analyze its parameterized complexity under measures that capture practically relevant instance features: the number of variables $n$ (instance scale), the maximum coefficient magnitude $k$ (numeric range), and structural parameters of the constraint graph such as treewidth $tw$ (decomposability) and vertex cover size $vc$ (density). We show that MAXSTP is W[1]-hard parameterized by $n$, implying that $n$ and parameters that depend on $n$ (including $tw$ and $vc$) are insufficient for fixed-parameter tractability. For combined parameters, we give an $O^*(k^n)$-time algorithm, yielding single-exponential solvability for fixed $k$. While $k+tw$ remains W[1]-hard, MAXSTP is in XP via an $O^*((n\cdot k)^{tw})$ algorithm. Our results suggest that MAXSTP is often computationally harder than optimizing qualitative CSPs. We verify that many such problems (including RCC-8 and Allen's algebra) are FPT when parameterized by $n$ or $tw$. However, we also demonstrate that FPT algorithms for MAXSTP are indeed possible but with other parameters such as $k + vc$.

Supporting Autonomous Process Execution within a Multi-Perspective Constraint Frame via Numeric Planning

AI-Augmented Business Process Management Systems (ABPMS) enhance traditional BPMS by leveraging advanced AI techniques to define, execute, and monitor complex process structures. Within this landscape, Framed Autonomy denotes the capability of a system to autonomously advance the execution of a Business Process (BP) instance while strictly adhering to a predefined frame, i.e., a set of constraints that may span multiple perspectives. Existing research on framed autonomy has predominantly focused on control-flow constraints, either declarative or procedural, and typically relies on their transformation into automata-based representations. In this study, we extend this line of work by introducing a novel tool for what-if analysis that augments the process frame with multi-perspective constraints, including data-aware and temporal conditions. Given a partial process execution, the proposed approach exploits this enriched frame to recommend optimal continuations in compliance with the underlying process specifications. We additionally report an empirical evaluation demonstrating the scalability and effectiveness of the technique, thereby highlighting its potential for supporting autonomous and constraint-aware decision making in ABPMS.

Towards Detecting Inconsistencies in End-to-end Generated TODs

Generative AI is profoundly transforming the core technologies behind conversational systems, shifting from component-based to end-to-end approaches. However, Large Language Models (LLMs) may still generate inconsistencies, a critical issue particularly in Task-Oriented Dialogues (TODs), where system responses must strictly adhere to information from a domain knowledge base (e.g., restaurants in a city). A single hallucination (e.g., suggesting a non-existent restaurant) can lead to severe task failures. We investigate a method for automatically detecting inconsistencies by conceptualizing TODs as a Constraint Satisfaction Problem (CSP), where variables represent dialogue segments referencing the conversational domain, and constraints among variables capture dialogue properties such as turn coherence and adherence to domain knowledge. We propose a pipeline that first identifies variables in a target dialogue and then applies a CSP solver to identify valid solutions. By comparing the target dialogue with valid variable assignments, we can detect inconsistencies and suggest minimal changes to ensure dialogue consistency. We demonstrate the high accuracy of the CSP-based approach in detecting inconsistencies, and provide a detailed analysis of our findings.

RLVP: Penalize the Path, Reward the Outcome

Agents acting on our behalf in the real world (e.g. placing phone calls) must learn online from costly, often irreversible interactions rather than cheap simulator steps. Two things follow. First, deployability depends on the path, not only the outcome. An agent must respect outcome-neutral constraints such as not repeatedly calling an unresponsive user, respecting business hours, or completing required authentication constraints that outcome-based rewards cannot express, since violating them frequently improves apparent success. Second, because each interaction is expensive, the agent must learn efficiently from very few examples. Reinforcement learning from verifiable rewards (RLVR) is blind to both challenges: it optimizes solely on the outcome and wastes expensive rollouts on all-fail groups where group-relative advantage collapses to zero. Attempts to densify supervision by rewarding progress target the hard-to-verify direction. In contrast, real agentic environments can cheaply detect bad moves. Since group-relative advantage is equivalent to within-group variance, a dense signal helps only when it supplies variance the outcome lacks. A verifiable penalty on the path meets this condition reliably, while a progress potential helps only where partial progress is reachable. The resulting recipe "penalize the path, reward the outcome" achieves high task success with near-zero violations, where outcome-only training violates constraints on nearly every episode. We provide four design rules for effective penalties, including avoidance of the inaction trap that arises when a penalty is used in isolation.

StructuredEdit: Constraint-Aware Graphic Design Editing via Differentiable Parameter Propagation

Graphic design editing requires precise manipulation of typography, layout, and visual hierarchy under strict design constraints. Following the introduction of large language models, organizations have increasingly promoted vision-language models to enhance productivity. However, current models operate on pixels and achieve only 52% constraint satisfaction on structured design edits, thereby limiting their reliability for professional workflows. We present StructuredEdit, a pipeline that reframes design editing as parameter manipulation rather than pixel generation. Our core technical contribution is Differentiable Parameter Propagation (DPP), a training method that embeds hard design constraints into vision-language model fine-tuning by backpropagating pixel-level constraint violations through a lightweight differentiable rasterizer. A hybrid candidate-and-filter pipeline produces 125k validated edit triplets. The resulting system reaches 89% constraint satisfaction versus 52% for GPT-4V, 0.82 matched-element Intersection over Union, and 76% top-1 font accuracy over the 100 most-frequent design typefaces. In a user study (N=35), editing time drops 33% and correction iterations drop 44% relative to a GPT-4V baseline.

G-RRM: Guiding Symbolic Solvers with Recurrent Reasoning Models

In this work, we focus on SE-RRMs, a symbol-equivariant instantiation of RRMs that exhibits improved extrapolation to larger problem sizes. We propose a neuro-symbolic approach, ``Guiding with Recurrent Reasoning Models'' (G-RRM), which integrates SE-RRMs with symbolic solvers for constraint satisfaction problems. SE-RRMs act as neural solvers that generate full solution proposals and guide classical symbolic solvers, such as backtracking or SAT-based methods like Glucose 4.1 and CaDiCaL 3.0.0, that produce globally correct solutions. Centrally, we investigate when neural guidance with G-RRM improves the search efficiency of symbolic solvers. % Our experiments show that the efficacy of G-RRM depends on two conditions: first, the problem instances must have an expansive combinatorial search space to expose potential gains, and second, the solver architecture must be capable of dynamically overwriting its branching choices to recover when neural hints are imperfect. When these conditions hold, guidance drives median conflict counts to zero and yields significant wall-clock speedups: on $9\times9$ Sudoku, where the SE-RRM correctly solves $91.1\%$ of instances, backtracking accelerates by $33.3\times$ and Glucose 4.1 by $1.70\times$ (median, $p<0.001$), with Glucose 4.1 retaining a $1.17\times$ speedup on perfect-hint $25\times25$ grids. In contrast, CaDiCaL 3.0.0, whose runtime is overhead-dominated and which always respects the injected branching hints rather than overwriting them, shows no significant speedup (median $1.02\times$, n.s.) and even a small significant mean slowdown ($0.90\times$) on $9\times9$. These results delineate the regimes in which neural guidance translates into practical speedups.

Constrained Tabular Diffusion for Finance

Generative models in finance face the dual challenge of producing realistic data while satisfying strict regulatory and economic objectives, a requirement that standard tabular diffusion models cannot provide. To address this difficulty, we introduce Constrained Tabular Diffusion for Finance (CTDF), a novel integration of sampling-time feasibility operations with mixed-type tabular diffusion in financial applications. By incorporating a training-free feasibility operator into the reverse-diffusion sampling loop, CTDF enforces hard constraints for applications such as simulation, legal compliance, and extrapolation. Extensive experiments on large-scale financial datasets demonstrate zero constraint violations and improvement in scarce data utility. CTDF establishes a robust method for generating trustworthy and compliant synthetic data, opening new avenues for rigorous generative modeling and analysis in the financial domain.

VGB for Masked Diffusion Model: Efficient Test-time Scaling for Reward Satisfaction and Sample Editing

Inference-time scaling is a promising paradigm to improve generative models, especially when outputs must satisfy structural constraints or optimize downstream rewards. We consider Masked Diffusion Model (MDM) and introduce MDM-VGB, a discrete diffusion sampler that augments unmasking generation with theoretically principled reward-guided remasking. Inspired by the recent success of the classical Jerrum-Sinclair backtracking Markov chain in reward-tilted generation, MDM-VGB extends the backtracking random walk from a fixed prefix tree to a masked-state graph, allowing tokens to be unmasked and remasked at arbitrary positions. The resulting sampler favors unmasking and remasking moves that lead to higher-value partial configurations, enabling both effective high-reward generation and efficient repair of low-reward samples. We prove that MDM-VGB is robust to process-verifier noise and achieves quadratic complexity, while popular test-time heuristics such as best-of-$N$ can incur exponential complexity due to error accumulation. Our theoretical findings are corroborated by strong empirical performance, particularly on popular constraint-satisfaction and scientific benchmarks such as Sudoku and QM9.

AdaPlanBench: Evaluating Adaptive Planning in Large Language Model Agents under World and User Constraints

Planning for real-world problems by language models often involves both world and user constraints, which may not be fully specified upfront and are progressively disclosed through interaction. However, existing benchmarks still underexplore adaptive planning under such progressively revealed dual constraints. To address this gap, we introduce AdaPlanBench, a dynamic interactive benchmark for evaluating whether Large Language Model (LLM) agents can adaptively plan and re-plan under progressively revealed world and user constraints. AdaPlanBench is built on 307 household tasks, with a scalable constraint construction pipeline that augments each task with dual constraints. At runtime, agents interact with the environment in a multi-turn protocol where hidden constraints are revealed only when the agent proposes a plan that violates them, requiring iterative plan revision under accumulating feedback. This makes planning challenging, as agents must infer and track constraints from feedback while re-planning effectively. Experiments on ten leading LLMs show that adaptive planning under dual constraints remains challenging, with the best model reaching only 67.75% accuracy. We further observe that performance degrades as more constraints accumulate, with user constraints posing a particularly large challenge and failures often stemming from weaker physical grounding and reduced effectiveness. These results establish AdaPlanBench as a testbed for dual-constrained interactive planning and highlight the challenge of reliable adaptation to dynamically revealed constraints in LLM agents.

DiBS: Diffusion-Informed Branch Selection

Sudoku is a representative constraint satisfaction problem that requires global structural reasoning under strict discrete constraints. The existing works of solving Sudoku mainly focus on two dominant approaches, i.e., traditional heuristic and deep learning solver. However, they suffer from two complementary limitations: learning-based solvers lack hard correctness guarantees, while complete symbolic solvers are still prone to long-tail search. To address these shortcomings, we propose a novel diffusion model-guided approach, termed as DiBS, for the branch selection search process. Specifically, DiBS keeps the symbolic solver complete and uses the diffusion model as a branch-ordering guide. The core method is ranking candidate values under the current partial assignment and lightweight consistency signal. Furthermore, we provide an in-depth theoretical proof to reveal how it works and why it works. Experiments on the challenging Royle 17-clue Sudoku benchmark show that our DiBS substantially reduces search cost relative to strong heuristic baselines, especially in nodes, backtracks, and long-tail percentiles. Besides, these results confirm that learned global guidance is effective on hard instances where branch-order mistakes are most expensive. All codes are available at https://github.com/shanxierdan/DiBS.

Bridging Auxiliary Constraints to Resolve Instruction Following in Large Reasoning Models

Large Reasoning Models (LRMs) have demonstrated impressive capabilities in many tasks, yet they struggle with reliably following multiple instructions, either by failing to satisfy individual constraints or by struggling to balance competing constraints simultaneously. We formalize this challenge as the Constraint Adherence Problem (CAP). This paper introduces a novel framework that addresses CAP by representing instructions as a structured knowledge graph of constraints. Our approach, Constraint Relationship Graph Completion (CRGC), explicitly models relationships between constraints, identifies adherence challenges, and discovers ``bridge constraints'' that help the model better focus on and reconcile requirements. Bridge constraints act as auxiliary instructions that make primary constraints more salient and compatible. Unlike existing approaches that enhance instruction following through general training methods, CRGC specifically improves constraint satisfaction by leveraging the model's own knowledge to create better pathways for generation. Experiments across three popular instruction following datasets demonstrate that our approach reduces constraint violations by 39% compared to standard prompting while maintaining reasoning abilities of large reasoning models.

Position: Certified Correctness in Neural Constraint Reasoning Requires Symbolic Integration

Neural solvers for constraint satisfaction problems have achieved remarkable in-distribution accuracy, yet they suffer from a fundamental limitation persistent constraint violations occur under distribution shifts even when the model reports high confidence. This position paper argues that when hard constraints exist and the cost of verification is relatively low, neural constraint reasoning must prioritize symbolic integration over pure learning. We justify our focus on Sudoku as a representative NP-complete testbed because it exhibits a sharp asymmetry between easy verification and hard solving: checking a candidate solution requires only polynomial time $O(n^{2})$, while finding a solution may require exponential search. Through a comprehensive survey of solving methods spanning deterministic algorithms, metaheuristic optimization, learning-based approaches, and language-conditioned reasoning, we demonstrate that neural-only methods without instance-level certification fail to achieve the provable correctness that symbolic and neuro-symbolic approaches provide. We advocate for a bidirectional integration in which neural methods enhance symbolic solvers by learning heuristics and converting percepts into symbols, while symbolic methods verify neural outputs to ensure their reliability. To operationalize this position, we propose a multi-agent certified reasoning framework that demonstrates how this integration can achieve both computational efficiency and provable correctness.