Daily Papers

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. We give one counterexample on c_0 and another on ell^1 with its usual norm. 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.

Mathematical programming formulations are routinely modified through algebraic reformulations, perturbations of constraint functions, and the addition or removal of constraints. Some of these modifications preserve the feasible set, whereas others reflect newly imposed modeling requirements and therefore change the optimization problem itself. This paper develops a metric framework for quantifying the robustness of formulation-dependent properties. Formulations are modeled as typed collections of constraint functions. Within each fixed typed-cardinality class, their distance is defined by optimally matching constraints of the same type and measuring the resulting discrepancies in a norm on the underlying function space. As a concrete demonstration of the framework, we study the Linear Independence Constraint Qualification (LICQ). We introduce the pointwise LICQ radius, defined as the distance from a feasible formulation to the set of formulations that remain feasible at a prescribed point but fail LICQ there. Under suitable assumptions, we derive an explicit formula for this radius and characterize the effect of adding a single equality or inequality constraint.

This paper derives necessary optimality conditions for free end-time optimal control problems governed by sweeping process dynamics. In contrast to classical optimal control problems, the presence of the normal cone term in the state equation introduces discontinuities with respect to the state variable and prevents the standard Lipschitz regularity assumptions typically used in optimal control theory. As a result, both the analysis of trajectories and the formulation of optimality conditions require refined tools. We address problems with general endpoint constraints and time-dependent data, considering both the case in which the dynamics are Lipschitz continuous in time and the more challenging setting of merely measurable time dependence. Special attention is devoted to the additional transversality conditions associated with the free end-time variable. In the Lipschitz case, these conditions are expressed in terms of a function of bounded variation that coincides almost everywhere with the maximized Hamiltonian. In the measurable case, we show that a suitable interpretation can be obtained via the notions of sub- and super-essential values of the maximized Hamiltonian, recently introduced in the literature, leading to strengthened transversality conditions. These conditions also involve an additional term reflecting the interaction between the costate arc and the normal cone to the moving set at the optimal endpoints. Our approach combines suitable perturbation techniques with a penalization method tailored to sweeping processes. The moving set is modelled as a finite intersection of inequality-defined sets satisfying suitable constraint qualifications, including a positive linear independence condition and a diagonal dominance property of the associated Gramian matrix. We also introduce a local version of the constraint qualification condition. Our results apply to a broad class of problems, including those involving unbounded moving sets such as polyhedra. The resulting optimality system extends and sharpens recent results for classical free end-time problems to the non-Lipschitz, discontinuous framework of sweeping processes. The relevance of the transversality conditions obtained in this article is illustrated through two simple examples.

Optimisation-based parking planners usually impose collision constraints only at the time samples, so a vehicle corner can cut an obstacle between samples, and no executable trajectory exists until the solver converges. We present a planner for car-like vehicles with reverse gear in which every iterate of the optimisation phase satisfies the discretised dynamics exactly and keeps the whole vehicle rectangle clear of obstacles between the samples. Each time interval receives one convex corridor that holds all vehicle corners at both ends and is shrunk by a sweep margin bounding how far the corner paths leave their chords. Separating half-planes give the corridors a direction out of obstacles when the initial guess is in collision; later, heading-aligned boxes are grown from the speed, curvature and step of the current iterate and rebuilt after accepted steps. A feasibility-perturbed trust-region sequential quadratic programming method projects each step onto the dynamics by feedback and verifies it exactly; the cost decreases monotonically, and once the corridors stop changing, limit points are Karush-Kuhn-Tucker points of the corridor-constrained problem or violate a constraint qualification. On 820 benchmark cases the planner succeeds in 818 without penetration (797 from the first initial guess), none of the 7103 evaluated optimisation-phase iterates is unusable, and it succeeds in 96.5% of the cases when 99% of the initial guesses intersect an obstacle. Its maneuvers take 0.7% longer in the median than those of a similarly certified exact-collision baseline. The guarantees hold for the planning model, not for a physical vehicle.

Solving problems through tool use under explicit constraints constitutes a highly challenging yet unavoidable scenario for large language models (LLMs), requiring capabilities such as function calling, instruction following, and self-refinement. However, progress has been hindered by the absence of dedicated evaluations. To address this, we introduce CCTU, a benchmark for evaluating LLM tool use under complex constraints. CCTU is grounded in a taxonomy of 12 constraint categories spanning four dimensions (i.e., resource, behavior, toolset, and response). The benchmark comprises 200 carefully curated and challenging test cases across diverse tool-use scenarios, each involving an average of seven constraint types and an average prompt length exceeding 4,700 tokens. To enable reliable evaluation, we develop an executable constraint validation module that performs step-level validation and enforces compliance during multi-turn interactions between models and their environments. We evaluate nine state-of-the-art LLMs in both thinking and non-thinking modes. Results indicate that when strict adherence to all constraints is required, no model achieves a task completion rate above 20%. Further analysis reveals that models violate constraints in over 50% of cases, particularly in the resource and response dimensions. Moreover, LLMs demonstrate limited capacity for self-refinement even after receiving detailed feedback on constraint violations, highlighting a critical bottleneck in the development of robust tool-use agents. To facilitate future research, we release the data and code.

Twenty-seven years ago, E. Freuder highlighted that "Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it". Nowadays, CP users have great modeling tools available (like Minizinc and CPMpy), allowing them to formulate the problem and then let a solver do the rest of the job, getting closer to the stated goal. However, this still requires the CP user to know the formalism and respect it. Another significant challenge lies in the expertise required to effectively model combinatorial problems. All this limits the wider adoption of CP. In this position paper, we investigate a possible approach to leverage pre-trained Large Language Models to extract models from textual problem descriptions. More specifically, we take inspiration from the Natural Language Processing for Optimization (NL4OPT) challenge and present early results with a decomposition-based prompting approach to GPT Models.

Combinatorial problems are present in a wide range of industries. Constraint Programming (CP) is a well-suited problem-solving paradigm, but its core process, namely constraint modelling, is a bottleneck for wider adoption. Aiming to alleviate this bottleneck, recent studies have explored using Large Language Models (LLMs) as modelling assistants, transforming combinatorial problem descriptions to executable constraint models, similar to coding assistants. However, the existing evaluation datasets for constraint modelling are often limited to small, homogeneous, or domain-specific instances, which do not capture the diversity of real-world scenarios. This work addresses this gap by introducing CP-Bench, a novel benchmark dataset that includes a diverse set of well-known combinatorial problem classes sourced from the CP community, structured explicitly for evaluating LLM-driven CP modelling. With this dataset, and given the variety of constraint modelling frameworks, we compare and evaluate the modelling capabilities of LLMs for three distinct constraint modelling systems, which vary in abstraction level and underlying syntax: the high-level MiniZinc language and Python-based CPMpy library, and the lower-level Python interface of the OR-Tools CP-SAT solver. In order to enhance the ability of LLMs to produce valid constraint models, we systematically evaluate the use of prompt-based and inference-time compute methods adapted from existing LLM-based code generation research. Our results underscore the modelling convenience provided by Python-based frameworks, as well as the effectiveness of documentation-rich system prompts, which, augmented with repeated sampling and self-verification, achieve further improvements, reaching up to 70\% accuracy on this new, highly challenging benchmark.

Regardless of the particular task we want them to perform in an environment, there are often shared safety constraints we want our agents to respect. For example, regardless of whether it is making a sandwich or clearing the table, a kitchen robot should not break a plate. Manually specifying such a constraint can be both time-consuming and error-prone. We show how to learn constraints from expert demonstrations of safe task completion by extending inverse reinforcement learning (IRL) techniques to the space of constraints. Intuitively, we learn constraints that forbid highly rewarding behavior that the expert could have taken but chose not to. Unfortunately, the constraint learning problem is rather ill-posed and typically leads to overly conservative constraints that forbid all behavior that the expert did not take. We counter this by leveraging diverse demonstrations that naturally occur in multi-task settings to learn a tighter set of constraints. We validate our method with simulation experiments on high-dimensional continuous control tasks.

Large language models (LLMs) face a dual challenge in creative capability evaluation: existing benchmarks (e.g., Story Cloze Test, HellaSwag) measure models' discriminative ability over narrative continuation using multiple-choice recognition paradigms, rather than directly measuring creative generation capability; rubric-based scoring and LLM-as-Judge methods rely on subjective dimension assessment or natural language model outputs, and cannot provide objective, automated scoring mechanisms. This paper proposes QUIET (Quality Understanding via Interlocked Evaluation Testing), a diagnostic benchmark for LLM creative capability based on multi-blank cascaded story cloze. QUIET sets N blanks (10-20) in a story with complete structure, with each blank accompanied by an explicit content constraint, and cascade dependency relationships between blanks -- the content filled into earlier blanks constrains the feasible solution space for later blanks. The evaluated model (or human participants) fills all blanks in open-ended generation mode; the results are scored by an information-theoretic automated scoring protocol without human grading. The scoring protocol directly operationalizes the "calibrated surprise" theoretical framework (Zou & Xu, 2026a). For each blank k, a composite score is computed: score = satisfy * (1 + lambda * surprise), where lambda = 1.0. Here, "satisfy" measures how well the blank filling satisfies the content constraint (objective logical reasoning judgment, not subjective aesthetic scoring), and "surprise" measures the degree of surprise given that the constraint is satisfied. Creative answers that do not satisfy the constraint score zero; answers that satisfy the constraint but are mediocre score low; answers that satisfy the constraint and are surprising score high.

It is crucial for large language models (LLMs) to follow instructions that involve multiple constraints. However, it is an unexplored area to enhance LLMs' ability to follow soft constraints. To bridge the gap, we initially design a pipeline to construct datasets with high-quality outputs automatically. Additionally, to fully utilize the positive and negative samples generated during the data construction process, we choose Direct Preference Optimization (DPO) as the training method. Furthermore, taking into account the difficulty of soft constraints indicated by the number of constraints, we design a curriculum learning training paradigm based on the constraint quantity. We experimentally evaluate the effectiveness of our methods in improving LLMs' soft constraint following ability and analyze the factors driving the improvements.The datasets and code are publicly available at https://github.com/Rainier-rq/FollowSoftConstraint.

Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or near-optimal solutions for small instances, they do not scale well to large ones, i.e., they require long computation times or yield low-quality solutions. Therefore, real-world scheduling applications often resort to fast, handcrafted, priority-based dispatching heuristics to find a good initial solution and then refine it using optimization methods. This paper proposes a novel end-to-end approach to solving scheduling problems by means of CP and Reinforcement Learning (RL). In contrast to previous RL methods, tailored for a given problem by including procedural simulation algorithms, complex feature engineering, or handcrafted reward functions, our neural-network architecture and training algorithm merely require a generic CP encoding of some scheduling problem along with a set of small instances. Our approach leverages existing CP solvers to train an agent learning a Priority Dispatching Rule (PDR) that generalizes well to large instances, even from separate datasets. We evaluate our method on seven JSSP datasets from the literature, showing its ability to find higher-quality solutions for very large instances than obtained by static PDRs and by a CP solver within the same time limit.

This paper proposes a novel column generation framework for combinatorial software testing. In particular, it combines Mathematical Programming and Constraint Programming in a hybrid decomposition to generate covering arrays. The approach allows generating parameterized test cases with coverage guarantees between parameter interactions of a given application. Compared to exhaustive testing, combinatorial test case generation reduces the number of tests to run significantly. Our column generation algorithm is generic and can accommodate mixed coverage arrays over heterogeneous alphabets. The algorithm is realized in practice as a cloud service and recognized as one of the five winners of the company-wide cloud application challenge at Oracle. The service is currently helping software developers from a range of different product teams in their testing efforts while exposing declarative constraint models and hybrid optimization techniques to a broader audience.

Structural modeling is a fundamental component of computational engineering science, in which even minor physical inconsistencies or specification violations may invalidate downstream simulations. The potential of large language models (LLMs) for automatic generation of modeling code has been demonstrated. However, non-executable or physically inconsistent outputs remain prevalent under stringent engineering constraints. A framework for physics-consistent automatic building modeling is therefore proposed, integrating domain knowledge construction, constraint-oriented model alignment, and verification-driven evaluation. CivilInstruct is introduced as a domain-specific dataset that formalizes structural engineering knowledge and constraint reasoning to enable simulation-ready model generation. A two-stage fine-tuning strategy is further employed to enforce constraint satisfaction and application programming interface compliance, substantially reducing hallucinated and non-conforming outputs. MBEval is presented as a verification-driven benchmark that evaluates executability and structural dynamics consistency through closed-loop validation. Experimental results show consistent improvements over baselines across rigorous verification metrics. Our code is available at https://github.com/Jovanqing/AutoBM.

Large language models can produce creative and diverse responses. However, to integrate them into current developer workflows, it is essential to constrain their outputs to follow specific formats or standards. In this work, we surveyed 51 experienced industry professionals to understand the range of scenarios and motivations driving the need for output constraints from a user-centered perspective. We identified 134 concrete use cases for constraints at two levels: low-level, which ensures the output adhere to a structured format and an appropriate length, and high-level, which requires the output to follow semantic and stylistic guidelines without hallucination. Critically, applying output constraints could not only streamline the currently repetitive process of developing, testing, and integrating LLM prompts for developers, but also enhance the user experience of LLM-powered features and applications. We conclude with a discussion on user preferences and needs towards articulating intended constraints for LLMs, alongside an initial design for a constraint prototyping tool.

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such constraints can be softly imposed via loss function penalties, recent advancements in differentiable physics and optimization improve performance by incorporating PDE-constrained optimization as individual layers in neural networks. This enables a stricter adherence to physical constraints. However, imposing hard constraints significantly increases computational and memory costs, especially for complex dynamical systems. This is because it requires solving an optimization problem over a large number of points in a mesh, representing spatial and temporal discretizations, which greatly increases the complexity of the constraint. To address this challenge, we develop a scalable approach to enforce hard physical constraints using Mixture-of-Experts (MoE), which can be used with any neural network architecture. Our approach imposes the constraint over smaller decomposed domains, each of which is solved by an "expert" through differentiable optimization. During training, each expert independently performs a localized backpropagation step by leveraging the implicit function theorem; the independence of each expert allows for parallelization across multiple GPUs. Compared to standard differentiable optimization, our scalable approach achieves greater accuracy in the neural PDE solver setting for predicting the dynamics of challenging non-linear systems. We also improve training stability and require significantly less computation time during both training and inference stages.

Multi-constraint planning involves identifying, evaluating, and refining candidate plans while satisfying multiple, potentially conflicting constraints. Existing large language model (LLM) approaches face fundamental limitations in this domain. Pure reasoning paradigms, which rely on long natural language chains, are prone to inconsistency, error accumulation, and prohibitive cost as constraints compound. Conversely, LLMs combined with coding- or solver-based strategies lack flexibility: they often generate problem-specific code from scratch or depend on fixed solvers, failing to capture generalizable logic across diverse problems. To address these challenges, we introduce the Scalable COde Planning Engine (SCOPE), a framework that disentangles query-specific reasoning from generic code execution. By separating reasoning from execution, SCOPE produces solver functions that are consistent, deterministic, and reusable across queries while requiring only minimal changes to input parameters. SCOPE achieves state-of-the-art performance while lowering cost and latency. For example, with GPT-4o, it reaches 93.1% success on TravelPlanner, a 61.6% gain over the best baseline (CoT) while cutting inference cost by 1.4x and time by ~4.67x. Code is available at https://github.com/DerrickGXD/SCOPE.

Instruction following evaluates large language models (LLMs) on their ability to generate outputs that adhere to user-defined constraints. However, existing benchmarks often rely on templated constraint prompts, which lack the diversity of real-world usage and limit fine-grained performance assessment. To fill this gap, we propose a multi-dimensional constraint framework encompassing three constraint patterns, four constraint categories, and four difficulty levels. Building on this framework, we develop an automated instruction generation pipeline that performs constraint expansion, conflict detection, and instruction rewriting, yielding 1,200 code-verifiable instruction-following test samples. We evaluate 19 LLMs across seven model families and uncover substantial variation in performance across constraint forms. For instance, average performance drops from 77.67% at Level I to 32.96% at Level IV. Furthermore, we demonstrate the utility of our approach by using it to generate data for reinforcement learning, achieving substantial gains in instruction following without degrading general performance. In-depth analysis indicates that these gains stem primarily from modifications in the model's attention modules parameters, which enhance constraint recognition and adherence. Code and data are available in https://github.com/Junjie-Ye/MulDimIF.

Large Language Models (LLMs) struggle to directly generate correct plans for complex multi-constraint planning problems, even with self-verification and self-critique. For example, a U.S. domestic travel planning benchmark TravelPlanner was proposed in Xie et al. (2024), where the best LLM OpenAI o1-preview can only find viable travel plans with a 10% success rate given all needed information. In this work, we tackle this by proposing an LLM-based planning framework that formalizes and solves complex multi-constraint planning problems as constrained satisfiability problems, which are further consumed by sound and complete satisfiability solvers. We start with TravelPlanner as the primary use case and show that our framework achieves a success rate of 93.9% and is effective with diverse paraphrased prompts. More importantly, our framework has strong zero-shot generalizability, successfully handling unseen constraints in our newly created unseen international travel dataset and generalizing well to new fundamentally different domains. Moreover, when user input queries are infeasible, our framework can identify the unsatisfiable core, provide failure reasons, and offers personalized modification suggestions. We show that our framework can modify and solve for an average of 81.6% and 91.7% unsatisfiable queries from two datasets and prove with ablations that all key components of our framework are effective and necessary. Project page: https://sites.google.com/view/llm-rwplanning.

Intelligent document processing pipelines extract structured entities (tables, images, and text) from documents for use in downstream systems such as knowledge bases, retrieval-augmented generation, and analytics. A persistent limitation of existing pipelines is that extraction output is produced without any intrinsic mechanism to verify whether it faithfully represents the source. Model-internal confidence scores measure inference certainty, not correspondence to the document, and extraction errors pass silently into downstream consumers. We present Reconstruction as Validation (RaV-IDP), a document processing pipeline that introduces reconstruction as a first-class architectural component. After each entity is extracted, a dedicated reconstructor renders the extracted representation back into a form comparable to the original document region, and a comparator scores fidelity between the reconstruction and the unmodified source crop. This fidelity score is a grounded, label-free quality signal. When fidelity falls below a per-entity-type threshold, a structured GPT-4.1 vision fallback is triggered and the validation loop repeats. We enforce a bootstrap constraint: the comparator always anchors against the original document region, never against the extraction, preventing the validation from becoming circular. We further propose a per-stage evaluation framework pairing each pipeline component with an appropriate benchmark. The code pipeline is publicly available at https://github.com/pritesh-2711/RaV-IDP for experimentation and use.

Numerous real-world decision-making problems can be formulated and solved using Mixed-Integer Linear Programming (MILP) models. However, the transformation of these problems into MILP models heavily relies on expertise in operations research and mathematical optimization, which restricts non-experts' accessibility to MILP. To address this challenge, we propose a framework for automatically formulating MILP models from unstructured natural language descriptions of decision problems, which integrates Large Language Models (LLMs) and mathematical modeling techniques. This framework consists of three phases: i) identification of decision variables, ii) classification of objective and constraints, and iii) finally, generation of MILP models. In this study, we present a constraint classification scheme and a set of constraint templates that can guide the LLMs in synthesizing a complete MILP model. After fine-tuning LLMs, our approach can identify and synthesize logic constraints in addition to classic demand and resource constraints. The logic constraints have not been studied in existing work. To evaluate the performance of the proposed framework, we extend the NL4Opt dataset with more problem descriptions and constraint types, and with the new dataset, we compare our framework with one-step model generation methods offered by LLMs. The experimental results reveal that with respect to the accuracies of generating the correct model, objective, and constraints, our method which integrates constraint classification and templates with LLMs significantly outperforms the others. The prototype system that we developed has a great potential to capture more constraints for more complex MILPs. It opens up opportunities for developing training tools for operations research practitioners and has the potential to be a powerful tool for automatic decision problem modeling and solving in practice.

Constraint programming is known for being an efficient approach for solving combinatorial problems. Important design choices in a solver are the branching heuristics, which are designed to lead the search to the best solutions in a minimum amount of time. However, developing these heuristics is a time-consuming process that requires problem-specific expertise. This observation has motivated many efforts to use machine learning to automatically learn efficient heuristics without expert intervention. To the best of our knowledge, it is still an open research question. Although several generic variable-selection heuristics are available in the literature, the options for a generic value-selection heuristic are more scarce. In this paper, we propose to tackle this issue by introducing a generic learning procedure that can be used to obtain a value-selection heuristic inside a constraint programming solver. This has been achieved thanks to the combination of a deep Q-learning algorithm, a tailored reward signal, and a heterogeneous graph neural network architecture. Experiments on graph coloring, maximum independent set, and maximum cut problems show that our framework is able to find better solutions close to optimality without requiring a large amounts of backtracks while being generic.

Deep Generative Models (DGMs) have been shown to be powerful tools for generating tabular data, as they have been increasingly able to capture the complex distributions that characterize them. However, to generate realistic synthetic data, it is often not enough to have a good approximation of their distribution, as it also requires compliance with constraints that encode essential background knowledge on the problem at hand. In this paper, we address this limitation and show how DGMs for tabular data can be transformed into Constrained Deep Generative Models (C-DGMs), whose generated samples are guaranteed to be compliant with the given constraints. This is achieved by automatically parsing the constraints and transforming them into a Constraint Layer (CL) seamlessly integrated with the DGM. Our extensive experimental analysis with various DGMs and tasks reveals that standard DGMs often violate constraints, some exceeding 95% non-compliance, while their corresponding C-DGMs are never non-compliant. Then, we quantitatively demonstrate that, at training time, C-DGMs are able to exploit the background knowledge expressed by the constraints to outperform their standard counterparts with up to 6.5% improvement in utility and detection. Further, we show how our CL does not necessarily need to be integrated at training time, as it can be also used as a guardrail at inference time, still producing some improvements in the overall performance of the models. Finally, we show that our CL does not hinder the sample generation time of the models.

Multi-constraint instruction following requires verifying whether a response satisfies multiple individual requirements, yet LLM judges are often assessed only through overall-response judgments. We introduce MCJudgeBench, a benchmark for constraint-level judge evaluation in multi-constraint instruction following. Each instance includes an instruction, a candidate response, an explicit constraint list, per-constraint gold labels in {yes, partial, no}, and controlled response-side perturbations. The evaluation protocol further includes evaluation prompt variants to test judge stability. We evaluate proprietary and open-source LLM judges using both correctness and inconsistency metrics, distinguishing intrinsic inconsistency under stochastic decoding from procedural inconsistency under prompt and response perturbations. Our results show that judge reliability has multiple dimensions: strong overall performance does not guarantee equally reliable detection across label categories, especially for rarer partial and no cases. Judges with higher correctness do not always have lower inconsistency. Evaluation with reasoning improves correctness but does not uniformly improve stability. These findings motivate evaluating LLM judges at the constraint level to study these failure modes.

Recently, a large amount of work has focused on improving large language models' (LLMs') performance on reasoning benchmarks such as math and logic. However, past work has largely assumed that tasks are well-defined. In the real world, queries to LLMs are often underspecified, only solvable through acquiring missing information. We formalize this as a constraint satisfaction problem (CSP) with missing variable assignments. Using a special case of this formalism where only one necessary variable assignment is missing, we can rigorously evaluate an LLM's ability to identify the minimal necessary question to ask and quantify axes of difficulty levels for each problem. We present QuestBench, a set of underspecified reasoning tasks solvable by asking at most one question, which includes: (1) Logic-Q: Logical reasoning tasks with one missing proposition, (2) Planning-Q: PDDL planning problems with initial states that are partially-observed, (3) GSM-Q: Human-annotated grade school math problems with one missing variable assignment, and (4) GSME-Q: a version of GSM-Q where word problems are translated into equations by human annotators. The LLM is tasked with selecting the correct clarification question(s) from a list of options. While state-of-the-art models excel at GSM-Q and GSME-Q, their accuracy is only 40-50% on Logic-Q and Planning-Q. Analysis demonstrates that the ability to solve well-specified reasoning problems may not be sufficient for success on our benchmark: models have difficulty identifying the right question to ask, even when they can solve the fully specified version of the problem. Furthermore, in the Planning-Q domain, LLMs tend not to hedge, even when explicitly presented with the option to predict ``not sure.'' This highlights the need for deeper investigation into models' information acquisition capabilities.

Making language models solve constraint problems reliably often means having them translate the problem into a formal specification and delegating the search to a sound solver. But the translation is itself a language-model task, and an unfaithful translation makes the solver faithfully solve the wrong problem. Existing pipelines repair only translations that crash, returning the solver's error message and falling silent when the program runs but is wrong. We replace the error message with a proof: when the generated program is unsatisfiable, we extract a minimal unsatisfiable core over the model's own constraints and hand it back the exact set that cannot hold together, a leakage-free signal that localizes the fault. On a new benchmark of 77 problems with an exact oracle, translation to Answer Set Programming is faithful on six of seven domains and fails only on aggregate coverage scheduling, which concentrates the translation tax in one diagnosable pattern. A minimal core, rather than a bare error, is what stops a weaker model from fabricating solutions to infeasible problems, cutting fabrication from 79% to 7%. A strong chain-of-thought baseline meanwhile matches the symbolic route on accuracy, so the route's value is not accuracy but certificates and its refusal to fabricate.

State-of-the-art neural network (NN) verifiers demonstrate that applying the branch-and-bound (BaB) procedure with fast bounding techniques plays a key role in tackling many challenging verification properties. In this work, we introduce the linear constraint-driven clipping framework, a class of scalable and efficient methods designed to enhance the efficacy of NN verifiers. Under this framework, we develop two novel algorithms that efficiently utilize linear constraints to 1) reduce portions of the input space that are either verified or irrelevant to a subproblem in the context of branch-and-bound, and 2) directly improve intermediate bounds throughout the network. The process novelly leverages linear constraints that often arise from bound propagation methods and is general enough to also incorporate constraints from other sources. It efficiently handles linear constraints using a specialized GPU procedure that can scale to large neural networks without the use of expensive external solvers. Our verification procedure, Clip-and-Verify, consistently tightens bounds across multiple benchmarks and can significantly reduce the number of subproblems handled during BaB. We show that our clipping algorithms can be integrated with BaB-based verifiers such as α,β-CROWN, utilizing either the split constraints in activation-space BaB or the output constraints that denote the unverified input space. We demonstrate the effectiveness of our procedure on a broad range of benchmarks where, in some instances, we witness a 96% reduction in the number of subproblems during branch-and-bound, and also achieve state-of-the-art verified accuracy across multiple benchmarks. Clip-and-Verify is part of the α,β-CROWN verifier (http://abcrown.org), the VNN-COMP 2025 winner. Code available at https://github.com/Verified-Intelligence/Clip_and_Verify.

Optimization modeling via mixed-integer linear programming (MILP) is fundamental to industrial planning and scheduling, yet translating natural-language requirements into solver-executable models and maintaining them under evolving business rules remains highly expertise-intensive. While large language models (LLMs) offer promising avenues for automation, existing methods often suffer from low data efficiency, limited solver-level validity, and poor scalability to industrial-scale problems. To address these challenges, we present EvoOpt-LLM, a unified LLM-based framework supporting the full lifecycle of industrial optimization modeling, including automated model construction, dynamic business-constraint injection, and end-to-end variable pruning. Built on a 7B-parameter LLM and adapted via parameter-efficient LoRA fine-tuning, EvoOpt-LLM achieves a generation rate of 91% and an executability rate of 65.9% with only 3,000 training samples, with critical performance gains emerging under 1,500 samples. The constraint injection module reliably augments existing MILP models while preserving original objectives, and the variable pruning module enhances computational efficiency, achieving an F1 score of ~0.56 on medium-sized LP models with only 400 samples. EvoOpt-LLM demonstrates a practical, data-efficient approach to industrial optimization modeling, reducing reliance on expert intervention while improving adaptability and solver efficiency.

Recent progress in o1-like models has significantly enhanced the reasoning abilities of Large Language Models (LLMs), empowering them to tackle increasingly complex tasks through reflection capabilities, such as making assumptions, backtracking, and self-refinement. However, effectively evaluating such reflection capabilities remains challenging due to the lack of appropriate benchmarks. To bridge this gap, we introduce LR^2Bench, a novel benchmark designed to evaluate the Long-chain Reflective Reasoning capabilities of LLMs. LR^2Bench comprises 850 samples across six Constraint Satisfaction Problems (CSPs) where reflective reasoning is crucial for deriving solutions that meet all given constraints. Each type of task focuses on distinct constraint patterns, such as knowledge-based, logical, and spatial constraints, providing a comprehensive evaluation of diverse problem-solving scenarios. We conduct extensive evaluation on both conventional models and o1-like models. Our experimental results reveal that even the most advanced reasoning-specific models, such as DeepSeek-R1 and OpenAI o1-preview, struggle with tasks in LR^2Bench, achieving an average Exact Match score of only 20.0% and 23.6%, respectively. These findings underscore the significant room for improvement in the reflective reasoning capabilities of current LLMs. The leaderboard of our benchmark is available at https://huggingface.co/spaces/UltraRonin/LR2Bench

Incorporating prior knowledge or specifications of input-output relationships into machine learning models has attracted significant attention, as it enhances generalization from limited data and yields conforming outputs. However, most existing approaches use soft constraints by penalizing violations through regularization, which offers no guarantee of constraint satisfaction, especially on inputs far from the training distribution--an essential requirement in safety-critical applications. On the other hand, imposing hard constraints on neural networks may hinder their representational power, adversely affecting performance. To address this, we propose HardNet, a practical framework for constructing neural networks that inherently satisfy hard constraints without sacrificing model capacity. Unlike approaches that modify outputs only at inference time, HardNet enables end-to-end training with hard constraint guarantees, leading to improved performance. To the best of our knowledge, HardNet is the first method that enables efficient and differentiable enforcement of more than one input-dependent inequality constraint. It allows unconstrained optimization of the network parameters using standard algorithms by appending a differentiable closed-form enforcement layer to the network's output. Furthermore, we show that HardNet retains neural networks' universal approximation capabilities. We demonstrate its versatility and effectiveness across various applications: learning with piecewise constraints, learning optimization solvers with guaranteed feasibility, and optimizing control policies in safety-critical systems.

Agents based on large language models (LLMs) have demonstrated effectiveness in solving a wide range of tasks by integrating LLMs with key modules such as planning, memory, and tool usage. Increasingly, customers are adopting LLM agents across a variety of commercial applications critical to reliability, including support for mental well-being, chemical synthesis, and software development. Nevertheless, our observations and daily use of LLM agents indicate that they are prone to making erroneous plans, especially when the tasks are complex and require long-term planning. In this paper, we propose PDoctor, a novel and automated approach to testing LLM agents and understanding their erroneous planning. As the first work in this direction, we formulate the detection of erroneous planning as a constraint satisfiability problem: an LLM agent's plan is considered erroneous if its execution violates the constraints derived from the user inputs. To this end, PDoctor first defines a domain-specific language (DSL) for user queries and synthesizes varying inputs with the assistance of the Z3 constraint solver. These synthesized inputs are natural language paragraphs that specify the requirements for completing a series of tasks. Then, PDoctor derives constraints from these requirements to form a testing oracle. We evaluate PDoctor with three mainstream agent frameworks and two powerful LLMs (GPT-3.5 and GPT-4). The results show that PDoctor can effectively detect diverse errors in agent planning and provide insights and error characteristics that are valuable to both agent developers and users. We conclude by discussing potential alternative designs and directions to extend PDoctor.

We study reasoning in Rule-Governed Decision Tasks (RGDTs), where models apply external rules to case facts and justify decisions, as required in policy, contract, and compliance settings. Beyond the deductive capability emphasized by standard mathematical and logical reasoning tasks, RGDTs require interpreting rules and their applicability, assessing conditions from evidence, combining judgments under rules and exceptions, and providing checkable justifications. These demands motivate a benchmark assessing both decisions and their stated grounds. We introduce RGDT-Bench, providing 202.1K condition-level supervision slots across four task tracks and eight supported task-probe combinations that vary access to supporting information. Label-blind extraction and deterministic checks produce labels for warrant completeness: source-referenced coverage and consistency of stated decision grounds. The benchmark attributes failures to four process layers: rule use, condition, evidence, and aggregation, and checks the final outcome. Among evaluable correct responses, warrant incompleteness averages 40.2% across six evaluated LLMs and supported task-probe combinations. Such warrant incompleteness poses potential safety risks and remains difficult to detect: the best of seventeen existing evaluators reaches only 57.69% (random: 50%) task-averaged area under the receiver operating characteristic curve (AUROC). To address this difficulty, we train a simple reward model with warrant supervision. It achieves 69.24% task-averaged AUROC among correct answers, exceeding the matched outcome-supervised baseline by 10.37 pp (percentage points) and the best existing evaluator by 11.55 pp. Beyond completeness assessment, the model outperforms both outcome-supervised baselines across nearly all response-selection comparisons, supporting RGDT-Bench's warrant supervision for RGDT reasoning.

We introduce the first version of KWBench (Knowledge Work Bench), a benchmark for unprompted problem recognition in large language models: can an LLM identify a professional scenario before attempting to solve it. Existing frontier benchmarks have saturated, and most knowledge-work evaluations to date reduce to extraction or task completion against a specification. KWBench targets the step before that: recognizing the governing structure of the situation from raw inputs alone. The benchmark contains 223 tasks sourced from practitioners across acquisitions, contract negotiations, clinical pharmacy, organizational politics, fraud analysis, and incentive design. Each task encodes a formal game-theoretic pattern (principal-agent conflict, signaling, mechanism design failure, strategic omission, coalitional dynamics, strategic interdependence) and carries structured ground truth recording the expert reading of the situation and the anticipated failure modes. Models receive raw data and a task prompt with no indication of problem type. Scoring is a three-tier rubric gated by a mandatory conjunctive check. Mandatory criteria encode the predicted wrong paths. We evaluate 16 models. The best model passes on 27.9% of tasks. The top two models agree on only 31.7% of their passes. Among the top 8, 44 tasks are solved by exactly one model; routing across the top 8 covers 50.7% of the benchmark, nearly double the best single model. Conditional on passing, quality scores converge (approx 83% across models); unconditional scores do not. Same models articulate the relevant game-theoretic concept correctly when asked, then fail to apply it unprompted. We release KWBench to shift how frontier models are evaluated on knowledge work, scoring them on whether they recognize the right problem from the situation alone, not only on how well they execute once the problem has been framed for them.

Authoring a multi-actor scenario for a living 3D world, where every action changes its state, and each action's validity depends on the state accumulated before it, demands the freedom of storytelling and the rigor of simulation at once. We author such scenarios with LLM agents, as Graphs of Events in Space and Time (GESTs) that a simulation engine executes deterministically into narrative videos with per-frame spatial, temporal, and semantic ground truth. A staged pipeline driving a flagship LLM, the standard design in video generation, failed outright: the model violates rules stated verbatim in its prompt, and cannot track the dynamic world state. We answer with a constraint-enforcing tool layer: our Director and Scene Builder agents explore the world's capabilities page by page and build every scene through operations checked against simulator state, so every specification they emit is valid by construction. Because we generate each seed text from an existing scenario graph, we can measure reconstruction: the agent authors its own graph from the text alone, yet matches the original at 0.83 F1 on its events, each action with its participants (0.55 for a random scenario of the same kind), and 0.77 on their ordering (0.43 random). End to end: the standard staged pipeline produced 0 executable specifications in 50 attempts; our agents, driving a budget model, execute 20 of 25 (80%), and are, to our knowledge, the first to exercise the full expressive capacity of GEST.

The adeptness of Large Language Models (LLMs) in comprehending and following natural language instructions is critical for their deployment in sophisticated real-world applications. Existing evaluations mainly focus on fragmented constraints or narrow scenarios, but they overlook the comprehensiveness and authenticity of constraints from the user's perspective. To bridge this gap, we propose CFBench, a large-scale Comprehensive Constraints Following Benchmark for LLMs, featuring 1,000 curated samples that cover more than 200 real-life scenarios and over 50 NLP tasks. CFBench meticulously compiles constraints from real-world instructions and constructs an innovative systematic framework for constraint types, which includes 10 primary categories and over 25 subcategories, and ensures each constraint is seamlessly integrated within the instructions. To make certain that the evaluation of LLM outputs aligns with user perceptions, we propose an advanced methodology that integrates multi-dimensional assessment criteria with requirement prioritization, covering various perspectives of constraints, instructions, and requirement fulfillment. Evaluating current leading LLMs on CFBench reveals substantial room for improvement in constraints following, and we further investigate influencing factors and enhancement strategies. The data and code are publicly available at https://github.com/PKU-Baichuan-MLSystemLab/CFBench

The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of DGP instances. In this paper, we study the Discretizable Molecular Distance Geometry Problem whose feasible solutions provide a discretization scheme for the DGP. We propose the first constraint programming formulations as well as a set of checks for proving infeasibility, domain reduction techniques, symmetry breaking constraints and valid inequalities. Our computational results indicate that our formulations outperform the state-of-the-art integer programming formulations, both for feasible and infeasible instances.

In critical applications, it is vital for classifiers to defer decision-making to humans. We propose a post-hoc method that makes existing classifiers selectively abstain from predicting certain samples. Our abstaining classifier is incentivized to maintain the original accuracy for each sub-population (i.e. no harm) while achieving a set of group fairness definitions to a user specified degree. To this end, we design an Integer Programming (IP) procedure that assigns abstention decisions for each training sample to satisfy a set of constraints. To generalize the abstaining decisions to test samples, we then train a surrogate model to learn the abstaining decisions based on the IP solutions in an end-to-end manner. We analyze the feasibility of the IP procedure to determine the possible abstention rate for different levels of unfairness tolerance and accuracy constraint for achieving no harm. To the best of our knowledge, this work is the first to identify the theoretical relationships between the constraint parameters and the required abstention rate. Our theoretical results are important since a high abstention rate is often infeasible in practice due to a lack of human resources. Our framework outperforms existing methods in terms of fairness disparity without sacrificing accuracy at similar abstention rates.

A modified LAB algorithm is introduced in this paper. It builds upon the original LAB algorithm (Reddy et al. 2023), which is a socio-inspired algorithm that models competitive and learning behaviours within a group, establishing hierarchical roles. The proposed algorithm incorporates the roulette wheel approach and a reduction factor introducing inter-group competition and iteratively narrowing down the sample space. The algorithm is validated by solving the benchmark test problems from CEC 2005 and CEC 2017. The solutions are validated using standard statistical tests such as two-sided and pairwise signed rank Wilcoxon test and Friedman rank test. The algorithm exhibited improved and superior robustness as well as search space exploration capabilities. Furthermore, a Clustering-Based Search Space Reduction (C-SSR) method is proposed, making the algorithm capable to solve constrained problems. The C-SSR method enables the algorithm to identify clusters of feasible regions, satisfying the constraints and contributing to achieve the optimal solution. This method demonstrates its effectiveness as a potential alternative to traditional constraint handling techniques. The results obtained using the Modified LAB algorithm are then compared with those achieved by other recent metaheuristic algorithms.

Writing competitive programming problems is exacting. Authors must: set constraints, input distributions, and edge cases that rule out shortcuts; target specific algorithms (e.g., max-flow, dynamic programming, data structures); and calibrate complexity beyond the reach of most competitors. We argue that this makes for an ideal test of general large language model capabilities and study whether they can do this reliably. We introduce AutoCode, which uses multiple rounds of validation to yield competition-grade problem statements and test cases. On held-out problems, AutoCode test suites approach 99% consistency with official judgments, a significant improvement over current state-of-the-art methods like HardTests, which achieve less than 81%. Furthermore, starting with a random seed problem, AutoCode can create novel variants with reference and brute-force solutions. By cross-verifying these generated solutions against test cases, we can further filter out malformed problems. Our system ensures high correctness, as verified by human experts. AutoCode successfully produces novel problems judged by Grandmaster-level (top 0.3%) competitive programmers to be of contest quality.

Quantified formulas with Uninterpreted Functions (UFs) over non-linear real arithmetic pose fundamental challenges for Satisfiability Modulo Theories (SMT) solving. Traditional quantifier instantiation methods struggle because they lack semantic understanding of UF constraints, forcing them to search through unbounded solution spaces with limited guidance. We present AquaForte, a framework that leverages Large Language Models to provide semantic guidance for UF instantiation by generating instantiated candidates for function definitions that satisfy the constraints, thereby significantly reducing the search space and complexity for solvers. Our approach preprocesses formulas through constraint separation, uses structured prompts to extract mathematical reasoning from LLMs, and integrates the results with traditional SMT algorithms through adaptive instantiation. AquaForte maintains soundness through systematic validation: LLM-guided instantiations yielding SAT solve the original problem, while UNSAT results generate exclusion clauses for iterative refinement. Completeness is preserved by fallback to traditional solvers augmented with learned constraints. Experimental evaluation on SMT-COMP benchmarks demonstrates that AquaForte solves numerous instances where state-of-the-art solvers like Z3 and CVC5 timeout, with particular effectiveness on satisfiable formulas. Our work shows that LLMs can provide valuable mathematical intuition for symbolic reasoning, establishing a new paradigm for SMT constraint solving.

Effective scheduling under tight resource, timing, and operational constraints underpins large-scale planning across sectors such as capital projects, manufacturing, logistics, and IT fleet transitions. However, the reliability of large language models (LLMs) when reasoning under high-constraint regimes is insufficiently characterized. To address this gap, we present R-ConstraintBench, a scalable framework that evaluates models on Resource-Constrained Project Scheduling Problems (RCPSP), an NP-Complete feasibility class, while difficulty increases via linear growth in constraints. R-ConstraintBench incrementally increases non-redundant precedence constraints in Directed Acyclic Graphs (DAGs) and then introduces downtime, temporal windows, and disjunctive constraints. As an illustrative example, we instantiate the benchmark in a data center migration setting and evaluate multiple LLMs using feasibility and error analysis, identifying degradation thresholds and constraint types most associated with failure. Empirically, strong models are near-ceiling on precedence-only DAGs, but feasibility performance collapses when downtime, temporal windows, and disjunctive constraints interact, implicating constraint interaction, not graph depth, as the principal bottleneck. Performance on clean synthetic ramps also does not guarantee transfer to domain-grounded scenarios, underscoring limited generalization.

Large language models (LLMs) are increasingly expected to tackle complex tasks, driven by their expanding applications and users' growing proficiency in crafting sophisticated prompts. However, as the number of explicitly stated requirements increases (particularly more than 10 constraints), LLMs often struggle to accurately follow such complex instructions, which limits their applicability in complex real-world scenarios. To the best of our knowledge, existing datasets do not exceed 10 constraints per instance. To address this challenge, we propose RECAST, an efficient and scalable framework for synthesizing datasets where each example incorporates far more constraints than those in existing benchmarks, aiming to challenge and extend the boundaries of models' ability to follow complex instructions. These constraints are extracted from real-world prompt-response pairs to ensure practical relevance. Using this framework, we construct RECAST-30K, a large-scale, high-quality dataset comprising 30k instances spanning 19 constraint types. Experimental results demonstrate that models finetuned on RECAST-30K substantially improve in following complex instructions while maintaining their general capabilities without degradation. Moreover, RECAST enables automatic verification of constraint satisfaction via rule-based validators for quantitative constraints and LLM-based validators for qualitative ones; the verifiability provided by RECAST enables the design of reward functions for reinforcement learning, which further boosts model performance on complex and challenging tasks.

Large language models (LLMs) exhibit degraded performance under prompt compression, but the mechanisms remain poorly understood. We introduce the Compression-Decay Comprehension Test (CDCT), a benchmark that independently measures constraint compliance (CC) and semantic accuracy (SA) across compression levels. We evaluate 9 frontier LLMs across 8 concepts using 5 compression levels from extreme (c=0.0, ~2 words) to none (c=1.0, ~135 words). A three-judge LLM jury achieves almost perfect inter-rater agreement on CC (Fleiss' appa=0.90). We observe a universal U-curve pattern in constraint compliance (97.2% prevalence), with violations peaking at medium compression (c=0.5, ~27 words). Counterintuitively, models perform better at extreme compression than medium lengths. The dimensions are statistically orthogonal (r=0.193, p=0.084), with constraint effects 2.9x larger than semantic effects. Experimental validation via RLHF ablation confirms our constraint salience hypothesis: removing "helpfulness" signals improves CC by 598% on average (71/72 trials, p<0.001), with 79% achieving perfect compliance. This demonstrates that RLHF-trained helpfulness behaviors are the dominant cause of constraint violations at medium compression. Reasoning models outperform efficient models by 27.5% (Cohen's d=0.96). Our findings reveal a fundamental tension between RLHF alignment and instruction-following, providing actionable guidelines for improving deployed systems.

With the widespread adoption of large language models (LLMs), hallucinations, which are non-factual fabrications in model outputs, have become serious concerns. Reasoning capabilities have received attention as a self-verification process to improve output reliability. However, the effect of reasoning within a closed system where LLMs cannot rely on external tools or knowledge has yet to be clarified. We therefore conduct experiments under strict constraints (recommending peer-reviewed journal articles in computer science) to examine the effect of reasoning across multiple models (GPT-5.2 and Gemini 3 Flash). Our results reveal a problematic trade-off between constraint compliance and factual accuracy. Non-reasoning models exhibit high constraint violation rates (66-75%) but maintain factual accuracy, while reasoning models reduce violations (13-26%) but systematically distort known facts to satisfy constraints and increase complete fabrication. This trade-off pattern is consistent across both models despite different architectures, indicating a fundamental limitation of reasoning. Furthermore, reasoning does not uniformly improve output authenticity: effects diverge by model, reflecting different allocations of the compliance-truthfulness trade-off. These findings challenge the assumption that reasoning universally improves reliability: reasoning models trade honest constraint violations for detection-resistant distortions.

As Large Language Model (LLM) agents increasingly execute complex, autonomous software engineering tasks, developers rely on natural language instruction files such as AGENTS.md to express project-specific coding conventions, tooling restrictions, and architectural boundaries. However, because these instructions remain passive text, agents frequently violate documented constraints due to context window saturation or conflicting local context. In autonomous settings without real-time human supervision, such violations rapidly compound into technical debt. To ground autonomous agents in repository constraints, we introduce ContextCov, a framework that transforms passive natural language instructions into executable guardrails. Unlike prompt-only or reflection-only compliance approaches, ContextCov compiles documented constraints into three complementary checks: static AST queries for code patterns, runtime shell shims that intercept prohibited commands, and architectural validators that enforce structural rules. Acting as an automated, continuous reviewer, ContextCov intercepts agent actions and returns immediate, reproducible violation traces, enabling self-correction before non-compliant changes are finalized. We evaluate ContextCov on SWE-bench Lite (12 repositories, 300 tasks). Compared to prompt-only and LLM reflection baselines, ContextCov achieves 88.3% constraint compliance (vs. 67.0% and 50.3%) with 3.4x lower feedback cost, while maintaining functional correctness. The source code and evaluation results are available at https://github.com/reSHARMA/ContextCov.

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.

Scaling verifiable training signals remains a key bottleneck for Reinforcement Learning from Verifiable Rewards (RLVR). Logical reasoning is a natural substrate: constraints are formal and answers are programmatically checkable. However, prior synthesis pipelines either depend on expert-written code or operate within fixed templates/skeletons, which limits growth largely to instance-level perturbations. We propose SSLogic, an agentic meta-synthesis framework that scales at the task-family level by iteratively synthesizing and repairing executable Generator--Validator program pairs in a closed Generate--Validate--Repair loop, enabling continuous family evolution with controllable difficulty. To ensure reliability, we introduce a Multi-Gate Validation Protocol that combines multi-strategy consistency checks with Adversarial Blind Review, where independent agents must solve instances by writing and executing code to filter ambiguous or ill-posed tasks. Starting from 400 seed families, two evolution rounds expand to 953 families and 21,389 verifiable instances (from 5,718). Training on SSLogic-evolved data yields consistent gains over the seed baseline at matched training steps, improving SynLogic by +5.2, BBEH by +1.4, AIME25 by +3.0, and Brumo25 by +3.7.

Background and Objective: Clinicians expect recurrence risk to climb with cancer severity. In a UK multicentre trial, an unconstrained XGBoost model learnt that higher tumour stage and carcinoma in situ predicted lower recurrence risk, and discrimination, calibration, and SHAP were all blind to it. We developed a counterfactual testing framework to detect this inversion and a monotonic-constraint framework to remove it without hurting performance. Methods: BOXIT enrolled 472 patients with protocol-mandated cystoscopy across 51 UK sites (2007-2012); 435 had at least two years' follow-up (153 recurrences, 35.2%). We developed a counterfactual direction test and a monotonic-constraint correction, with constraint directions drawn from the EORTC and EAU risk systems, and evaluated both against unconstrained XGBoost and logistic regression on 18 predictors (seven directed) over 50 cross-validation folds. The test worsened each patient on one directed feature at a time to check whether risk fell; SHAP direction and calibration were also assessed. Key Findings and Limitations: Tumour stage and carcinoma in situ were associated with lower recurrence, opposite to medical intuition; the unconstrained model reversed carcinoma in situ counterfactuals in 90.2% of cases and stage in 74.3%. Discrimination (ΔAUC 0.005, p=0.47), calibration, and SHAP magnitude were all blind to the inversion. Monotonic constraints eliminated every violation at no cost to discrimination (0.723 vs 0.718) and outperformed EORTC (p=8.9e-16). Limitations: single trial, internal-external validation only. Conclusions and Clinical Implications: A model that had learned this inversion passed every conventional check. A counterfactual direction test, run as a single refit with pre-specified monotonic constraints, catches this failure at no cost to performance and should be routine before clinical deployment.

Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM reasoning. Whereas olympiad-style problems measure step-by-step reasoning alone, research-level problems use such reasoning to advance the frontier of mathematical knowledge itself, emerging as a compelling alternative. Yet research-level math benchmarks remain scarce because such problems are difficult to source (e.g., Riemann Bench and FrontierMath-Tier 4 contain 25 and 50 problems, respectively). To support reliable evaluation of next-generation frontier models, we introduce Soohak, a 439-problem benchmark newly authored from scratch by 64 mathematicians. Soohak comprises two subsets. On the Challenge subset, frontier models including Gemini-3-Pro, GPT-5, and Claude-Opus-4.5 reach 30.4%, 26.4%, and 10.4% respectively, leaving substantial headroom, while leading open-weight models such as Qwen3-235B, GPT-OSS-120B, and Kimi-2.5 remain below 15%. Notably, beyond standard problem solving, Soohak introduces a refusal subset that probes a capability intrinsic to research mathematics: recognizing ill-posed problems and pausing rather than producing confident but unjustified answers. On this subset, no model exceeds 50%, identifying refusal as a new optimization target that current models do not directly address. To prevent contamination, the dataset will be publicly released in late 2026, with model evaluations available upon request in the interim.

It is imperative for Large language models (LLMs) to follow instructions with elaborate requirements (i.e. Complex Instructions Following). Yet, it remains under-explored how to enhance the ability of LLMs to follow complex instructions with multiple constraints. To bridge the gap, we initially study what training data is effective in enhancing complex constraints following abilities. We found that training LLMs with instructions containing multiple constraints enhances their understanding of complex instructions, especially those with lower complexity levels. The improvement can even generalize to compositions of out-of-domain constraints. Additionally, we further propose methods addressing how to obtain and utilize the effective training data. Finally, we conduct extensive experiments to prove the effectiveness of our methods in terms of overall performance and training efficiency. We also demonstrate that our methods improve models' ability to follow instructions generally and generalize effectively across out-of-domain, in-domain, and adversarial settings, while maintaining general capabilities.

Large Language Models (LLMs) excel at generating fluent text but struggle to enforce external constraints because they generate tokens sequentially without explicit control mechanisms. GenCP addresses this limitation by combining LLM predictions with Constraint Programming (CP) reasoning, formulating text generation as a Constraint Satisfaction Problem (CSP). In this paper, we improve GenCP by integrating Masked Language Models (MLMs) for domain generation, which allows bidirectional constraint propagation that leverages both past and future tokens. This integration bridges the gap between token-level prediction and structured constraint enforcement, leading to more reliable and constraint-aware text generation. Our evaluation on COLLIE benchmarks demonstrates that incorporating domain preview via MLM calls significantly improves GenCP's performance. Although this approach incurs additional MLM calls and, in some cases, increased backtracking, the overall effect is a more efficient use of LLM inferences and an enhanced ability to generate feasible and meaningful solutions, particularly in tasks with strict content constraints.

This paper introduces an approach for learning to solve continuous constraint satisfaction problems (CCSP) in robotic reasoning and planning. Previous methods primarily rely on hand-engineering or learning generators for specific constraint types and then rejecting the value assignments when other constraints are violated. By contrast, our model, the compositional diffusion continuous constraint solver (Diffusion-CCSP) derives global solutions to CCSPs by representing them as factor graphs and combining the energies of diffusion models trained to sample for individual constraint types. Diffusion-CCSP exhibits strong generalization to novel combinations of known constraints, and it can be integrated into a task and motion planner to devise long-horizon plans that include actions with both discrete and continuous parameters. Project site: https://diffusion-ccsp.github.io/

Inference-time planning with large language models frequently breaks under partial observability: when task-critical preconditions are not specified at query time, models tend to hallucinate missing facts or produce plans that violate hard constraints. We introduce Self-Querying Bidirectional Categorical Planning (SQ-BCP), which explicitly represents precondition status (Sat/Viol/Unk) and resolves unknowns via (i) targeted self-queries to an oracle/user or (ii) bridging hypotheses that establish the missing condition through an additional action. SQ-BCP performs bidirectional search and invokes a pullback-based verifier as a categorical certificate of goal compatibility, while using distance-based scores only for ranking and pruning. We prove that when the verifier succeeds and hard constraints pass deterministic checks, accepted plans are compatible with goal requirements; under bounded branching and finite resolution depth, SQ-BCP finds an accepting plan when one exists. Across WikiHow and RecipeNLG tasks with withheld preconditions, SQ-BCP reduces resource-violation rates to 14.9\% and 5.8\% (vs.\ 26.0\% and 15.7\% for the best baseline), while maintaining competitive reference quality.

Statutes are increasingly parsed by machines before people read them, and the parsers disagree: on Missouri's statutes, two independently written extractors diverge on numeric-threshold presence at a false-negative rate of 0.43. We ask what formal logic survives such noise. We build a passive survival certificate for the Duquenne-Guigues implication basis of machine-extracted statutory contexts: per-attribute inter-extractor disagreement is measured, replayed against the basis in 1,000 Monte Carlo trials, and an implication is certified only when a one-sided Wilson 95% lower bound on survival reaches 0.95; every certified implication carries premise spans and a minimal counterexample. On 29,365 Missouri sections and 502 Indian central-Act sections, the preregistered held-out gate passes (10 statute families across 7 Titles exact; 16 across 11 with 5% tolerance), yet under one globally deployed error model 93.2% of held-out chapters fall below the informativeness floor, and a 2x2 factorial assigns that to calibration-rate transfer, not selection. The certificate is usable but fragile: deploy it per-chapter-calibrated or error-tolerant. Code, data products, and the audit trail, including one retracted claim, are released.

The ACPBench dataset provides atomic reasoning tasks required for efficient planning. The dataset is aimed at distilling the complex plan generation task into separate atomic reasoning tasks in their easiest possible form, boolean or multiple-choice questions, where the model has to choose the right answer from the provided options. While the aim of ACPBench is to test the simplest form of reasoning about action and change, when tasked with planning, a model does not typically have options to choose from and thus the reasoning required for planning dictates an open-ended, generative form for these tasks. To that end, we introduce ACPBench Hard, a generative version of ACPBench, with open-ended questions which the model needs to answer. Models that perform well on these tasks could in principle be integrated into a planner or be used directly as a policy. We discuss the complexity of these tasks as well as the complexity of validating the correctness of their answers and present validation algorithms for each task. Equipped with these validators, we test the performance of a variety of models on our tasks and find that for most of these tasks the performance of even the largest models is still subpar. Our experiments show that no model outperforms another in these tasks and with a few exceptions all tested language models score below 65%, indicating that even the current frontier language models have a long way to go before they can reliably reason about planning. In fact, even the so-called reasoning models struggle with solving these reasoning tasks. ACPBench Hard collection is available at the following link: https://ibm.github.io/ACPBench

We develop a method for training neural networks on Boolean data in which the values at all nodes are strictly pm 1, and the resulting models are typically equivalent to networks whose nonzero weights are also pm 1. The method replaces loss minimization with a nonconvex constraint formulation. Each node implements a Boolean threshold function (BTF), and training is expressed through a divide-and-concur decomposition into two complementary constraints: one enforces local BTF consistency between inputs, weights, and output; the other imposes architectural concurrence, equating neuron outputs with downstream inputs and enforcing weight equality across training-data instantiations of the network. The reflect-reflect-relax (RRR) projection algorithm is used to reconcile these constraints. Each BTF constraint includes a lower bound on the margin. When this bound is sufficiently large, the learned representations are provably sparse and equivalent to networks composed of simple logical gates with pm 1 weights. Across a range of tasks -- including multiplier-circuit discovery, binary autoencoding, logic-network inference, and cellular automata learning -- the method achieves exact solutions or strong generalization in regimes where standard gradient-based methods struggle. These results demonstrate that projection-based constraint satisfaction provides a viable and conceptually distinct foundation for learning in discrete neural systems, with implications for interpretability and efficient inference.

We propose a constraint learning schema for fine-tuning Large Language Models (LLMs) with attribute control. Given a training corpus and control criteria formulated as a sequence-level constraint on model outputs, our method fine-tunes the LLM on the training corpus while enhancing constraint satisfaction with minimal impact on its utility and generation quality. Specifically, our approach regularizes the LLM training by penalizing the KL divergence between the desired output distribution, which satisfies the constraints, and the LLM's posterior. This regularization term can be approximated by an auxiliary model trained to decompose the sequence-level constraints into token-level guidance, allowing the term to be measured by a closed-form formulation. To further improve efficiency, we design a parallel scheme for concurrently updating both the LLM and the auxiliary model. We evaluate the empirical performance of our approach by controlling the toxicity when training an LLM. We show that our approach leads to an LLM that produces fewer inappropriate responses while achieving competitive performance on benchmarks and a toxicity detection task.

Humanity's Last Exam (HLE) has become a widely used benchmark for evaluating frontier large language models on challenging, multi-domain questions. However, community-led analyses have raised concerns that HLE contains a non-trivial number of noisy items, which can bias evaluation results and distort cross-model comparisons. To address this challenge, we introduce HLE-Verified, a verified and revised version of HLE with a transparent verification protocol and fine-grained error taxonomy. Our construction follows a two-stage validation-and-repair workflow resulting in a certified benchmark. In Stage I, each item undergoes binary validation of the problem and final answer through domain-expert review and model-based cross-checks, yielding 641 verified items. In Stage II, flawed but fixable items are revised under strict constraints preserving the original evaluation intent, through dual independent expert repairs, model-assisted auditing, and final adjudication, resulting in 1,170 revised-and-certified items. The remaining 689 items are released as a documented uncertain set with explicit uncertainty sources and expertise tags for future refinement. We evaluate seven state-of-the-art language models on HLE and HLE-Verified, observing an average absolute accuracy gain of 7--10 percentage points on HLE-Verified. The improvement is particularly pronounced on items where the original problem statement and/or reference answer is erroneous, with gains of 30--40 percentage points. Our analyses further reveal a strong association between model confidence and the presence of errors in the problem statement or reference answer, supporting the effectiveness of our revisions. Overall, HLE-Verified improves HLE-style evaluations by reducing annotation noise and enabling more faithful measurement of model capabilities. Data is available at: https://github.com/SKYLENAGE-AI/HLE-Verified

Seven years ago, researchers proposed a postprocessing method to equalize the error rates of a model across different demographic groups. The work launched hundreds of papers purporting to improve over the postprocessing baseline. We empirically evaluate these claims through thousands of model evaluations on several tabular datasets. We find that the fairness-accuracy Pareto frontier achieved by postprocessing contains all other methods we were feasibly able to evaluate. In doing so, we address two common methodological errors that have confounded previous observations. One relates to the comparison of methods with different unconstrained base models. The other concerns methods achieving different levels of constraint relaxation. At the heart of our study is a simple idea we call unprocessing that roughly corresponds to the inverse of postprocessing. Unprocessing allows for a direct comparison of methods using different underlying models and levels of relaxation.

Assurance cases can be used to argue for the safety of products in safety engineering. In safety-critical areas, the construction of assurance cases is indispensable. Trustworthiness Derivation Trees (TDTs) enhance assurance cases by incorporating formal methods, rendering it possible for automatic reasoning about assurance cases. We present Trustworthiness Derivation Tree Analyzer (Trusta), a desktop application designed to automatically construct and verify TDTs. The tool has a built-in Prolog interpreter in its backend, and is supported by the constraint solvers Z3 and MONA. Therefore, it can solve constraints about logical formulas involving arithmetic, sets, Horn clauses etc. Trusta also utilizes large language models to make the creation and evaluation of assurance cases more convenient. It allows for interactive human examination and modification. We evaluated top language models like ChatGPT-3.5, ChatGPT-4, and PaLM 2 for generating assurance cases. Our tests showed a 50%-80% similarity between machine-generated and human-created cases. In addition, Trusta can extract formal constraints from text in natural languages, facilitating an easier interpretation and validation process. This extraction is subject to human review and correction, blending the best of automated efficiency with human insight. To our knowledge, this marks the first integration of large language models in automatic creating and reasoning about assurance cases, bringing a novel approach to a traditional challenge. Through several industrial case studies, Trusta has proven to quickly find some subtle issues that are typically missed in manual inspection, demonstrating its practical value in enhancing the assurance case development process.

We study the ability of state-of-the art models to answer constraint satisfaction queries for information retrieval (e.g., 'a list of ice cream shops in San Diego'). In the past, such queries were considered to be tasks that could only be solved via web-search or knowledge bases. More recently, large language models (LLMs) have demonstrated initial emergent abilities in this task. However, many current retrieval benchmarks are either saturated or do not measure constraint satisfaction. Motivated by rising concerns around factual incorrectness and hallucinations of LLMs, we present KITAB, a new dataset for measuring constraint satisfaction abilities of language models. KITAB consists of book-related data across more than 600 authors and 13,000 queries, and also offers an associated dynamic data collection and constraint verification approach for acquiring similar test data for other authors. Our extended experiments on GPT4 and GPT3.5 characterize and decouple common failure modes across dimensions such as information popularity, constraint types, and context availability. Results show that in the absence of context, models exhibit severe limitations as measured by irrelevant information, factual errors, and incompleteness, many of which exacerbate as information popularity decreases. While context availability mitigates irrelevant information, it is not helpful for satisfying constraints, identifying fundamental barriers to constraint satisfaction. We open source our contributions to foster further research on improving constraint satisfaction abilities of future models.

Enterprise agents must follow long-horizon, conditional, safety-critical standard operating procedures (SOPs). We compile machine-readable SOP constraints into executable pseudo-code and run them with a program-guided (PG) stack machine that pages the active frame while an LLM performs semantic execution. A three-arm SOPBench study across six models separates representation from runtime: compiled text never significantly hurts and gains up to 16.0 points where official prose underperforms. Runtime guidance is capability-gated. Two strong models independently show positive seven-domain PG contrasts (58:19 and 75:31 discordant pairs), whereas weak models are harmed. A full-program cursor ablation (active frame first, complete program retained) recovers much of the strong-model refusal gain; selective visibility adds a smaller improvement. Paired probe and audit measurements track this divide to spontaneous state discipline rather than reconstruction ability. On Bank the three primary arms rise from 70.4 to 86.4 to 92.8, with 100% refusal correctness. Practical guidance: compile first; enable active-frame paging only after a model-level discipline check.

Planning is a fundamental capability for large language models (LLMs) because such complex tasks require models to coordinate goals, constraints, resources, and long-term consequences into executable and verifiable solutions. Existing planning benchmarks, however, usually treat planning data as fixed collections of instances rather than controllable generation targets. This limits scenario coverage, ties difficulty to surface-level proxies rather than structural sources, and offers limited support for scalable generation, automatic verification, or planning-oriented training. We introduce PlanningBench, a framework for generating scalable, diverse, and verifiable planning data for both evaluation and training. PlanningBench starts from real planning scenarios and abstracts practical workflows into a structured taxonomy of more than 30 task types, subtasks, constraint families, and difficulty factors. Guided by this taxonomy, a constraint-driven synthesis pipeline instantiates self-contained planning problems with adaptive difficulty control, quality filtering, and instance-level verification checklists. This shifts planning data construction from fixed benchmark collection to controllable generation while preserving realistic task grounding. We use PlanningBench to evaluate open-source and closed-source frontier LLMs, and find that current models still struggle to produce complete solutions under coupled constraints. Beyond evaluation, reinforcement learning on verified PlanningBench data improves performance on unseen planning benchmarks and broader instruction-following tasks. Further analysis suggests that determinate or well-specified optimal solutions provide clearer reward signals and more stable training dynamics. Overall, PlanningBench provides a controllable source of planning data for diagnosing and improving generalizable planning abilities in LLMs.

Recent advancements in prompt engineering strategies, such as Chain-of-Thought (CoT) and Self-Discover, have demonstrated significant potential in improving the reasoning abilities of Large Language Models (LLMs). However, these state-of-the-art (SOTA) prompting strategies rely on single or fixed set of static seed reasoning modules like "think step by step" or "break down this problem" intended to simulate human approach to problem-solving. This constraint limits the flexibility of models in tackling diverse problems effectively. In this paper, we introduce Auto-Evolve, a novel framework that enables LLMs to self-create dynamic reasoning modules and downstream action plan, resulting in significant improvements over current SOTA methods. We evaluate Auto-Evolve on the challenging BigBench-Hard (BBH) dataset with Claude 2.0, Claude 3 Sonnet, Mistral Large, and GPT 4, where it consistently outperforms the SOTA prompt strategies. Auto-Evolve outperforms CoT by up to 10.4% and on an average by 7% across these four models. Our framework introduces two innovations: a) Auto-Evolve dynamically generates reasoning modules for each task while aligning with human reasoning paradigm, thus eliminating the need for predefined templates. b) We introduce an iterative refinement component, that incrementally refines instruction guidance for LLMs and helps boost performance by average 2.8% compared to doing it in a single step.

Neural networks (NN) perform well in diverse tasks, but sometimes produce nonsensical results to humans. Most NN models "solely" learn from (input, output) pairs, occasionally conflicting with human knowledge. Many studies indicate injecting human knowledge by reducing output constraints during training can improve model performance and reduce constraint violations. While there have been several attempts to compare different existing algorithms under the same programming framework, nonetheless, there has been no previous work that categorizes learning algorithms with output constraints in a unified manner. Our contributions are as follows: (1) We categorize the previous studies based on three axes: type of constraint loss used (e.g. probabilistic soft logic, REINFORCE), exploration strategy of constraint-violating examples, and integration mechanism of learning signals from main task and constraint. (2) We propose new algorithms to integrate the information of main task and constraint injection, inspired by continual-learning algorithms. (3) Furthermore, we propose the Hβ-score as a metric for considering the main task metric and constraint violation simultaneously. To provide a thorough analysis, we examine all the algorithms on three NLP tasks: natural language inference (NLI), synthetic transduction examples (STE), and semantic role labeling (SRL). We explore and reveal the key factors of various algorithms associated with achieving high Hβ-scores.

Large language models are increasingly deployed as autonomous agents for multi-step tasks in executable environments, yet their ability to perform realistic operations research (OR) work remains unclear. Existing OR evaluations often decouple modeling from solving, rely on pre-formalized or text-only instances, and rarely test the full workflow from operational artifacts to validated decisions. In this work, we introduce ORAgentBench, an execution-grounded benchmark for evaluating autonomous agents on challenging end-to-end operations research tasks. It contains 107 human-reviewed tasks across diverse operational scenarios, each packaged in an isolated environment with a natural-language brief, multi-file data, configuration artifacts, and a required submission schema. Agents must write and run solution code, and their submissions are evaluated by hidden validators for schema validity, hard-constraint feasibility, and normalized objective quality. Experiments with fourteen frontier agent-model configurations show that current agents remain far from reliable OR practice. The best agent passes only 35.51% of all tasks and 20.59% of hard tasks, and many feasible submissions still fall below the required quality threshold. Failure analysis further shows that errors are dominated by strategic weaknesses, including missed operational rules, brittle formulations, weak feasible-solution construction, and insufficient solution improvement. OR-specific procedural skills increase hard-task feasibility, but do not reliably improve solution quality or pass rate. These results suggest that progress in OR agents requires moving beyond plausible optimization code toward dependable, high-quality operational decision-making.

Vision-language process reward models (VL-PRMs) are increasingly used to score intermediate reasoning steps and rerank candidates under test-time scaling. However, they often function as black-box judges: a low step score may reflect a genuine reasoning mistake or simply the verifier's misperception of the image. This entanglement between perception and reasoning leads to systematic false positives (rewarding hallucinated visual premises) and false negatives (penalizing correct grounded statements), undermining both reranking and error localization. We introduce Explicit Visual Premise Verification (EVPV), a lightweight verification interface that conditions step scoring on the reliability of the visual premises a step depends on. The policy is prompted to produce a step-wise visual checklist that makes required visual facts explicit, while a constraint extractor independently derives structured visual constraints from the input image. EVPV matches checklist claims against these constraints to compute a scalar visual reliability signal, and calibrates PRM step rewards via reliability gating: rewards for visually dependent steps are attenuated when reliability is low and preserved when reliability is high. This decouples perceptual uncertainty from logical evaluation without per-step tool calls. Experiments on VisualProcessBench and six multimodal reasoning benchmarks show that EVPV improves step-level verification and consistently boosts Best-of-N reranking accuracy over strong baselines. Furthermore, injecting controlled corruption into the extracted constraints produces monotonic performance degradation, providing causal evidence that the gains arise from constraint fidelity and explicit premise verification rather than incidental prompt effects. Code is available at: https://github.com/Qwen-Applications/EVPV-PRM

Natural-language software requirements are often ambiguous, inconsistent, and underspecified; in safety-critical domains, these defects propagate into formal models that verify the wrong specification and into implementations that ship unsafe behavior. We show that large language models, equipped with an SMT solver, can audit such requirements: translating them into formal logic, detecting ambiguity through stochastic variation in the generated formalization, and exposing inconsistency, vacuousness, and safety violations through solver queries on the resulting specification. We present VERIMED, a neurosymbolic pipeline that operationalizes this idea for medical-device software requirements, and report two findings. First, stochastic variation across independent formalizations is a signal of ambiguity: requirements that admit multiple plausible interpretations produce SMT-inequivalent formalizations, and bidirectional SMT equivalence checking turns this disagreement into a solver-checkable test. Second, the usefulness of symbolic feedback depends on its granularity: in counterexample-guided repair on a hemodialysis question-answering benchmark, concrete SMT counterexamples raise verified accuracy from 55.4% to 98.5%. Over an extensive experimental evaluation on open-source hemodialysis safety requirements, we show that the LLM-based approach in VERIMED successfully reduces ambiguity-sensitive requirements and enables rigorous auditing of software requirements through SMT-based queries.

The increasing complexity of enterprise business scenarios has promoted the widespread adoption of long SKILL documents in agent systems, posing new challenges for compliance detection: large models incur substantial inference costs, while small models may fail to maintain detection accuracy. To address this gap, we propose SkillCDG, a graph-based framework for long SKILL compliance detection. SkillCDG represents complex business policies as a two-layer constraint dependency graph, where the upper layer indexes SKILL descriptions for scenario routing and the lower layer captures dependencies among atomic constraints within each SKILL. During inference, two-level retrieval followed by dependency closure supports compliance judgment and source traceability. We comprehensively evaluate the framework on three enterprise datasets and two controlled public benchmark variants. Experimental results demonstrate that SkillCDG outperforms baseline methods by up to 12.8 percentage points in detection F1 score, while reducing token consumption by a maximum 64.3\%. Moreover, we further investigate the inherent relationships among policy-graph complexity, model scale, and detection performance. Comparative experiments conducted on four checkpoints from a single model family validate a concise and effective scaling trend: end-to-end detection correctness exhibits a complexity-differentiated scaling pattern, and the complexity metric derived from the constraint dependency graph can effectively quantify instance difficulty and the performance improvement potential of models. Leveraging this insightful scaling trend, we conduct adaptive training sample selection and adopt on-policy distillation to efficiently enhance the compliance detection capability of small-scale models.

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification that the model is truly robust against all future attacks. Unfortunately, when faced with adversarially trained models, all existing approaches have significant trouble making certifications that are strong enough to be practically useful. Linear programming (LP) techniques in particular face a "convex relaxation barrier" that prevent them from making high-quality certifications, even after refinement with mixed-integer linear programming (MILP) and branch-and-bound (BnB) techniques. In this paper, we propose a nonconvex certification technique, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. The nonconvex relaxation makes strong certifications comparable to much more expensive SDP methods, while optimizing over dramatically fewer variables comparable to much weaker LP methods. Despite nonconvexity, we show how off-the-shelf local optimization algorithms can be used to achieve and to certify global optimality in polynomial time. Our experiments find that the nonconvex relaxation almost completely closes the gap towards exact certification of adversarially trained models.

Instance-specific algorithm configuration and algorithm portfolios have been shown to offer significant improvements over single algorithm approaches in a variety of application domains. In the SAT and CSP domains algorithm portfolios have consistently dominated the main competitions in these fields for the past five years. For a portfolio approach to be effective there are two crucial conditions that must be met. First, there needs to be a collection of complementary solvers with which to make a portfolio. Second, there must be a collection of problem features that can accurately identify structural differences between instances. This paper focuses on the latter issue: feature representation, because, unlike SAT, not every problem has well-studied features. We employ the well-known SATzilla feature set, but compute alternative sets on different SAT encodings of CSPs. We show that regardless of what encoding is used to convert the instances, adequate structural information is maintained to differentiate between problem instances, and that this can be exploited to make an effective portfolio-based CSP solver.

Large Language Models (LLMs) have demonstrated a powerful ability for text generation. However, achieving optimal results with a given prompt or instruction can be challenging, especially for billion-sized models. Additionally, undesired behaviors such as toxicity or hallucinations can manifest. While much larger models (e.g., ChatGPT) may demonstrate strength in mitigating these issues, there is still no guarantee of complete prevention. In this work, we propose formalizing text generation as a future-constrained generation problem to minimize undesirable behaviors and enforce faithfulness to instructions. The estimation of future constraint satisfaction, accomplished using LLMs, guides the text generation process. Our extensive experiments demonstrate the effectiveness of the proposed approach across three distinct text generation tasks: keyword-constrained generation (Lin et al., 2020), toxicity reduction (Gehman et al., 2020), and factual correctness in question-answering (Gao et al., 2023).

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees, while achieving competitive empirical performance.

We introduce the Endless Exam, a benchmark spanning fourteen parameterised families of mathematical construction problems, with verifiable scores that distinguish progress before and beyond published mathematical frontiers. Each submitted object is checked automatically for validity and assigned a relative quality score against a published frontier or construction baseline, without capping improvements at 1. The benchmark draws long-term challenges from open mathematical problems and generates larger instances by varying their parameters. Compact certificates allow large constructions to be verified without listing every element. Across nine models evaluated on 69 distinct instances, continuous quality scores distinguish performance even though none of the 30 published-frontier references is surpassed. Size-quality curves show how construction quality changes as problem size increases. We release the generators, verifiers, references, model responses and analysis to support continued measurement before and beyond human frontiers.

Creating CAD digital twins from the physical world is crucial for manufacturing, design, and simulation. However, current methods typically rely on costly 3D scanning with labor-intensive post-processing. To provide a user-friendly design process, we explore the problem of reverse engineering from unconstrained real-world CAD images that can be easily captured by users of all experiences. However, the scarcity of real-world CAD data poses challenges in directly training such models. To tackle these challenges, we propose CADCrafter, an image-to-parametric CAD model generation framework that trains solely on synthetic textureless CAD data while testing on real-world images. To bridge the significant representation disparity between images and parametric CAD models, we introduce a geometry encoder to accurately capture diverse geometric features. Moreover, the texture-invariant properties of the geometric features can also facilitate the generalization to real-world scenarios. Since compiling CAD parameter sequences into explicit CAD models is a non-differentiable process, the network training inherently lacks explicit geometric supervision. To impose geometric validity constraints, we employ direct preference optimization (DPO) to fine-tune our model with the automatic code checker feedback on CAD sequence quality. Furthermore, we collected a real-world dataset, comprised of multi-view images and corresponding CAD command sequence pairs, to evaluate our method. Experimental results demonstrate that our approach can robustly handle real unconstrained CAD images, and even generalize to unseen general objects.

Sequential agent search accumulates changes from its current champion but discards alternative branches; independent proposals preserve breadth but restart from the root. Loreley instead retains complete repository states in a Quality-Diversity (QD) archive and samples them as parents or supplies them as context for later edits. Candidates are Git commits produced in isolated worktrees and judged by a project-supplied evaluator. We compare configured Loreley QD, sequential champion editing, and independent root proposals in a matched Zstandard experiment: seven paired blocks and 48 physical candidate jobs per policy and block (1,008 total), with root-only initialization and each policy's native concurrency. Validation selected a winner at each budget checkpoint; an agent-hidden holdout measured the fixed candidate. At 48 jobs, QD was 0.135% below Sequential Champion (95% BCa interval for the paired effect: -0.556% to +0.161%) and 0.320% above Independent Root (-0.082% to +0.686%). Neither contrast established a QD advantage; Sequential had the highest observed 48-job mean and median. Archive retention and later sampling did occur. Four of seven final QD winners had a non-incumbent state in their primary-parent ancestry under a retrospective one-incumbent rule applied only to the observed QD stream. Including inspiration edges raised the count to six, without showing that supplied context caused an edit. Three earlier capability campaigns produced generation-4, multi-file improvements in two Python libraries and a separate Zstandard revision. Loreley engaged the intended stepping-stone mechanism, but the controlled experiment did not show an endpoint benefit at 48 jobs.

We introduce SATBench, a benchmark for evaluating the logical reasoning capabilities of large language models (LLMs) through logical puzzles derived from Boolean satisfiability (SAT) problems. Unlike prior work that focuses on inference rule-based reasoning, which often involves deducing conclusions from a set of premises, our approach leverages the search-based nature of SAT problems, where the objective is to find a solution that fulfills a specified set of logical constraints. Each instance in SATBench is generated from a SAT formula, then translated into a story context and conditions using LLMs. The generation process is fully automated and allows for adjustable difficulty by varying the number of clauses. All 2100 puzzles are validated through both LLM-assisted and solver-based consistency checks, with human validation on a subset. Experimental results show that even the strongest model, o4-mini, achieves only 65.0% accuracy on hard UNSAT problems, close to the random baseline of 50%. SATBench exposes fundamental limitations in the search-based logical reasoning abilities of current LLMs and provides a scalable testbed for future research in logical reasoning.

We consider a binary classification problem under group fairness constraints, which can be one of Demographic Parity (DP), Equalized Opportunity (EOp), or Equalized Odds (EO). We propose an explicit characterization of Bayes optimal classifier under the fairness constraints, which turns out to be a simple modification rule of the unconstrained classifier. Namely, we introduce a novel instance-level measure of bias, which we call bias score, and the modification rule is a simple linear rule on top of the finite amount of bias scores.Based on this characterization, we develop a post-hoc approach that allows us to adapt to fairness constraints while maintaining high accuracy. In the case of DP and EOp constraints, the modification rule is thresholding a single bias score, while in the case of EO constraints we are required to fit a linear modification rule with 2 parameters. The method can also be applied for composite group-fairness criteria, such as ones involving several sensitive attributes.

Advancing complex reasoning in large language models relies on high-quality, verifiable datasets, yet human annotation remains cost-prohibitive and difficult to scale. Current synthesis paradigms often face a recurring trade-off: maintaining structural validity typically restricts problem complexity, while relaxing constraints to increase difficulty frequently leads to inconsistent or unsolvable instances. To address this, we propose Agentic Proposing, a framework that models problem synthesis as a goal-driven sequential decision process where a specialized agent dynamically selects and composes modular reasoning skills. Through an iterative workflow of internal reflection and tool-use, we develop the Agentic-Proposer-4B using Multi-Granularity Policy Optimization (MGPO) to generate high-precision, verifiable training trajectories across mathematics, coding, and science. Empirical results demonstrate that downstream solvers trained on agent-synthesized data significantly outperform leading baselines and exhibit robust cross-domain generalization. Notably, a 30B solver trained on only 11,000 synthesized trajectories achieves a state-of-the-art 91.6% accuracy on AIME25, rivaling frontier-scale proprietary models such as GPT-5 and proving that a small volume of high-quality synthetic signals can effectively substitute for massive human-curated datasets.

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, including mathematical reasoning. However, the current evaluation mostly focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing or contradictory conditions, known as ill-defined problems. To further study this problem, we develop a largescale benchmark called Problems with Missing and Contradictory conditions ( PMC) containing over 5,000 validated ill-defined mathematical problems. Our preliminary experiments through PMC reveal two challenges about existing methods: (1) traditional methods exhibit a trade-off between solving accuracy and rejection capabilities, and (2) formal methods struggle with modeling complex problems. To address these challenges, We develop Variable-Constraint Search (VCSEARCH), a trainingfree framework that leverages formal language to detect ill-defined problems, where a variableconstraint pair search strategy is incorporated to improve the modeling capability of formal language. Extensive experiments demonstrate that VCSEARCH improves the accuracy of identifying unsolvable problems by at least 12% across different LLMs, thus achieving stronger robust mathematical reasoning ability.

In industrial procurement, an LLM answer is useful only if it survives a standards check: recommended material must match operating condition, every parameter must respect a regulated threshold, and no procedure may contradict a safety clause. Partial correctness can mask safety-critical contradictions that aggregate LLM benchmarks rarely capture. We introduce IndustryBench, a 2,049-item benchmark for industrial procurement QA in Chinese, grounded in Chinese national standards (GB/T) and structured industrial product records, organized by seven capability dimensions, ten industry categories, and panel-derived difficulty tiers, with item-aligned English, Russian, and Vietnamese renderings. Our construction pipeline rejects 70.3% of LLM-generated candidates at a search-based external-verification stage, calibrating how unreliable industrial QA remains after LLM-only filtering.Our evaluation decouples raw correctness, scored by a Qwen3-Max judge validated at κ_w = 0.798 against a domain expert, from a separate safety-violation (SV) check against source texts. Across 17 models in Chinese and an 8-model intersection over four languages, we find: (i) the best system reaches only 2.083 on the 0--3 rubric, leaving substantial headroom; (ii) Standards & Terminology is the most persistent capability weakness and survives item-aligned translation; (iii) extended reasoning lowers safety-adjusted scores for 12 of 13 models, primarily by introducing unsupported safety-critical details into longer final answers; and (iv) safety-violation rates reshuffle the leaderboard -- GPT-5.4 climbs from rank 6 to rank 3 after SV adjustment, while Kimi-k2.5-1T-A32B drops seven positions.Industrial LLM evaluation therefore requires source-grounded, safety-aware diagnosis rather than aggregate accuracy. We release IndustryBench with all prompts, scoring scripts, and dataset documentation.

Test-time scaling has enabled Large Language Models (LLMs) with remarkable reasoning capabilities, particularly in mathematical domains, through intermediate chain-of-thought (CoT) reasoning before generating final answers. However, the specific sources and mechanisms underlying these reasoning capabilities remain insufficiently understood. Optimization reasoning, i.e. finding extrema under constraints, represents a fundamental abstraction that underpins critical applications in planning, control, resource allocation, and prompt search. To systematically evaluate this capability, we introduce ExtremBench, a benchmark dataset for solving mathematical extremal problems, curated from inequality exercises used for Chinese Mathematical Olympiad and transformed into 93 standardized extrema-finding problems. We conduct extensive evaluations across various state-of-the-art open-source model families, including the Qwen3, GPT-OSS, and DeepSeek. Our results reveal that LLMs' extremal-solving reasoning capabilities do not always align with those of current mathematical benchmarks such as AIME25 and MATH-500, with some models showing strong general mathematical reasoning but poor extremal-solving skills, and vice versa. This discrepancy highlights a critical gap in current evaluation practices and suggests that existing benchmarks may not comprehensively capture the full spectrum of mathematical reasoning abilities.

Large language models (LLMs) have advanced significantly in code generation, yet their ability to follow complex programming instructions with layered and diverse constraints remains underexplored. Existing benchmarks often prioritize functional correctness, overlooking the nuanced requirements found in real-world development. We introduce MultiCodeIF, a comprehensive benchmark designed to evaluate instruction-following in code generation across multiple dimensions: constraint type, hierarchical levels, and iterative refinement. Built upon a structured taxonomy of 9 categories and 27 constraint types, MultiCodeIF enables granular assessment of both functional and non-functional instruction adherence. Using an automated pipeline, ConstraGen, we synthesize and evolve 2,021 code tasks sourced from 14 programming languages, supporting multi-turn evaluation through feedback-driven task variants. Empirical evaluation of six state-of-the-art LLMs uncovers substantial performance disparities. The top-performing model, Claude-3-7-Sonnet, achieves 63.0% average constraint satisfaction, while smaller models like Qwen3-1.7B fall to 44.8%. Models perform well on explicit constraints, but struggle with implicit or abstract constraints. Tasks with multiple hierarchical constraints significantly reduce model success rates, from 54.5% in single-level to just 18.8% in multi-level scenarios. However, structured feedback enables progressive improvement: average constraint satisfaction rises from 63.0% to 83.4% over four iterative refinement rounds. MultiCodeIF provides a scalable, constraint-aware, and feedback-sensitive framework to benchmark LLMs under realistic code generation scenarios, bridging the gap between synthetic evaluations and real-world instruction complexity. The full benchmark dataset, evaluation pipeline, and source code are available at https://github.com/SYSUSELab/MultiCodeIF.

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural language proofs be checked for errors. LLM judges are increasingly being adopted to meet the growing demand for evaluating such proofs. While verification is considered easier than generation, what model capability does reliable verification actually require? We systematically evaluate four open-source and two frontier LLMs on datasets of human-graded natural language proofs of competition-level problems. We consider two key metrics: verifier accuracy and self-consistency (the rate of agreement across repeated judgments on the same proof). We observe that smaller open-source models are only up to ~10% behind frontier models in accuracy but they are up to ~25% more inconsistent. Furthermore, we see that verifier accuracy is sensitive to prompt choice across all models. We then demonstrate that the smaller models, in fact, do possess the mathematical capabilities to verify proofs at the level of frontier models, but they struggle to reliably elicit these capabilities with general judging prompts. Through an LLM-guided prompt search, we synthesize an ensemble of specialized prompts that overcome the specific failure modes of smaller models, boosting their performance by up to 9.1% in accuracy and 15.9% in self-consistency. These gains are realized across models and datasets, allowing models like Qwen3.5-35B to perform on par with frontier models such as Gemini 3.1 Pro for proof verification.

User alignment is crucial for adapting general-purpose language models (LMs) to downstream tasks, but human annotations are often not available for all types of instructions, especially those with customized constraints. We observe that user instructions typically contain constraints. While assessing response quality in terms of the whole instruction is often costly, efficiently evaluating the satisfaction rate of constraints is feasible. We investigate common constraints in NLP tasks, categorize them into three classes based on the types of their arguments, and propose a unified framework, ACT (Aligning to ConsTraints), to automatically produce supervision signals for user alignment with constraints. Specifically, ACT uses constraint verifiers, which are typically easy to implement in practice, to compute constraint satisfaction rate (CSR) of each response. It samples multiple responses for each prompt and collect preference labels based on their CSR automatically. Subsequently, ACT adapts the LM to the target task through a ranking-based learning process. Experiments on fine-grained entity typing, abstractive summarization, and temporal question answering show that ACT is able to enhance LMs' capability to adhere to different classes of constraints, thereby improving task performance. Further experiments show that the constraint-following capabilities are transferable.

This paper introduces an approach to endow generative diffusion processes the ability to satisfy and certify compliance with constraints and physical principles. The proposed method recast the traditional sampling process of generative diffusion models as a constrained optimization problem, steering the generated data distribution to remain within a specified region to ensure adherence to the given constraints. These capabilities are validated on applications featuring both convex and challenging, non-convex, constraints as well as ordinary differential equations, in domains spanning from synthesizing new materials with precise morphometric properties, generating physics-informed motion, optimizing paths in planning scenarios, and human motion synthesis.

Generative Adversarial Networks (GANs) struggle to generate structured objects like molecules and game maps. The issue is that structured objects must satisfy hard requirements (e.g., molecules must be chemically valid) that are difficult to acquire from examples alone. As a remedy, we propose Constrained Adversarial Networks (CANs), an extension of GANs in which the constraints are embedded into the model during training. This is achieved by penalizing the generator proportionally to the mass it allocates to invalid structures. In contrast to other generative models, CANs support efficient inference of valid structures (with high probability) and allows to turn on and off the learned constraints at inference time. CANs handle arbitrary logical constraints and leverage knowledge compilation techniques to efficiently evaluate the disagreement between the model and the constraints. Our setup is further extended to hybrid logical-neural constraints for capturing very complex constraints, like graph reachability. An extensive empirical analysis shows that CANs efficiently generate valid structures that are both high-quality and novel.

Task-oriented dialogues must maintain consistency both within the dialogue itself, ensuring logical coherence across turns, and with the conversational domain, accurately reflecting external knowledge. We propose to conceptualize dialogue consistency as a Constraint Satisfaction Problem (CSP), wherein variables represent segments of the dialogue referencing the conversational domain, and constraints among variables reflect dialogue properties, including linguistic, conversational, and domain-based aspects. To demonstrate the feasibility of the approach, we utilize a CSP solver to detect inconsistencies in dialogues re-lexicalized by an LLM. Our findings indicate that: (i) CSP is effective to detect dialogue inconsistencies; and (ii) consistent dialogue re-lexicalization is challenging for state-of-the-art LLMs, achieving only a 0.15 accuracy rate when compared to a CSP solver. Furthermore, through an ablation study, we reveal that constraints derived from domain knowledge pose the greatest difficulty in being respected. We argue that CSP captures core properties of dialogue consistency that have been poorly considered by approaches based on component pipelines.

While tool-augmented Large Language Models have significantly improved multi-step reasoning in quantitative STEM tasks, a critical residual failure mode remains: intermediate reasoning steps that are syntactically well-formed, mathematically executable, and unit-consistent, yet contextually ungrounded. Current approaches either rely on formal verifiers that cannot assess semantic intent, or burden Process Reward Models (PRMs) with the dual task of checking both arithmetic and logic. In this paper, we propose a neuro-symbolic framework that cleanly decouples reasoning into two formal dimensions: Symbolic Validity (V) and Semantic Groundedness (G). We guarantee V by construction using a deterministic symbolic verifier acting as a hard filter. To assess G, we train a PRM conditionally on the verifier-accepted manifold. To train this PRM efficiently, we introduce Counterfactual Symbolic Perturbation (CSP), a novel data synthesis strategy that algorithmically generates constraint-preserving hard negatives (steps that perfectly pass the verifier but are logically flawed). At inference, we deploy a verifier-first constrained search that guarantees execution consistency for verifier-covered operations while relying on the PRM solely to rank semantic grounding. By targeting the exact residual error class of strong tool-using LLMs, our method significantly improves reasoning reliability without the sprawling heuristics of prior frameworks.

Chain-of-thought (CoT) prompting can fail severely on constraint-dense logical reasoning tasks, where unverified errors accumulate silently across steps. We introduce SymStep: an LLM makes one atomic claim at a time (DEDUCE: Alice, pet, Cat), then a lightweight constraint propagator checks the claim for consistency with prior accepted deductions, rejects contradictions, and cascades implied facts automatically. SymStep+G additionally provides MRV guidance after each accepted step, directing the LLM toward the most constrained unresolved variable. On a 35-puzzle retained subset of ZebraLogicBench, a benchmark of 1,000 Einstein-style logic puzzles, Direct and CoT both achieve 0%, while SymStep+G reaches 97%. On AR-LSAT analytical reasoning problems, SymStep achieves 100% vs. CoT's 87%. On LGP-14, SymStep+G achieves 100% vs. 0% for CoT and Logic-LM, the strongest prior symbolic+LLM baseline we compare against. Ablation studies reveal that MRV guidance is a key mechanism for reducing directionless cycling, while consistency checking provides a safety net against explicit contradictions. Across six benchmarks spanning five task domains, SymStep variants match or exceed every baseline on constraint-dense and arithmetic tasks. Experiments on AQUA-RAT algebra confirm the advantage is constraint-density-specific.

The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a CTL formula, for a given (possibly infinite-state) program. We propose a method based on encoding the problem as a set of Horn constraints. The method takes a program, modeled as a transition system, and a property given by a CTL formula as input. It first generates a set of forall-exists quantified Horn constraints and well-foundedness constraints by exploiting the syntactic structure of the CTL formula. Then, the generated set of constraints are solved by applying an off-the-shelf Horn constraints solving engine. The program is said to satisfy the property if and only if the generated set of constraints has a solution. We demonstrate the practical promises of the method by applying it on a set of challenging examples. Although our method is based on a generic Horn constraint solving engine, it is able to outperform state-of-art methods specialised for CTL verification.

We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles benchmark ZebraLogicBench. Instead of letting the LLM attempt to directly solve the puzzles, our method prompts the model to formalise the problem in a logic-focused domain-specific language (DSL) called Logic.py. This formalised representation is then solved using a constraint solver, leveraging the strengths of both the language model and the solver. Our approach achieves a remarkable 65% absolute improvement over the baseline performance of Llama 3.1 70B on ZebraLogicBench, setting a new state-of-the-art with an accuracy of over 90%. This significant advancement demonstrates the potential of combining language models with domain-specific languages and auxiliary tools on traditionally challenging tasks for LLMs.

Knowledge graphs (KGs) are increasingly used to support large lan guage model (LLM) reasoning, but standard triplet-based KGs treat each relation as globally valid. In many settings, whether a relation should count as evidence depends on the context. We therefore formulate triplet validity as a triplet-specific function of context and refer to this formulation as a Quantum Knowledge Graph (QKG). We instantiate QKG in medicine using a diabetes-centered PrimeKG subgraph, whose 68,651 context-sensitive relations are further annotated with patient-group-specific constraints. We evaluate it in a reasoner--validator pipeline for medical question answering on a KG-grounded subset of MedReason containing 2,788 questions. With Haiku-4.5 as both the Reasoner and the Validator, KG-backed validation significantly improves over a no-validator baseline (+0.61 pp), and QKG with context matching yields the largest gain, outperforming both KG validation without context matching (+0.79 pp) and the no-validator baseline (+1.40 pp; paired McNemar, all p<0.05). Under a stronger validator (Qwen-3.6-Plus), the raw QKG gain over the no-validator baseline grows from +1.40 pp to +5.96 pp; the context-matching gap is non-significant (p=0.73) on the raw set but becomes borderline significant (p=0.05) after adjustment for knowledge leakage and suspicious questions, consistent with a benchmark-gold ceiling rather than a QKG limitation. Taken together, the results support the view that the value of a KG in LLM-based clinical reasoning lies not merely in storing medically related facts, but in representing whether those facts are applicable to the specific patient context. For reproducibility and further research, we release the curated QKG datasets and source code.https://github.com/HKAI-Sci/QKG

Recent advances in Hierarchical Multi-label Classification (HMC), particularly neurosymbolic-based approaches, have demonstrated improved consistency and accuracy by enforcing constraints on a neural model during training. However, such work assumes the existence of such constraints a-priori. In this paper, we relax this strong assumption and present an approach based on Error Detection Rules (EDR) that allow for learning explainable rules about the failure modes of machine learning models. We show that these rules are not only effective in detecting when a machine learning classifier has made an error but also can be leveraged as constraints for HMC, thereby allowing the recovery of explainable constraints even if they are not provided. We show that our approach is effective in detecting machine learning errors and recovering constraints, is noise tolerant, and can function as a source of knowledge for neurosymbolic models on multiple datasets, including a newly introduced military vehicle recognition dataset.

Automated science needs agents that can work out the rules of an unfamiliar environment by interacting with it. Interactive rule-discovery puzzles offer a controlled setting for studying this ability: an agent infers hidden rules through experimentation and uses what it has inferred to reach a stated goal. We ask what limits current language models on these puzzles and whether reinforcement learning (RL) improves performance on rules held out from training. To study both, we introduce WITNESS, a 2D grid-based puzzle environment with ground-truth ASCII observations and controlled access to rules. An agentic pipeline generates games for WitnessGym, the RL training suite, and WitnessBench, comprising public validation and private test games. The validation set separately tests new compositions of trained rule primitives and primitives absent from training. Under a shared harness, the best of 18 frontier proprietary and open-weight models solves only 24\% of private test level slots, with scores sensitive to the observation interface and agent configuration. Providing ground-truth rules raises Opus-5's validation RHAE-L5 (relative human action efficiency over the first five levels) from 59.9 to 97.8, whereas a 27B open-weight model gains only 2.1 points and remains limited even with the rules provided. RL on WitnessGym raises the 27B model's private test RHAE-L5 from 2.1 to 5.4 and yields a mean gain of 4.1 points on four external discovery benchmarks. Together, these results point to rule acquisition as a major difficulty for frontier models like Opus-5 while smaller models further struggle on rule-based execution, and indicate that RL on hidden-rule puzzles transfers to broader rules and real-world tasks beyond training. Benchmark is available at: https://witnessbench.ai

Recent agent frameworks and inference-time algorithms often struggle with complex planning problems due to limitations in verifying generated plans or reasoning and varying complexity of instances within a single task. Many existing methods for these tasks either perform task-level verification without considering constraints or apply inference-time algorithms without adapting to instance-level complexity. To address these limitations, we propose PlanGEN, a model-agnostic and easily scalable agent framework with three key components: constraint, verification, and selection agents. Specifically, our approach proposes constraint-guided iterative verification to enhance performance of inference-time algorithms--Best of N, Tree-of-Thought, and REBASE. In PlanGEN framework, the selection agent optimizes algorithm choice based on instance complexity, ensuring better adaptability to complex planning problems. Experimental results demonstrate significant improvements over the strongest baseline across multiple benchmarks, achieving state-of-the-art results on NATURAL PLAN (sim8%uparrow), OlympiadBench (sim4%uparrow), DocFinQA (sim7%uparrow), and GPQA (sim1%uparrow). Our key finding highlights that constraint-guided iterative verification improves inference-time algorithms, and adaptive selection further boosts performance on complex planning and reasoning problems.

Character animation in real-world scenarios necessitates a variety of constraints, such as trajectories, key-frames, interactions, etc. Existing methodologies typically treat single or a finite set of these constraint(s) as separate control tasks. They are often specialized, and the tasks they address are rarely extendable or customizable. We categorize these as solutions to the close-set motion control problem. In response to the complexity of practical motion control, we propose and attempt to solve the open-set motion control problem. This problem is characterized by an open and fully customizable set of motion control tasks. To address this, we introduce a new paradigm, programmable motion generation. In this paradigm, any given motion control task is broken down into a combination of atomic constraints. These constraints are then programmed into an error function that quantifies the degree to which a motion sequence adheres to them. We utilize a pre-trained motion generation model and optimize its latent code to minimize the error function of the generated motion. Consequently, the generated motion not only inherits the prior of the generative model but also satisfies the required constraints. Experiments show that we can generate high-quality motions when addressing a wide range of unseen tasks. These tasks encompass motion control by motion dynamics, geometric constraints, physical laws, interactions with scenes, objects or the character own body parts, etc. All of these are achieved in a unified approach, without the need for ad-hoc paired training data collection or specialized network designs. During the programming of novel tasks, we observed the emergence of new skills beyond those of the prior model. With the assistance of large language models, we also achieved automatic programming. We hope that this work will pave the way for the motion control of general AI agents.

Large language models systematically fail when a salient surface cue conflicts with an unstated feasibility constraint. We study this through a diagnose-measure-bridge-treat framework. Causal-behavioral analysis of the ``car wash problem'' across six models reveals approximately context-independent sigmoid heuristics: the distance cue exerts 8.7 to 38 times more influence than the goal, and token-level attribution shows patterns more consistent with keyword associations than compositional inference. The Heuristic Override Benchmark (HOB) -- 500 instances spanning 4 heuristic by 5 constraint families with minimal pairs and explicitness gradients -- demonstrates generality across 14 models: under strict evaluation (10/10 correct), no model exceeds 75%, and presence constraints are hardest (44%). A minimal hint (e.g., emphasizing the key object) recovers +15 pp on average, suggesting the failure lies in constraint inference rather than missing knowledge; 12/14 models perform worse when the constraint is removed (up to -39 pp), revealing conservative bias. Parametric probes confirm that the sigmoid pattern generalizes to cost, efficiency, and semantic-similarity heuristics; goal-decomposition prompting recovers +6 to 9 pp by forcing models to enumerate preconditions before answering. Together, these results characterize heuristic override as a systematic reasoning vulnerability and provide a benchmark for measuring progress toward resolving it.

Code generation, symbolic math reasoning, and other tasks require LLMs to produce outputs that are both syntactically and semantically correct. Constrained LLM generation is a promising direction to enforce adherence to formal grammar, but prior works have empirically observed that strict enforcement of formal constraints often diminishes the reasoning capabilities of LLMs. In this work, we first provide a theoretical explanation for why constraining LLM outputs to very restrictive grammars that only allow syntactically valid final answers reduces the reasoning capabilities of the model. Second, we demonstrate that by augmenting the output grammar with carefully designed additional rules, it is always possible to preserve the reasoning capabilities of the LLM while ensuring syntactic and semantic correctness in its outputs. Building on these theoretical insights, we propose a reasoning-augmented constrained decoding algorithm, CRANE, which effectively balances the correctness of constrained generation with the flexibility of unconstrained generation. Experiments on multiple open-source LLMs and benchmarks show that CRANE significantly outperforms both state-of-the-art constrained decoding strategies and standard unconstrained decoding, showing up to 10% points accuracy improvement over baselines on challenging symbolic reasoning benchmarks GSM-symbolic and FOLIO.

We pursue a vision for self-improving language models in which the model does not merely generate problems or traces to imitate, but constructs the environments that train it. In zero-data reasoning RL, this reframes self-improvement from a data-generation loop into an environment-construction loop, where each artifact is a reusable executable object that samples instances, computes references, and scores responses. Whether this vision sustains improvement hinges on a single property: the environments must exhibit stable solve--verify asymmetry, the model must be able to write an oracle once that it cannot reliably execute in natural language on fresh instances. This asymmetry takes two complementary forms. Some tasks are algorithmically hard to reason through but trivial as code: a dynamic program or graph traversal, compiled once, yields unboundedly many calibrated instances. Others are intrinsically hard to solve but easy to verify, like planted subset-sum or constraint satisfaction. Both create a durable gap between proposing and solving that the policy cannot close by gaming the verifier, and it is this gap that keeps reward informative as the learner improves. We instantiate this view in EvoEnv, a single-policy generator, solver method that synthesizes Python environments from ten seeds and admits them only after staged validation, semantic self-review, solver-relative difficulty calibration, and novelty checks. The strongest evidence comes from the already-strong regime: on Qwen3-4B-Thinking, fixed public-data RLVR and fixed hand-crafted environment RLVR reduce the average, while EvoEnv improves it from 72.4 to 74.8, a relative gain of 3.3%. Stable self-improvement, we suggest, depends not on producing more synthetic data, but on models learning to construct worlds whose difficulty stays structurally beyond their own reach.

Remarkable performance of large language models (LLMs) in a variety of tasks brings forth many opportunities as well as challenges of utilizing them in production settings. Towards practical adoption of LLMs, multi-agent systems hold great promise to augment, integrate, and orchestrate LLMs in the larger context of enterprise platforms that use existing proprietary data and models to tackle complex real-world tasks. Despite the tremendous success of these systems, current approaches rely on narrow, single-focus objectives for optimization and evaluation, often overlooking potential constraints in real-world scenarios, including restricted budgets, resources and time. Furthermore, interpreting, analyzing, and debugging these systems requires different components to be evaluated in relation to one another. This demand is currently not feasible with existing methodologies. In this postion paper, we introduce the concept of reasoning capacity as a unifying criterion to enable integration of constraints during optimization and establish connections among different components within the system, which also enable a more holistic and comprehensive approach to evaluation. We present a formal definition of reasoning capacity and illustrate its utility in identifying limitations within each component of the system. We then argue how these limitations can be addressed with a self-reflective process wherein human-feedback is used to alleviate shortcomings in reasoning and enhance overall consistency of the system.

Technical hiring has increasingly become a skill system of its own, requiring candidates to prepare for processes that only partially resemble the position being filled. This paper reconstructs how the software-engineering community remembers that process across four eras from 2005 to 2026. Retrospective ratings from 911 respondents show a history of expanding interview work and burden, while an analysis of public preparation questions finds that most tested knowledge has a plausible use in an ordinary software-engineering project. The contradiction is only apparent: relevant topics can still form an invalid process when they are accumulated beyond the vacancy, presented under artificial constraints, or selected and interpreted without a common job-derived standard. The paper responds with the Ticket-Based Pragmatic Assessment Framework, a prescriptive reference framework that derives a bounded assessment from declared responsibilities, near-term tickets, and project-entry work. It preserves normal tools, defines three explicit evidence gates, limits repeated sessions, and stops when the decision is supported. The objective is to make an interview a compressed version of the job rather than a parallel profession that candidates must learn merely to obtain it.

Recent progress in reasoning models suggests that generating plausible attempts for research-level mathematics may be within reach, but verification remains a bottleneck, consuming scarce expert time. We hypothesize that a meaningful solution should contain enough method-level information that, when applied to a neighborhood of related questions, it should yield better downstream performance than incorrect solutions. Building on this idea, we propose Consequence-Based Utility, an oracle-free evaluator that scores each candidate by testing its value as an in-context exemplar in solving related yet verifiable questions. Our approach is evaluated on an original set of research-level math problems, each paired with one expert-written solution and nine LLM-generated solutions. Notably, Consequence-Based Utility consistently outperforms reward models, generative reward models, and LLM judges on ranking quality. Specifically, for GPT-OSS-120B, it improves Acc@1 from 67.2 to 76.3 and AUC from 71.4 to 79.6, with similarly large AUC gains on GPT-OSS-20B (69.0 to 79.2). Furthermore, compared to LLM-Judges, it also exhibits a larger solver-evaluator gap, maintaining a stronger correct-wrong separation even on instances where the underlying solver often fails to solve.

Deep research requires agents to find answers that jointly satisfy multiple constraints. Discovering such answers is costly, whereas verifying a candidate can often be decomposed into tractable constraint-wise checks. This discovery--verification asymmetry suggests that a research agent should do more than simply search longer: it should recursively improve its current answer by verifying intermediate results and using the partially verified state to guide subsequent refinement. We introduce AREX, a family of Recursively Self-Improving (RSI) deep research agents. AREX alternates between an inner research loop that gathers evidence and constructs a provisional answer, and an outer self-improvement loop that audits the answer constraint-wise, identifies unresolved claims, and launches targeted follow-up research. To sustain RSI over long horizons, AREX learns an autonomous context-update tool that compresses growing interaction history into a compact improvement state preserving verified evidence and unresolved constraints, without relying on an external model. We train AREX on verified synthetic tasks and high-quality trajectories through agentic mid-training and long-horizon reinforcement learning. To mitigate sparse final rewards during long horizon learning, we emphasize key steps where decisive evidence is acquired or erroneous research directions are corrected. We instantiate a dense 4B model and a 122B-A10B Mixture-of-Experts model. Across BrowseComp, WideSearch, DeepSearchQA, Humanity's Last Exam (HLE), and other reasoning and tool-use benchmarks, AREX substantially outperforms comparable-scale baselines and remains competitive with models using substantially more activated parameters.

Traditional vulnerability detection methods rely heavily on predefined rule matching, which often fails to capture vulnerabilities accurately. With the rise of large language models (LLMs), leveraging their ability to understand code semantics has emerged as a promising direction for achieving more accurate and efficient vulnerability detection. However, current LLM-based approaches face significant challenges: instability in model outputs, limitations in context length, and hallucination. As a result, many existing solutions either use LLMs merely to enrich predefined rule sets, thereby keeping the detection process fundamentally rule-based, or over-rely on them, leading to poor robustness. To address these challenges, we propose a constraint-solving approach powered by LLMs named VULSOLVER. By modeling vulnerability detection as a constraint-solving problem, and by integrating static application security testing (SAST) with the semantic reasoning capabilities of LLMs, our method enables the LLM to act like a professional human security expert. We assess VULSOLVER on the OWASP Benchmark (1,023 labeled samples), achieving 96.29% accuracy, 96.55% F1-score, and 100% recall. Applied to popular GitHub repositories, VULSOLVER also identified 15 previously unknown high-severity vulnerabilities (CVSS 7.5-9.8), demonstrating its effectiveness in real-world security analysis.

Text generation under constraints have seen increasing interests in natural language processing, especially with the rapidly improving capabilities of large language models. However, existing benchmarks for constrained generation usually focus on fixed constraint types (e.g.,generate a sentence containing certain words) that have proved to be easy for state-of-the-art models like GPT-4. We present COLLIE, a grammar-based framework that allows the specification of rich, compositional constraints with diverse generation levels (word, sentence, paragraph, passage) and modeling challenges (e.g.,language understanding, logical reasoning, counting, semantic planning). We also develop tools for automatic extraction of task instances given a constraint structure and a raw text corpus. Using COLLIE, we compile the COLLIE-v1 dataset with 2080 instances comprising 13 constraint structures. We perform systematic experiments across five state-of-the-art instruction-tuned language models and analyze their performances to reveal shortcomings. COLLIE is designed to be extensible and lightweight, and we hope the community finds it useful to develop more complex constraints and evaluations in the future.

Real-world instructions with multiple constraints pose a significant challenge to existing large language models (LLMs). An observation is that the LLMs exhibit dramatic performance fluctuation when disturbing the order of the incorporated constraints. Yet, none of the existing works has systematically investigated this position bias problem in the field of multi-constraint instruction following. To bridge this gap, we design a probing task where we quantitatively measure the difficulty distribution of the constraints by a novel Difficulty Distribution Index (CDDI). Through the experimental results, we find that LLMs are more performant when presented with the constraints in a ``hard-to-easy'' order. This preference can be generalized to LLMs with different architecture or different sizes of parameters. Additionally, we conduct an explanation study, providing an intuitive insight into the correlation between the LLM's attention and constraint orders. Our code and dataset are publicly available at https://github.com/meowpass/PBIF.

Parametric computer-aided design (CAD) tools are the predominant way that engineers specify physical structures, from bicycle pedals to airplanes to printed circuit boards. The key characteristic of parametric CAD is that design intent is encoded not only via geometric primitives, but also by parameterized constraints between the elements. This relational specification can be viewed as the construction of a constraint program, allowing edits to coherently propagate to other parts of the design. Machine learning offers the intriguing possibility of accelerating the design process via generative modeling of these structures, enabling new tools such as autocompletion, constraint inference, and conditional synthesis. In this work, we present such an approach to generative modeling of parametric CAD sketches, which constitute the basic computational building blocks of modern mechanical design. Our model, trained on real-world designs from the SketchGraphs dataset, autoregressively synthesizes sketches as sequences of primitives, with initial coordinates, and constraints that reference back to the sampled primitives. As samples from the model match the constraint graph representation used in standard CAD software, they may be directly imported, solved, and edited according to downstream design tasks. In addition, we condition the model on various contexts, including partial sketches (primers) and images of hand-drawn sketches. Evaluation of the proposed approach demonstrates its ability to synthesize realistic CAD sketches and its potential to aid the mechanical design workflow.

Large language models (LLMs) have achieved unprecedented performances in various applications, yet evaluating them is still challenging. Existing benchmarks are either manually constructed or are automatic, but lack the ability to evaluate the thought process of LLMs with arbitrary complexity. We contend that utilizing existing relational databases based on the entity-relationship (ER) model is a promising approach for constructing benchmarks as they contain structured knowledge that can be used to question LLMs. Unlike knowledge graphs, which are also used to evaluate LLMs, relational databases have integrity constraints that can be used to better construct complex in-depth questions and verify answers: (1) functional dependencies can be used to pinpoint critical keywords that an LLM must know to properly answer a given question containing certain attribute values; and (2) foreign key constraints can be used to join relations and construct multi-hop questions, which can be arbitrarily long and used to debug intermediate answers. We thus propose ERBench, which uses these integrity constraints to convert any database into an LLM benchmark. ERBench supports continuous evaluation as databases change, multimodal questions, and various prompt engineering techniques. In our experiments, we construct LLM benchmarks using databases of multiple domains and make an extensive comparison of contemporary LLMs. We show how ERBench can properly evaluate any LLM by not only checking for answer correctness, but also effectively verifying the rationales by looking for the right keywords.

Identifying subtle technical errors within complex scientific and technical documents, especially those requiring multimodal interpretation (e.g., formulas in images), presents a significant hurdle for Large Language Models (LLMs) whose inherent error-correction tendencies can mask inaccuracies. This exploratory proof-of-concept (PoC) study investigates structured LLM context conditioning, informed by Persistent Workflow Prompting (PWP) principles, as a methodological strategy to modulate this LLM behavior at inference time. The approach is designed to enhance the reliability of readily available, general-purpose LLMs (specifically Gemini 2.5 Pro and ChatGPT Plus o3) for precise validation tasks, crucially relying only on their standard chat interfaces without API access or model modifications. To explore this methodology, we focused on validating chemical formulas within a single, complex test paper with known textual and image-based errors. Several prompting strategies were evaluated: while basic prompts proved unreliable, an approach adapting PWP structures to rigorously condition the LLM's analytical mindset appeared to improve textual error identification with both models. Notably, this method also guided Gemini 2.5 Pro to repeatedly identify a subtle image-based formula error previously overlooked during manual review, a task where ChatGPT Plus o3 failed in our tests. These preliminary findings highlight specific LLM operational modes that impede detail-oriented validation and suggest that PWP-informed context conditioning offers a promising and highly accessible technique for developing more robust LLM-driven analytical workflows, particularly for tasks requiring meticulous error detection in scientific and technical documents. Extensive validation beyond this limited PoC is necessary to ascertain broader applicability.

Test-time scaling via sequential revision has emerged as a powerful paradigm for enhancing Large Language Model (LLM) reasoning. However, standard post-training methods primarily optimize single-shot objectives, creating a fundamental misalignment with multi-step inference dynamics. While recent work treats this as multi-turn reinforcement learning (RL), conventional approaches optimize over the multi-step trajectories directly, failing to further exploit the high-quality mistakes in intermediate steps that model can learn from correcting them. We propose a two-stage iterative framework that alternates between online data/prompt augmentation and policy optimization. By converting the intermediate steps (``near-miss'' answers) in the successful recovery trajectories into decoupled revision and verification prompts, our approach concentrates training on both effective answer transformation and error identification. This approach enables efficient off-policy data generation and reduces the computational overhead of long-horizon sampling compared to standard multi-turn RL. On LiveCodeBench, using publicly available test cases as feedback, we observe gains of +6.5 points over the RL baseline and +4.0 points over standard multi-turn training. Beyond coding, our approach matches the previously reported SOTA result on circle packing while using the smallest base model (4B) and far fewer rollouts than the much larger evolutionary search systems. Math results under ground-truth verification further confirm improved correction ability. It also generalizes to out-of-distribution constraint-satisfaction puzzles such as n\_queens and mini\_sudoku, where correctness is defined entirely by problem constraints. Code is available at https://github.com/yxliu02/REVES.git.

Large Language Models (LLMs) excel at code generation, but ensuring their outputs to be functionally correct, especially in complex programming tasks, is a persistent challenge. While traditional Test-Driven Development (TDD) offers a path for code refinement, its efficacy with LLMs is often undermined by the scarcity of high-quality test cases or the pitfalls of automated test generation, including biased tests or inaccurate output predictions that can misdirect the correction process. This paper introduces Property-Generated Solver, a novel framework that leverages Property-Based Testing (PBT) to validate high-level program properties or invariants, instead of relying on specific input-output examples. These properties are often simpler to define and verify than directly predicting exhaustive test oracles, breaking the "cycle of self-deception" where tests might share flaws with the code they are meant to validate. Property-Generated Solver employs two collaborative LLM-based agents: a Generator dedicated to code generation and iterative refinement, and a Tester that manages the PBT life-cycle and formulate semantically rich feedback from property violations. The resulting comprehensive and actionable feedback then guides the Generator in its refinement efforts. By establishing PBT as the core validation engine within this iterative, closed-loop paradigm, Property-Generated Solver provides a robust mechanism for steering LLMs towards more correct and generalizable code. Extensive experimental results on multiple code generation benchmarks demonstrate that Property-Generated Solver achieves substantial pass@1 improvements, ranging from 23.1% to 37.3% relative gains over established TDD methods.

Code LLMs still struggle with code execution reasoning, especially in smaller models. Existing methods rely on supervised fine-tuning (SFT) with teacher-generated explanations, primarily in two forms: (1) input-output (I/O) prediction chains and (2) natural-language descriptions of execution traces. However, intermediate execution steps cannot be explicitly verified during SFT, so the training objective can reduce to merely matching teacher explanations. Moreover, training data is typically collected without explicit control over task difficulty. We introduce ExecVerify, which goes beyond text imitation by incorporating verifiable white-box rewards derived from execution traces, including next-statement prediction and variable value/type prediction. Our work first builds a dataset with multiple difficulty levels via constraint-based program synthesis. Then, we apply reinforcement learning (RL) to reward correct answers about both intermediate execution steps and final outputs, aligning the training objective with semantic correctness at each execution step. Finally, we adopt a two-stage training pipeline that first enhances execution reasoning and then transfers to code generation. Experiments demonstrate that a 7B model trained with ExecVerify achieves performance comparable to 32B models on code reasoning benchmarks and improves pass@1 by up to 5.9\% on code generation tasks over strong post-training baselines.

Instruction-following machine translation (IF-MT) requires respecting prompt-level rules on terminology, formatting, and register. Rule compliance typically trades off against translation quality, a tension that general-purpose IF data augmentation methods do not address. We propose Reference-Grounded Data Curation, a two-phase pipeline that extracts every supervised constraint from a reference translation that already satisfies it, ensuring feasibility by construction. Phase 1 applies Instruction-Following Difficulty (IFD) scoring to retain the hardest-but-learnable instances from an English-Thai parallel pool. Phase 2 extracts constraints from each reference target and keeps only generations satisfying every constraint, yielding the 1.97M-record Grounded dataset. We fine-tune open-weight bases on Grounded to produce ChindaMT, a Thai-English translation family at 4B, 2B, and 0.8B parameters. Under length-controlled pairwise judging, ChindaMT outperforms or matches every same-size baseline at every tier on both plain translation and under explicit rules, reaching up to a 68.4% win rate against the strongest baseline. The recipe transfers cleanly across Qwen generations. We release model weights, the Grounded dataset, and evaluation suites.

Reasoning is a cognitive process of using evidence to reach a sound conclusion. The reasoning capability is essential for large language models (LLMs) to serve as the brain of the artificial general intelligence agent. Recent studies reveal that fine-tuning LLMs on data with the chain of thought (COT) reasoning process can significantly enhance their reasoning capabilities. However, we find that the fine-tuned LLMs suffer from an Assessment Misalignment problem, i.e., they frequently assign higher scores to subpar COTs, leading to potential limitations in their reasoning abilities. To address this problem, we introduce an Alignment Fine-Tuning (AFT) paradigm, which involves three steps: 1) fine-tuning LLMs with COT training data; 2) generating multiple COT responses for each question, and categorizing them into positive and negative ones based on whether they achieve the correct answer; 3) calibrating the scores of positive and negative responses given by LLMs with a novel constraint alignment loss. Specifically, the constraint alignment loss has two objectives: a) Alignment, which guarantees that positive scores surpass negative scores to encourage answers with high-quality COTs; b) Constraint, which keeps the negative scores confined to a reasonable range to prevent the model degradation. Beyond just the binary positive and negative feedback, the constraint alignment loss can be seamlessly adapted to the ranking situations when ranking feedback is accessible. Furthermore, we also delve deeply into recent ranking-based alignment methods, such as DPO, RRHF, and PRO, and discover that the constraint, which has been overlooked by these approaches, is also crucial for their performance. Extensive experiments on four reasoning benchmarks with both binary and ranking feedback demonstrate the effectiveness of AFT.

Large language models must satisfy hard orthographic constraints during controlled text generation, yet systematic cross-architecture evaluation remains limited. We evaluate 28 configurations spanning three model families (Qwen3, Claude Haiku-4.5, GPT-5-mini) on 58 word puzzles requiring character-level constraint satisfaction. Architectural differences produce substantially larger performance gaps (2.0-2.2x, F1=0.761 vs. 0.343) than parameter scaling within families (83% gain from eightfold scaling), suggesting that constraint satisfaction may require specialized architectural features or training objectives beyond standard language model scaling. Thinking budget sensitivity proves heterogeneous: high-capacity models show strong returns (+0.102 to +0.136 F1), while mid-sized variants saturate or degrade. These patterns are inconsistent with uniform compute benefits. Using difficulty ratings from 10,000 human solvers per puzzle, we establish modest but consistent calibration (r=0.24-0.38) across all families, yet identify systematic failures on common words with unusual orthography ("data", "poop", "loll": 86-95% human success, 89-96% model miss rate). These failures reveal over-reliance on distributional plausibility that penalizes orthographically atypical but constraint-valid patterns, suggesting architectural innovations may be required beyond simply scaling parameters or computational budgets.

The Bernays-Sch\"onfinkel first-order logic fragment over simple linear real arithmetic constraints BS(SLR) is known to be decidable. We prove that BS(SLR) clause sets with both universally and existentially quantified verification conditions (conjectures) can be translated into BS(SLR) clause sets over a finite set of first-order constants. For the Horn case, we provide a Datalog hammer preserving validity and satisfiability. A toolchain from the BS(LRA) prover SPASS-SPL to the Datalog reasoner VLog establishes an effective way of deciding verification conditions in the Horn fragment. This is exemplified by the verification of supervisor code for a lane change assistant in a car and of an electronic control unit for a supercharged combustion engine.

As LLM-based agents increasingly operate in high-stakes domains with real-world consequences, ensuring their behavioral safety becomes paramount. The dominant oversight paradigm, LLM-as-a-Judge, faces a fundamental dilemma: how can probabilistic systems reliably supervise other probabilistic systems without inheriting their failure modes? We argue that formal verification offers a principled escape from this dilemma, yet its adoption has been hindered by a critical bottleneck: the translation from natural language requirements to formal specifications. This paper bridges this gap by proposing , a neuro-symbolic framework that employs a bidirectional Formal-of-Thought architecture: LLMs serve as specification compilers that top-down decompose high-level human intent into atomic, verifiable constraints, then bottom-up prove compliance using Dafny specifications and Z3 Satisfiability modulo theories solving, which produces mathematical guarantees rather than probabilistic scores. We validate across three benchmarks spanning behavioral safety, multi-domain constraint adherence, and agentic upward deception detection. Experiments on 7 agent models demonstrate that achieves an average improvement of 16.6% over LLM-as-a-Judge baselines, enables weak-to-strong generalization where a 7B judge achieves over 90% accuracy detecting deception from 72B agents, and provides near-linear safety improvement through iterative refinement.

Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated multi-step reasoning data. To generate high-quality reasoning data, many recent methods generate synthetic reasoning paths and filter them based on final answer correctness, often overlooking flaws in intermediate reasoning steps. To enhance the verification of intermediate reasoning steps, prior work primarily resorts to code execution or symbolic reasoning engines. However, code-based validation is restricted to code or mathematical tasks, and reasoning engines require a well-structured and complete context. As a result, existing methods fail to function effectively in natural language reasoning tasks that involve ambiguous or incomplete contexts. In these tasks, synthetic data still lack reliable checks for verifying each reasoning step. To address this challenge, we introduce ORACLE, a structured data generation framework inspired by syllogistic reasoning. ORACLE integrates the generative strengths of LLMs with symbolic supervision: the LLM produces step-wise reasoning contexts, while a symbolic reasoning engine verifies the validity of each intermediate step. By employing a unified prompting template to elicit modular reasoning chains, ORACLE enables fine-grained, step-level validation, facilitating the construction of high-quality multi-step reasoning data. Across six logical, factual, and commonsense reasoning benchmarks, our ORACLE consistently outperforms strong baselines on multiple models.

We present JEC-QA, the largest question answering dataset in the legal domain, collected from the National Judicial Examination of China. The examination is a comprehensive evaluation of professional skills for legal practitioners. College students are required to pass the examination to be certified as a lawyer or a judge. The dataset is challenging for existing question answering methods, because both retrieving relevant materials and answering questions require the ability of logic reasoning. Due to the high demand of multiple reasoning abilities to answer legal questions, the state-of-the-art models can only achieve about 28% accuracy on JEC-QA, while skilled humans and unskilled humans can reach 81% and 64% accuracy respectively, which indicates a huge gap between humans and machines on this task. We will release JEC-QA and our baselines to help improve the reasoning ability of machine comprehension models. You can access the dataset from http://jecqa.thunlp.org/.

The ability to follow instructions is crucial for Large Language Models (LLMs) to handle various real-world applications. Existing benchmarks primarily focus on evaluating pure response quality, rather than assessing whether the response follows constraints stated in the instruction. To fill this research gap, in this paper, we propose FollowBench, a Multi-level Fine-grained Constraints Following Benchmark for LLMs. FollowBench comprehensively includes five different types (i.e., Content, Situation, Style, Format, and Example) of fine-grained constraints. To enable a precise constraint following estimation on diverse difficulties, we introduce a Multi-level mechanism that incrementally adds a single constraint to the initial instruction at each increased level. To assess whether LLMs' outputs have satisfied every individual constraint, we propose to prompt strong LLMs with constraint-evolution paths to handle challenging open-ended instructions. By evaluating ten closed-source and open-source popular LLMs on FollowBench, we highlight the weaknesses of LLMs in instruction following and point towards potential avenues for future work. The data and code are publicly available at https://github.com/YJiangcm/FollowBench.