Structural Constraints

When a decoder-only transformer is forced to process matched correct and incorrect single-token continuations of a factual query, the two pathways through hidden-state space diverge: displacement vectors from the query-only representation keep near-equal magnitude but rotate apart, with angular separation growing through mid-depth before late layers resolve an asymmetric outcome. A logit-lens preference in the incorrect run falls far below the equal-probability prior (roughly 11.5x more mass on the incorrect token than the correct one). We read this pattern, rotational divergence then late-layer asymmetric commitment, as the geometric signature of the model externally appearing to reject a wrong continuation, while staying explicit that it is observational, not causal: the incorrect run could equally reflect the model conforming to the token it is forced to carry, which only a random-token control can settle. It holds across six decoder-only transformers spanning four architecture families (Llama, Mistral, Gemma, StableLM) from 1B to 13B parameters; a seventh (Qwen2 1.5B) is flat under our protocol, plausibly a tokenizer artefact, leaving an emergence threshold open. Linear probes recover the distinction at intermediate depth, and cross-domain transfer is structurally asymmetric, a financial-medical corridor transferring far better than transport pairs. Where single-layer activation patching is cleanly interpretable (LLaMA-2 13B, Mistral 7B) it yields no layer band of consistent recovery; a third model (StableLM-2 1.6B) recovers uniformly above the ceiling, which we diagnose as a code-path artefact and exclude. Under this scoped null the late-layer asymmetry is not localized to a single component, fitting a distributed-by-trajectory account rather than single-layer localized recall. We document this with forced-completion probing across seven models, three domains, and 300 queries.

This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the Optimal Decision Tree and Set Cover. We study these two fundamental tasks under precedence constraints, that is, if a test (or set) $X$ is a predecessor of $Y$, then in any feasible decision tree $X$ needs to be an ancestor of $Y$ (or respectively, if $Y$ is added to set cover, then so must be $X$). For the Optimal Decision Tree we consider two optimization criteria: worst case identification time (height of the tree) or the average identification time. Similarly, for the Set Cover we study two cost measures: the size of the cover or the average cover time. Our approach is to develop a number of algorithmic reductions, where an approximation algorithm for one problem provides an approximation for another via a black-box usage of a procedure for the former. En route we introduce other optimization problems either to complete the `reduction landscape' or because they hold the essence of combinatorial structure of our problems. The latter is brought by a problem of finding a Maximum Density Precedence-Closed Subfamily, where the density is defined as the ratio of the number of items the family covers to its size. We provide $\mathcal{O}^*(\sqrt{m})$-approximation polynomial-time algorithms for all aforementioned problems. The picture is complemented by a number of hardness reductions that provide $\mathcal{O}(m^{1/12-ε})$-inapproximability results for the decision tree and covering problems. Besides giving a complete set of results for general precedence constraints, we also provide polylogarithmic approximation guarantees for two most typically studied and applicable graph types, outforests and inforests. By providing corresponding hardness results, we show most of these results to be tight.

We develop a computational approach to Metric Answer Set Programming (ASP) to allow for expressing quantitative temporal constraints, like durations and deadlines. A central challenge is to maintain scalability when dealing with fine-grained timing constraints, which can significantly exacerbate ASP's grounding bottleneck. To address this issue, we leverage extensions of ASP with difference constraints, a simplified form of linear constraints, to handle time-related aspects externally. Our approach effectively decouples metric ASP from the granularity of time, resulting in a solution that is unaffected by time precision.

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.

LLMs excel at reasoning, but validating their steps remains challenging. Formal verification offers a solution through mechanically checkable proofs. Interactive theorem provers (ITPs) dominate mathematical reasoning but require detailed low-level proof steps, while auto-active verifiers offer automation but focus on software verification. Recent work has begun bridging this divide by evaluating LLMs for software verification in ITPs, but the complementary direction, LLMs for mathematical theorem proving in auto-active verifiers, remains unexplored. We present MINIF2F-DAFNY, the first translation of the widely-used mathematical benchmark miniF2F to an auto-active verifier: Dafny. We find that Dafny's automation alone solves 39-44% of problems with empty proofs, whereas many require substantial proof guidance in ITPs. We evaluate 8 off-the-shelf LLMs on proof generation, with the best model (Claude Opus 4.6) achieving 62.7% cumulative pass@4 on the full test set, improving over the 38.9% empty-proof baseline by 23.8 percentage points. These results show that auto-active verification offers a complementary empirical setting for AI-assisted mathematical reasoning, where LLMs provide high-level guidance while SMT automation handles low-level details. Our benchmark and evaluation infrastructure are publicly available on https://github.com/dafny-lang/miniF2F.

Hydrogen crossover is a critical safety and efficiency constraint in high-pressure polymer electrolyte membrane water electrolysis (PEMWE), but accurate prediction remains difficult because data are limited, transport physics are strongly coupled, and industrial operation requires reliable extrapolation beyond observed conditions. This study develops a hard-constraint physics-residual network (PR-Net) for hydrogen crossover prediction in PEMWE and compares it with a purely data-driven neural network (NN) and a soft-constraint physics-informed neural network (PINN). PR-Net embeds Henry's, Fick's, and Faraday's laws as a deterministic backbone and learns only a residual correction for unmodelled nonlinear effects. The benchmark includes 184 observations from eight peer-reviewed sources across six membrane types, covering 1-200 bar, $25-85°C$, and $0.05-5.0 A cm^{-2}$. PR-Net achieves $R^2 = 99.57 \pm 0.16$, with 9-fold lower prediction variability than NN and PINN. In pressure-axis extrapolation, PR-Net attains $R^2 = 94.02 \pm 0.92$ at 200 bar, 2.5 times beyond the training pressure range, compared with $68.06 \pm 5.52$ for PINN and $58.00 \pm 8.60$ for NN (p < 0.001). Residual analysis indicates that the learned correction captures part of the high-pressure gas-phase non-ideality and recovers a transport-regime transition near $0.23 A cm^{-2}$ between Fickian diffusion-dominated and Faradaic production-dominated transport. With a computation time of $1.08 \pm 0.34 ms$ on low-power embedded hardware, PR-Net provides a practical framework for real-time crossover monitoring, adaptive process control, and safer high-pressure green-hydrogen operation.

Accurately synthesizing 3D scenes from user-provided text descriptions is crucial for developing embodied agents. Despite the importance of scene-description alignment, existing evaluation methods for such text-guided 3D scene synthesis either capture only coarse similarity between the synthesized scene and the user description, or ignore the spatial reasoning for verifying object placement. None of them addressed the fine-grained constraints (e.g., X needs to be in the scene in a Y manner) implied by the description from users. To address this, we introduce LEGO, a benchmark dataset that pairs each user description with human-annotated constraints and a reference scene, and LEGO-Eval, an evaluation framework that decomposes a description into atomic constraints and verifies each one using tools that ground textual references to 3D objects and reason about their spatial relationships. We show that (i) LEGO-Eval evaluates misalignment far more accurately than existing methods and (ii) current scene synthesis approaches achieve at most 10% success rate in LEGO-Eval.

Optimizing a single advertising campaign across heterogeneous channels is a central challenge in industrial autobidding. Auction mechanisms vary across channels in ranking rules (pure eCPM vs. UE-augmented scoring), pricing formats (first- vs. second-price), and bidding conventions (uniform vs. non-uniform), while advertisers impose shared campaign-level constraints. We propose HOB, which makes marginal cost (MC) computable and alignable across heterogeneous channels, especially for first-price auctions (FPA) with organic-paid coexistence, where existing bidding formulations do not yield a practical aligned MC form. At the global level, HOB derives channel-specific MC forms and coordinates disparate channels through a shared MC target. At the local level, HOB models free-win probability and winning-price uncertainty with a zero-inflated exponential distribution, yielding an efficient surplus-optimal bidding strategy for non-uniform first-price auctions. We show that any interior optimum satisfies MC equalization across channels. Experiments on a controlled offline benchmark, industrial log replay, and large-scale online A/B tests demonstrate that HOB consistently delivers significant performance gains. Deployed on a large-scale commercial DSP, HOB delivers a 3.0% lift in GMV while maintaining return on advertising spend (ROAS) constraints.

We study \emph{online episodic Constrained Markov Decision Processes} (CMDPs) under both stochastic and adversarial constraints. We provide a novel algorithm whose guarantees greatly improve those of the state-of-the-art best-of-both-worlds algorithm introduced by Stradi et al. (2025). In the stochastic regime, \emph{i.e.}, when the constraints are sampled from fixed but unknown distributions, our method achieves $\widetilde{\mathcal{O}}(\sqrt{T})$ regret and constraint violation without relying on Slater's condition, thereby handling settings where no strictly feasible solution exists. Moreover, we provide guarantees on the stronger notion of \emph{positive} constraint violation, which does not allow to recover from large violation in the early episodes by playing strictly safe policies. In the adversarial regime, \emph{i.e.}, when the constraints may change arbitrarily between episodes, our algorithm ensures sublinear constraint violation without Slater's condition, and achieves sublinear $α$-regret with respect to the \emph{unconstrained} optimum, where $α$ is a suitably defined multiplicative approximation factor. We further validate our results through synthetic experiments, showing the practical effectiveness of our algorithm.

Video Temporal Grounding (VTG) aims to localize specific video segments corresponding to natural language queries. While recent Large Vision-Language Models (LVLMs) employ Reinforcement Learning to generate Chains-of-Thought (CoT), they typically rely solely on outcome-based supervision. Consequently, this often leads to hallucinations, where the reasoning process becomes disconnected from the visual content and the final prediction. Existing attempts to mitigate this by relying on external supervision from larger models or separate reward models are computationally expensive and prone to rigid patterns. To address these challenges, we propose TAR (Temporal Anchor-Constrained Reasoning), a framework that introduces the temporal anchor (T-anchor) as a transparent and auditable checkpoint mechanism. T-anchor enforces progressive refinement within the CoT, compelling the model to continuously ground its intermediate thoughts in visual evidence and iteratively calibrate temporal predictions, thereby significantly enhancing the faithfulness and autonomy of the reasoning process and final accuracy. Furthermore, we introduce a bootstrapping paradigm that automatically harvests high-quality CoT data using only a standard 7B model, eliminating the dependency on ultra-large models. Extensive experiments demonstrate that TAR achieves state-of-the-art performance and generates faithful, autonomous, and progressively refined reasoning traces.

Trajectory prediction, as a critical component of autonomous driving systems, has attracted the attention of many researchers. Existing prediction algorithms focus on extracting more detailed scene features or selecting more reasonable trajectory destinations. However, in the face of dynamic and evolving future movements of the target vehicle, these algorithms cannot provide a fine-grained and continuous description of future behaviors and lane constraints, which degrades the prediction accuracy. To address this challenge, we present BLNet, a novel dualstream architecture that synergistically integrates behavioral intention recognition and lane constraint modeling through parallel attention mechanisms. The framework generates fine-grained behavior state queries (capturing spatial-temporal movement patterns) and lane queries (encoding lane topology constraints), supervised by two auxiliary losses, respectively. Subsequently, a two-stage decoder first produces trajectory proposals, then performs point-level refinement by jointly incorporating both the continuity of passed lanes and future motion features. Extensive experiments on two large datasets, nuScenes and Argoverse, show that our network exhibits significant performance gains over existing direct regression and goal-based algorithms.

Chinese ASR correction is challenging because errors are often \emph{phonetic} (many characters share similar Pinyin) while the correction model must also obey a \emph{length constraint} under noisy N-best hypotheses. Existing approaches either exploit Pinyin only at the prompt/feature level without integrating it into model representations or rely on generative decoding that can drift in length. We propose \textbf{PERL}, a \textbf{constrained rephrasing pipeline} for Chinese N-best ASR correction that (i) predicts the target length and enforces it via mask budgeting, and (ii) fuses \emph{semantic} and \emph{phonetic} (Pinyin) representations through token-wise gates conditioned on sentence semantics. Experiments on Aishell-1 and our new domain N-best benchmark \textbf{DoAD} show that PERL consistently reduces CER (29.11% on Aishell-1 and up to $\sim$70% on DoAD) while maintaining low latency. We also provide analyzes of length generalization and phonetic--semantic interactions, showing when PERL relies on phonetic cues versus semantic constraints.

Large Language Models (LLMs) possess extensive foundational knowledge and moderate reasoning abilities, making them suitable for general task planning in open-world scenarios. However, it is challenging to ground a LLM-generated plan to be executable for the specified robot with certain restrictions. This paper introduces CLMASP, an approach that couples LLMs with Answer Set Programming (ASP) to overcome the limitations, where ASP is a non-monotonic logic programming formalism renowned for its capacity to represent and reason about a robot's action knowledge. CLMASP initiates with a LLM generating a basic skeleton plan, which is subsequently tailored to the specific scenario using a vector database. This plan is then refined by an ASP program with a robot's action knowledge, which integrates implementation details into the skeleton, grounding the LLM's abstract outputs in practical robot contexts. Our experiments conducted on the VirtualHome platform demonstrate CLMASP's efficacy. Compared to the baseline executable rate of under 2% with LLM approaches, CLMASP significantly improves this to over 90%.

We study a variation of the Stable Marriage problem, where every man and every woman express their preferences as preference lists which may be incomplete and contain ties. This problem is called the Stable Marriage problem with Ties and Incomplete preferences (SMTI). We consider three optimization variants of SMTI, Max Cardinality, Sex-Equal and Egalitarian, and empirically compare the following methods to solve them: Answer Set Programming, Constraint Programming, Integer Linear Programming. For Max Cardinality, we compare these methods with Local Search methods as well. We also empirically compare Answer Set Programming with Propositional Satisfiability, for SMTI instances.

In this document, we introduce PyCSP$3$, a Python library that allows us to write models of combinatorial constrained problems in a declarative manner. Currently, with PyCSP$3$, you can write models of constraint satisfaction and optimization problems. More specifically, you can build CSP (Constraint Satisfaction Problem) and COP (Constraint Optimization Problem) models. Importantly, there is a complete separation between the modeling and solving phases: you write a model, you compile it (while providing some data) in order to generate an XCSP$3$ instance (file), and you solve that problem instance by means of a constraint solver. You can also directly pilot the solving procedure in PyCSP$3$, possibly conducting an incremental solving strategy. In this document, you will find all that you need to know about PyCSP$3$, with more than 50 illustrative models.

TCSPs (Temporal Constraint Satisfaction Problems) [Dechter et al. 1991] get rid of unary constraints by binarizing them after having added an "origin of the world" variable. In this work, we look at the constraints between the "origin of the world" variable and the other variables, as the (binarized) domains of these other variables. With this in mind, we define a notion of arc-consistency for TCSPs, which we will refer to as binarized-domains Arc-Consistency, or bdArc-Consistency for short. We provide an algorithm achieving bdArc-Consistency for a TCSP, which we will refer to as bdAC-3, for it is an adaptation of Mackworth's [1977] well-known arc-consistency algorithm AC-3. We show that if an STP is bdArc-Consistent, and connected, i.e., its "origin of the world" variable is disconnected from none of the other variables, its binarized domains are minimal. We provide two polynomial backtrack-free procedures: one for the task of getting a solution from a connected bdArc-Consistent STP; the other for the task of getting, from a bdArc-Consistent STP, either that it is inconsistent or, in case of consistency, a connected bdArc-Consistent STP refinement. We then show how to use our results both in a general TCSP solver and in a TCSP-based job shop scheduler. The work also provides an experimental comparison on STPs of bdAC-3 with an existing arc-consistency algorithm, ACSTP, restricted to STPs [Kong et al. 2018]; an experimental comparison of three TCSP-based job shop schedulers, two of which use weak versions of bdAC-3 as the filtering procedure during the search, the third [Schwalb and Dechter 1997] a weak version of path-consistency; and the swi-prolog source codes used by these comparisons. Last but not least, we provide an incremental version of bdAC-3.

Accurate tactile forecasts need not improve force-constrained control. We study a 652,157-parameter action-conditioned visuotactile world model with matched behavior cloning, policy learning in imagination, independent reactive implicit Q-learning, and model-assisted force feedback. A fixed protocol executes 34 policies on 120 fresh MuJoCo environments spanning geometry and physical-parameter shifts, plus 324 independently replayed action branches on 12 additional ID environments. Visuotactile dynamics reduce force action-effect MAE from 0.413 N for persistence to 0.338 N. Model-assisted feedback raises ID force-budgeted success from 73.3% to 93.3%, with paired difference +20.0 [+6.7,+33.4] percentage points (95% CI), with the difference occurring during scripted lowering. Its pooled difference is +3.9 [-4.5,+11.7] points. Imagined RL achieves 11.9% pooled joint success versus 25.0% for reactive IQL. An empirical tactile-residual stress test adds 330 executions. The evidence concerns rigid-box lifting after a common approach, without physical-robot transfer or a closed-loop safety guarantee.