Structural Constraints

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We revisit contextual optimization from the perspective of policy class design. A desirable policy class should be expressive enough to learn rich context-decision relationships, should enforce hard feasibility constraints rather than soft penalty terms, and should remain smooth enough for gradient-based training on downstream decision losses. Existing approaches usually emphasize only part of these requirements. We propose Legendre-regularized policies, which parameterize decisions as solutions of regularized optimization problems over the original feasible region. This construction yields policies that are feasible by construction and differentiable with respect to learned latent parameters. We prove that the associated optimizer map is single-valued, maps onto the relative interior of the feasible set, admits an explicit Jacobian, is Lipschitz continuous, and can be made arbitrarily smooth. We also establish a universal approximation result showing that the proposed class can approximate any continuous feasible policy on compact context sets. The framework unifies explicitly regularized optimizers and implicit perturbation-based smooth optimizers. Experiments on contextual newsvendor and resource allocation problems show that our approach improves prescriptive performance relative to the benchmark methods.

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.

Generating realistic interior furniture layouts that strictly adhere to architectural constraints (e.g., walls, doors, and windows) remains a fundamental challenge in automated spatial design. Existing approaches, primarily based on one-shot generation using diffusion models or Large Language Models (LLMs), lack explicit mechanisms for intermediate geometric constraint verification, often resulting in structural collisions and functionally infeasible arrangements under complex room constraints. To address these challenges, we propose Agentic Designer, a progressive, multi-agent framework that formulates structure-aware interior layout generation as an iterative and constraint-verified decision process. By decomposing layout synthesis into modular stages of proposal, verification, and adjustment, the framework coordinates three specialized agents, a Generator, an Evaluator, and a Refiner, through a Progressive Consensus Mechanism. This mechanism enforces stepwise geometric validation and correction before each placement is committed, thereby preventing error accumulation. To facilitate this structure-aware paradigm and standardize evaluation, we establish InStruct, a comprehensive benchmark that integrates a dataset comprising over 18,000 high-quality, parametrically annotated samples with a novel suite of structure-centric metrics. Extensive quantitative evaluations, qualitative analyses, and user studies show that Agentic Designer significantly outperforms state-of-the-art methods, demonstrating substantial improvements in strict structural adherence and functional design coherence.

General intelligence, of the kind that underwrites the full range of human cognitive achievement, is not a property of computational architecture alone. This paper advances a single thesis: the structural constraints on general intelligence occupy distinct levels of description and are mutually non-reducible, in the sense that the special-sciences tradition gives to that term. It follows that no single architectural advance, and no continuation of the scaling programme by itself, can produce artificial general intelligence (AGI), and that research programmes must be evaluated against the full constraint profile rather than against performance on any one benchmark. The thesis is developed through a method that reads general intelligence through four evidential lenses, AI systems research, anthropology, law, and economics, each anchored to a distinct level of description, supplemented by speculative fiction used as a disciplined heuristic in the context of discovery rather than the context of justification. Applying the method yields a taxonomy of twenty-three structural constraints organised into eight clusters; six are examined in depth and ordered as an ascending ladder of levels, with explicit bridges showing why progress at one level cannot carry to the next. The argument issues in five falsifiable predictions, each stated with a named benchmark family and a disconfirmation condition, converting a descriptive framework into a research programme with a longer horizon than the scaling hypothesis implies.

Autonomous racing exposes the sim-to-real gap under extreme operating conditions characterized by high speed, tight stability margins, and stringent real-time constraints. Although simulation is indispensable for development, controllers that perform well in simulation often degrade abruptly on physical platforms due to interacting effects of dynamics mismatch, estimation delay, and execution-layer latency. This paper frames sim-to-real transfer in autonomous racing as a full-stack, real-time systems problem. We introduce a structured three-layer perspective (Physical/Cyber/Execution) to analyze how mismatches propagate and amplify through closed-loop feedback. We present diagnostic metrics beyond nominal lap time, including performance flip, stability-oriented measures, sensitivity to delay and noise, and latency distribution characterization. Mitigation strategies are synthesized from a deployment-oriented viewpoint, emphasizing execution-aware and delay-aware design. Finally, we outline benchmarking guidelines that enable reproducible and fair sim-to-real evaluation under compute and timing constraints. The resulting framework clarifies cross-layer failure mechanisms and provides practical design principles for deployable autonomous racing systems operating near dynamic limits.

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

Introduction: Biological systems face anatomical and metabolic constraints, including costly synaptic maintenance and limited connectivity. These constraints favor neural codes that compress behaviorally relevant information into low-redundancy patterns. We test whether an excitatory competitive Hebbian rule can support synaptic resource allocation under such constraints and whether the resulting representations occupy a more favorable cost-performance regime than reference learning rules. Methods: Representational cost is quantified using mutual-information-based measures derived from the Variational Information Bottleneck. Experiments use fixed audiovisual embeddings from three audiovisual benchmarks (AVE, Kinetics-Sounds, VGGSound100) to isolate downstream associative plasticity. Hebbian learning is compared with Dense Difference Target Propagation (DDTP) and backpropagation (BP) under matched sparsity and architectural constraints. Results: Hebbian learning achieves lower task-information cost (CTI) than sparse BP and DDTP in the main compressed comparisons, while reaching CTI values comparable to shallow BP with nonnegative weights. Rather than uniformly improving classification performance, Hebbian learning shifts the trade-off between task-relevant information and representational cost, yielding lower CTI at comparable functional performance in several settings. Discussion: The results indicate a cost-performance trade-off rather than uniform accuracy gains. For a given level of task-relevant information, Hebbian representations retain less input information while preserving functional performance, although accuracy is slightly reduced on some datasets. These findings support interpreting Hebbian learning as a mechanism for synaptic resource allocation rather than as a general strategy for maximizing audiovisual classification accuracy.

Reliable perception under diverse weather conditions remains a major challenge for autonomous driving systems. A common strategy to improve robustness is either to synthesize adverse weather conditions for training perception models or to apply weather-removal techniques to recover clean inputs. However, existing approaches typically rely on synthetic data augmentation or physics-based, task-specific models that require paired training data and often struggle to generate realistic weather effects or generalize robustly to out-of-domain scenarios. Toward this problem, we present Cyclone, a unified framework for weather editing based on latent diffusion, equipped with cycle-consistent constraints and knowledge from image-text models. Cyclone enables the generation of multiple weather conditions across diverse scenes while eliminating the need for paired data. Experimental results show that our approach produces more realistic, structure-preserving outputs than existing baselines and leads to consistent improvements across several downstream driving perception tasks. Furthermore, we demonstrate that Cyclone can be distilled to a video diffusion model for temporally consistent weather editing.

The rapid deployment of machine learning systems across cloud, edge, and enterprise environments has brought model optimization to the forefront of systems-engineering. Despite a rich literature spanning quantization, pruning, knowledge distillation, parameter-efficient fine-tuning (PEFT), and inference-time optimization, practitioners are often left navigating these techniques through heuristics rather than principled methodology. We argue that optimization should be formulated as a constraint-driven, multi-objective engineering decision and introduce a unified framework that characterizes any production deployment along five interacting constraint dimensions: data availability, latency budget, memory budget, accuracy tolerance, and retraining budget. Building on this taxonomy, we synthesize empirical gains reported across the research literature and map them to operational constraints rather than algorithmic categories. To ensure practical relevance, we selected these techniques by reviewing recent literature for methods that report measurable improvements against critical deployment bottlenecks. We propose a prescriptive decision framework and provide optimization pipelines for four representative industrial scenarios to illustrate it in practice. To the best of our knowledge, this work provides one of the first structured attempts to formalize model optimization as a constraint-aware, multi-objective engineering process, synthesizing quantitative evidence from the research literature.

Large language models now evolve faster than production inference systems can be ported and optimized. New releases change attention, MoE routing, quantization formats, KV-cache layout, and parallel execution patterns, while deployed accelerator fleets remain heterogeneous across hardware generations, framework forks, operator libraries, compiler backends, and communication runtimes. Serving a new model on existing hardware is therefore a model-framework-kernel-hardware co-adaptation problem. We present MetaInfer, an LLM-agent system that formulates inference adaptation as route search over a costed execution-adaptation graph. The graph connects model semantics, framework dispatch, kernel choices, hardware capabilities, runtime evidence, and serving objectives. MetaInfer constructs and updates this graph during execution, restores missing or blocked routes through patches, and reduces route cost through staged validation and end-to-end profiling. Three real episodes -- DeepSeek V4 Flash on NVIDIA A800, GLM 5.3 Flash on NVIDIA A800, and DeepSeek V4 Flash on Hygon K100AI DCU -- demonstrate deployment repair, cross-model knowledge transfer, and portability across heterogeneous accelerator software stacks.

Reinforcement Learning has revolutionized the landscape of robotic research, allowing robust learning of complex robotic skills in simulation. However, real-world deployment in open-ended environments requires strong safety guarantees to prevent dangerous or harmful behaviors. Safe Reinforcement Learning methods address this requirement by enforcing safety constraints. Nevertheless, learning under constraints often reduces learning speed and could lead to suboptimal task performance, as the agent must solve a more complex constrained optimization problem compared to unconstrained settings. To tackle this issue, in this work, we propose an extension of the ATACOM framework, a state-of-the-art reliable safety layer that can be integrated with existing Reinforcement Learning algorithms to enforce constraints derived from prior knowledge of the system or learned directly from data. Our proposed method, named ATACOM Directional Constraints (ATACOM-DC), significantly improves the safety-performance trade-off by introducing directional constraints that distinguish between actions approaching and moving away from constraint boundaries, activating constraint enforcement only when necessary. We evaluate our method across a range of challenging robotic control tasks in simulation, analyzing both constraint-violation costs and achieved task performance. Code and additional material at https://atacom-dc.robot-learning.net.

Evolved sequences can be used to infer the rules of evolution. Orally transmitted folk melodies are evolved sequences whose similarity to protein sequences (one-dimensional, drawn from a limited alphabet) invites application of bioinformatics methods to study cultural evolution. A major obstacle is that melodies encode rhythm, which breaks some assumptions of standard sequence-alignment algorithms. We develop a rhythm-aware alignment method and apply it to \num{40000} Irish dance tune variants, enabling the first large-scale automated melodic alignment. Four canonical bioinformatics analyses -- mutability, substitution matrices, positional conservation, and covariance -- reveal patterns distinct from those of molecular evolution, revealing the forces that shape each domain: biochemical and biophysical constraints for proteins; memory, motor, and social biases for melodies. Together the results show that bioinformatics provides a powerful framework -- conceptual as much as algorithmic -- for studying cultural evolution. Although the cultural transmission of music has been discussed for centuries, here we show how to analyze it at large scale.

Structural optimization problems often involve a large number of decision variables and highly non-convex feasible regions, making convergence to the true Pareto front extremely challenging. Even when convergence is achievable, it typically requires thousands of function evaluations, resulting in significant computational cost. This highlights the need for efficient and robust optimization algorithms for real-world engineering applications. In this study, we introduce a novel constrained multi-objective evolutionary algorithm, termed DPCME. The algorithm employs two interacting populations that exchange information, enabling effective global exploration and reducing the risk of convergence to local optima. To further enhance performance, a recent repair-based constraint-handling technique is incorporated, and alternative repair approaches are proposed and systematically evaluated. The proposed algorithm is tested on three engineering problems: the 72-bar truss, the 120-bar truss, and a chemical tanker structure, each involving hundreds of nonlinear failure constraints. Its performance is evaluated against state-of-the-art constrained multi-objective optimization algorithms from the latest PlatEMO package. A total of 43 algorithms are initially tested, from which the 12 best-performing methods are selected for detailed comparison. The results demonstrate that DPCME achieves superior or competitive convergence and diversity across all test cases, and that the inclusion of repair-based constraint handling further improves its performance.

Physics-Informed Neural Networks (PINNs) provide a meshless approach for solving partial differential equations (PDEs), but suffer severe degradation in stiff and shock-dominated problems, where small PDE residuals can correspond to globally inaccurate solutions. We show these failures are multi-causal, arising from the concurrent interplay of (i) spectral bias against sharp features, (ii) imbalanced multi-term optimization and loss-weight collapse, (iii) violation of temporal causality, and (iv) under-resolved collocation. We present SPARC-Net, a unified architecture and training framework that jointly addresses all four pathologies. SPARC-Net leverages an adaptive multi-scale spectral encoder with a learnable spectral gate, a gated residual backbone, adaptive activations, and a hard-constraint output ansatz that exactly enforces initial and boundary conditions, structurally eliminating loss-weight collapse. Training employs stabilized gradient-norm loss balancing, floored causality-respecting residual weighting, and residual-based adaptive collocation (RAD). Validated against exact analytic and high-order spectral reference solutions across four canonical benchmarks -- viscous Burgers', Allen-Cahn, convection (beta=30), and reaction -- SPARC-Net yields substantial improvements over vanilla PINNs: relative L2 error drops from 1.47e-1 to 1.14e-1 on Burgers' (22% reduction), 9.93e-1 to 5.78e-2 on Allen-Cahn (94% reduction), and 9.82e-1 to 3.54e-3 on reaction (100% reduction). A characteristic-coordinate encoder for hyperbolic transport further reduces convection error from 5.14e-1 to 9.88e-5 (100% reduction). We report five-seed mean +/- standard deviation errors, Wilcoxon significance tests, full ablation studies, hyperparameter sensitivities, an extension to the 2D heat equation, and comparisons against parameter-matched baselines.

The problem of constrained online convex optimization is considered, where at each round, once a learner commits to an action $x_t \in \mathcal{X} \subset \mathbb{R}^d$, a convex loss function $f_t$ and a convex constraint function $g_t$ that drives the constraint $g_t(x)\le 0$ are revealed. The objective is to simultaneously minimize the static regret and cumulative constraint violation (CCV) compared to the benchmark that knows the loss functions and constraint functions $f_t$ and $g_t$ for all $t$ ahead of time, and chooses a static optimal action that is feasible with respect to all $g_t(x)\le 0$. Currently, the best known algorithm is OGD+Projection algorithm of [Vaze and Sinha, 2025] that has simultaneous regret of $O(\sqrt{T})$ and CCV of $O(T^{1/3})$ for $d=2$ [Balasundaram et al., 2026], and simultaneous regret of $O(\sqrt{T})$ and CCV of $O(\sqrt{T})$ for any $d$ [Sarkar and Sinha, 2026]. In this paper, we show that the CCV of the OGD+Projection algorithm is $Ω(T^{\frac{d-1}{2d}})$. This is the first such lower bound result.

We study a symbolic search space for the Collatz conjecture based on finite exponent codes of the accelerated map. Each code records the number of divisions by two after every 3n + 1 step and determines three quantities: real drift, a 2-adic start representative, and a 3-adic endpoint representative. Their combination defines the 2-3-infinity diagnostic. Counterexample-like codes should exhibit near-critical drift, small 2-adic start representatives, and endpoints compatible with growth on the scale of (3/2)^k. We prove that every infinite code generated by a fixed positive integer has asymptotically vanishing 2-adic and 3-adic residue rates. Experiments with random critical codes, mechanical critical codes, and adaptive evolutionary search at lengths 100, 200, and 400 show that adaptive search improves finite-length trade-offs, while all methods retain clearly positive residue rates. The proposed framework is not a verification method for the Collatz conjecture, but a symbolic diagnostic approach for investigating obstruction structures in exponent-code space.

Over the last few years, there has been an increased interest in making machine learning models more interpretable. Although a great deal of effort goes into developing techniques for interpreting the interactions learned by a given model, fewer studies focus on assessing the quality of such explanations. Even fewer focus on how to adjust the model to produce explanations faithful to prior knowledge, a process known as explanation-guided learning. Furthermore, most approaches in this area focus on classification problems and usually assume prior knowledge about which input features or regions are most important. In this work, we introduce a new approach to steering neural networks based on partial dependence, such that their average response to certain features aligns with specific functional domain knowledge about the problem. We empirically demonstrate on a range of regression problems, including dynamical systems forecasting, that models whose training has been controlled using our method perform better than unconstrained models and are more data-efficient. Moreover, we highlight that interpretations obtained from the former actually align with the user-provided knowledge, whereas those obtained from the latter do not.

Large language models (LLMs) are increasingly trusted to draft the artifacts of safety analysis such as, losses, hazards, Unsafe Control Actions (UCAs), and safety constraints, inside rigorous processes such as Systems-Theoretic Process Analysis (STPA). Yet a blind spot runs through this fast-growing literature: every system gets analysed except the LLM-assisted tool doing the analysing, which is itself a safety-relevant system that can hallucinate standards, emit unverifiable constraints, and leave no audit trail from prompt to artifact. We take seriously the question the field has skipped -- {who analyses the analyser?} and answer it by turning STPA on the tool itself. We present {Constitutional Meta-STPA}, an LLM-assisted STPA tool built around a closed loop: the tool runs a {meta-STPA} of the class of AI-assisted safety tools and {derives} rather than asserts, its governance constitution from the resulting loss$\to$hazard$\to$UCA$\to$constraint chain, yielding a published constitution of $21$ Tool Principles and $8$ Meta-Safety Principles, each bound to a code enforcement point. We formalise the measured object as a constitution-marginal coverage operator over a principle set $P$ ($|P|{=}29$) with a soundness lemma that isolates coverage from model and scanner, and report four findings. {(i)~Self-derivation:} a frontier ensemble ({claude-opus-4.8}${+}${claude-sonnet-4}) recovers $18/21$ canonical and all $8/8$ governance principles from the tool's own design, while a weaker pair recovers $12/21$ and $3/8$, so the meta layer is model-limited, not constitution-limited, and the same $8/8$ re-emerge from a second, independently authored tool.

This paper presents a Spatiotemporal Tube (STT)-based control framework for general unknown nonlinear Euler-Lagrange (EL) systems subject to input constraints, with the objective of satisfying Signal Temporal Logic (STL) specifications, where confinement of the system trajectory within the STT guarantees the satisfaction of the corresponding STL task. For both single and multi-agent scenarios, the STT corresponding to each agent is modeled as a time-varying ball, whose center and radius are jointly parameterized using a physics-informed neural network (PINN). The robustness metric associated with the STL specification corresponding to the agents is incorporated into the training process as a loss function, enabling the learned tube to encode task-level temporal requirements. For a multi-agent scenario, we introduce an additional robustness metric corresponding to the global task, which, when satisfied, ensures the tubes do not collide with each other. To ensure that the system trajectory remains within the learned STT and thereby satisfies the local and global STL specifications, we propose a control strategy that explicitly accounts for input constraints. In particular, a closed-form control law is developed to keep the trajectory inside the tube while regulating the motion of the tube by enforcing bounds on its evolution depending on the input constraints of the system. The proposed approach has been validated over several case studies.

Vision-language alignment powers open-vocabulary recognition, retrieval, and LVLM grounding, yet natural captions are often underspecified, making similarity brittle and overly confident under paraphrase and omitted details. We aim to learn representations whose matching is stable across caption views and whose confidence reflects how strongly text constrains an image. We propose Text as Partial Constraint (TPC), a core-residual alignment framework that treats multi-view captions as incomplete supervision. It distills a consensus semantic core as the alignment target, learns a single-view core predictor for standard inference with one query, and explicitly discourages vision-language similarity from depending on the orthogonal unsaid residual. An uncertainty-aware contrastive objective further softens alignment when caption views disagree, reducing overconfident updates under weak language constraints. Across zero-shot recognition and adversarial robustness, TPC achieves 81.42/64.05 Top-1 clean/robust accuracy on ImageNet and 76.19/52.03 on an Avg-14 transfer suite, while improving LVLM transfer with 85.16 POPE F1 and 59.57 OKVQA accuracy under an LLaVA-1.5-7B stack. These results suggest that modeling text as a partial constraint is a practical and principled route to more reliable vision-language representations under underspecified language supervision.

Training-free controllable motion generation has attracted growing interest for enabling flexible constraint enforcement without constraint-specific training. However, existing training-free methods require constraints to be continuous objective-based with differentiable losses, while many real-world requirements are criterion-based and provide only discontinuous, sparse, or even black-box feedback. In this paper, we propose Motion-Inference-as-Control (MIC), the first training-free motion generation framework that handles both continuous objective-based and criterion-based motion constraints under a shared mechanism. The key idea is to cast diffusion-based motion generation as a stochastic control problem. This perspective not only provides principled and practically effective step-wise control laws that support criterion-based constraints without requiring differentiability and naturally accommodate objective-based constraints as a special case, but also motivates a control-oriented constraint coordination mechanism that adaptively balances and reconciles motion constraints during generation. Experiments across diverse constraint settings demonstrate the effectiveness of our framework.

Visual-spatial understanding, defined as the ability to infer object relationships and scene layouts from visual inputs, is fundamental to downstream tasks such as robotic navigation and embodied interaction. However, pre-trained vision-language models (VLMs) remain constrained by spatial uncertainty stemming from inherently 2D observations and by the scarcity of data for 3D spatial understanding. To address these limitations, we proposed a novel framework, SpaceEra, in the NeurIPS 2025 Spotlight paper. Although it achieved significant performance gains, we further observed that its effectiveness is hindered by insufficient input from scanning videos and weak reasoning constraints. To tackle these newly emerged challenges, we extend the original framework into a comprehensive system, termed SpaceEra++, which spans data construction, model design, training optimization, and prompting inference. Specifically, to alleviate input insufficiency, we introduce ScenePick, a frame sampling strategy that balances spatial coverage with object semantics to produce compact yet comprehensive scene representations. In addition, to enhance spatial reasoning, we develop SpaceAlign, which enforces pairwise object constraints by jointly exploiting absolute coordinates and relative spatial relations, thereby aligning optimization with spatial accuracy. Extensive experiments across multiple benchmarks demonstrate consistent improvements over strong baselines, while ablation studies validate both the individual and joint contributions of each component, and further analyses provide guidance for future research.

The game of Taboo requires describing a target word without using a set of forbidden words, so that other players can guess it. This deceptively simple task combines strict lexical constraints with the need for communicatively effective descriptions, making it a compelling playground for examining how LLMs navigate competing demands at inference time. We evaluate two open-weight models under conditions that intervene at progressively deeper levels of the generative process, from prompting to generation-time constraints to internal representations manipulations. We assess their outputs through forbidden word violation detection, LLM-as-a-judge measuring the degree to which generated descriptions successfully evoke the target concept for both human and machine guessers, and examining whether the strategies models adopt under constraint align with those of human players. Our results show that compliance with the rules of the game and communicative effectiveness trade off differently across conditions, and that models remain substantially weaker than humans as guessers, suggesting that lexical grounding under constraint is an open challenge for current language models.

Despite advances in indoor scene generation, synthesizing coherent building exteriors consistent with generated interiors remains largely unexplored. Existing methods can generate floor plans and wall layouts but typically stop at a structural shell, lacking stylistically consistent facades and roofs. Completing these exteriors is challenging because the footprint, wall geometry, and opening semantics must remain fixed-constraints that unconstrained generative models often violate. We introduce ShellMaker, a language-guided exterior completion framework that operates under these structural constraints. Given a building scaffold and a text style prompt, ShellMaker generates a complete exterior mesh with PBR materials by combining parametric roof generation, LLM-based part-aware prompt refinement, joint wall-roof material retrieval, and geometry-aware assembly. Operating on a format agnostic scaffold representation, ShellMaker generalizes to indoor generators, CityGML, and CAD inputs, while maintaining structural consistency and improving architectural coherence over retrieval and unconstrained generative baselines. The project page is available at https://ruiqixu37.github.io/ShellMaker_web/