Uncoupled Learning

Generating realistic 3D dance from music is a challenging task that requires accurate synchronization with musical rhythms while capturing the spatial complexity of human motion. Although existing methods can generate physically plausible dance motions, they often struggle to achieve precise alignment with music, such as the beat. To address this limitation, we propose a novel diffusion-based framework, BeatDance, with two components: 1) We present a Hierarchical Decoupled Attention (HDA) module, which first disentangles the learning of human pose and temporal dynamics. A hierarchical structure is then employed to capture both short-term and long-term dependencies, thereby enhancing spatial-temporal modeling. 2) We adopt cycle-consistent learning by introducing an auxiliary dance-to-music module. During training, discrepancies between the reconstructed and original music induce a stronger loss signal, effectively encouraging the consistency property between the music and dance motion. Extensive experimental results demonstrate that our proposed approach outperforms recent competitive methods on two benchmark datasets.

Multi-task visual grounding requires models to jointly understand linguistic semantics and perform accurate visual localization and segmentation. Despite the success of multimodal large language models, effectively adapting them to multiple grounding objectives remains challenging. Existing methods commonly enforce task cooperation through shared representations, while overlooking the intrinsic conflict between task-oriented feature interests. In this paper, we introduce $\textbf{DeCo}$, an efficient $\textbf{De}$couple-to-$\textbf{Co}$uple learning framework that resolves this dilemma through a two-stage paradigm: task-specific representation decoupling followed by complementary prior coupling. Specifically, we first propose Task-aware Semantic Decoupling (TSD) to route shared visual cues into individual features under salient word-level guidance, alleviating representation interference between localization and segmentation. Furthermore, we observe that segmentation naturally provides informative localization priors due to dense supervision. Based on this insight, we introduce Hybrid Prior Coupling (HPC), which integrates sentence-level semantic prior with mask-derived spatial prior for enhanced grounding. Built upon a frozen multimodal encoder, DeCo requires lightweight trainable parameters while achieving strong generalization across multiple grounding objectives. Extensive experiments on RefCOCO/+, G-Ref, ReferIt, Flickr, DIOR-RSVG, SARVG1.0, RRSIS-D, RIS-LAD, and RefDIOR demonstrate that DeCo achieves state-of-the-art performance on both natural and remote sensing benchmarks. The code and models are available at https://github.com/xiaoqiang-lu/DeCo.

Operator learning for parametric partial differential equations (PDEs) typically builds global models over prescribed domains, requiring cross-condition data or costly physics-constrained training. Here we show that the output Jacobian of a neural solution model trained at one condition defines a reusable response space for cross-condition solution variations. We introduce Linearized Subspace Transfer (LST) to exploit this space and recover target solutions by minimizing the target PDE-system residual over response-space coordinates. Because any single response space has finite coverage, Active Transfer Modeling (ATM) uses post-transfer residuals as coverage indicators to selectively acquire response spaces from additional single-condition models. Across six systems, single-condition response spaces supported cross-condition transfer, with enrichment improving accuracy when added spaces expanded representation capacity. Relative to evaluated physics-informed operator baselines, ATM reduced error and offline construction cost, with orders-of-magnitude accuracy gains in representative cases and millisecond-to-second target adaptation. These results establish neural solvers as reusable local parametric models.

Many learning systems return a single point estimate even when admissible outputs form disconnected or non-convex sets. Under squared loss, an ambiguous conditional distribution can therefore have a Bayes-optimal conditional mean that is invalid. We formalize this failure as conditional mean collapse and introduce Settling, an equilibrium-based inference operator that separates proposal generation, consistency evaluation, and test-time equilibrium selection. The operator treats a mean-seeking proposal as an initialization and refines it toward a locally stable configuration; conditional on initialization, refinement is deterministic. We establish exact-gradient descent, local convergence, and an inexact-gradient robustness condition relevant to learned consistency critics. In a reproducible 100-context geometric diagnostic, the mean-seeking baseline succeeds in 0/100 contexts, stochastic denoising in 100/100, and Settling in 99/100 while producing substantially lower trajectory roughness. A 1,200-run sensitivity study yields 97-100% success across obstacle-jitter ranges up to 0.20 and 94-100% across one-time initialization perturbations from 0.05 to 0.50. Cross-domain panels remain mechanism illustrations; learned high-dimensional validation remains an open empirical test.

We introduce an uncoupled learning algorithm which, when employed by all players of an arbitrary $N$-player normal form game with up to $K$ actions per player, guarantees $O(N^3\log^2 K)$ individual regret, uniformly over the horizon of play. The proposed algorithm - which we call higher-order optimism with discounting (HOOD) is a variant of optimistic follow-the-regularized-leader (OptFTRL) that combines a discounted $(N+1)$-th order predictor with entropic regularization over a suitable "lifting" of the game's strategy space. This combination of ingredients is purposefully designed to dampen large oscillations of the induced sequence of play in a controlled manner, removing in this way a key stumbling block of previous attempts to achieve constant regret in general games. Our approach bears several striking similarities to the concurrent - and completely independent - work of Liu, Farina, and Ozdaglar (arXiv:2608.31166), who very recently derived an $O(N^{21}\log^{4} K)$ regret bound through the use of higher-order optimism and an exponential moving average estimator.

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.

Activity-cliff ranking remains difficult because local structural changes can cause large activity differences, while high-quality data that resolve the underlying mechanisms remain limited. To use available activity labels more effectively, we combine absolute-activity regression with ranking-consistency learning. CliffRank trains two parallel predictors with mean squared error, a thresholded listwise loss, and Pairwise Preference Consistency (PPC), which aligns relative ordering in the preference-probability space. On three antimicrobial peptide datasets, CliffRank with ESM2-t12 achieved the highest mean Spearman correlation of 0.5393 and mean Recall@50 of 21.4, although the leading method varied across individual datasets. On three small-molecule datasets, CliffRank with PNA, where PPC was activated after 120 epochs, achieved the highest mean Spearman correlation of 0.6890, while its mean Recall@50 of 30.4 matched that of ACANet-PNA. The PPC results also define its practical limits. Asymmetric initialization improved the MolCLR-GIN averages but did not improve every target. For PNA without pretrained weights, delayed PPC improved selected metrics, but no schedule was best for both mean Spearman correlation and mean Recall@50. Future work should evaluate more targets and antimicrobial peptide systems, develop adaptive PPC schedules, and incorporate protein or membrane context when available.

In this work, we study radically uncoupled learning in discounted general-sum Markov games. Assuming ``$\mathsf{ETH}$ for $\mathsf{PPAD}$", we show that, for every fixed discount factor, there is no polynomial-time algorithm for computing inverse-polynomially accurate coarse correlated equilibria in discounted general-sum Markov games when players learn independently in decentralized settings. Complementing this hardness result, we provide what appears to be the first \emph{radically uncoupled} algorithm with sub-exponential convergence guarantees to coarse correlated equilibria in discounted general-sum Markov games without imposing any structural restrictions on the game. Our algorithm is a \emph{layered} variant of optimistic mirror descent with an increasing step-size schedule tailored to the multi-agent setting. Finally, we develop both full-feedback and partial feedback versions of the aforementioned algorithm and establish sub-exponential convergence guarantees for each case.

Pairwise constrained clustering typically relies on hard must-link/cannot-link labels, whereas realistic pairwise supervision may be real-valued and entangle intrinsic ambiguity, expert judgment, and stochastic corruption. Existing deep constrained clustering (DCC) methods mainly target hard, expert-agnostic constraints, treating soft labels mostly numerically rather than semantically. We formalize this setting as uncertainty-aware probabilistic constrained clustering (UPCC), defining a canonical aleatoric target through a heterogeneous observation process and analyzing its conditional identifiability. We introduce ProbPair, an angular pairwise objective for probabilistic relations, and build ECI-PP, an estimator--corrector--integrator framework that refines imperfect supervision via belief estimation, correction, and reliability-aware integration. Across challenging probabilistic supervision settings, experiments on diverse benchmarks show that ECI-PP outperforms state-of-the-art DCC methods and remains robust with a shared default configuration.

Large traveling salesman problem (TSP) instances require a solver to allocate limited computation while preserving the validity of its outputs. Existing neural--operations-research (OR) hybrids predict guidance without requiring learned transitions to satisfy constraints discovered during search. DualCert introduces \emph{constraint-coupled learning}, in which current degree equations and dynamically separated subtour-elimination constraints (SECs) define each learned transition. At each refinement, the degree equations and selected, strictly satisfied SEC equations, with positive slacks, define an iterate-dependent primal-slack Karush--Kuhn--Tucker (KKT) manifold. Repaired dual variables and violated SEC rows define a local cost field. An exact constrained mirror-descent step maps each finite state to a positive state on the same manifold. Where selected rows and deterministic ties remain fixed, implicit differentiation maps parameter perturbations into the manifold tangent space and reuses the forward constraint operator for the local-cost-field derivative. The terminal edge state allocates computation across Held--Karp ascent, candidate-graph edge tests, and tour construction under a fixed budget. Deterministic verification recomputes original costs and accepts only verified candidate-graph lower bounds and edge decisions. On 1,000 held-out TSP1000 instances, DualCert attains a mean tour-cost gap of $0.0573\%$ from Lin--Kernighan--Helsgaun version 3 (LKH-3) reference tours in $9.55$ batch-amortized seconds per instance. It returns a verified candidate-graph lower bound for every instance and achieves $81.46\%$ edge-decision coverage. The mean gap is $67.1\%$ smaller than the reported NeuroLKH mean gap. Thus, optimization constraints govern learning, while deterministic verification preserves output validity.

We study constrained statistical learning over infinite-dimensional hypothesis classes in the fully nonconvex setting, and establish universal PACC learnability of the solutions of dual algorithms: Probably Approximately Correct on Constraints, guaranteeing optimality and constraint satisfaction at once. This strengthens near-PACC results, whose feasibility residual no amount of data can remove. Optimality is caught between generalization, governed by Rademacher complexity and favoring small classes, and strong Lagrangian duality, which rests on Lyapunov convexity for vector measures and needs decomposability, a demand pulling the other way. We reconcile the two by posing the population problem over a universal RKHS $\mathcal{H}_K$, dense in a decomposable envelope, and learning over norm balls of growing radius. This yields the Tikhonov complexity $\mathfrak{T}^{\varepsilon}_{n}$, the least RKHS norm reaching an $\varepsilon$-optimal Lagrangian level set; we prove it finite, obtain exact learnability of the optimal value, and make the sample threshold explicit and polynomial in $1/\varepsilon$ under a source condition. Feasibility is harder: absent convexity the Lagrangian may not attain its infimum, and dual information pins down only an averaged constraint-risk vector, not the risks of any returned predictor. We introduce the closure-realization gap $\varepsilon^\star_\infty$, an index of how well $\mathcal{H}_K$ retrieves feasible solutions from dualization; it is a property of the problem, not of a modeling choice. Learnability is exact when $\varepsilon^\star_\infty=0$, in particular under dual differentiability, and near-PACC with residual exactly $\varepsilon^\star_\infty$ otherwise. Finally, no distribution-free threshold exists already in the unconstrained specialization, so universality is the canonical frame for dual algorithms over large hypothesis classes.

Physical learning rules such as equilibrium propagation (EP), coupled learning (CL), and adjoint coupled learning (AL) train resistive networks through local measurements. In the small-nudge limit EP and CL exactly conserve the conductance mass K = (1/2) sum_e kappa_e^2, a property that stabilizes training. We show that conservation also governs the inductive bias of these rules. For a single output we prove that EP and CL are trajectory equivalent, so single-output experiments cannot distinguish what the two rules learn. We prove that AL does not conserve the mass but dissipates it at exactly twice its own loss. In linear circuits we prove that the conserved mass has no functional consequence: all three vector fields are homogeneous in the conductances, so the selected solution is independent of the initialization scale. Fixed nonlinear elements break this protection. In diode circuits the learned input-output function depends on the initialization scale by up to about forty percent, an effect absent in linear controls, and the conservative rules retain this memory permanently while the dissipative rule partially erases it. At matched training loss the dissipative rule typically generalizes worse than the conservative rules, although it reaches low training loss faster; the penalty correlates with the mass dissipated en route and fades in larger circuits, where little mass is lost. The conservation structure of a local learning rule thus sets its initialization memory, its training speed, and, where dissipation is appreciable, its generalization; it should be treated as a design parameter of physical learning machines.

We propose Dynamic Constraint Learning (DCL), a data-driven framework for constrained optimization when constraint functions are unknown and cannot be queried during optimization. At each iteration, the method learns a local surrogate from nearby data and solves a subproblem within a data-supported trust region. Compared with offline global constraint learning, the approach uses local surrogates that adapt to the data distribution during optimization and can achieve solution quality comparable to that of global models while using simpler local models and smaller optimization subproblems. We demonstrate the performance of DCL on a synthetic test problem and two case studies from the literature.

As constrained learning becomes increasingly common, models are trained under explicit feasibility requirements to enforce fairness, safety, robustness, regulariza- tion, and physics or logic constraints. Understanding how training samples in- fluence the model solution (e.g., learned parameters) is crucial for interpretability and robustness. The classical influence function (IF) estimates sample contribu- tions via local sensitivity analysis, measuring how the solution changes when a specific training sample is perturbed or removed. However, IF becomes unreli- able in constrained settings: data perturbations can reshape both the objective and the feasible region, leading to estimates that violate feasibility. In response, we propose the Directional Influence Function (DIF), a novel estimator that explicitly incorporates these constraints into influence estimation. DIF formulates the opti- mality conditions of constrained learning as a variational inequality (VI) and ana- lyzes how perturbing training data affects this VI. We validate DIF on constrained linear regression and demonstrate that it recovers leave-one-out retraining results, whereas IF and penalty-based IF exhibit significant bias. We further apply DIF to fairness-constrained CNNs, where DIF accurately predicts test loss changes under data removal and aligns closely with actual retraining. Our results establish DIF as an efficient and reliable tool for data attribution in constrained learning.

Deep Metric Learning (DML) often struggles with zero-shot generalization because standard objectives inherently capture what co-occurs rather than what causes similarity. Consequently, DML models are vulnerable to shortcut learning driven by two structurally distinct confounders: background spurious correlations (which create backdoor paths via scene context) and foreground nuisance perturbations (which inject non-semantic variations like pose or illumination). Although existing methods have proposed targeted solutions for each pathway individually, none can simultaneously address both due to their fundamentally distinct causal roles. To bridge this gap, we propose the Counterfactual Causal Embedding (CouCE), a unified causal framework that explicitly models and neutralizes both confounders. Specifically, we introduce Orthogonal Dictionary-Based Backdoor Adjustment (ODBA), which isolates spurious background patterns into a variance-gated dictionary and stably disentangles them from the learned embeddings via soft orthogonal regularization. Simultaneously, we propose Multi-Scale Randomized Causal Intervention (MSRCI) to enforce causal invariance against foreground nuisances through multi-scale Fourier amplitude randomization and a symmetric KL invariance constraint. Notably, CouCE seamlessly integrates with any proxy-based loss, incurring modest training overhead without requiring architectural modifications during inference. Extensive experiments on CUB-200-2011, Cars-196, and Stanford Online Products demonstrate that CouCE consistently achieves state-of-the-art performance, providing a principled and robust solution for debiased DML.

Maternal-fetal US is the primary imaging modality for monitoring fetal development, yet accurate automated segmentation remains challenging due to the scarcity of pixel-level annotations. To address this issue, we propose DACL, a semi-supervised framework for robust fetal US image segmentation. DACL jointly trains a deployment-oriented lightweight convolutional network (1.47\thinsp\mathrm{M} parameters) and a Transformer-based network, leveraging labeled data for supervised learning and unlabeled data via CPS. To enhance prediction stability, we introduce a dual-agreement consistency loss that couples pixel-wise probabilistic divergence with entropy-guided confidence alignment. Unlike conventional CPS methods that enforce agreement only at the prediction level, DACL explicitly regularizes both distributional alignment and uncertainty, thereby suppressing unreliable pseudo-labels and enabling stable cross-architecture pseudo-label learning under extreme annotation scarcity. Furthermore, an interpolation-based consistency strategy using mixup is applied to unlabeled samples to enhance robustness. Under 5% labeled data, DACL improves Dice by up to 2.77% and reduces HD95 by up to 14.69 mm compared with the strongest recent semi-supervised methods, demonstrating significant improvements in boundary accuracy on both fetal head and abdomen datasets. These results demonstrate the effectiveness of agreement-based consistency learning for annotation-efficient fetal US segmentation. Our code is on GitHub.

Machine learning models are increasingly used to model chemical process systems, yet they often lack principled uncertainty quantification and mechanisms to enforce physical constraints. We propose a probabilistic neural network framework that guarantees satisfaction of linear equality constraints within a given tolerance, while capturing aleatoric uncertainty. Compared to state-of-the-art methods, our formulation demonstrates improved predictive accuracy, uncertainty calibration, and adherence to constraints on reduced data. It also demonstrates competitive performance, but with significantly faster training times when evaluated on large data regimes. We evaluated this on two batch reactor case studies, enforcing mass balances.

In this paper we show that the physical learning methods known as coupled learning (CL) and equilibrium propagation (EP) conserve a mass-like quantity in the trainable parameters in the continuous-time, small-nudging limit. We prove that this conservation holds in a broad range of physically relevant settings. We then show that the conservation law constrains the training dynamics in a way that makes convergence reliable in important settings for linear circuits. We conclude by discussing some practical implications of this conservation law.

Physical learning methods train physical networks to perform computational tasks using only local update rules, exploiting the physics of the system to handle the global transfer of information. We provide the first local convergence analysis of three such methods -- Equilibrium Propagation (EP), Coupled Learning (CL), and a new method we call Adjoint Coupled Learning (AL) -- for linear circuits, in the limit of small-nudging for both discrete and continuous time. EP and AL perform gradient descent on a natural loss function, while CL follows modified dynamics with an additional cubic correction. Assuming the existence of a solution, we identify a coercivity condition, expressed as a rank condition on a matrix built from the network's incidence structure, under which the training loss decays exponentially and the parameters converge to the solution manifold. We show that coercivity can fail by exhibiting a kite circuit in which a symmetry causes the coercivity constant to degenerate on the solution manifold, but prove using Sard's theorem that such degeneracies are non-generic: coercivity holds at every point of the solution manifold for almost every choice of desired output.

Hard-constraint decision systems usually veto infeasible candidates. This is too rigid when the system can act: if a known affordable repair would make an infeasible candidate feasible and valuable, rejection is a false veto rather than a ranking error. We introduce Q-RACL (Quantum Repair-Augmented Constraint Learning), a repair-before-veto framework that first defines RACL decision semantics and then identifies the single inference link where quantum feature access can be load-bearing. RACL accepts a candidate when a sequential repair plan restores feasibility and preference; otherwise it returns structured rejection credit. The hard link is repair-feasibility inference: which repair class restores feasibility from an observed candidate and context. We construct a discrete-logarithm-hidden RACL family where the repair class is a shifted interval rule in the latent exponent a = log_g(x), while the learner observes only x = g^a mod p. Under standard DLP-based learning separation, this coordinate is inaccessible to efficient raw-input classical policies but accessible to a quantum agent through Shor/Fourier structure. Across six primes and ten seeds, bounded raw-input classical policies and a wrong raw-Fourier encoding remain near chance, whereas the Q-DLP policy keeps false-veto rate below 1.1%, wins all paired seeds, and yields QNI_cond = 0.9777 to 0.9972. A classical DLog oracle matches it, isolating feature access rather than classifier capacity. Thus quantum AI is not added as a generic model upgrade; for this DLP-hidden repair family, it supplies the missing feature that closes the repair-before-veto loop.

Hard constraints are usually treated as terminal vetoes: once a candidate violates a requirement, the learned rule rejects it and any repair is handled outside the decision semantics. This misses a common deployed regime in which the system already knows a finite menu of modifications, such as adding a ticket option, changing a configuration, or requesting an available service upgrade. Existing constraint-learning, soft-relaxation, and recourse methods address nearby problems, but they do not learn whether an option should be repaired before being vetoed. We introduce Repair-Augmented Constraint Learning (RACL), a contextual decision framework that lifts known repair operators into the classifier semantics. A candidate is accepted when an affordable repair makes it feasible and preferred enough; otherwise the system returns a structured rejection credit and, when applicable, a repair plan. This repair-before-veto view strictly generalizes no-repair HASSLE-style semantics, reveals an irreducible false-veto gap for terminal-veto rules, separates binary-label non-identifiability from decision-rule learnability, and gives capacity and calibration bounds for the observed-feasibility shared-weight setting. Across controlled and DB1B-derived benchmarks, RACL recovers the intended credit and repair structure. On the hardest raw-data-derived tier, validation-selected RACL reduces false vetoes to 10/4039 (FVR 0.0025), versus about 1064/4039 for the strongest repair-search black-box baseline, while making the FVR/EDR trade-off explicit.

Evolutionary model merging provides a powerful framework for the automated, training-free composition of LLMs through parameter-space search. However, existing methods predominantly rely on stochastic, hand-crafted operators that overlook the underlying performance landscape of the coefficient space. We propose Evolutionary Generative Merging (EvoGM), a framework that transcends manual heuristics by employing learnable generative modeling to optimize merging coefficients. Specifically, EvoGM features a dual-generator architecture with cycle-consistent learning to adaptively sample and refine promising merging candidates. By constructing winner-loser pairs from historical search trajectories, our framework effectively captures high-performance parameter distributions and maximizes data efficiency. This generative process is seamlessly integrated into a multi-round evolutionary pipeline, where elite merged models iteratively serve as new expert foundations. Extensive experiments across diverse benchmarks demonstrate that EvoGM significantly outperforms state-of-the-art baselines, exhibiting robust performance on both seen and unseen tasks. Code and data are available at https://github.com/JiangTao97/evogm.

City-wide traffic forecasting is important for congestion management, route guidance, and intelligent transportation systems, but accurate prediction remains challenging when future traffic must be generated as spatial maps over an entire urban network. Existing traffic movie prediction methods have improved frame-level accuracy, yet many still treat forecasting mainly as image reconstruction. This can produce traffic maps that are numerically close to the ground truth but weakly constrained by road layout, connectivity, travel direction, and congestion propagation, especially in cross-city settings where both traffic behavior and road structure change. To address this limitation, this study proposes RCSNet, a road-conditioned spatiotemporal network that reformulates traffic movie prediction as topology-guided future-state generation. RCSNet extracts road-aware representations from static road maps, models multi-horizon traffic dynamics from historical observations, aligns directional traffic features with local road structure, and progressively generates future traffic maps for improved temporal consistency. A structure-consistent learning objective further encourages predictions to remain accurate, road-aligned, and spatially stable. Experiments across multiple cities show that RCSNet improves both forecasting accuracy and structural consistency. In same-city forecasting on Berlin, Antwerp, and Moscow, RCSNet reduces average MAE, MSE, and RMSE by 11.5%, 10.0%, and 5.1%, respectively, compared with the closest baseline. In cross-city testing on unseen Chicago and Bangkok, it reduces RMSE by 10.6% and 10.5% without target-city fine-tuning. Additional horizon-wise, road-structure, explainability, statistical, and efficiency analyses show that RCSNet produces more accurate, transferable, road-aligned, and computationally efficient traffic forecasts.

Vision-Language-Action (VLA) models have shown strong performance on embodied manipulation, yet they remain brittle under visual observation changes, paraphrased language instructions, and compounded perturbations. This limitation suggests that existing methods still rely heavily on shallow correlations in the training distribution, rather than learning stable couplings among task semantics, environment states, and action generation. Although recent efforts improve robustness through larger-scale training, post-training adaptation, or enhanced predictive modeling, they rarely enforce invariance-oriented consistency within the end-to-end policy itself. To address this issue, we propose RoVLA, a robust vision-language-action framework with multi-consistency constraints. RoVLA enforces consistency under three complementary transformations: instruction semantics, trajectory evolution, and observation perturbation. Specifically, Instructional Consistency (IC) promotes stable grounding under semantically equivalent instruction rewrites, Evolutionary Consistency (EC) preserves coherent action intent throughout the generation process, and Observational Consistency (OC) improves robustness to visual and proprioceptive perturbations by enforcing consistent predictions before and after targeted disturbances. By explicitly modeling these invariances during training, RoVLA reduces reliance on superficial correlations and improves robustness and generalization. Experiments on LIBERO-Plus, RoboTwin 2.0, and real-world manipulation tasks show that RoVLA consistently outperforms strong baseline methods and exhibits superior robustness under diverse task and observation shifts. These results demonstrate the effectiveness of multi-consistency learning for robust embodied control. Codes will be available at https://github.com/HCPLab-SYSU/RoVLA.

Constrained machine learning enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. Despite its practical importance, no general method exists for the non-convex, non-smooth, stochastic setting that arises naturally in deep learning. We propose the Stochastic Penalty-Barrier Method (SPBM), which extends classical penalty and barrier methods to this setting via exponential dual averaging, a stabilized penalty schedule, and the Moreau envelope to handle non-smoothness. Experiments across multiple settings show that SPBM matches or outperforms existing constrained optimization baselines while incurring only linear runtime overhead compared to unconstrained Adam for up to 10,000 constraints.

Diffusion models are rapidly redefining 3D anomaly detection in point cloud data. As 3D sensing becomes integral to modern manufacturing, reliable anomaly detection is essential for high-throughput quality assurance and process control. Yet practical deployment on resource-constrained, latency-critical systems remains limited. Existing methods are often computationally prohibitive or unreliable in complex, unmasked regions, and diffusion pipelines are inherently bottlenecked by iterative denoising. In this work, we address this bottleneck by reformulating reconstructionbased anomaly detection through consistency learning, enabling direct prediction of anomaly-free geometry in one or two network evaluations. We further introduce a novel hybrid loss formulation that explicitly enforces reconstruction toward clean data. This design substantially reduces inference cost, achieving up to 80x faster runtime than the current state-of-the-art method, without GPU acceleration, while preserving strong detection performance. It outperforms R3D-AD on Anomaly-ShapeNet with 76.20% I-AUROC and remains competitive on Real3DAD with 72.80% I-AUROC, enabling efficient, low-latency anomaly detection on resource-constrained platforms, including drones, smart industrial cameras, and other edge devices.

Neural processes are meta-learning models that map context sets to predictive distributions. While inspired by stochastic processes, NPs do not generally satisfy the Kolmogorov consistency conditions required to define a valid stochastic process. This inconsistency is widely acknowledged but poorly understood. Practitioners note that NPs work well despite the violation, without quantifying what this means. We address this gap by defining the conditioning consistency gap, a KL divergence measuring how much a conditional neural process's (CNP) predictions change when a point is added to the context versus conditioned upon. Our main results show that for CNPs with bounded encoders and Lipschitz decoders, the consistency gap is $O(1/n^2)$ in context size $n$, and that this rate is tight. These bounds establish the precise sense in which CNPs approximate valid stochastic processes. The inconsistency is negligible for moderate context sizes but can be significant in the few-shot regime.

Off-policy learning in constrained MDPs with large binary state spaces faces a fundamental tension: causal identification of transition dynamics requires structural assumptions, while sample-efficient policy learning requires state-space compression. We introduce PI-CMDP, a framework for CMDPs whose constraint dependencies form a layered DAG under a Lifecycle Ordering Assumption (LOA). We propose an Identify-Compress-Estimate pipeline: (i) Identify: LOA enables backdoor identification of causal edge weights for cross-layer pairs, with formal partial-identification bounds when LOA is violated; (ii) Compress: a Markov abstraction compresses state cardinality from 2^(WL) to (W+1)^L under layer-priority regularity and exchangeability; and (iii) Estimate: a physics-guided doubly-robust estimator remains unbiased and reduces the variance constant when the physics prior outperforms a learned model. We instantiate PI-CMDP on constraint repair in engineering simulation pipelines. On the TPS benchmark (4,206 episodes), PI-CMDP achieves 76.2% repair success rate with only 300 training episodes versus 70.8% for the strongest baseline (+5.4 pp), narrowing to +2.8 pp (83.4% vs. 80.6%) in the full-data regime, while substantially reducing cascade failure rates. All improvements are consistent across 5 independent seeds (paired t-test p < 0.02).

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the last-iterate to a Nash equilibrium. Although the non-bandit case has been studied extensively, this setting has only been explored recently, with a bound of $\mathcal{O}(T^{-1/8})$ on the exploitability gap. We show that, for uncoupled algorithms, guaranteeing convergence of the policy profiles to a Nash equilibrium is detrimental to the performance, with the best attainable rate being $Ω(T^{-1/4})$ in contrast to the usual $Ω(T^{-1/2})$ rate for convergence of the average iterates. We then propose two algorithms that achieve this optimal rate up to constant and logarithmic factors. The first algorithm leverages a straightforward trade-off between exploration and exploitation, while the second employs a regularization technique based on a two-step mirror descent approach.