Papers

Most vision-language-action models represent future motion as fixed-rate action chunks, tying temporal resolution and prediction horizon to a fixed output budget. This pointwise representation wastes capacity on highly correlated neighboring actions, leaves temporal continuity and smoothness to be learned implicitly, and forces a tradeoff between long-horizon coverage and the local precision required for contact-rich manipulation. To address these limitations, we introduce Vela, a vision-language-action foundation model that represents future robot behavior as continuous trajectories. Vela combines a compact spline-based action representation with motion-dependent temporal support and a shared action interface for heterogeneous embodiments, allowing a fixed output budget to adapt its temporal resolution across motions. We pretrain Vela on large-scale multi-embodiment robot data and evaluate it on LIBERO-X, EBench, and two real-world long-horizon tasks, egg-cake cooking and potato shredding, obtaining promising results across simulation and physical manipulation. These results highlight the potential of continuous action representations as a foundation for future embodied foundation models. Project page and more results: https://clementine24.github.io/Vela/ .

Explainable artificial intelligence (XAI) encompasses methods that draw on different sources of information and address different explanatory needs. A common framework is needed to describe how this information becomes evidence and is communicated as an explanation for a particular recipient. We propose the General Framework for Generating Explanations (GFGE), grounded in interpretative frameworks and the complementary activities of sense-reading and sense-giving. Its conceptual foundation is the Interpret/Explain Schema (IES), which connects an analyst's interpretation of system evidence, the communication of a selected account, and the recipient's interpretation of that account. GFGE operationalises this schema through five roles: data interpretation, model interpretation, output interpretation, optional post-hoc analysis, and aggregation. A role-typed operation graph records method-specific dependencies, while evidence records retain the sources, assumptions, and limitations of explanatory claims. The explanatory question, audience, and context guide the procedure. We instantiate GFGE for attribution, surrogate, counterfactual, concept and prototype, intrinsic rule, argumentation, and language-model methods. These instantiations show how intrinsic, post-hoc, and hybrid workflows can be represented through the same roles while preserving their distinct evidential requirements. GFGE provides a common basis for analysing explanation workflows, tracing communicated claims to their evidence, and identifying unresolved explanatory dependencies.

The architecture of modern LLMs consists of a profound cognitive polarization. LLMs possess implicit intuition encoded in their parameters, yet rely on a disconnected, explicit mechanism to access the outside world. Agentic frameworks have not bridged this gap; instead, models are often compelled into pathological "induced amnesia." Under the prevailing "Retrieve-Always" paradigm, agents must distrust their internal knowledge, making every user interaction a "tabula rasa" event that must be checked externally. This creates reflexive dependence that can be thermodynamically wasteful, cognitively fragile, and susceptible to irrelevant context. We propose a return to first principles, operationalizing the biological maxim "Look Before You Leap." We introduce MARTA (Metacognitive Adaptive Retrieval and Thought Architecture), a neuro-symbolic framework that bridges parametric and non-parametric knowledge. Rather than treating retrieval as mandatory, MARTA models it as a cost, taking the leap only when perceived internal inadequacy warrants external information. By allowing the agent to gauge the entropy of its own thoughts before acting, MARTA enables deliberative retrieval and uncertainty-aware decision making. Our approach suggests that giving agents the capacity for introspection can restore a more efficient balance between internal knowledge and external information.

Carousel interfaces allow a recommender system to directly observe how far a user has browsed. This signal distinguishes displayed but unclicked items from items that were never displayed, whereas conventional ranking-bandit models, including cascade and position-based models, generally treat examination as latent. We formulate a ranking-bandit problem in which a learner presents a list of $L$ items, observes the user's maximum browsing depth, and receives click feedback only for positions up to that depth. The objective is to maximize the expected number of clicks under an unknown item-attractiveness vector and a browsing-depth distribution. We propose three algorithms based on UCB, Thompson Sampling, and DMED, all of which update item statistics only from observed exposures. We derive an instance-dependent logarithmic upper bound for our UCB-based algorithm and an asymptotic upper bound for our DMED-based algorithm that coincides with the lower bound as its parameter $\alpha\downarrow 0$, establishing asymptotic optimality in this limit. Simulations in synthetic shallow- and deep-browsing environments, together with experiments parameterized from RecGaze interaction logs, show that OD-TS attains final mean regret similar to PBM-TS, while the proposed methods achieve lower final mean regret than PBM-UCB.

Most Large Language Models exhibit a fundamental tension between two sequential tasks, such as logical reasoning and safety alignment. The high-variance internal states required for sophisticated Chain-of-Thought (CoT) deduction can geometrically interfere with latent representations encoding safety constraints. We identify this phenomenon as Sequential Subspace Interference, showing that standard fine-tuning on logical tasks such as multi-step mathematics and code generation can result in a 23.3% interference penalty on alignment benchmarks, substantially weakening the model's safety priors. This Reasoning Drift is not adequately captured by current adaptation methods because gradients for logical tasks are rarely orthogonal to safety objectives. To address this issue, we propose AURA (Adaptive Unique Residual Allocation), a spectral regularization framework that enforces Spectral Independence between reasoning and safety. By explicitly estimating the null space of the alignment manifold and constraining reasoning updates to its orthogonal complement, AURA enables models to improve logical reasoning without compromising safety. Empirically, AURA recovers 23.0% of the lost performance while preserving greater than 0.98 cosine fidelity to the safe state, demonstrating that reasoning and alignment can be effectively decoupled through geometric regularization.

Speech watermarking offers proactive traceability for synthetic speech, yet most existing models operate only after text-to-speech (TTS) synthesis by adding a watermark perturbation to the generated waveform. This post-hoc design leaves watermarking as an external step that can be omitted or bypassed and restricts the watermark to a shallow waveform representation. We propose NeuMark-Native, a TTS-native watermarking framework for neural codec-based synthesis. It embeds payload information into every generated codec-latent layer before waveform decoding, improving watermark persistence under downstream digital signal processing (DSP) and neural codec resynthesis. NeuMark-Native keeps the pretrained TTS model and the neural codec frozen, while optimizing only the watermark modules on generated codec tokens. Experiments on two corpora under 11 DSP attacks and 9 neural-codec attacks demonstrate robust watermark detection while preserving naturalness, intelligibility, and speech quality close to synthetic speech.

Semantic-driven time-series generation offers a promising way to improve downstream learning in few-shot forecasting, but directly generating numerical sequences from language often fails to preserve the intended temporal structure. We propose VisualBridge, which uses time-series plots as a visual intermediate to bridge high-level temporal semantics and numerical sequences. An MLLM first converts plotted series into structured semantic representations, enabling explicit control over temporal properties such as trend, seasonality, and volatility. We then learn a semantic editing policy with downstream forecasting rewards, allowing the generation process to favor temporal patterns that are beneficial for the target task. The resulting sequences are further modeled by a temporal VAE to produce consistent multivariate augmentations. Experiments on standard public forecasting benchmarks demonstrate that VisualBridge improves few-shot forecasting over conventional augmentation methods, with ablations validating the roles of visual semantic grounding, learned semantic control, and VAE-based generation.

Feed-forward 3D models provide strong multi-view geometric priors, while on- line simultaneous localization and mapping (SLAM) relies mainly on local mea- surements and can accumulate drift over long sequences. Existing attempts to combine the two typically treat feed-forward predictions as an external geomet- ric state that is aligned or fused with the online estimate after the fact, which keeps broader multi-view evidence outside the optimizer that refines the SLAM state. We present F2SLAM, which instead converts feed-forward geometry di- rectly into optimization-native target-weight measurements attached to a persis- tent dense factor graph. A high-frequency stream maintains local tracking con- straints and graph connectivity, while a low-frequency stream uses wider multi- view context to selectively refresh existing measurements after a state-consistency check. Both streams constrain the same poses, inverse depths, and optional cam- era intrinsics through a single dense bundle adjustment. Experiments on multiple benchmarks demonstrate consistently strong trajectory estimation and improved dense reconstruction in both calibrated and uncalibrated settings. Notably, the uncalibrated configuration reduces the average ATE RMSE from 0.030 m for the strongest feed-forward baseline to 0.002 m on the Replica dataset.

On-policy self-distillation (OPSD) of large language models (LLMs) has demonstrated the ability to improve reasoning capabilities while preserving previously acquired knowledge. Despite substantial empirical success, the dynamics of OPSD in continual reasoning remain incompletely understood. Modeling LLM reasoning as search over a directed acyclic graph, we provide a unified theoretical analysis of both the dynamics of post-training—OPSD and supervised fine-tuning (SFT) in continual learning—and the impact of pre-training on subsequent performance. Our findings establish three key insights with an optimization guarantee: (i) OPSD with hints from correct outputs enables continual learning without forgetting by sparse yet effective gradient descent updates induced by the hint structure. (ii) SFT on correct reasoning paths can lead to catastrophic forgetting due to dense updates along the training paths, which overwrite the information previously acquired. (iii) Diversity in pre-training is crucial for enabling a post-trained model to reach a correct output when a rollout starts from an intermediate state. Our results, supported by theoretical analysis, show that reliable continual reasoning depends on how post-training updates interact with the reasoning structure established during pre-training.

How strongly do the remaining diffusion-sampling steps amplify a perturbation at a late latent state? Standard measurements answer this question with newly sampled isotropic noise, even though perturbations encountered during sampling have already been transformed by earlier steps. We compare these two cases directly. For each trajectory, we transport a centered perturbation from an earlier step to a late state, then replay its direction at the same magnitude as a newly sampled isotropic perturbation; both then undergo the same remaining updates. Across the samplers we study, median paired shaped-to-fresh angular-gain ratios range from $1.14$ to $2.35$. Shaped angular gain exceeds its matched fresh counterpart in every trajectory in the original main cohorts. The same pattern appears when endpoint change is measured by latent RMS. The effect also appears in perceptual feature representations: earlier-sampling directions cause larger feature changes at the endpoint, even when the corresponding pixel-space change is comparable. Permuting shaped directions across trajectories weakens the effect, including within class, indicating that the advantage depends on alignment with the receiving trajectory as well as on shared directional structure.

Patient world models used for clinical trial simulation can agree on transition kernels and arm-specific risks, yet disagree on the fraction of patients harmed by switching treatment—the counterfactual quantity that matters for intervention-aware reasoning. We audit this reliability gap in a two-stage shared-response SCM: a categorical intermediate health state is followed by common terminal care. Under independent stages, the sharp harm interval has closed-form endpoints for at most three intermediate states, with an exactness boundary at four states. Declared dependence and response-mismatch budgets yield calibrated outer bounds when stage independence or complete mediation is relaxed; in a symmetric three-state model the entire sensitivity frontier is sharp, $[0,\min\{1/2,1/3+(\rho+\delta)/2\}]$, and shows exactly how budgets erase the gain over endpoint-only bounds. Two eight-variable response LPs propagate interventional uncertainty for finite-sample audits. Exact witnesses verify attainability. On public clinical simulators (EpiCare; sepsis), native configurations show little resolved stage dependence and no additional joint-compatibility gain over pairwise transport—honest negative results for reliability claims. All experiments are locally reproducible; guarantees remain conditional on the stated causal model. The results provide a concrete protocol for deciding when a patient world model is safe to trust for counterfactual harm.

Data-driven mechanistic hypotheses are essential to scientific discovery because they explain how underlying processes produce observed phenomena. AI agents and AI scientists increasingly support scientific data analysis. However, their ability to turn empirical findings into mechanistic hypotheses remains insufficiently examined. To address this gap, we introduce MechHypoBench, the first benchmark for evaluating whether AI agents and AI scientists can generate such hypotheses from empirical data. It combines paper-derived mechanisms from 14 scientific fields with real-world datasets containing 17.98 million records. The construction retains the observational complexity of empirical data while providing a specified underlying mechanism. Agents analyze the observations and propose open-form hypotheses. We develop an evaluation framework that assesses open-form mechanistic hypotheses through their consequences under withheld conditions. Experiments with general agents and AI scientists reveal a substantial gap between generated hypotheses and the underlying mechanisms.

Risk regulation imposes directional constraints on scores; we adopt their strict per-input form – the score monotone non-decreasing in every exposure input – as a normative commitment. Deployed pipelines – monotone hand-crafted aggregates feeding sign-constrained gradient boosting – already satisfy it by composition, so constrained-versus-unconstrained comparisons price a guarantee the incumbent has for free. We instead hold admissibility fixed on both sides and measure what learning the aggregation is worth. Our instrument is a recurrent network whose state is classical risk statistics (an exponentially weighted moving average and a high-water mark with learned transforms), monotone by construction in every input and per MC-dropout sample. The central finding, by functional regression, is a subsumption boundary: a learned monotone channel reproduces the geometrically weighted separable family of hand-crafted statistics, one channel per member, to Spearman $\rho \ge 0.996$, approximates window statistics with measurable ceilings, and fails at consecutivity ($\rho = 0.924$) and time localization (0.628), both structural, and at the exposure floor (0.829), a learnability boundary. One explicit admissible basis repairs each failure (rank correlation 1.000). In or near the separable family, learned and engineered aggregation are substitutes, and the learned channel is never statistically behind at full sample size and specified capacity. Its advantages are incumbent-specific: a committed grid pays up to 0.019 AUC in decay regions it leaves uncovered (the learned channel stays within 0.004 of the strongest engineered consumer at every swept point); the highest-dimensional comparator degrades fastest with scarce data; and beyond the training support, grid-fed tree-ensemble scores go flat while a strictly increasing head keeps ranking. No single incumbent is dominated on all three axes.

The next generation of multimodal research agents must reason over long-lived research histories rather than short model completions. During a single task, an agent may repeatedly search the web, inspect visual evidence, revisit earlier hypotheses, and accumulate tens of thousands of tokens of multimodal context. Despite this trend, online RL for multimodal research agents remains largely confined to shorter contexts and interaction horizons. We push online RL training to 128k context and 75+ tool-interaction turns. To our knowledge, this is the first online multimodal deep-research RL study trained at 128k context, and the first trained with a 75 tool-turn horizon. Scaling to this regime exposes several practical limitations of conventional RL training. Early in training, weak policies make poor use of large interaction budgets, causing expensive rollouts with little reward improvement. Later, policy entropy can collapse before performance has saturated, prematurely ending useful learning. We introduce Long-MDR, a three-component training recipe designed specifically for this setting: On-Policy Distillation Warmup, Progressive Horizon Expansion, and Entropy-Triggered Rescue. Together, these techniques improve both the learning efficiency and stability of long-horizon RL, enabling continued gains in a regime where direct training is slow and costly. Code will be available at https://github.com/navileon/Long-MDR

DETR-style detectors use one-to-one bipartite matching during training to assign object queries to ground-truth objects, enabling end-to-end set prediction without non-maximum suppression (NMS). However, without an explicit de-duplication procedure, multiple queries can still produce highly similar hypotheses for the same object, making training unstable and predictions less decisive. Inspired by the sequential ordering of NMS, we propose DETRNN, a plug-and-play module that turns unordered object queries into a competition-aware sequence for recurrent refinement. DETRNN builds an explicit confidence-and-similarity based order from prior predictions, then refines queries with an RNN along this order to model competition inside the decoder. This ordered recurrent refinement reduces redundant predictions, stabilizes optimization, and improves final detection accuracy. Experiments on multiple DETR-style detectors show consistent gains with comparable efficiency. Code repository: https://github.com/nigelwoo2008-coder/DETRNN.

Generative large language models (LLMs) inherit undesirable behaviors from pre-training, including demographic bias and toxic generation, that often emerge only after deployment and affect a small subset of inputs. A repair should eliminate the identified defect, preserve the model's overall functionality and, ideally, provide correctness guarantees. Existing approaches address this only partially: gradient-based fine-tuning lacks per-instance guarantees and becomes unstable with few defect samples; model editing assumes explicit knowledge replacement rather than behavioral correction; and constraint-based repair is largely restricted to discriminative models with unique target outputs. We present FORGE, a framework for targeted behavioral repair of generative language models that separates defect localization, weight editing, and behavioral verification into independent stages. Its core is a repair abstraction that converts localized defective generation into explicit optimization objectives, enabling verification-oriented repair techniques to operate on autoregressive generation. FORGE is editing-mechanism agnostic: we instantiate it with (1) a constraint-based quadratic optimization method that provides per-sample repair certificates and (2) a null-space projection editor that minimizes interference with the original model distribution, both under the same localization and verification protocol. On five open-source LLMs, FORGE consistently achieves larger reductions in bias and toxicity than gradient-based fine-tuning with minor perplexity degradation. The two backends exhibit complementary performance across architectures, which a lightweight causal probe traces to where toxicity-related signals concentrate. FORGE also remains effective with only a handful of defective examples, where conventional fine-tuning often oscillates or fails to converge.

Surrogate modelling is important to enhance the computational efficiency of uncertainty quantification for physical processes involving random parameters. The advantage of Fourier neural operator (FNO) compared to conventional surrogates is its cross-resolution prediction capability. In the current study, a cross-resolution surrogate based on FNO is built for two-phase transient Darcy flows in porous media with random parameters. A multiresolution Sobolev learning method is proposed for FNO to enhance the cross-resolution prediction accuracy by incorporating first and second-order gradients in the loss function using training samples of different resolutions. The gradients are approximated by resolution-related finite difference schemes compatible with the grid for numerical simulation. Experimental results demonstrate the effectiveness of the new method in training FNO for building cross-resolution surrogates.

We revisit the Gentzen-style monadic translation of Gödel's System T. The translation is parametrized by a nucleus, a monad-like structure that need not satisfy the monad laws. A fundamental theorem of logical relations provides a uniform correctness argument for its instances. By choosing suitable nuclei, we obtain majorants, moduli of pointwise and uniform continuity, internal dialogue trees, and functionals of general bar recursion, all represented by terms of T. The internal dialogue-tree application gives a simpler construction, with correctness established directly using Church-encoded terms. We also extend the translation and its fundamental theorem to sums and finite lists. Finally, we develop the Kuroda-style translation and its continuity instance, comparing the moduli obtained with those of the Gentzen-style translation.

We prove that no single rank ordered adversary strategy is globally optimal for the prediction with expert advice problem with six or more experts, in both the geometric stopping and finite time horizon settings. The proof is based on establishing a leading order correction when one expert moves far ahead of the others. This allows us to connect optimal strategies between $n$ and $j<n$ experts and utilize recent results on the exact optimality set for the five expert problem.

GUI grounding is a critical capability for GUI agents powered by vision-language models, helping them execute user instructions by locating the corresponding elements in screenshots. Single-step grounding struggles with small elements and dense layouts, motivating multi-step visual search. However, existing approaches commonly rely on textual reasoning misaligned with visual space or costly multi-round interactions with external visual tools. To make multi-step visual search an explicit spatial process within the model, we propose ReLaViS, which performs Recurrent Latent Visual Search in a single interaction round. At each step, a spatial search head uses the hidden state to query the screenshot's visual tokens, producing a spatial search distribution that explicitly represents the search focus. This distribution then aggregates the visual tokens into latent visual evidence, which is recurrently fed back as the next input embedding to condition subsequent search. We further introduce a GUI-aware coarse-to-fine inductive bias through trajectories constructed from flat element annotations, supervising search from the global interface through intermediate element groups to the target. Built on Qwen2.5-VL-7B, ReLaViS improves ScreenSpot-Pro accuracy by 3.1 percentage points to 56.3% with only a 3.5% increase in inference FLOPs and outperforms the matched single-step baseline on all five benchmarks.

Infrared image super-resolution is currently led by Mamba-based networks with 26 to 37 million parameters, which are difficult to deploy on the airborne and handheld platforms where thermal imaging is most needed. This paper presents TIRMamba, a network with 896K to 910K parameters for single-channel thermal imagery. A Thermal Prior Highway computes gradient, local-contrast and spectral cues once at the input and, through one adapter per residual group, modulates a weight-tied bidirectional state-space trunk and gates its dual-scale detail branch; a tri-path reconstruction adds the learned residual to a bicubic radiometric baseline. Because the standard benchmark provides only 265 infrared training images and evaluates fusion products on full images, we train with a replay strategy: grayscale DIV2K pre-training followed by fine-tuning on 64-pixel patches drawn with equal probability from the infrared and natural corpora. At scale factor 4, TIRMamba matches the strongest protocol-trained methods on both official test sets with 29 to 40 times fewer parameters and 2.8 to 9.4 times lower latency; at scale factor 2 it gives the highest SSIM on both. A variant with prior-conditioned selectivity, TIRMamba-Rad, corrects a 3 dB raw-thermal failure of an intermediate size-invariant design and gives the best results at scale factor 4 on raw-thermal, unmanned-aerial-vehicle and independent-sensor test sets. Code and trained models will be released at https://github.com/julian135707/TIRMamba upon acceptance.

Learning dexterous manipulation benefits from human demonstration datasets that capture diverse and natural hand-object interactions. In particular, contact points and forces provide supervision on where and how strongly to interact, which cannot be fully captured by motion trajectories alone. However, methods for jointly capturing hand and object motion, contact points, and forces remain limited. Moreover, severe occlusion from hand-object interaction challenges accurate tracking of both hands and objects. To address these limitations, we present a Visual-Inertial-CONtact based hand-object tracking (VICON) framework. It holistically captures both hand and object motion along with contact information during manipulation, even under severe occlusion. First, we adopt a visual-inertial glove and an RGB-D camera for accurate hand tracking, and redesign the glove to incorporate contact sensing. Specifically, force-sensitive resistors (FSRs) are placed on the glove based on human grasp frequency to synchronously record contact states and calibrated normal forces. Second, without requiring pre-existing CAD models, we estimate object poses using RGB-D images and a mesh reconstructed from a monocular video. We propose factor-graph-based object trajectory estimation that fuses object-pose estimates weighted by visibility under hand-object occlusion, FSR measurements, and a hand-motion prior. Across 40 motion-capture sessions with five objects, VICON achieves a 2.5% failed-frame rate compared with 50.9-64.6% for the baselines, with median errors of 3.9 mm and 3.0 degrees under occlusion. Using VICON, we construct a dataset containing synchronized hand-object motion, contact points, and normal forces, and will publicly release an expanded dataset covering 10 object categories at https://github.com/VICON-dataset/dataset.

Effective adaptive instructional systems require robust measures of learner engagement that go beyond static user profiles. This study employs Multimodal Learning Analytics (MMLA) to investigate the relationship between self-reported instructional modality preferences and objective neurophysiological markers of engagement. Thirty-seven participants engaged with learning content delivered via varying modalities (visual, auditory, reading/writing, kinesthetic). We captured real-time neural activity using two EEG devices: the Emotiv EpocX (14 channels, 128 Hz) and OpenBCI (16 channels, 125 Hz). Preferences were assessed using the VARK questionnaire. Consistent with literature challenging the "meshing hypothesis," aligning instructional modality with stated preferences did not significantly predict performance gains. However, spectral analysis of EEG data revealed divergent engagement patterns: when content aligned with preferences, distinct neural activity patterns emerged in theta and alpha frequency bands-markers associated with attention and cognitive processing. These signals were used to train a binary logistic regression classifier, achieving a mean accuracy of 83.21% with OpenBCI and 56.27% with Emotiv EpocX. These findings suggest that while self-reported preferences may not dictate learning outcomes, they significantly influence neurophysiological engagement, offering a viable, non-invasive input for adaptive educational algorithms.

Large language model (LLM)-based multi-agent systems increasingly rely on memory to transform execution trajectories into reusable procedural knowledge. Yet repeated retrieval also makes memory errors persistent: memory pollution arises when outdated, weakly supported, or spuriously successful procedures become recurring components of future reasoning. Multi-agent execution introduces an additional structural risk. Scope collapse occurs when procedural knowledge escapes the coordination scope in which it was shown effective and is repeatedly reused at incompatible decision levels, allowing local errors to influence cascades of downstream decisions. Meanwhile, task-level failures provide ambiguous supervision because they rarely reveal which recalled knowledge was responsible. We introduce AECG, a framework for asymmetric experience consolidation and governance for multi-agent systems. AECG turns memory from static experience storage into a dynamic reliability-governance loop, preserving coordination scope and using multi-scale, confidence-aware reliability to detect degradation. It then combines degradation with downstream impact to prioritize high-risk knowledge under a bounded review budget, applies targeted interventions, and reactivates revised skills only after paired replay. Across three multi-agent frameworks and four benchmarks, AECG achieves the best score in 11 of 12 framework–benchmark settings and improves over the strongest competing memory method by as much as 10.23 percentage points; removing scope preservation reduces accuracy by up to 16.89 points. AECG thereby reframes multi-agent memory from passive accumulation into auditable reliability governance. Code is available at https://github.com/fenhg297/AECG

A kernel $k(x,y)$ is LSHable if there exists a locality sensitive hashing scheme $H$ such that $k(x,y)=\Pr_{h\sim H}[h(x)=h(y)]$ for all $x,y$. This notion plays a key role in efficient kernel methods in high dimensions. In this work, we show that the $p$-exponential kernel $k(x,y)=\exp(-\lVert x-y \rVert_p)$ is LSHable in bounded regions for all $1<p\leq2$. Previously, this was known only for $p=1$. Our new "mosaic LSH" scheme is based on a Poisson hyperplane process with hyperplanes sampled as $\ell_1$-biased $p$-stable vectors, for which we develop efficient sampling procedures. As applications, our results yield new and efficient density estimation methods based on LSHability for those $p$-exponential kernels.

We analyse a divergence form stochastic differential equation featuring a Leray-Lions flux function that satisfies standard Carathéodory, growth, monotonicity, and coercivity conditions. We consider two types of noise: multiplicative Lipschitz continuous noise and a transport noise. Our approach utilises the gradient discretisation method, a generic framework encompassing various numerical schemes such as conforming and nonconforming finite element methods, hybrid mimetic mixed methods, and hybrid high order methods. For both types of noise, we propose a stable generic scheme, prove that scheme solutions converge to a strong solution in the probabilistic sense. For the multiplicative Lipschitz continuous noise, we establish the rate of convergence.

Test-time compute has become a central way to improve code generation: systems sample multiple candidate programs and use verifier-visible evidence to select the final output. This paradigm implicitly assumes that the verifier provides a corrective signal independent from the generator. We challenge this assumption under misleading task premises. When the generator and verifier share a false premise, they become coupled through a mistaken belief: the generator produces premise-consistent shortcuts, while the verifier supplies evidence that fails to expose them. Consequently, the selector may choose a hidden-test-wrong candidate even when a hidden-test-correct program exists in the pool. We call this failure mode Verification Trap. Across three code-generation benchmarks and five code models, false premises consistently degrade first-sample correctness, reduce selector-chosen correctness after 64-sample test-time selection, and amplify recoverable mis-selection. Mechanistically, verifier-written tests inherit the premise-level blind spot, reshaping verifier-visible candidate space away from hidden-test correctness. These traces make Verification Trap predictable before hidden execution: a lightweight gold-free predictor using verifier-visible features reaches 0.846 AUROC. Our results identify decoupled evidence as a key mitigation axis: coupled scaling provides limited recovery, whereas premise-agnostic robustness auditors recover substantial oracle headroom.

For four finite discrete random variables, we prove that the negative of the Ingleton expression, divided by the joint entropy, is at most $19/124 \approx 0.15323$, improving the previously reported upper bound $3/19$ by $11/2356$. The proof uses a copy program with four copy steps and six auxiliary variables, certified by exact rational linear-programming certificates. We also show that two published information inequalities, due to Dougherty-Freiling-Zeger and Csirmaz, imply the bound $5/32$ by an explicit nonnegative combination with Shannon inequalities, and that $5/32$ is the exact optimum both of the union of the three published inequality catalogues considered here and of the full copy-lemma extensions of all 213 distinct copy programs occurring in them. The new program is not among these programs, and the bound $19/124$ remains optimal when all of them and all catalogue inequalities are added. Ancillary files provide the parsed catalogues, exact primal and dual certificates, exact extension certificates, and verifiers that use only the Python standard library.

Inspired by cognitive science, we present CREATIVEFLOW, an analogical generation framework that explicitly models analogical divergent thinking to mitigate creative homogenization in text-to-3D pipelines. Our method derives a series of meaningful yet relationally similar source-target asset pairs, each featuring distinct geometric configurations. Expert evaluations demonstrate that our framework substantially enhances creative novelty and visual fascination. This workflow and its resulting assets establish a foundational dataset and benchmark for future relation-aware 3D model training.

A safe action is not necessarily a viable one. A frozen vision-language-action (VLA) policy can favor a locally admissible move that leaves no policy-supported route to safe task completion. We call this the feasibility-likelihood gap: likelihood ranks the next move, while feasibility depends on the futures it leaves open. To bring those futures into the decision, we derive the exact next-block marginal of the history-conditioned policy-environment trajectory law restricted to safe task completion. The derivation reveals a candidate-dependent feasible-future mass: its support records whether safe completion remains possible under the frozen continuation process, while its magnitude measures how much weighted safe-completion mass remains. Since exact evaluation is impractical online, we develop a selective finite-candidate approximation and establish conditions for recovering the best retained viable candidate. Our alarm-triggered, training-free reranker VICS-G lowers mean cumulative safety cost by 1.9%-57.5% across six Safety-CHORES settings while remaining within 2.5 percentage points of policy sampling in success and 0.82 steps in mean episode length. Our approach offers a promising and practical path toward safer task completion, grounded in an exact policy-relative target yet requiring neither policy retraining nor online rollouts.