Papers

Time-dependent, three-dimensional (3D) oceanic multi-variables define coherent states of the evolving ocean to facilitate ocean diagnosis and advance ocean science to better inform environmental and hazard management. However, extracting quantitative evidence from these variables requires substantial and complex analytical effort. We introduce OceanMind, a multi-agent AI system that directly couples large language models (LLMs) with comprehensive time-dependent 3D ocean states for swift and effective diagnosis. OceanMind organizes the analytical process into four coordinated complexity stages: Query Routing, Skill-based Planning, Tool Execution, and Evidence-based Summary Generation. Specialized agents interpret user requests, construct and execute multi-step computational workflows, and synthesize quantitative evidence. To ensure reliable workflow construction, 63 reusable ocean-specific analysis skills serve as procedural manuals that guide the LLM agent in selecting data, conducting diagnostics, and applying analytical tools. With reflection and replanning mechanisms that use execution feedback to repair invalid plans, OceanMind ensures reliable analysis workflows across diverse needs. On a benchmark of 240 computational-workflow queries spanning the four stages, OceanMind outperformed general ReAct agents with the same registered tool pool, achieving relative improvements of 41.2% in effectiveness and 21.5% in efficiency. Beyond the benchmark, OceanMind reproduced published oceanic diagnostics, validated hypotheses, and supported environmental decision-making over global oceans. Overall, OceanMind advances LLMs by integrating them with time-dependent 3D ocean analysis, enabling scientific interpretation and enhancing formulation of environmental policies based on quantitative ocean evidence.

Flow matching models excel at generative modeling, and many downstream applications require their samples to satisfy prescribed constraints, such as observed measurements and physical laws. However, existing constrained samplers often face a trade-off: enforcing constraints can substantially displace samples from the pretrained data distribution. To address this trade-off, we introduce MintFlow, a training-free constrained sampling framework that formulates constraint enforcement as a minimal intervention on the pretrained flow trajectory. MintFlow seeks the minimal perturbation of an intermediate flow state such that its subsequent evolution under the pretrained flow field satisfies the target constraint. By minimally perturbing the flow state while keeping the pretrained flow field unchanged, MintFlow enforces the constraint while minimizing unnecessary deviation from the pretrained distribution. An adjoint formulation yields a closed-form expression for this perturbation, eliminating expensive iterative optimization. Furthermore, MintFlow adaptively selects the intervention time to balance the required perturbation magnitude with its amplification by the remaining flow. Across a range of tasks in generative vision and physical system modeling, MintFlow achieves competitive constraint satisfaction while preserving the pretrained generative distribution substantially better than state-of-the-art constrained methods.

Online feature stores decouple feature computation from model serving, materializing features from upstream event streams into a low-latency store that inference reads at request time. This decoupling introduces a freshness gap - the interval between an event occurring at the source and its effect becoming visible in the served feature vector - that is widely documented as a cause of training-serving skew but has no formal treatment as a bounded, cost-quantified quantity. We model the online feature store as a materialized view over an event stream and define a per-feature freshness budget: the difference between the decision window a feature is consumed within and the staleness the serving pipeline imposes on it. We prove two propositions - a per-feature staleness bound, and a closed-form threshold below which a feature can never be served within budget - and validate them in a seeded, reproducible discrete-event simulation and on a real Apache Kafka, Redis, and PostgreSQL pipeline. The predicted collapse threshold reproduces on real infrastructure, with the decision-error transition landing where the closed form predicts. Reconciling simulated and real drop rates surfaces a methodological result of independent interest: the dominant simulation-to-infrastructure gap is not latency but a sampling-phase artifact - a simulation whose request clock and recomputation cadence are phase-locked systematically under-observes staleness. Randomizing that phase reconciles simulation and infrastructure to within 0.018 mean absolute error in per-feature drop rate. Results are scoped to the studied workloads and configurations and are not claims about any specific production feature-store implementation.

We study online convex optimization with one unbiased stochastic subgradient per round and an unknown finite conditional $p$th noise moment, $1<p\le2$. For every fixed interval $I$ of length $n$ and comparator path with $\Lambda_I=1+P_I/D$, one learner achieves \[ E[Regret_I(u)]\le\min(GDn, C[GD\sqrt{n(\Lambda_I+\log^2(2T))} +\sigma Dn^{1/p}(\Lambda_I+\log^2(2T))^{(p-1)/p}]). \] The learner uses none of $G,\sigma,p,I,P_I$, and the constant is universal. Interval adaptation adds to comparator complexity, preserving the distinct mean-gradient and noise exponents. The analysis controls calibration in expectation and limits the cost of observation-scale changes. Its general theorem compares to distributions over predictably available experts with relative-entropy dependence on a nonuniform prior. A common prior favors long windows and long restart lengths. With the statistics supplied, the interval cost becomes $1+\log(T/n)$, including the optimal full-horizon static rate. A change-of-measure lower bound identifies the noise power of this logarithm for learners retaining a full-horizon optimal guarantee, under explicit conditions. Static comparisons and deterministic partitions follow from the same decisions.

Electricity price forecasting (EPF) supports scheduling, bidding, and risk management in electricity markets, yet existing benchmarks focus mainly on numerical inputs, leaving the forecasting value of forecast-time textual context insufficiently evaluated. We introduce TRACE, a reproducible benchmark of 7,300 zone–day instances pairing prices from five zones in a major U.S. market with official operational text available at the forecast cutoff. TRACE reconstructs official operational text at each cutoff, preventing post-cutoff information leakage. We evaluate TRACE for semantic alignment and forecasting value. Semantic assessments align with central movement and both tail risks in ground-truth prices, most consistently for upper-tail price risk. Forecasting value is reflected in a median 7.4% reduction in upper-tail pinball loss across time-series foundation models. A controlled cross-day text-mismatch ablation reverses the gains, falling below the no-text baseline.

Time series forecasting remains a critical challenge across numerous domains. Despite significant advancements, existing approaches struggle with complex phenomena such as regime shifts, cross-domain knowledge transfer, and multimodal data integration. This paper introduces Multi-Agent Collaborative Time Series Forecasting with Emergent Memory (MACTS-EM), a novel framework where specialised agents collaborate to achieve superior forecasting performance. The MACTS-EM architecture integrates: (1) domain-specialised forecasting agents for pattern recognition, anomaly detection, causal inference, and uncertainty quantification; (2) a meta-cognitive layer for dynamic agent allocation; (3) an emergent memory mechanism enabling cross-domain pattern transfer; (4) multimodal contextual integration; and (5) adversarial robustness components. Evaluation across financial markets, climate patterns, energy consumption, and pandemic propagation demonstrates that MACTS-EM outperforms existing approaches in most scenarios, with 8-12% improvement in forecasting accuracy, 22-27% better zero-shot transfer capability, 16-21% enhanced resilience during regime shifts, and 15-18% faster recovery after distribution shifts. Our findings suggest that collaborative, agentic approaches to time series forecasting represent a promising direction beyond traditional architectures, particularly for complex real-world scenarios requiring multi-resolution temporal understanding and contextual adaptation.

Interpretive Structural Modeling (ISM) is a well-known process for multi-criteria decision making. The success of ISM over other methodologies is its ability to model causal relationships, the binary scale of factors, and resulting hierarchical representation. Traditionally, the modeling process is performed by repeated interactions with subject matter experts until consensus is reached. This process is tedious, labor-intense, and most importantly limits the ability of ISM to scale to studies with hundreds of variables. Drawing on existing work of causal graph discovery with large language models (LLM) as imperfect experts, this work explores an integrated LLM-ISM approach for ISM. Pairwise, k-wise, rowwise, and full graph discovery methodologies are compared and evaluated. It is shown that causal graph discovery methods for ISM perform best using rowwise (SHD=160, F1-score=0.77) and full graph methods (SHD=135, F1-score=0.73).

The universal approximation property of dropout neural networks does not by itself describe the network size required for an accurate random realization. In this work, we study approximation of the unit ball of $W^{n,\infty}([0,1]^d)$ by ReLU networks whose edges are retained independently with probability $p$. The approximation error is measured uniformly over the input domain, and the guarantee holds with probability at least $1-\delta$ for a single sampled network. We construct networks of constant depth and size $\widetilde O_{n,d}(p^{-9}\varepsilon^{-\max\{d/n,2\}} \log(1/\delta))$. The construction combines bounded local subnetworks, localization on a successful approximation event, and a multiscale Taylor decomposition. Conversely, Sobolev capacity imposes a lower bound on the number of surviving edges, while approximation of a fixed affine function requires an output-layer cost of order $((1-p)/p)\varepsilon^{-2}\log(1/\delta)$ at sufficiently high confidence. For fixed $p\in(0,1)$ and $\delta<\min\{1/2,1-p\}$, the upper and lower bounds match in the accuracy exponent under a fixed or logarithmic depth budget. When $d\leq2n$, they also match in confidence up to logarithms of accuracy. We extend the lower bounds to $W^{n,r}$ targets with $L^s$ error, and distinguish this extension from the upper bound for $W^{n,\infty}$. The optimal retention dependence and logarithmic factors remain open.

Many scientific questions require reasoning about what was never observed: What if the conditions, interventions, or history had been different? Models can predict accurately on observed data yet fail on such what-if queries when correlated inputs are varied independently. A common remedy is to add controlled simulation data in which these factors are explicitly disentangled, but this requires access to a simulator, can be computationally expensive, and inherits the simulator's modeling assumptions. We introduce ReRoute, a framework for targeted scientific what-if prediction that combines factual data with partial mechanistic knowledge, without requiring controlled intervention data for adaptation. ReRoute fixes the queried input of a pretrained backbone to a reference value, reintroduces its variation through a known mechanistic pathway, and fine-tunes on the original factual data, while leaving downstream effects to the learned dynamics. We provide a causal identification result for this construction under explicit structural assumptions, with the core argument machine-checked in Lean. After showing that ReRoute achieves highly accurate counterfactual predictions in a controlled advection-diffusion system where exact responses are available, we turn to state-of-the-art climate emulation. On held-out coupled-climate interventions, ReRoute reduces aggregate climate error by 18.2-31.8% under severe CO$_2$ distribution shifts while preserving skill under standard conditions, at a small fraction of the cost of retraining on additional controlled simulations, without even accounting for the substantial expense of generating such data. Finally, on an emulator trained from historical ERA5 reanalysis, where no counterfactual reference exists, ReRoute preserves substantially more of the surface warming implied by the observed boundary conditions under a fixed-CO$_2$ counterfactual.

Speculative sampling accelerates diffusion generation by verifying inexpensive draft states in parallel while preserving the target law. Recent tree-based methods allocate the parallel compute budget more effectively than single-chain drafts, as demonstrated by Diffusion Greedy Rejection Sampling (D-GRS). D-GRS generates $K$ conditionally independent candidates per node, and sequentially tests them in their generation order. Yet the sampled candidates admit an informative ranking without additional target-model evaluations. To exploit this, we introduce Rank-Aware Speculative Sampling (RASS), a verification rule for speculative draft trees based on rank-aware list coupling. RASS orders draft candidates along the proposal-target mean displacement and samples a rank with weights optimized to minimize total variation between the selected-proposal and target laws. Finally, the selected candidate is maximally coupled with the target, with residual correction ensuring exact sampling for any choice of rank weights. We evaluate RASS on a Gaussian-mixture target, unconditional pixel-space generation on FFHQ, conditional generation on CIFAR-10, and latent diffusion with Stable Diffusion 3.5 using COCO2014 prompts. Measured by the ratio of standard to speculative sampling's target-model evaluation counts, RASS improves on D-GRS across the evaluated settings, with gains reaching approximately 20% on CIFAR-10 at matched compute budgets.

It has recently been shown that nearest-neighbour retrieval provides a strong baseline for molecular fingerprint prediction from MS/MS spectra, with several variants matching or outperforming current deep learning models (Khoo and Barzilay, 2026; Liu et al., 2026; Gupta et al., 2026). Importantly, "nearest neighbour" encompasses a family of retrieval methods that differ in the information assumed to be available at inference. In this report, we systematically compare several nearest-neighbour variants and show how these differing assumptions affect performance. Our goal is to establish stricter baselines that enable more rigorous benchmarking and better measure progress in this area.

Operational land surface forecasting systems built on Mamba-family Structured State Space Models absorb non-stationary confounding events (unrecorded irrigation booms, dam-operation shifts, sensor recalibrations) into their state-transition matrices, silently biasing NDVI, LST, and crop phenology predictions long after the physical cause ends. This paper introduces SSU-LSF (State-Space Unlearning for Land Surface Forecasting), the first machine-unlearning framework purpose-built for geoscientific Mamba-based SSMs. We develop EKFac influence functions specialized to the Mamba state matrices via a closed-form matrix-exponential gradient, use spectral-radius-weighted elbow thresholding to localize a temporal confounding footprint $\Phi$, and apply Hessian-free projected gradient ascent within a KL-divergence trust region augmented by spatial total-variation (TV) regularization. Proposition 1 establishes that residual confounding is bounded by $\mathcal{O}\big((1-\rho(\bar{A})^{T_c})/((1-\rho(\bar{A}))\mu)\big)$, which grows with the window length $T_c$. Across three heterogeneous benchmarks and eleven baselines, SSU-LSF achieves confounding reduction rates of $0.773$ (CropHarvest), $0.821$ (NDVI-LST), and $0.859$ (ERA5), with worst-case clean-domain RMSE degradation of $4.2\%$ on ERA5, converging in 3–5 epochs at $8.4\times$ lower GPU-cost per unlearning request than full retraining. Code: https://github.com/Anidipta/SSU-LSF

Artificial intelligence increasingly serves as a natural-language interface to complex technical systems, letting people accomplish sophisticated tasks by describing what they want rather than specifying how to do it. Extending this interface to living systems is harder: unlike code or images, a biological intervention has no closed-form linguistic meaning, and the paired language-intervention-outcome data needed to learn such a mapping is expensive to collect, since each example requires its own wet-lab experiment. One way around this is to treat an existing archive of interventions and their already-observed outcomes as a fixed, offline dataset, and use a vision-language model to judge, without any new experiments, whether an archived outcome matches a natural-language description. But whether that judgment is reliable enough to train a language-to-intervention mapping on – without new experiments and without human validation – has remained unclear. Here we show that a natural-language interface for a living organism – a xenobot, a synthetic multicellular construct with no nervous system – can be learned entirely offline this way, using a vision-language model's own judgment as the sole training reward: an instruction is mapped to the intervention already on record as producing the described behavior. This mapping generalizes to entirely new instructions, evaluated against archive data withheld from training (80.0% held-out accuracy vs a $66.7% chance baseline, matching a network trained directly on ground-truth labels).

Amortized simulation-based inference (SBI), which is trained on radiative-transfer simulators, recovers exoplanet atmospheres accurately on synthetic James Webb Space Telescope (JWST) spectra but collapses when it comes to real reduced spectra. The flow posterior collapsed on real WASP-39b (importance-sampling effective sample size (ESS) = 1, best-fit ḩi}2/N = 301), and such a failure is usually blamed on missing the forward-model physics, but ruling these levers out with nested sampling first (a temperature gradient, SO2 opacity, and a high-fidelity opacity set) leaves the fit unchanged, meaning the collapse is not from the simulator misspecification but instead from a missing latent, the planet radius. To fix this, we build MIRAGE, a radius-augmented flow-matching posterior calibrated against an independent nested-sampling reference with importance sampling and an optimal-transport map, which yields a physical and literature-consistent retrieval of real WASP-39b (with ḩi}2/N from 301 to 0.06). This same method transfers unchanged across two instruments and three real JWST targets, including one spectrum self-reduced end-to-end from raw Mikulski Archive for Space Telescopes(MAST) data. The lesson is cross-domain, as a latent the simulator encodes but the inference omits can masquerade as misspecification.

For quantum machine learning, the exact boundary between classical and quantum advantage is still poorly understood. Direct comparison between quantum neural networks (QNNs) and existing classical models, which encompass fundamentally different function classes, often fails to provide broader insight into the difference between the two. Inspired by the techniques of Neural Quantum States and Random Fourier Features, this work introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network architecture for efficiently learning coefficients over the same finite Fourier series support as quantum neural networks. Testing on a selection of tabular benchmark datasets, we find that NFS is an effective classifier architecture broadly competitive with established classical baselines, including a comparable Random Fourier Features model, and possessing comparable performance to data-reuploading QNNs; combined with additional analysis comparing the learned Fourier spectra of QNNs and NFS on synthetic data, these results establish NFS as a natural classical baseline for evaluating QNN performance.

Transformer-based large language models (LLMs) such as RoBERTa represent text using contextual word embeddings (CWEs), which alter the embeddings associated with each token based on surrounding context. We construct token-wise incremental trajectories by repeatedly recomputing a token's CWE as successive words are added to a sentence, yielding a representation of how contextualized embeddings evolve as the utterance unfolds. We evaluate this approach using garden-path sentences as a test case with characteristic features. Token-wise trajectories reproduce known features of garden-path processing, including disruption around the critical region, and reliably distinguish garden-path sentences from matched disambiguated controls. We introduce several metrics for quantifying representational displacement across contextual increments and show that trajectory information can be highly predictive of sentence type. We find that ambiguity-related information is recoverable not only from the sentence-level CLS representation but also from ordinary vocabulary tokens, suggesting that utterance-level information is distributed across multiple representational scales. In exploratory analyses, we find qualitatively similar trajectory structures in other ambiguity- and misdirection-related linguistic phenomena. Together, these results establish token-wise incremental trajectories as a promising framework for studying utterance-specific meaning construction using LLMs.

Large language models (LLMs) deployed through text-only APIs face model extraction risks, as adversaries can collect their responses to train surrogates that reproduce their capabilities. While prior work has developed diverse attacks and defenses, evaluations remain fragmented across access assumptions, model configurations, query budgets, and security objectives, limiting comparability across methods. To address this gap, we introduce a unified benchmark covering six extraction attacks, ten defenses, and two adaptive attacks that paraphrase or back-translate protected responses before surrogate training. The benchmark controls model configurations, query data, budgets, and held-out evaluation conditions within each comparison while preserving attack-specific querying and training procedures. We measure surrogate capability, fidelity to the victim, output quality using Rep-4, and query-budget sensitivity; defenses use their own security metrics paired with surrogate performance. For the adaptive attacks, we jointly measure provenance-detector scores and the capability and fidelity of surrogates trained on rewritten responses. The benchmark thus provides a reproducible basis for comparing extraction methods and their interactions with defenses under text-only access. Code and artifacts are available at https://github.com/sliu11-byte/MEA-Bench.

Agentic reinforcement learning (RL) trains a large language model (LLM) to act over long, multi-step interactions. However, a single localized error can cause task failure, while trajectory-level rewards provide limited guidance for assigning credit to individual decisions. To address this limitation, we introduce Segment-level Hindsight Advantage Reweighting for Policy Optimization (SHARPO), a credit-assignment mechanism that refines Group Relative Policy Optimization (GRPO) at the level of environment-facing segments. Inspired by the existing on-policy self-distillation (OPSD) method, SHARPO computes teacher-student log-probability gaps within each segment and uses the resulting signal to compute a bounded multiplier on the GRPO advantage. This multiplier is shared by all tokens within the segment, allowing credit to vary across different segments. With Qwen2.5-7B-Instruct, SHARPO outperforms existing baselines on the ALFWorld and WebShop benchmarks, including GRPO, SDAR, RLSD, and StepOPSD.

For every constant-width CNF, we show that linear degree in polynomial calculus (PC) implies exponential size in resolution over constant-degree polynomials, over the same prime field. Applications include exponential lower bounds for CNFs in $\operatorname{Res}(\operatorname{PC}_r/\mathbb{F}_p)$ and hence in $\operatorname{Res}(\oplus_p)$, separations between different moduli, improved lower bounds for $\operatorname{Res}(k)$ up to $k=\varepsilon\log n$, proof-search consequences, and an implication of super-polynomial $AC^0[p]$-Frege bounds from very strong PC degree lower bounds. The proof uses the common-multiplier idea isolated from Braun [arXiv:2609.23015] to construct a Razborov–Smolensky approximation that preserves inferences, without introducing extension variables. The approximation errors are measured by ranks of the multiplication maps induced by the error-witness polynomials, modulo bounded-degree PC consequences.

Text-to-music generation models are trained on massive music collections, creating a growing need for data attribution methods that can quantify the contribution of individual training samples. However, existing attribution methods are difficult to rigorously evaluate due to the lack of reliable ground truth, making it challenging to reliably assess their actual effectiveness. To address this gap, we introduce TrueMuse, a controlled dataset and benchmark for text-to-music data attribution. TrueMuse is constructed by fine-tuning three diffusion-based text-to-music models on carefully curated attribution samples, whose known inclusion in fine-tuning provides controlled attribution targets for evaluation. The benchmark covers four attribution settings, spanning melodic structure, timbral characteristics, artist-level stylistic signatures, and genre-level shared patterns, and includes 133 attributes, 648 fine-tuned models, and 95,456 generated samples across two prompt types. Using TrueMuse, we systematically evaluate existing black-box attribution methods along four dimensions: fine-tuning improvement, prompt-type difficulty, multi-task training, and fine-tuning data size. Our results show that attribution remains challenging, with existing methods exhibiting substantial variation across evaluation settings, highlighting the need for more reliable and generalizable attribution methods for text-to-music generation.

ARC-AGI-3 evaluates agents in interactive environments whose rules and objectives must be inferred from observation. We present Kepler, an open-source harness that represents hypotheses as executable world models and validates them through retrospective transition checks and conditional prediction checks. Under one frozen Claude Opus 5 configuration, Kepler obtained a server-verified 100.00 RHAE on all 25 public games, with no per-game model selection or score-conditioned reruns. On 181 of 183 completed levels, the final Opus attempt used no more actions than the corresponding median-human baseline. The retained board runs used 8,256 environment actions, of which 7,292 occurred in scored levels. Retained local provider-session records yield 858.0 million tokens, 97.37% cache reads, and a \$777.72 cost at September 1, 2026 API list-equivalent rates. We also report three evaluation failures: source-code leakage that produced an invalid perfect run, agents reconstructing a removed harness in a control condition, and autonomous repair masking a broken planner. A single-game observation case study showed that animation frames contained task-relevant information absent from settled text grids. Across the final Claude Opus 5 and GPT-5.6 Sol boards, 48 of 50 game-model cells reached 100. These results indicate that public-set score alone has limited discriminative value and motivate first-attempt, cost-conditioned, and verification-aware reporting.

Fluent LLM explanations may not follow the evidence from a structured system. We present VERITYGATE, a four-gate checker for declared evidence IDs, entities, numbers, and claim types. It checks a fixed schema; it does not verify every fact in the prose. At r=0 and r=1, we test 900 instances per setting (450 grounded-ungrounded pairs) with GPT-4o-mini, Llama-3.3-70B, and Claude Sonnet 4.6. Under this schema-level contract and before repair, 80.3% of mini claims and 47.9% of Sonnet claims fail. These are verifier rejection rates, not prose-hallucination rates. One repair pass raises claim survival from 19.7% to 28.0% for mini and from 52.1% to 54.3% for Sonnet. Verified claims per example change by +0.14 for mini, -0.71 for Llama, and -0.47 for Sonnet, so survival and output volume must be reported together. A second Sonnet pass gives no clear gain. At r=1, Gate 4 covers 97.0%, 98.7%, and 100% of failing claims for mini, Llama, and Sonnet. Small human studies support the rules but show gaps between schema checks and correct prose. A domain-specific GPT-4o judge test shows an order effect, so it is only a usefulness check. We release the code and data.

A typed decision is a choice among a fixed set of options, returned as a probability rather than as text. Systems that need typed decisions today use models trained for that purpose. This report describes AnyJev, which reads a typed decision from one prefill of a pretrained instruction-tuned language model. The readout restricts the next-token distribution at the answer position to the option tokens. It has two defects: the model assigns higher probability to some labels whatever the input, and to some positions in the option list. AnyJev corrects both with no gradient steps and no parameter changes: it divides out a label prior estimated from unlabelled inputs, and it averages log-probabilities over the K cyclic rotations of the option list. On two 20-option tasks the rotations lower the order-flip rate from 0.33 to 0.14 and from 0.33 to 0.18, and raise accuracy on 11 of 11 models on both. Reading every rotation requires K prefills. A stopping rule selected against the full-rotation decision on unlabelled states cuts that. Selecting the threshold on one unlabelled split and bounding its disagreement on a second, it reads 10.6 rotations of 18 at a verified 0.008 bound on two of four cells; selected and bounded on one split, as our serving run did, it reads 7.3 and serves 2.2 times as many decisions per second on vLLM. The code is open source.

This paper develops a new moment-matching order reduction method for multi-input quadratic-bilinear descriptor systems. The proposed approach accommodates multiple inputs acting on both the differential and algebraic equations and constructs separate projection spaces associated with different input channels and input combinations. The method uses a matrix-free algorithm, allowing the reduced-order matrices and tensors to be computed without explicitly assembling or storing the full-order system matrices and tensors. This feature makes the proposed method particularly suitable for large-scale computational fluid dynamics problems. Numerical experiments carried out for two-dimensional flow problems demonstrate that the resulting reduced-order models accurately reproduce the transient responses of the full-order models under multiple time-varying inputs.

Let $K_t$ be obtained by attaching a pendant path of length $t$ to a fixed rooted graph $K$. We prove that $\mathrm{Mo}(L(K_t))-\mathrm{Mo}(K_t)$, the difference between its line-graph and original Mostar indices, is exactly affine on each parity class beyond a sharp uniform cutoff. The slope depends on distance-level neighbor counts and is positive for every non-bipartite core. Triangle chains give infinitely many graphs with $\mathrm{Mo}(L(G))>\mathrm{Mo}(G)$ at every positive cyclomatic number $c$, with maximum degree three, resolving Alex-Indulal Problem 3.3. At zero slope, a cactus branch-mass formula decides equality; identical vertex profiles need not give identical intercepts. Fixed cores giving equality for all sufficiently long attachments exist exactly when $c$ is odd. Maximum degree three suffices, and at every even $c$ a binary-tree construction gives equality on one eventual parity class.

We prove a complexity classification of counting planar graph homomorphisms with non-negative weights. For a real symmetric matrix $M$ with nonnegative entries, the problem $\GH(M)$ is either (1) P-time computable over all graphs, or (2) \#P-hard in general but P-time computable over planar graphs, or (3) \#P-hard over planar graphs. Furthermore, $\GH(M)$ in (2) consists of precisely those that involve the P-time FKT algorithm to count planar perfect matchings with a holographic transformation. The dichotomy for entrywise positive and full rank matrices lies at the core of the proof. In this setting, the main tool is a matrix algebra ${A}$ (a vector space with bilinear multiplication) formed by taking the real span of (centered) entrywise logarithms of all realizable matrices from $M$ using planar edge gadgets and polynomial interpolation. We then define a multiplicative homomorphism $F(\cdot)$ on the algebra ${A}$, which turns out to be a polynomial map. The exponents of prime factorization of component polynomials of $F$ induce graph distances for distance-regular graphs. These graphs are either the Hamming graphs or Doob graphs using a classification result for distance-regular graphs (if $\PlGH(M)$ is not \#P-hard), after obtaining their intersection numbers. The dichotomy is proved in either case. We then extend the complexity classification to all nonnegative matrices.

Large language models carry an internal notion of uncertainty in their sampling distribution, i.e., the probabilities they place on generating one answer rather than another. They can also be asked to state a confidence, in words or as a number: a verbalized uncertainty. Prior work suggests that internal probabilities track relative frequencies in the training data, and that verbalized probabilities track explicit probabilistic assertions in the training data. However, we do not know whether these two readouts are aligned, except when frequencies and probabilistic assertions in the training data happen to align. This limits our understanding of when we can use verbalized uncertainties as a proxy for either training data frequencies, or a model's internal distribution. We resolve this gap by systematically exploring how LLMs probability readouts are impacted by training and in-context data, via intervening on the underlying uncertainty sources in the data. We find that both internal and verbalized probability readouts are impacted by both distributional and asserted uncertainty in the training data. Further, we find that verbalized and internal probabilities are aligned beyond what would be expected by independently tracking the same uncertainty sources, suggesting that verbalized probabilities can be used to probe a model's internal distribution.

Dubbing quality control requires a reference-free judge that can determine whether a candidate text line matches a speaker's visible articulation in both content and timing, using only silent video and text because dubbed audio may not yet exist. Existing visual speech recognizers and video-language models are poorly suited to this setting: even when fine-tuned to recover spoken content from lip motion, they remain largely insensitive to temporal errors. We introduce $\textit{Align Then Reason}$ (ATR), a multilingual lip-sync judge that first establishes a monotonic alignment between frame-level lip representations and the phonetic units of the candidate line, then reasons over this alignment to make the final judgment. An alignment scorer provides the LLM with both local evidence for each phonetic unit and a calibrated global alignment score, enabling it to reason jointly about content and timing. On a seven-language benchmark, our method improves mean AUC over the corresponding Qwen3.5 SFT baselines by 59.4%, 50.2%, and 50.8% with 2B, 4B, and 9B reasoners, respectively. The gains generalize across LLM families, reaching mean AUC improvements of 45.9% and 46.6% over the best baseline for LLaMA-3.1-8B and Mistral-7B, respectively. They also transfer across datasets to three unseen MuAViC languages. Furthermore, we evaluate on two downstream tasks built from real dubbing lines. On dub-line reranking, ATR-9B outperforms the best lip-reading baseline by 52.0%, while on script-to-clip assignment, ATR-9B improves over the best lip-reading baseline by 17.7%.

We present a planning and control approach to reactively use hand contacts to stabilize a humanoid in low stability scenarios, where only using feet contacts may result in a fall. Candidate contacts are sampled within the robot's reachable workspace, and a preview is computed by rolling out the centroidal dynamics through pre-impact, impact and post-impact phases. Sampled points are scored based on the Center of Pressure (CoP) control authority at the post-impact phase. Central to our approach is a learned model of the robot's CoP region during post-impact, which enables rapid evaluation of candidate contact points compared to traditional optimization-based methods. The presented planner has two stages: the first selects an optimal bracing region and the second computes an optimal bracing point within the region. Our simulation results demonstrate an average increase in impulse resilience of 89% over recovery without hand contacts and 17% over a naive planning strategy (closest reachable region). We validate our framework on hardware, performing push tests while standing and walking. The standing trials show an average 43% reduction in stabilization time compared to naive hand placement and the walking trials demonstrate a 18% reduction compared to baseline recovery (without hand contacts).

Share the light, not the map. We study next-best-view selection for a team of robots, each of which builds its own 3D Gaussian Splatting map and keeps it private. A robot picks the view with the largest expected information gain (EIG) about the splats along its own path. This gain depends on the other maps. Their splats occlude its own and shine behind them, so the gain has to be evaluated against the pooled map. No robot has this map. We show that the coupling passes through only two ray quantities, the transmittance in front of a splat and the radiance behind it, and that both are sums over the hits of the ray. Hence, they decompose across the robots, and each robot sums them over depth bins in its own map, along the rays of a candidate view, and sends the sums with their pose derivatives. The robot planning the view turns them into its EIG and gradient on SO(3). Transmittance and Radiance Aggregates, communicated for the EIG, give the protocol its name: TRACE. No robot shares its splats, and the message size does not grow with a map. We prove that the reconstruction is exact unless a depth bin behind a splat mixes hits of two robots, and we bound the error otherwise. Over 100 next-best-view decisions in Habitat-Sim, TRACE picks a heading within 15 degrees of the centralized one in 83.3% of the cases, and its views reach 97.9% of the centralized EIG.