Vector-field-based methods are widely used for robot control and are often applied to the path-tracking problem. Some vector field approaches require repeatedly computing the distance between the robot configuration and the curve, as well as the corresponding closest point. Recently, vector fields have been extended to Lie Groups. In this case, this computation can be expensive, especially when performed at high control frequencies on embedded platforms. This paper proposes a method for efficiently computing the distance between a point and a curve represented as what is called a G-polynomial curve, which is a curve representation that generalizes polynomial curves to matrix Lie groups. The proposed approach exploits the structure of these curves to reduce the problem to a small number of polynomial root-finding computations. Simulation results show that the method significantly reduces computation time while maintaining accuracy compared to existing optimization-based approaches. Practical formulas are also provided for the case of the group SE(3), and the method is validated experimentally on a robotic manipulator. The methodology is implemented in a computational package, available online.

Reduced-order modeling of high-dimensional dynamical systems is often hindered by the non-Markovian closure term that represents the effect of unresolved variables on the resolved dynamics. Inspired by the Mori--Zwanzig formalism, in which the closure takes the form of a memory functional of the resolved trajectory, we recast closure modeling as a sequence modeling problem and propose the Mamba-Assisted Closure (MAC) framework: a Mamba-based sequence model, trained to predict the closure from the resolved trajectory, is coupled with the reduced-order governing equations through a numerical integrator to advance the resolved variables in time. A key feature of the framework is its exploitation of the dual representation of state-space models -- the model is trained in a sequence-to-sequence fashion via the convolutional form, and deployed for step-by-step autoregressive rollout via the recurrent form, yielding both efficient long-trajectory training and constant per-step inference cost. On the viscous Burgers' equation and the chaotic two-scale Lorenz '96 system, the MAC model substantially outperforms the Markovian reduced-order model, the GRU-based sequence model, and the Wilks method in predictive accuracy and long-time rollout stability.

We investigate whether task-vector arithmetic, successful for cross-speaker emotional intensity control in modular text-to-speech (TTS), transfers to large-scale TTS systems built on language-model backbones with in-context learning (LM-TTS). Through a systematic elimination study over four progressively narrower operands on Qwen3-TTS-12Hz-1.7B - model weights via LoRA fine-tuning, continuous codec embeddings, discrete codec tokens, and the speaker embedding (x-vector) produced by an ECAPA-TDNN encoder jointly trained with the synthesis backbone - we localize the dominant carrier of emotional prosody to the x-vector. Building on this finding, we propose a training-free method based on centroid arithmetic in x-vector space: an emotion direction $τ= \mathbb{E}_i[x(s_i,\text{emo})] -\mathbb{E}_i[x(s_i,\text{neutral})]$ applied to an unseen target speaker as $x_{\text{new}} = x(\text{target},\text{neutral}) + α\cdotτ$. Using ESD (English) as the $τ$ source and emoUERJ (Brazilian Portuguese) as a cross-lingual ground-truth target, we observe average gains of $+0.29$ in emotion2vec cosine over the ICL baseline on English held-out speakers and $+0.09$ on Brazilian Portuguese held-out speakers, while largely preserving identity (WavLM SECS $\gtrsim 0.88$ for the multi-speaker $τ$ variant) and intelligibility (WER $\approx 0$ in PT-BR). These results offer initial evidence that the reported incompatibility of centroid-arithmetic style control with token-based TTS architectures may be circumvented when the arithmetic operates on the speaker embedding.

In this paper, we propose RePHO, a method to reconstruct physically plausible human-object interactions (HOI) from monocular videos. While existing kinematic-based approaches produce visually plausible motion, they often result in physically implausible artifacts such as interpenetration and object floating. To overcome these issues, we introduce a physics-guided reconstruction framework. We begin with a kinematic estimate and then refine it by training a policy with reinforcement learning (RL). This policy is optimized to reproduce the interaction in a physics simulator. Because kinematic estimates are typically noisy, naive RL training can fail. Therefore, we propose an adaptive sampling strategy with a dual self-updating mechanism that can identify the frames with the most informative and reliable kinematic reconstruction. Our process progressively improves reconstruction quality and yields physically consistent HOI sequences. We demonstrate our approach on two standard HOI benchmarks and achieve clear improvements in physical plausibility metrics over state-of-the-art methods. Project Page: https://dingbang777.github.io/RePHO/

Purpose: To develop an interpretable and trustworthy AI framework that combines deep learning based MRI Osteoarthritis Knee Score (MOAKS) prediction with interpretable statistical modeling to study structure-pain relationships at scale using data from the Osteoarthritis Initiative (OAI). Materials and Methods: We first developed a deep learning framework to predict MOAKS features directly from knee MRIs and incorporated conformal prediction to provide prediction uncertainty quantification. This uncertainty-aware strategy enables explicit filtering of model outputs, retaining only high-confidence MOAKS predictions at the knee level. Second, we applied a longitudinal latent class mixed model (LCMM) to examine associations between key structural abnormalities and four complementary knee pain measurements. Results: Among the three MRI-defined abnormalities (i.e., bone marrow lesions (BML), cartilage loss (CART), and meniscal extrusion (ME)), our framework substantially improved the Matthews correlation coefficient (MCC) and some other metrics. For example, MCC increased from 0.69 to 0.91 for BML, from 0.45 to 0.80 for CART, and from 0.59 to 0.89 for ME. Using these high-confidence predictions, we expanded the sample size to 2,175 knees for the LCMM analysis. Two distinct pain trajectories were identified (rapid and stable pain progression). The estimated odds ratios (95% CI) for the rapid progression group were 1.62 (1.12-2.35) for BML, 1.83 (1.24-2.70) for CART loss, and 2.50 (1.75-3.57) for ME. Conclusion: These results highlight the importance of these structural abnormalities as risk factors for pain and functional progression in osteoarthritis.

Retinal blood vessel segmentation plays a vital role in the early detection of diabetic retinopathy and glaucoma. While recent deep learning models have achieved great segmentation accuracy, they typically require heavy computational resources, making real-world deployment on edge devices difficult. In this paper, we propose LightVesselNet, an efficient neural network designed for retinal vessel segmentation in a resource-constrained environment. Despite containing only 75K parameters, LightVesselNet performs competitively with much larger models. The network employs a compact encoder decoder architecture enhanced with channel and spatial attention mechanisms, a multi-scale feature aggregation module at the bottleneck, and a subpixel upsampling strategy in the decoder. A dedicated edge residual connection preserves fine vessel detail throughout decoding. Extensive experiments on five publicly available datasets: DRIVE, STARE, CHASEDB1, FIVES, and HRF, yield sensitivity scores of 0.8189, 0.8499, 0.8640, 0.8634, 0.8096, and Dice coefficients of 0.8070, 0.8072, 0.8181, 0.8649, and 0.7686, respectively. LightVesselNet shows improved efficiency (Performance vs Parameter or GFlops) compared to State-of-the-Art models. Cross-dataset evaluation confirms the model's generalisation capability. Overall, LightVesselNet is a strong candidate for deployment in low-resource clinical settings and mobile screening tools.

Every new clinical imaging device creates a domain shift where dense gland masks are expensive yet cheap clinical signals -- eyelid outlines, Pult grades, morphometric ratios -- are routinely recorded. We present TopoPult-SSL, a two-stage framework for cross-device meibomian gland segmentation. Stage 1 adapts a source-trained model without target gland masks in the training loss, using four weak-prior anchors driven by target eyelid masks and clinical metadata only. Stage 2, when target gland masks are available, distils complementary Stage-1 teachers into a single compact student via supervised self-distillation. We develop and validate the technique on the public MGD-1k to CAMG research benchmark (1,000 to 100 images, different device), where the distilled model achieves Dice 0.716+/-0.006 (best 0.726), surpassing UA-MT (0.710) and the ensemble teacher (0.720) -- with a single pass. The gland-mask-free Stage-1 variant reaches Precision 0.694 vs. 0.30-0.34 for SAM/MedSAM (p<0.001), enabling deployment without dense gland contouring. Code and reproducibility scripts are released.

Human language comprehension unfolds sequentially: each word is processed in the context of those that came before, and the interpretation builds incrementally over time. Surprisal, the negative log probability of a word given its context, has been the dominant predictor of incremental processing cost. But surprisal reduces rich sequential representations to a single scalar at each word, discarding information about the direction in which the interpretation has been evolving. Dynamical-systems approaches suggest that the trajectory of the evolving interpretive state, not just its position at each moment,should shape processing, and language itself may have local momentum, since speakers plan utterances a few words at a time. We introduce trajectory extrapolation error: at each word, we fit a linear trajectory to the preceding hidden states of a transformer language model and measure deviation from the extrapolated path. On the Natural Stories corpus, this measure is nearly orthogonal to surprisal (r = .044) and independently predicts self-paced reading times. The effect is especially pronounced in garden-path sentences, strengthens with model scale (GPT-2 Small to Large), and replicates across architectures with different positional encoding schemes (GPT-2 vs. Pythia/RoPE). A displacement control shows the effect is not reducible to representational change magnitude: displacement and extrapolation error predict in opposite directions. These findings reveal two dissociable components of processing cost: word-level prediction error (surprisal) and sensitivity to the local momentum of the unfolding interpretation (trajectory extrapolation error).

We unify RoPE's Fourier phase, Jordan-RoPE's finite jets, and ALiBi's affine recency into a single learnable relative-position space, and study which regions of this space are selected by different tasks. PJ-RoPE is a Fourier-Jet-Affine formulation for relative attention, with an optional Poincare-type reading as the affine completion of a homogeneous Fourier-jet positional representation. Algebraically, the same primitives form a finite constant-coefficient difference module: simple roots of the lag-shift operator give Fourier/RoPE characters, repeated nonzero roots give Jordan/Fourier jets, and the repeated unit root gives ALiBi-like affine recency. The framework separates scalar PJ-bias kernels from exact PJ-rotary feature transforms, introduces adaptive sector diagnostics, and uses LC/rapidity coordinates to stabilize high-order jets. Controlled probes verify sector containment and selection; small language runs expose an affine/recency boundary; music-token streams provide the clearest case where LC/affine variants remain strong while carrying measurable high-order corrections; and LC diagnostics show a scale-stability gain coupled to phase-resolution loss.

Personalizing large language models (LLMs) has become a central challenge as LLMs are deployed across recommendation, search, dialogue, and content generation -- settings where the same query should yield different answers given different users. A promising route is to summarize each user's interaction history into a natural-language memory or profile and prepend it to the prompt to facilitate personalization. Existing methods learn such profile generators with explicit rewards derived from labeled downstream tasks, which are expensive and sparse as they require annotated supervision for every target task. In light of this challenge, we introduce Bidirectional User Modeling via Profiles (BUMP), a self-supervised framework that trains a profile generator without any downstream labels. Specifically, given a user's interaction history, we use GRPO to train an LLM to emit a free-form textual profile under a bidirectional in-batch ranking objective: a small LLM judge measures (i) how well the generated profile, used as a query, ranks the user's own held-out interactions above interactions from other users in the batch, and (ii) how well a held-out interaction, used as a query, ranks the user's own profile above profiles of other users. Both directions are scored with multi-positive NDCG and combined into a dense reward per rollout; other users in the batch supply free negatives, so every training example yields supervision from raw interaction logs alone. Evaluated on the LaMP benchmark, BUMP matches or outperforms closed-source APIs and prior methods relying on labeled rewards, while requiring no task label at training.

Theoretical studies of machine learning models commonly consider different limiting regimes in which the learning dynamics of gradient descent becomes theoretically tractable. It is, however, desirable to have a systematically obtained picture of all qualitatively different extreme learning regimes for a particular type of models. In this paper we propose such a picture for large weight-tied linear autoencoders characterized by input and latent dimensions, initialization magnitude, and training set size. This model is nonlinear in the weights and its gradient flow does not have a general theoretical solution. We show that at the level of the formal loss-expansion hierarchy, its extreme regimes are naturally associated with faces of a triangular prism. In particular, there are five basic extreme regimes associated with the 2-faces of the prism: (1) large-data, (2) small-data, (3) mean-field, (4) narrow-latent, and (5) free. For regimes (1,2,3,4), we derive explicit expressions for both train and population limiting loss evolutions under gradient flow, obtaining very good agreement with experimental results.

Returned products in circular factories re-enter production with heterogeneous degradation states, usage histories, and remaining capability. Reuse cannot be decided from the current inspection alone, because future function fulfillment and component integrity may evolve differently under the next service scenario. Existing PHM approaches support degradation prediction, but often target fixed operating conditions or isolated component benchmarks, while material-fatigue assessment is rarely linked to system-level functional prognosis. This paper addresses this gap for an angle grinder by combining uncertainty-aware functional prediction with component-level fatigue assessment in an instance-specific reliability workflow. The proposed framework combines the current tool state with recent force--torque usage windows. A convolutional encoder extracts loading patterns from spindle forces and shaft torque, and an LSTM backbone predicts nine functional variables as Gaussian mean and variance estimates. In parallel, the same loading history is translated into output-shaft fatigue information through finite-element-supported stress reconstruction, S--N/Miner damage evaluation with Haibach extension, and Paris-law crack-growth analysis. A streaming replay algorithm consolidates both branches into functional, material, and system reliability trajectories. Held-out tests show mean \(2\%\)-tolerance accuracy of 0.9652 across nine outputs. Thermal variables are predicted near-perfectly, while drive motor current and load speed remain the most demanding dynamic outputs, with \(R^2\) values of 0.9750 and 0.9924. Torque history is especially important for these variables, and the conventional LSTM outperforms GRU and xLSTM in the short-history setting. Reliability calibration is most informative for drive motor current, where predicted and observed exceedance probabilities ...

Patch-based Time Series Foundation Models (TSFMs) suffer from context poisoning: structurally anomalous patches capture disproportionate attention and silently degrade zero-shot forecast quality. We propose improving TSFM accuracy at inference time by optimizing the input context rather than modifying model weights. We present GITCO (Gated Inference-Time Context Optimization), a lightweight three-component framework: Gate, Router, and Critic that selectively identifies and suppresses harmful patches without any parameter updates. Evaluated on TimesFM 2.5 across 53 GIFT-Eval datasets under K-fold cross-validation, GITCO achieves an average +1.95% MASE reduction on TimesFM 2.5 while capturing 89.9% of the improvement upper bound. We introduce context sensitivity profiles as a new characterizable property of TSFMs: the mapping from time series meta-features to expected accuracy improvement under inference-time context intervention, shaped jointly by model architecture and the statistical structure of the data.

Large language models can shift human beliefs across high-stakes domains, but most persuasion studies rely on pre/post belief change. These endpoint measures identify whether persuasion occurred, yet miss where and how beliefs moved within a dialogue. We present PERSUASIONTRACE, a framework for studying persuasion in human-LLM interaction. Built on a web-based experimental platform, PERSUASIONTRACE contributes a tool for multi-turn persuasion studies and a process-level evaluation protocol: it records multi-turn belief reports from human or simulated targets of persuasion, annotates persuader turns with rhetorical dimensions (logos/pathos/ethos), and evaluates simulators by fidelity to real human belief dynamics. Using this framework, we find that human targets group into two clusters of multi-turn belief updates and exhibit susceptibility to rhetorical strategies, and that LLMs are persuasive across generic and personalized topics, text and audio modalities, and multi-turn interactions. Prior work has chiefly used vanilla-prompted LLMs to simulate human targets, but we show that these simulators fail to replicate human belief dynamics. We introduce a Bayesian-network simulated target that maintains an explicit latent belief state over time so each persuader message yields cognitively realistic belief updates. In human-likeness evaluation, our Bayesian target scores near a human reference (81 vs 80), while baseline LLM targets score substantially lower (64). PERSUASIONTRACE reframes persuasion evaluation from endpoint movement alone to process fidelity, providing a stronger basis for scientific analysis and safer optimization of persuasive systems.

Flow matching (FM) has emerged as a powerful framework for learning dynamic transport maps between two empirical distributions. However, less explored is the setting with intermediate observed marginals that can help constrain the flows between the endpoints. This "multimarginal" regime is central to modeling temporal evolution in dynamical systems in many scientific domains that can sample sequential distributions. We tackle this problem with a novel approach that leverages the connection between FM and dynamic optimal transport (OT), softly steering the flow towards the intermediate marginals through potential terms in the dynamic OT action. By extending the conditional FM learning target to incorporate these potentials, we derive an efficient, simulation-free algorithm for multimarginal FM that offers considerable flexibility in the spatiotemporal dynamics of the learned flows. We demonstrate state-of-the-art performance and training efficiency of OT-potential FM (OTP-FM) on diverse single-cell RNA sequencing, oceanographic, and meteorological datasets. Our code is available at https://github.com/Bexorg-Inc/OTP-FM.

Multimodal memes are dynamic and often require up to date background knowledge for interpretation. Existing methods often overlook such knowledge or rely on fixed parametric knowledge of pretrained models that may be incomplete, outdated, or unavailable for emerging memes. We introduce Query Retrieve Conclude, a zero shot framework that identifies missing knowledge, retrieves open web evidence, and synthesizes evidence grounded background knowledge for meme understanding and detection. We also introduce a curated meme understanding benchmark of recent memes from 2024 to 2026 with external background knowledge annotations. Experiments on three meme understanding datasets and five meme detection tasks show that our framework improves knowledge recovery, meme understanding and downstream detection over zero shot baselines.

Implicit chain-of-thought (iCoT) methods aim to internalize reasoning in large language models, but often underperform explicit CoT prompting. We empirically find that hidden-state reasoning trajectories exhibit low-rank structure. Motivated by this observation, we propose a low-rank distillation framework that transfers reasoning by aligning teacher and student trajectories in a shared low-rank tensor subspace using first- and second-order statistics. The resulting formulation captures the global structure of reasoning while supporting a compact latent reasoning process. We evaluate the method across multiple model families, including LLaMA and Qwen, at different scales on mathematical reasoning benchmarks. Our approach consistently improves performance, especially on challenging multi-step tasks, approaching explicit CoT accuracy and outperforming prior iCoT distillation methods.

With PRECISE, we extended Prediction-Powered Inference to produce bias-corrected estimates of ranking evaluation metrics by combining a small human-labeled set with a large LLM-judged set. PPI is provably unbiased regardless of the LLM judge's error profile. We make it applicable to hierarchical metrics like Precision@K, where annotations are per-document but the metric is per-query, by reducing the output-space computation from O(2^|C|) to O(2^K). On the ESCI benchmark, augmenting 30 human annotations with Claude 3 Sonnet judgments reduces the standard error of Precision@4 estimates from 4.45 to 3.50 (a 21% relative reduction). In a production system, our framework correctly identified the best of three system variants from 100 human labels and 2 hours of domain-expert annotation; A/B testing confirmed this ranking with +407 bps in daily sales.

Multi-agent systems (MAS) built on large language models are typically organized around roles, pipelines, and turn schedules, while the content that agents pass to one another is often left as unconstrained natural language. However, this free-form communication can rapidly inflate token usage, consume the shared context window, and ultimately affect both system performance and inference cost. We analyze five common inter-agent communication strategies across two MAS topologies, finding that no fixed strategy is universally optimal. Instead, effective inter-agent messages consistently preserve action-centered information needed by downstream agents. Building on this, we propose the PACT (Protocolized Action-state Communication and Transmission), which treats inter-agent communication as a public state-update problem and projects each raw agent output into a compact action-state record before it enters shared history. Across different MAS topologies, PACT consistently improves the performance-cost trade-off, achieving comparable or stronger task performance with substantially fewer tokens. The gains extend to production coding harnesses: PACT lifts OpenHands' resolve rate at -10% tokens-per-resolved, and is resolve-neutral on SWE-agent while halving input tokens. Our code is publicly available at https://github.com/iNLP-Lab/PACT.

LLM agents operate in two distinct regimes: open-weight agents amenable to reinforcement learning (RL) and black-box agents whose behaviour must be controlled purely at test time. Although black-box agents are often backed by state-of-the-art proprietary LLMs, API-only access precludes parameter-level optimization, rendering most RL methods inapplicable. To address this limitation, we turn to a known equivalence between RL and Bayesian inference. We propose Agentic Monte Carlo (AMC) to directly sample from the optimal policy of a black-box agent rather than training it through RL. The optimal policy is a posterior over trajectories whose prior we define as the fixed black-box LLM agent. We employ Sequential Monte Carlo to sample from this posterior by learning a value function to steer the agent while leaving the underlying black-box model unchanged. We validate AMC on three diverse environments from the AgentGym benchmark, demonstrating significant improvements over prompting baselines and even outperforming Group Relative Policy Optimization (GRPO) as we scale the test-time compute of our method. AMC demonstrates the feasibility of performing principled RL-style optimization of black-box LLM agents. Code is available at https://github.com/layer6ai-labs/Agentic-Monte-Carlo

Recent progress in generative modeling has made safety control a central challenge, yet existing approaches remain largely model-specific, requiring retraining or tailored interventions for each new architecture. In this work, we ask whether safety can be represented as a portable latent direction, learned once and reused across heterogeneous generators. We introduce the first framework for cross-model safety steering, in which a safety direction is estimated in a source LLM from paired safe-unsafe prompts, transported to a target generator through a lightweight alignment fitted on benign data alone, and applied at inference time. Crucially, our pipeline never accesses unsafe data on the target side, isolating whether safety can be transferred through shared representation geometry. Beyond a single global direction, we also identify a multi-vector extension that captures category-specific safety behaviors, enabling more selective control. We evaluate our approach in text-to-image and text-to-video generation across diverse source-target model pairs. Across models, transferred safety directions achieve ASR reduction and CLIP-Score/FID trade-offs comparable to directions learned natively on the target model using unsafe data, while requiring no target-side unsafe data. This indicates that safety improvements do not come at the expense of generation quality. Our results point to a modular view of safety: safety-relevant behavior is not purely model-local, but can be controlled through latent directions that persist across models. This suggests a new path toward lightweight, reusable safety mechanisms that do not require target-side unsafe data.

We study the personal camera roll visual question answering setting. In this setting, a conversational AI assistant can access a user's personal camera roll and retrieve relevant photos to answer queries, ranging from simple factual questions (e.g., ``Name of the food I tried yesterday?'') to more open-ended ones (e.g., ``Recommend some dishes I have never eaten before''). Given the vast nature of the personal camera roll (i.e., multiple years, hundreds to thousands of photos), a successful AI assistant needs to understand a long-horizon, highly personalized visual content stream in order to navigate and locate the correct and/or relevant information. To support this, we collect and manually annotate questions that mimic real-world usage. The final dataset, camroll, contains 50 users, 31,476 images, and 2,500 QA pairs. We further design camroll-agent, a conversational AI agent equipped with hierarchical memory and a minimal set of tools for efficient navigation over large, personalized visual memory. Experimental results show that camroll-agent outperforms numerous baselines and methods for long-context understanding AI agents system. Together, the camroll dataset and camroll-agent highlight the gap in AI agents' long-context reasoning: personalized visual memory requires different approaches from standard long-context textual memory, especially when consistency, visual details, and user-specific context are present.

Electro-Hydrostatic Actuators (EHAs) are widely used in aerospace and industrial systems, where timely detection of sensor anomalies is essential to ensure safe and reliable operation. However, the large volume and high sampling frequency of EHA sensor data pose challenges for accurate and efficient anomaly detection. Conventional statistical and classical machine-learning methods such as Z-score, Interquartile Range (IQR), Median Absolute Deviation (MAD), Isolation Forest, Gaussian Mixture, and k-means often fail to capture the temporal dependencies inherent in EHA signals, resulting in limited detection accuracy and elevated false-alarm rates. Furthermore, systematic evaluations of data-driven anomaly detection approaches for EHA systems remain scarce, particularly under varying operational conditions. This study presents an offline anomaly-detection framework for univariate EHA sensor signals, focusing on temperature and pressure data collected from a controlled test bench. The method employs a reconstruction-based Long Short-Term Memory (LSTM) autoencoder, calibrated and evaluated using validation-set reconstruction-error distributions. Performance is assessed across multiple fault-injection scenarios using accuracy, precision, recall, and F1-score, complemented by sensitivity analyses under varying operating conditions. The LSTM autoencoder achieved an average accuracy of 99.0\%, precision up to 100\%, recall between 90.2\% and 99.6\%, and F1-scores from 93.1\% to 99.8\%, demonstrating high detection sensitivity and a very low false-alarm rate across all evaluated sensors. These results highlight the feasibility of data-driven offline anomaly detection for EHAs. Future work will focus on adapting the developed framework for an online (real-time) environment.

Neural rough differential equations (NRDEs) stay accurate under irregular sampling while taking far fewer integration steps than standard neural differential equations, summarising a finely sampled driver by its log-signature and advancing the hidden state over coarse intervals using the log-ODE method. This efficiency rests on the shuffle algebra, the algebraic counterpart of Stratonovich calculus. This reliance means NRDEs cannot expose the quadratic-variation terms Itô dynamics require, nor the ordered covariant derivatives that govern Itô flows on connection-equipped manifolds. Ameliorating this, we introduce Branched Neural Rough Differential Equations (B-NRDEs), a Hopf-algebraic framework that recasts the NRDE log-ODE step as geometric numerical integration on the state-space manifold, matching the driving algebra to the governing calculus: Grossman--Larson rooted trees for Euclidean Itô dynamics, Munthe-Kaas--Wright planar rooted trees for ordered covariant derivatives on manifolds, and the shuffle algebra in the classical Stratonovich case. This yields intrinsic coarse-step dynamics that exactly preserve manifold constraints. Finally, we introduce a branched signature-kernel objective to enable Itô-consistent law matching by making quadratic-variation terms visible during training. On rough Bergomi volatility, sim-to-real $\mathrm{SO}(3)$ dynamics forecasting, and SPD covariance dynamics, B-NRDEs offer a unified, effective approach to stochastic and manifold-valued dynamics beyond the Euclidean--Stratonovich setting.

We establish the first sharp thresholds for low-degree polynomial tests in planted-vs-planted settings, where the goal is to determine with vanishing error which of two structured planted mechanisms generated the observed data. We prove matching low-degree upper and lower bounds for counting communities in the planted submatrix and planted dense subgraph models. The resulting testing threshold coincides, down to the sharp constant, with the known low-degree recovery threshold. In contrast, the task of weak testing, where the goal is to outperform random guessing, does not have a sharp threshold but rather a smooth transition, which we identify. To prove our results, we develop a framework for planted-vs-planted testing that builds on a latent-variable expansion originating in low-degree recovery and employs new methods to identify and prune non-signal contributions.

Near-real-time flood depth prediction demands surrogate models that are accurate, fast, and transferable across watersheds. Supervised surrogates can match physics-based simulators in accuracy but need millions of training rows per watershed and cannot extrapolate beyond their original mesh. We propose a domain-aware coreset construction pipeline that conditions a tabular foundation model at inference time. The pipeline stratifies storms by return period and most-affected watershed, then samples hexagons with a target-aware spatial selector. With 0.7% of the per-watershed training pool, the model attains a mean $R^2$ of 0.663 across nine Houston-area watersheds, within 98.5% of the supervised reference ($R^2$ = 0.673). It transfers to held-out watersheds without task-specific retraining, staying ahead of a coreset-trained supervised baseline. On real storms it exceeds the supervised reference on a far out-of-distribution case and trails it on a mostly in-distribution one. Domain-aware coreset construction lets tabular foundation models deliver data-efficient, watershed-transferable flood predictions without per-watershed training.

Reinforcement learning with verifiable rewards improves reasoning and tool use, yet long-horizon language agents still learn unsupported evidence chains, belief drift, and shortcut actions that satisfy terminal checks. Existing process rewards are mostly correlational: they reward retrieval-, reflection-, or verification-like steps without estimating whether the step contributes to final verified success under a specified intervention. We propose CVT-RL, a constrained policy-gradient algorithm with dense verifiable rewards, intervention-validity gating, and a policy-conditioned counterfactual contribution (PCCC) estimator. Deletion, semantic substitution, evidence substitution, and tool-output perturbation define separate controlled interventions; continuations are sampled from a frozen reference policy, and a selection-adjusted doubly robust estimator augments the advantage. Belief control uses only prefix-observable labels, while an augmented Lagrangian constrains unsupported claims, skipped verification, tool tampering, and unsafe calls. On long-context QA, ALFWorld, ScienceWorld, and web/tool tasks, CVT-RL improves average task success from 71.8% for compute-matched non-causal RL and 75.4% for an information-matched counterfactual-process baseline to 78.9%, improves evidence F1 from 78.9 to 82.8 over the information-matched baseline, and reduces measured hacking from 7.2% to 3.9%. Independent human audit estimates 4.6% hacking for CVT-RL versus 8.1% for the information-matched baseline, and adaptive detector-evasion attacks raise hacking only to 7.1%. Stratified bootstrap and mixed-effects tests give p<0.01 after Holm correction for all primary metrics. Carefully scoped counterfactual credit, paired with validity gating, diagnostics, and verifiable constraints, provides a reproducible route toward more reliable long-horizon RL for language agents.

Variable fonts enable continuous variation of glyph geometry along semantic design axes such as weight, width, slant, and optical size. However, constructing a variable font from a static font remains a labor-intensive process requiring expert typographic design and manual specification of glyph variation data. We introduce NIV (Neural Axis Variations), a method that automatically converts a static font into a fully functional variable font. Given glyph outlines and a set of desired design axes, NIV predicts per-point displacements. The model operates directly on vector glyph geometry and employs a novel Property Embedding mechanism that captures interactions between multiple axes, enabling consistent multi-axis variation within a unified framework. We train NIV on a newly constructed dataset derived from variable Google Fonts, comprising over one million variation tuples. The resulting model generalizes across unseen code points, unseen font styles, high-complexity CJK glyphs, and even out-of-distribution handwriting inputs. The generated outputs are standard variable font files supporting continuous interpolation via existing rendering engines. To facilitate research, we release the dataset, the complete training and inference implementation, and trained models at https://github.com/ndvbd/NIV. Beyond typography, our approach demonstrates how structured geometric objects with continuous parametric variation can be synthesized using neural deformations.

We introduce VideoKR, the first large-scale training corpus specifically designed to strengthen knowledge- and reasoning-intensive video understanding. It comprises 315K video reasoning examples over 145K newly collected, CC-licensed, expert-domain videos. We develop a human-in-the-loop, skill-oriented example generation pipeline that targets progressively deeper video reasoning capabilities while ensuring the difficulty, diversity, and reliability of both the examples and their CoT rationales. We also curate VideoKR-Eval, a new expert-annotated benchmark where questions require genuine video understanding and knowledge-intensive reasoning rather than textual shortcuts. Our experiments show that, under a standard SFT$\rightarrow$GRPO pipeline, models post-trained on VideoKR outperform prior post-training approaches on knowledge-intensive video reasoning while remaining competitive on general video reasoning, highlighting data design as a key driver of progress in video reasoning. We further conduct comprehensive ablations to isolate the contributions of VideoKR, providing actionable insights for future work.

Foundation models are increasingly trained on sequences of user actions in recommendation, payments, fraud, and commerce, but these models still lack the kind of compute calibration that scaling laws provide for language models. We study a common two-part behavioral-model architecture: a feature-based event embedder maps each multi-modal item to a vector, and a decoder-only transformer predicts the next event from the resulting sequence. Across roughly 600 runs on real interaction data, spanning $10^{15}$-$10^{19}$ training FLOPs, we jointly vary four deployment-relevant axes: the two-part parameter split, critical batch size, model/data allocation, and the number of sampled negatives used after freezing the embedder. A small embedder ($s^{\star}\!\approx\!2\%$ of parameters) is compute-optimal at every budget we test because embedder parameters are both more expensive per step and exposed to far more repeated items than contextualizer parameters. Compute-optimal training is data-heavy relative to text at low compute, but its $D/N$ ratio moves toward the Chinchilla heuristic as compute increases. The sampled training objective and deployed ranking metrics disagree in ways that themselves scale: critical batch size, optimal negative count after freezing, and the agreement between loss and ranking quality all shift with compute and with the chosen evaluation metric. For negative sampling, larger budgets increasingly prefer more negatives; by $10^{19}$ FLOPs the active constraint is candidate-axis memory rather than FLOPs. In behavioral foundation models, the evaluation metric is therefore part of the scaling law: changing it can change the compute-optimal recipe.