让下一篇重要论文，不再错过。

In low-rank matrix sensing of a rank-$D$ factor $U^\ast \in \mathbb{R}^{V \times D}$, replacing isotropic Gaussian designs with power-law measurement covariance $Σ= \mathrm{diag}(j^{-s})_{j=1}^V$ leaves the Burer--Monteiro landscape free of spurious local minima, yet division-normalised first-order optimizers stall above a critical exponent $s^\ast$. We trace this failure to a numerical precision wall. At the ground truth, the smallest non-gauge expected Hessian eigenvalue scales at leading order as $V^{-(s+1)}D^{-s}$. When this curvature drops below the effective denominator floor $ε_O$ of optimizer $O$, normalisation noise overwhelms rare-direction gradients, yielding the leading-order boundary $s^\ast_O(V, D) = [\log(1/ε_O) - \log V]/\log(VD) + δ_O$, where $δ_O$ is a metric-dependent detection lag. With $δ_{\mathrm{Adam}}$ calibrated on four configurations and frozen, this formula predicts Adam's onset within $0.45$ across all 16 cells of a held-out grid ($V \in \{64,128,256,512\} \times D \in \{4,8,16,32\}$), separates fixed-$VD$ pairs, and distinguishes denominator-precision walls from conditioning and sign-quantisation walls. The approximation fails at $D = 2$, reflects a finite-$D$ spectral crossover, and saturates below $\varepsilon_0 = 10^{-8}$ at a dynamical floor.

The determinantal complexity of a polynomial is the order of the smallest matrix whose entries are polynomials of degree at most one and whose determinant equals the polynomial. A lower bound for the permanent in this measure is the algebraic form of the question whether the permanent is harder to compute than the determinant. Over the complex numbers, the best known lower bound grows cubically in the size of the permanent. It holds even when the permanent only has to be a limit of such determinants. I prove that the cubic lower bound holds over every algebraically closed field of odd characteristic $p$, with a constant that depends on $p$. Hence the cubic bound does not depend on characteristic zero. I also prove the bound for Pfaffians, which are square roots of determinants of skew symmetric matrices. Lower bounds for Pfaffians imply the same bounds for determinants. Further, I prove the bound, divided by $a$, for matrices whose entries are polynomials of degree at most $a$. All three results come from one lower bound for smooth hypersurfaces. I prove it in every characteristic by counting intersection points together with their multiplicities.

Unlearning concerns the task of removing the influence of a sensitive portion of the training data, such as protected, copyrighted or private text, from a model without retraining it from scratch. While unlearning requests happen continuously during a model's lifetime, the vast majority of LLM unlearning methods are ill-suited for iterated removal, yielding steep decay in forgetting and utility upon sequential unlearning. This decay stems from interference between successive updates, as each new deletion can undo earlier ones or push the model further along directions already degraded by them. To address this, we introduce Continual Orthogonal Projection (COP), a gradient-projection scheme that restricts each update to the orthogonal complement of activation subspaces cached from prior forget sets. This approach provably guarantees first-order non-interference with earlier deletions. COP stores only a low-rank basis per layer, requiring neither past gradients nor previous forget sets, and plugs into unlearning methods that update the model through gradient steps on a differentiable loss without modifying its objective. Experiments on standard LLM unlearning benchmarks (TOFU and RWKU) show that COP preserves utility across sequential requests without weakening forgetting, preventing the collapse of standard objectives and forgetting more effectively than continual-specific baselines.

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive linearizations of the perturbed KKT conditions, we perform a simulation working directly with the nonlinear complementarity equations. Using a two-stage quantum eigenpath traversal schedule, this approach yields an algorithm for solving linear optimization problems involving $m$ constraints and $n$ variables to $\varepsilon$-optimality using $\widetilde{O}\!\left((m+n)^{3/2}\,\varepsilon^{-1}+(m+n)^{1/2}\,\varepsilon^{-3/2}\right)$ queries to an oracle that evaluates a potential function. In the standard gate model (i.e., without access to quantum RAM), our algorithm can obtain $\varepsilon$-precise solutions to LO problems using at most $$\widetilde{O}\!\left(\left[\frac{(m+n)^{3/2}}{\varepsilon} + \frac{(m+n)^{1/2}}{\varepsilon^{3/2}}\right] \cdot \mathrm{nnz}(A)\right)$$ elementary gates, where $\mathrm{nnz}(A)$ is the total number of non-zero elements found in the constraint matrix.

Financial AI workflows that reuse investor knowledge need persistent memory that integrates observations across sources and periods without losing identity or provenance. In a knowledge graph, recurring observations may use different surface forms, fragmenting relationship histories and preventing evidence from accumulating. We introduce Fusion and Identity Registry for Memory Evolution (FIRME), a registry-anchored memory graph that reconciles incoming observations to persistent canonical relationships and retains their source, time, and context. Within periods, rule-based fusion links investor-call discussions to portfolio cash-flow signals, directly or through a fixed product-topic ontology. Across periods, canonical identities and persistent aliases direct recurring observations to the same relationship history; deterministic updates summarize reinforcement, inactivity, and reactivation. We evaluate FIRME on proprietary investor-call and cash-flow records and on S&P 500 earnings-call transcripts. Compared with a historical registry that retains canonical identities and semantic fallback but omits alias memory, FIRME increases final-period Correct Match Rate by 7.8-12.1 percentage points across four dataset-backend settings under a fixed-judge and fallback-review protocol. A blinded human audit of 200 incoming observations per setting finds Correct Match Rate gains of 9.0-16.5 points and reattachment-recall gains of 22.5-29.0 points, with higher observed merge precision in all four samples. A separate audit finds valid evidence paths for 293 of 300 outputs from full within-period fusion in the investor-call setting. Extraction-faithfulness and round-trip diagnostics assess source grounding and preservation of extractor-derived graph content.

Recent advances in interactive world models have made it possible to generate controllable, dynamic environments from action inputs. Yet current models struggle to maintain coherence beyond roughly one minute of rollout, a limitation rooted not in model capacity but in the scarcity of long-horizon training data. Existing gameplay video datasets typically consist of clips under ten seconds, with captions that describe whole clips in coarse and undifferentiated text, which is insufficient for controllable long-horizon generation. We address this with GameVerse, a minute-scale gameplay video dataset purpose-built for long-horizon interactive world modeling. GameVerse contains 69.7K clips spanning 1,655 hours and 349.6 million frames across diverse first- and third-person gameplay, including 1,358 hours of continuous two-minute sequences, an order of magnitude longer than prior datasets. Clips pass through a unified pipeline of scene-consistent segmentation, quality filtering, camera pose estimation, and event-based caption annotation. Each clip is paired with a temporally stable camera trajectory that remains coherent across minutes, together with captions that separate static scene context from dynamic foreground events and align to event boundaries rather than fixed time windows. Comprehensive analysis shows that GameVerse surpasses existing public datasets in scale, diversity, and annotation quality. Experiments further demonstrate that training on GameVerse substantially extends the temporal horizon of interactive world models.

Audio-visual instance segmentation (AVIS) segments and tracks individual sound-producing objects in videos. Existing benchmarks predominantly use monaural audio, which lacks inter-channel cues for spatially distinguishing concurrent sound sources. We introduce AVPS-360 (Audio-Visual Person Segmentation 360), a spatial audio-visual benchmark bridging AVIS and sound event localisation and detection (SELD). Built upon STARSS23, it pairs first-order Ambisonics audio with synchronised 360° video across 230 recordings totalling 10.5 hours. Recordings average 164.0 seconds. The dataset captures intermittent sound production in real-world interactions dominated by speech, alongside laughter, clapping, and footsteps. It provides 31,678 manually reviewed instance masks linked to source identities and sound-event labels. We also present a baseline that integrates spatial audio with visual features for frame-level segmentation and identity association across frames. Experiments on AVPS-360 show that existing AVIS methods struggle with detection and identity association in long recordings with intermittent sound production, while our baseline substantially improves performance in both aspects.

State-of-the-art deep reinforcement learning (RL) methods have achieved remarkable performance in continuous control tasks, yet their computational complexity is often incompatible with the constraints of resource-limited hardware, due to their reliance on replay buffers, batch updates, and target networks. The emerging paradigm of streaming deep RL addresses this limitation through purely online updates, achieving strong empirical performance on standard benchmarks. In this work, we propose two novel streaming deep RL algorithms, Streaming Soft Actor-Critic (S2AC) and Streaming Deterministic Actor-Critic (SDAC), explicitly designed to be compatible with state-of-the-art batch RL methods, making them particularly suitable for on-device finetuning applications such as Sim2Real transfer. Both algorithms achieve performance comparable to state-of-the-art streaming baselines on standard benchmarks without requiring tedious per-environment hyperparameter tuning. We further investigate the batch-to-streaming transition, showing that a naive transition does not guarantee preservation of pre-trained policy performance, and propose a principled approach to address this challenge.

Standardized uptake value ratio (SUVR) quantification of amyloid PET commonly relies on a subject-specific T1-weighted MRI, yet a usable MRI is not always available. We therefore combined CT-to-MRI synthesis with conformal prediction for MRI-free PET quantification with reliability assessment. A slice-consistent Brownian Bridge Diffusion Model was strengthened with multi-dataset training and data-source conditioning to enrich the anatomical prior learned from MRI, and with expanded multi-slice CT context to exploit the through-plane continuity of subject-specific anatomy in CT. Synthetic MRI was used for FreeSurfer-based anatomical parcellation and PET quantification, while deep-ensemble uncertainty was calibrated with conformal prediction to estimate a plausible range for the corresponding real MRI-based SUVR. On $^{11}$C-PiB PET from OASIS-3, the proposed method achieved the highest synthesis and parcellation fidelity among the compared methods. Mean cortical SUVR from the proposed synthetic MRI agreed closely with the real MRI-based reference (MAE $0.016 \pm 0.015$, Pearson $r = 0.9987$) and yielded the same amyloid-positivity classification as the real MRI in all 87 test subjects at the prespecified cut-off. Conformal prediction achieved empirical coverage close to the prespecified levels, and at 90% target coverage, 85 of 87 subjects had prediction intervals that supported an unambiguous amyloid-positivity decision. Zero-shot evaluation on an independent external cohort showed that the proposed CT-to-MRI model could support PET quantification without retraining, although conformal calibration required target-cohort recalibration to recover the intended coverage. These findings support CT-to-MRI-based MRI-free PET quantification as a promising approach for providing accurate SUVR measurements and an explicit assessment of their reliability.

Service orchestration across the edge--cloud continuum increasingly uses language models (LMs) to translate intents and operational evidence into scheduling, configuration, diagnosis, and remediation decisions. Yet, useful model outputs do not by themselves establish dependable orchestration: reliability also depends on where the LM enters the decision process, what authority it is granted, how actions are constrained, and what system-level evidence supports the claimed effect. Existing surveys provide limited synthesis of the links between continuum-specific orchestration decisions, LM responsibility, operational authority, assurance controls, and supporting empirical evidence. We systematically review 39 primary studies and develop a five-dimensional analytical framework for connecting system context, orchestration decisions, LM agency, operational safeguards, and evaluation evidence. The synthesis reveals predominantly hybrid designs in which LMs support interpretation, candidate generation, and mitigation planning, while downstream components commonly retain feasibility enforcement and execution authority. Bounded closed-loop remediation is emerging, but continuum-specific constraints remain unevenly represented in decision formulations, and production-scale evidence across heterogeneous edge--cloud environments remains limited. These findings suggest that reliance on LM-enabled orchestration depends on aligning decision constraints, operational authority, safeguards, and evaluation evidence with the claimed system effect.

In psychiatric practice, the clinical intake interview remains a primary diagnostic instrument, requiring the clinician to establish rapport while disentangling complex, overlapping presentations. Here, we show that multi-turn reinforcement learning (RL) in simulation environments improves language model performance on structured text-based psychiatric intake, spanning history-taking, differential diagnosis, and initial management planning. In a randomized, double-blind crossover study ($N = 60$ matched scenario pairs, 120 encounters) comparing the RL-trained agent against its identically prompted base model, 32 board-certified psychiatrists role-played standardized patients while a separate panel of 15 independent, board-certified psychiatrists scored the de-identified transcripts. The trained agent outperformed the base model in 76.7% of matched scenario pairs ($p < 0.0001$), with gains on an adapted clinical-examination rubric ($d_z = 0.77$, $p < 0.0001$), patient-centered communication (82.0% vs. 65.2%, $p < 0.001$), and differential diagnosis appropriateness (68.3% vs. 33.3%, $p < 0.001$). Across 127 psychiatrist-validated simulated intake scenarios, the trained agent nearly doubled its base model's clinical rubric score (0.706 vs. 0.379; composite reward 0.564 vs. 0.294, $p < 0.0001$). To systematically probe conversational safety, we established two Delphi-consensus taxonomies, of clinical safety risks and relational competencies, from which 256 challenging adversarial presentations were derived; we find that training in simulation environments more than halved under-triage of acute safety risks (12.9% vs. 30.5%, $p < 0.0001$). Simulation environments thus provide a controlled testbed for training and stress-testing psychiatric conversational agents, with gains that transferred to psychiatrist-enacted encounters, though residual gaps require safeguards and clinician oversight.

Self-supervised speech models encode rich phonetic information, but it remains unclear how to transform this information into interpretable metrics for second-language (L2) pronunciation assessment in spontaneous speech. We propose a native-reference coordinate geometry in which phone-class averages from native speech define a low-dimensional reference subspace, and L2 speech is evaluated by its distance to matching native phone-class coordinates. Unlike prior distance-based approaches, our method does not require parallel recordings with matched linguistic content or dedicated pronunciation labels. Across different self-supervised encoders and modeling choices, the resulting native-reference distances show negative Spearman correlations up to -0.5 with speaking proficiency, indicating that higher-proficiency speakers tend to have smaller distances to the corresponding native phone-class coordinates.

Sampling-based reachability estimates reachable sets from finitely many simulated trajectory endpoints. Existing guarantees often control missed probability mass or approximation error relative to the convex hull of the reachable set, leaving the geometric error relative to the reachable set incompletely characterized. We study this error as a problem of support estimation under flow distortion. Our assumptions combine a uniform lower bound on the local volume density of the initial set, a lower bound on the sampling density, and a one-sided Lipschitz constant $μ$ for the vector field. These conditions admit initial sets with corners and dynamics that may expand or contract. In the fine-accuracy regime, $\tilde{\mathcal O}\bigl(2^ne^{nμT}(R/r)^n/(ρκ)\bigr)$ independent endpoint samples suffice for Hausdorff accuracy $r$ using the endpoint cloud. Here, $n$ is the state dimension, $T$ is the horizon, $R$ is the volume-equivalent radius, and $ρ$ and $κ$ quantify sampling density and local volume density. For $n\ge2$ and sufficiently small $κ$, a minimax lower bound over all estimators based only on independent endpoints matches these dependencies up to a dimension-dependent factor $2\cdot4^n$ and logarithmic factors, within the stated parameter range and when the state domain accommodates the construction. The exponential burden in dimension, and in the horizon for expanding systems, is therefore intrinsic to this observation model. Planar experiments illustrate the predicted effects of corners and contraction; robot-arm experiments show how empirical accuracy deteriorates with dimension.

Understanding natural Earth surface processes requires integrating topography, imagery, hydrology, and human infrastructure while remaining robust to geographic variation, yet few benchmarks support both challenges. We introduce EarthScape, a multimodal benchmark for geologic mapping and surface-aware learning under geographic domain shift. EarthScape combines aerial imagery, LiDAR-derived elevation, multi-scale terrain derivatives, and contextual vector data into 37 co-registered input channels per sample, together with pixel-level geologic masks. Its geographically separated regions share a common label space, enabling controlled evaluation of in-domain and cross-region generalization under realistic class imbalance and spatial complexity. Benchmark experiments show that engineered terrain representations transfer more robustly than raw elevation, while spatial support and multimodal terrain inputs strongly influence performance. Fusion effectiveness depends on backbone and evaluation domain, with more complex cross-attention providing no consistent advantage over simpler strategies. These representation trends extend across geospatial foundation models and semantic segmentation, while class-level results show that no single terrain feature or scale is optimal across geologic classes. Together, EarthScape provides a benchmark for studying representation design, multimodal fusion, and geographic robustness in surface-aware geospatial learning. Our source code is available at https://github.com/masseygeo/earthscape and the dataset at https://doi.org/10.13023/kgs.data.05.01.2025.

Reconstructing dynamic 3D scenes from monocular videos remains challenging because limited observations provide insufficient motion constraints. Conventional 4D Gaussian representations model spatiotemporal appearance efficiently, but the restricted temporal evolution of each primitive makes complex nonlinear dynamics difficult to represent compactly. We propose a motion-expressive 4D Gaussian representation with time-varying means and covariances. By analytically differentiating Gaussian trajectories, we obtain Gaussian velocities and introduce Flow Splatting to render optical flow while accounting for camera motion, enabling dense motion supervision. This formulation jointly models scene appearance and motion within a unified set of 4D Gaussian primitives. We further introduce an initialization strategy based on the sampling theorem and a velocity consistency regularizer to stabilize optimization. Experiments on DAVIS and NVIDIA Dynamic Scenes demonstrate a favorable trade-off between reconstruction quality and efficiency under challenging monocular settings.

Predictive models trained at well-resourced data-rich institutions often fail when deployed in new populations. Motivated by the goal of building clinical diagnosis and decision-making algorithms for data-scarce rural populations using the general knowledge learned from data-rich hospitals, we formulate the fundamental question of \emph{domain generalization with adversarially chosen domains}, which asks a learner to perform on any unseen target domain nearly as well as the worst hypothesis consistent with the evidence from the observed source domains. Assuming only that the hypothesis class contains a "universal" predictor with small error on all $k$ source domains, we characterize the sample complexity of this objective up to logarithmic factors. Letting $d$ denote the VC dimension of the hypothesis class, we find, somewhat surprisingly, that the sample complexity reduces significantly from $Ω(dk)$ to $O(d)$ under a small relaxation of the learning goal in which, roughly speaking, we allow the learned model to compete with hypotheses that perform well on 99% instead of 100% of the source domains. By applying this insight to the meta-distributional setting, in which source domains are selected according to a distribution on distributions, we obtain a corresponding improvement over known sample complexity upper bounds. We also study the effect of data access to the target domain and show that a small labeled sample from the target domain does not improve the worst-case sample complexity on the source domains.

Infant pose and shape estimation is essential for applications in childcare, developmental monitoring, and medical diagnosis. However, existing methods and datasets are largely designed for adults, and direct transfer to infants fails due to substantial differences in body proportions, articulation limits, and frequent self-occlusion. To address this gap, we introduce InfantNet, the largest real-image infant dataset to date, comprising 108,902 RGB images of infants aged 6-18 months. Each image is annotated with 2D keypoints, and a curated subset of 11,642 images additionally includes 3D pose and shape annotations with full SMIL parameters, verified through multi-view rendering and reprojection-error filtering. We use an iterative annotation pipeline to ensure high fidelity across both 2D and 3D labels. InfantNet establishes a large-scale, comprehensive benchmark for infant 2D keypoint detection and 3D pose-and-shape recovery. Baseline experiments demonstrate that state-of-the-art adult pose estimators do not generalize well to infants, whereas fine-tuning on InfantNet yields a consistent improvement. The gains are even more pronounced for 3D pose and shape estimation, where SMIL-based estimation demonstrates robust performance with accuracy comparable to results reported for SMPL-based models. By releasing the InfantNet dataset and benchmark, we provide a vital resource for advancing infant pose analysis and related healthcare applications.

Generative AI and misinformation research have evolved since our 2024 survey. This paper presents an updated perspective, transitioning from literature review to practical countermeasures. We report on changes in the threat landscape, including improved AI-generated content through Large Language Models (LLMs) and multimodal systems - addressing the adverse impacts of AI on information quality. This work focuses on our practical contributions: JudgeGPT, a platform to evaluate human perception of AI-generated news, and RogueGPT, a controlled stimulus generation engine for research. Together, these tools form an experimental pipeline for studying how humans perceive and detect AI-generated misinformation. Our findings show that detection capabilities have improved, but competition between generation and detection continues. We discuss mitigation strategies such as LLM-based detection, inoculation approaches, and the dual-use nature of generative AI.

Aerial imagery provides complementary spatial context for autonomous driving by exposing road structure beyond the immediate perception range of onboard sensors. Yet map construction from aerial imagery, aerial-assisted online HD mapping, and cross-view localization are typically studied on separate data and benchmarks. We introduce KITScenes Aerial, an extension of the KITScenes Multimodal dataset that augments synchronized onboard sensor data, vehicle poses, and rich Lanelet2 map annotations with spatially associated aerial imagery and higher-resolution neural representations, providing a common basis for a variety of research tasks. Our mapping evaluation focuses on all 53 KITScenes map classes across different model designs, spatial ranges, and aerial resolutions, while retaining compatibility with the widely used three-class setting. Representative baselines show that aerial context is particularly beneficial for fine-grained and extended-range mapping, more than doubling 53-class mAP at the larger mapping extent. Higher-resolution aerial imagery yields a further 4.3 mAP (+24 %) improvement, with gains extending to challenging map elements such as traffic lights. We additionally evaluate cross-view localization under geographically disjoint conditions, where an adapted fine-grained feature-matching baseline achieves a mean translation error of 5.13 m. KITScenes Aerial thus enables unified study of aerial and ground-level information across complementary mapping and localization tasks. Project page: https://kitscenes.com/aerial

Retrieval-augmented generation commonly serves separate models for reranking and answering, duplicating model residency and passage processing. We introduce Glance, which equips the generator with a lightweight decision adapter and pointer head to score candidate passages from a shared prefill. Short relevance probes branch from the cached context, producing one score per passage without separately prefilling each query-passage pair. A single resident 9B backbone supports generation, general decisions and reranking, with approximately 0.1 GiB of additional memory per decision skill. After 39 minutes of MS MARCO fine-tuning, Glance achieves nDCG@10 of 0.741 on SciFact and 0.345 on NFCorpus, compared with 0.721 and 0.326 for bge-reranker-v2-m3. On 300 HotpotQA questions, its selected context improves answer F1 by 0.045 over cross-encoder-selected context under the same base generator (paired bootstrap 95% CI [0.014, 0.076]). In a scaling study, reranking quality keeps rising up to 200 candidates (43k tokens) scored from one shared prefill, where it exceeds the cross-encoder by 0.058 nDCG@10, and a probe-only activated adapter lets generation continue from the original passage cache. These initial results demonstrate generator-based reranking with one resident backbone; evaluation currently covers two retrieval datasets, one QA dataset and one backbone family.

We present PhysInsert, a framework for physically plausible reference-based object insertion that jointly adapts objects and their surrounding scenes. Existing methods often rely on masked inputs, generation-based pairs, or training pairs with limited viewpoint variation, leaving pose and illumination adaptation and bidirectional object-scene interactions insufficiently constrained. We construct the Insert World dataset with strictly aligned Blender-rendered counterfactual pairs and object references across viewpoints and lighting conditions. Building on these data, Geometry-Guided Adaptation couples a VGGT geometry stream with image and text streams under target-scene feature supervision to guide spatially consistent insertion. Complementary 2D Object-Scene Spatial Supervision jointly supervises object occupancy and environmental changes while grounding spatial instructions in object regions through image-text attention. We introduce PhysInsert-Bench with dedicated cross-environment and cross-view cases requiring illumination and pose adaptation beyond appearance copying. Experiments on PhysInsert-Bench and DreamBooth demonstrate improved image fidelity; a user study further shows more accurate placement and improved lighting integration, perspective, and pose plausibility.

Controlling dynamical systems governed by partial differential equations (PDEs) remains a challenging task in scientific computing, owing to high-dimensional state spaces, distributed actuation, nonlinear dynamics, and stringent real-time constraints. Reinforcement learning (RL) has emerged as a promising paradigm for synthesizing feedback controllers that adapt to varying operating conditions and can be deployed efficiently in real-time. This review provides a unified perspective on RL and PDE-constrained optimization, and surveys model-free, model-based, and multi-agent RL approaches to PDE control, with particular emphasis on sample efficiency, generalization across parametric variations, and scalability to high-dimensional problems. Two demonstrative examples, the stabilization of a chaotic system and a flow control problem, illustrate the performance and pitfalls of RL agents in practice. Finally, we discuss evaluation and benchmarking practices, current limitations, and open research directions toward reliable, data-efficient, and scalable RL for scientific computing.

A central goal of biology is to predict the dynamics of multicellular systems. Lineage context (the states of a cell's sisters, cousins, etc.) could inform these predictions, but how best to leverage it remains unclear. Here we introduce lineage inpainting, a generative modeling approach that uses lineage context with tree-structured transformers and stochastic interpolants to model cell state dynamics across lineage trees. Applied to a lineage-traced transcriptional atlas of mouse embryogenesis, it recovers dynamics not resolved by gene expression alone, including multiple transcriptional convergence events where distinct lineages are drawn to a common state. Despite being fit on unperturbed development, lineage inpainting can generate hypotheses about perturbation responses by simulating counterfactuals. These simulations agree in many cases with observed developmental phenotypes, including a single-cell measurement of the Tbx5 knockout response. Our results show that lineage information provides a rich source of context for learning multicellular dynamics.

Tool-use benchmarks often score agents by final task success, but terminal outcomes can obscure whether the intermediate tool-call trajectory was executable. We propose prefix executability as a trajectory-level evaluation protocol for tool-using agents. The protocol measures whether every prefix of a predicted tool-call sequence remains executable under tool schemas, state preconditions, and data dependencies, and summarizes reliability using Prefix Executability Curves (PEC), First-Error Depth (FED), Trajectory Executability Rate (TER), horizon-normalized AUC-PEC, and Recovery Rate (RR). We instantiate the protocol on stratified samples from BFCL-v3 multi-turn and ToolSandbox, and on the complete Airline/Retail base splits of $τ^3$-bench. We observe that outcome-only and prefix-level rankings diverge: agents whose execution is conditioned on an unverified plan often achieve higher point-estimate final success than non-plan-conditioned baselines while substantially lowering TER and AUC-PEC. These divergences are precisely the failure modes that prefix executability is designed to expose: they reveal whether apparent success rests on an executable trajectory, where invalidity first enters, and whether success follows recovery from an earlier failure. As a validation intervention, explicit pre-execution plan checking can improve executable-prefix survival while maintaining competitive terminal success. These results show that final success alone is insufficient for evaluating tool-use agents and that prefix-level executability provides an actionable reliability signal for comparing agents, diagnosing failures, and assessing validation mechanisms.

Theoretical predictions of novel materials rely on a variety of techniques, from data-mining-based ion substitution methods to fully de novo generative models. Each approach imposes specific constraints and encounters unique challenges when extrapolating beyond the distribution of known materials to discover new ones. The foremost goal of materials generation is to produce stable, unique, and novel (S.U.N.) structures. Predicted structures that meet these criteria, however, typically result from novel chemical compositions mapped onto known structural prototypes or frameworks. We leverage this heuristic insight to present a new generative paradigm for the de novo prediction of inorganic crystalline materials constrained by their structural framework---i.e., the unit cell shapes and respective particle positions. Our method, termed OMatG-FC (Open Materials Framework-Conditional Generation), learns via a combination of discrete flow matching on the atomic species and stochastic interpolants for the volume scaling of the unit cell lattice, while fixing in-place the fractional coordinates and the unit-volume lattice vectors, dramatically reducing the dimensionality of the problem compared to unconstrained (framework-free) generation. Our method is more flexible than existing prototype-constrained methods, demonstrating capability for discovery of unseen, stable prototypes derived from known structural frameworks. We also investigate the number of unique frameworks in the MP-20 dataset, demonstrating the propensity of duplicate frameworks within the dataset and providing a framework-split version. We benchmark the performance of our model using the LeMat-GenBench suite using three ML interatomic potentials and achieve state-of-the-art S.U.N. rate below the convex hull, eschewing the need to learn atomic packings for materials discovery.

Language models have proven to be capable of learning the intricate latent structures in language. However, the dynamics of how such models acquire the components of that structure remain poorly understood, leaving them open to the criticism that models just remix training data. In this work, we use the Alchemy benchmark as a controlled setting in which we investigate how models acquire the different latent structure components of the data. We train a small decoder-only transformer on three controlled task variants: 1) inferring missing steps from partial contextual information, 2) composing simple rules to solve multi-step sequences, and 3) decomposing complex multi-step examples to infer intermediate states. By factorizing each task into interpretable components, we show that the model learns the different latent structure components in discrete $\textit{stages}$ and in a $\textit{coarse-to-fine}$ manner. Using inference-time ablations, we demonstrate that when certain latent structures are masked or replaced, the model can use an alternative intermediate latent structure to solve the task. We also observe an asymmetry: the model composes single step transitions robustly, but struggles to decompose complex examples to discover the atomic steps. Our findings provide insight into $\textit{how}$ a transformer model acquires latent structure, offering a detailed view of how capabilities evolve during training.

Continuum Glauber dynamics is a spatial birth-death process whose stationary distribution is a Gibbs distribution. We establish a spectral gap for Continuum Glauber dynamics applied to Gibbs point processes with repulsive pair potentials, a well-known special case of which is the hard sphere model. For arbitrary-range repulsive pair potentials, we show that a continuous version of Spectral Independence suffices to establish a spectral gap. This extends the regime of activity for which Continuum Glauber dynamics is known to mix, yielding a simple efficient sampling algorithm for arbitrary-range pair potentials that matches the known efficient sampling regime for finite-range pair potentials currently based on specialized algorithms. As a consequence, we also improve the threshold up to which packings of fixed size/density can be efficiently sampled from a bounded domain, the first improvement since Kannan, Mahoney and Montenegro (2003). To prove these results, we develop continuous analogs of Spectral Independence and negative fields localization. We show that a stronger variant of zero-freeness implies Spectral Independence, which in turn allows us to run the localization scheme to boost the spectral gap of Continuum Glauber dynamics from smaller activity to larger activity. While this follows the high-level blueprint of Chen and Eldan (2022) for the discrete setting, we have to address several novel difficulties due to the continuous setting. Notably, we avoid discretization in the algorithm and the analysis and work directly in the continuous setting.

Filtering has not yet had its foundation-model moment: state estimation is still dominated either by online Bayesian filtering algorithms that require known dy- namics as inputs, or by learning-based neural filters trained from scratch for a single system or parametric family. The core challenge is structural heterogene- ity: dynamical systems differ in their governing dynamics, physical scales, and noise levels, precluding a shared representation space for a reusable filter. To bridge this gap, we introduce FilterFM, the first pretrained model for Bayesian filtering that estimates latent states across heterogeneous dynamical systems with a single checkpoint. FilterFM employs a hierarchical two-level observation se- quence encoder and a prior-to-posterior state-reconstruction module that together handle varying observation and state dimensions across heterogeneous systems, while modeling state uncertainty via quantile prediction. Trained on a mixture of heterogeneous filtering tasks, FilterFM exhibits superior in-domain performance, delivering significant gains in estimation accuracy, runtime efficiency, and noise robustness compared to existing baselines. Beyond in-domain performance, it marks the first model to successfully enable zero-shot filtering on unseen dynamics, bridging the generalization gap in state estimation. Furthermore, we uncover clear scaling behaviors in foundation-model-based Bayesian filtering, which combined with comprehensive component ablation studies, validate the structural optimality of our design and broaden the generalization scope for this research field.

We introduce the Riemannian Lyapunov Framework (RLF), a unified framework that represents first order optimization as a closed loop controlled dynamical system on a Riemannian parameter manifold. Within this framework, optimizers are specified by a quadruple $(M, g, Φ, η)$ consisting of a Riemannian metric, an internal state transition map, a direction field generator, and a lifting parameter. Classical and modern methods including SGD, Adam, AdamW, Lion and Shampoo are recovered as specific instantiations of this quadruple. The central structural object of the framework is a time indexed family of target submanifolds in the extended state space of parameters, velocities, and internal memory, which we call the Normally Attracting Invariant Manifold (NAIM) family. These submanifolds organize training dynamics into two timescales: a fast contraction of the velocity state onto the current target submanifold, followed by a slow descent along it. Using Riemannian backstepping, we construct a strict Lyapunov function on the extended state space and prove Uniform Ultimate Boundedness (UUB) of the optimization trajectory under a descent alignment assumption and bounded stochastic disturbances. Under the additional Polyak-Lojasiewicz (PL) condition, the Lyapunov function converges linearly to a bounded neighborhood of the optimum, defined as the drift of the target direction field between consecutive iterates after parallel transport. To validate the framework's generativity, we derive three concrete instantiations of the quadruple, each exercising a distinct design axis, and show on geometric diagnostics, image classification benchmarks, and language modeling that their empirical behavior matches the theoretical predictions. The framework casts optimizer design as controller synthesis, complementing heuristic perspectives by providing a constructive template with provable guarantees.

Accurate soil moisture estimation is critical for precision agriculture, influencing irrigation, fertilization, and harvesting strategies. Traditional methods primarily rely on meteorological and soil property data, while recent approaches incorporate visual modalities such as aerial and geospatial imagery. However, these high-resolution images are expensive and computationally demanding to analyze. In this work, we propose Soil Moisture Distillation (SMD), a Knowledge Distillation (KD)-based multimodal learning framework that leverages unimodal teachers to enhance multimodal soil moisture estimation. SMD surpasses not only traditional multimodal fusion techniques, including MIS-ME, but also outperforms unimodal models, demonstrating the benefits of guided unimodal knowledge transfer. Additionally, we conduct a comparative analysis of soil patches and crop images, showing that crop images provide superior visual cues, leading to improved prediction accuracy. SMD achieves a 2% improvement in MAPE for soil patches and 1.2% for crops over state-of-the-art baselines, highlighting the effectiveness of leveraging both meteorological and visual data through knowledge distillation for enhanced soil moisture forecasting.