Papers

In this work, different from previous results, the explicit expression of numerical Onsager-Machlup action functional for Euler discretized SDEs driven by fractional Brownian motion is derived provided the drift coefficient and numerical reference path satisfy some suitable conditions. Then numerical fractional Euler-Lagrange equations for numerical Onsager-Machlup action functional are also obtained. Finally, numerical experiments to illustrate and support the theoretical findings.

We develop and analyse a symmetric weighted interior penalty polytopal discontinuous Galerkin (SWIP-PolyDG) method for multi-species reaction–diffusion systems with nonlinear reaction terms of up to cubic order. Such terms arise naturally when higher-order interactions are incorporated into population models, allowing non-additive effects among multiple species to influence local growth and conversion mechanisms. The proposed framework accommodates heterogeneous and possibly anisotropic diffusion tensors on general polygonal meshes. To control the nonlinear coupling, we consider a hierarchical block structure in the reaction operator, whereby each population block depends only on its own variables and on those associated with preceding blocks. In addition, the cubic self-interactions within each block are assumed to have a dissipative diagonal structure. Under these hypotheses and proceeding recursively over the hierarchy of population blocks, we derive local-in-time stability estimates in two spatial dimensions for the semi-discrete formulation in both the $L^2(\Omega)$-and dG-norms. We further establish an a priori error estimate in a combined $L^2(\Omega)$-dG energy norm for sufficiently regular solutions for the semi-discrete formulation. Finally, numerical experiments confirm the predicted convergence behaviour and illustrate the robustness of the method under heterogeneous diffusion.

We develop a complex balance relation for stellar pulsations whose real and imaginary parts give paired relations for the excitation rate and oscillation frequency. The formulation includes thermodynamic exchange, boundary power, and the inertial, compression, horizontal-area, and gravitational-stratification terms, without assuming weak nonadiabaticity. Applied to portions of an envelope, it provides cumulative diagnostics evaluated using the eigenfrequency and eigenfunctions of the complete pulsation problem. We show that a negligible global boundary contribution can coexist with substantial internal boundary power, which may largely compensate the thermodynamic exchange within the envelope. Applications to radial pulsations of post-AGB envelopes illustrate this behaviour for ordinary, strange, and anomalous-exchange modes. The latter have a negative effective norm and opposite signs of net exchange power and excitation rate. For a selected excited anomalous mode, the principal exchange occurs between the He II ionization region and the Z-bump, with less participation from the outer ionization layers than in the comparison modes. Classification by the largest response norm reveals distinct domains across the examined pulsation spectrum. The selected anomalous branch retains horizontal-area dominance across its transition from damping to excitation.

Digital quantum simulation (DQS) is one of the most promising applications of quantum computing. Trotterised DQS models quantum dynamics by decomposing the evolution into a sequence of gate-based Trotter steps. Using larger Trotter steps reduces the required gate count, but it is now understood that the Trotterisation step size cannot be increased beyond a certain threshold value, beyond which there is a sudden breakdown in simulation accuracy, due to the onset of quantum chaos. To date, this behaviour has only been studied for closed systems not subjected to the environmental noise and decoherence to which real-world quantum computers are highly sensitive. In this work, we study a range of experimentally relevant open-system quantum simulator models and show that Trotterisation thresholds persist even when open-system effects are included, even in the long-time, steady-state limit, once all coherence has been lost. We show that open DQS can accurately reproduce the dynamics of open target systems prior to the threshold, but still exhibits a sudden performance breakdown beyond it. We introduce new, statistical techniques to rigorously characterise the onset of quantum chaos beyond the Trotterisation threshold for both approximately unitary and genuine dissipative quantum chaos, based on random matrix theory (RMT), building on techniques developed for closed systems. Finally, we demonstrate that dissipative quantum chaos emerges when the dissipation is in balance with the presence of underlying unitary quantum chaos; the dissipation must be strong enough to induce genuinely dissipative behaviour, yet not so strong as to suppress the underlying chaotic structure.

Poisson denoising of scientific data requires methods that account for signal-dependent noise while accommodating different data dimensionalities and preserving quantitative intensity information. We present BMND, a dimension-independent extension of block matching and collaborative filtering for Gaussian and Poisson observations. Building on the two-stage structure of BM3D and BM4D, BMND processes Poisson data directly, without a variance-stabilizing transform, by combining noise-aware patch matching with propagation of signal-dependent noise variances through collaborative filtering and aggregation. A dimension-independent reference-patch traversal scheme supports arrays with an arbitrary number of axes. An optional aggregation-aware mass conservation preserves the observed total intensity after weighted overlap-add. We evaluate the framework on one-dimensional physiological signals, two-dimensional images, and three-dimensional volumes, using controlled noise experiments and measured fluorescence microscopy acquisitions. The experiments demonstrate improved reconstruction quality from noise-aware matching and Wiener filtering, while low-count phantom experiments show reduced denoising-induced intensity loss through mass conservation. The framework provides a unified, non-learning-based approach to denoising across arbitrary data dimensions and is released as an open-source library.

Native 3D texture generation synthesizes colors directly in 3D space for a given geometry, conditioned on multi-view reference images. It is generally believed that training such models requires large-scale, high-quality real 3D asset data, whose acquisition remains a long-standing and challenging problem. In this work, we propose Tex-Zero, demonstrating that a high-fidelity native 3D texture generation framework can be trained without 3D assets. Our key observation is that only high-quality and fine-grained color information is essential for 3D texture training, while the required geometric information is less critical and can be manually constructed rather than obtained from real 3D assets. This finding makes it possible to transform abundant, high-quality 2D images into effective training samples for 3D texture generation. Specifically, we convert high-quality 2D images into 3D training samples by representing each image as a plane in 3D space and applying patch-wise random rotations and aggregation to construct complex geometric structures. Using these constructed image data, we train the Tex-Zero VAE, which can reconstruct real 3D assets with high quality despite never observing them during training. Building upon the Tex-Zero VAE, we train the Tex-Zero DiT also exclusively on the constructed image data, where the conditioning 2D multi-view images are transformed into planes in 3D space and also encoded by the Tex-Zero VAE, thereby reducing the representation gap and improving generation quality. Extensive experiments show that Tex-Zero generates high-fidelity 3D textures with fine-grained details solely using images as training data, offering a promising perspective on the data paradigm for scaling 3D texture generation.

We lay out the analysis of the “Kronecker preconditioners” adopted in [24] for the linear wave equations. Importantly, we deliver the analysis justifying the claims in~[24, Section 4.2] about these preconditioners and we unpack all of the necessary numerical background for a full understanding of the observed phenomena.

MAS specifications express the effects of the actions of the agents and their environment, as well as other temporal phenomena, such as the intervals during which an agent may perform an action. The specification of a MAS should also be executable in order to allow for run-time monitoring. Constructing the specification of a MAS requires formal language expertise, while machine learning techniques depend on labelled data which are rarely available. To address these issues, we propose `genRTEC', a method that leverages pre-trained Large Language Models (LLMs) to generate executable MAS specifications, in the language of the `Run-Time Event Calculus' (RTEC), from natural language descriptions. genRTEC constructs MAS specifications with complex hierarchical and cyclic dependencies based only on short natural language descriptions of the concepts involved. We present an extensive empirical evaluation of genRTEC, spanning various MAS specifications, including both a qualitative and a quantitative assessment. Our results demonstrate that genRTEC constructs executable MAS specifications of high predictive accuracy without compromising reasoning efficiency.

Process-capture platforms promise to make the writing behind an assessed artefact visible, and vendors increasingly market them as a fairness measure rather than a detection tool. Their acceptability to the students who must write within them, however, is largely untested. This exploratory qualitative study examines how students' expectations of one such platform, Turnitin Clarity, compared with their experience of using it. Seven students at a UK university, given no onboarding to the platform, took part in pre-use focus groups. Six then completed an unassessed 500-word writing task over five days, before all seven returned for a post-use focus group. Data was analysed using reflexive thematic analysis, with Expectation-Confirmation Theory as an orienting frame. The overall pattern was one of mixed confirmation. Participants' functional expectations were largely met, and the sense of being watched that they had anticipated persisted after use: for some it was offset by perceived fairness, while for others it heightened self-monitoring. The bounded AI assistant divided them: its limits were welcomed for marking out acceptable use, but some felt it weakened their ownership of the work and worried it would flatten what they produced. Across both phases, participants weighed the costs of observation against perceived gains in fairness and asked for transparency to run in both directions. Several described already writing defensively in anticipation of accusations of AI misuse. Acceptance of process technologies was reported as being conditional on practice time, two-way transparency, and explicit data governance. Participants also questioned whether a single linear document can represent a writing process they described as messy and multimodal. Across these accounts, process capture did not sit outside the writing it recorded but reorganised the practice it set out to observe.

This study looks at how the entangling structure of a variational quantum classifier (VQC) relates to its performance in breast cancer diagnosis, using the Wisconsin Diagnostic Breast Cancer (WDBC) dataset. We tested three three-qubit configurations that share the same EfficientSU2 ansatz, COBYLA optimizer, and stratified five-fold cross-validation, but differ in their entangling structure: a single- repetition Ising-type coupling (A), a two-repetition linear Ising-type coupling (B), and a fully connected Heisenberg-type coupling (C). Entanglement was measured with the von Neumann entropy and the Wootters concurrence. From A to C, the mean entropy rose from 0.40 to 0.71, accuracy rose from 92.98% to 93.68%, and F1-score rose from 90.32% to 91.28%. Configuration C was also the most stable across folds. However, the fold-level correlations between entanglement and performance were weak and not significant. Richer topologies also increase circuit expressivity, so the two effects cannot be fully separated. These results show an association, not a proven causal link, between entangling structure and VQC performance.

For a graph \(F\), the Turán number \(\ex(n,F)\) is the maximum number of edges in an \(F\)-free graph on \(n\) vertices. Let \(q\ge 2\) be an integer and set \(n=q^{2}+q+1\). Brown and Erdős, Rényi and Sós independently proved that $\ex(n,C_{4})\ge \frac12 q(q+1)^{2}$ for every prime power \(q\), and Füredi subsequently established the upper bound $\frac12 q(q+1)^{2}$ for $\ex(n,C_{4})$ whenever \(q\notin\{1, 7,9,11,13\}\). In this article, we prove that every \(C_{4}\)-free graph \(G\) on \(n\) vertices with at most \(\frac12 q(q+1)^{2}\) edges satisfies $\tau(G)\le n^{(n-3)/2}$, where \(\tau(G)\) denotes the number of spanning trees of \(G\). In particular, for every prime power $q\notin\{7,9,11,13\}$, the above upper bound on $\tau(G)$ is attained precisely by the orthogonal polarity graphs, thereby proving London's conjecture for all such $q$.

We analyse a well-defined sample of galaxies from the final data release of the Kilo-Degree Survey (KiDS-DR5), selected using magnitude, photometric redshift, and stellar mass cuts, to measure their mean halo mass and circumgalactic dust content as a function of stellar mass. Our goal is to provide empirical constraints on dust transport mechanisms, such as stellar- and AGN-driven outflows, operating in galaxy halos. We develop and validate a new measurement and modelling framework using the MICE2 simulation, incorporating a realistic circumgalactic dust extinction scenario. Using this framework, we jointly model multiband ($ugriZYJHK_{\rm s}$) magnitude shifts and galaxy–galaxy lensing signals to infer the mean halo mass and dust mass of lens galaxies at $z_{\rm B} < 0.4$, analysed in five stellar-mass bins in KiDS-DR5. The modelling jointly describes the halo mass distribution and dust extinction, including dust associated with neighbouring halos. We demonstrate that the inclusion of a satellite fraction and dust extinction from neighbouring halos is required by the data. We find a linear relation between stellar mass and dust mass, consistent with previous observational studies, but flatter than predictions from the semi-analytic model Dusty-SAGE. This difference may indicate that current implementations of dust-related feedback in galaxy formation models require further refinement.

Managing water resources in mountainous regions depends heavily on reliable Snow Water Equivalent (SWE) and Snow Height (HS) data, yet these variables remain difficult to track at scale. This study evaluates three machine learning architectures (XGBoost, U-Net and SegFormer) for the joint estimation of SWE and HS variations from Sentinel-1 InSAR data over the Italian Alps, using the IT-SNOW reanalysis as reference. SegFormer achieves the best results on both targets, with an MAE of 10.391 cm for HS and 27.113 mm w.e. for SWE and the lowest variability across initializations. A feature sensitivity analysis shows that including all available features does not guarantee the lowest error, with model- and task-specific sensitivities. Spatial metrics (R2, Pearson's r) separate the three architectures far more clearly than mean error (MAE, RMSE) does, and decomposing the error per window attributes most of it to a systematic offset in the estimated mean variation rather than to the spatial pattern.

Flow matching (FM) has recently emerged as a promising framework for generative modeling due to its conceptual simplicity and strong empirical performance. In FM, samples are transported along a vector field parameterized by a neural network, inducing a probability path that evolves from a simple noise distribution to the target data distribution, governed by an ordinary differential equation (ODE). However, existing FM approaches predominantly rely on probability paths derived from optimal transport (OT) between Gaussian distributions, which may be suboptimal for capturing complex data with inhomogeneous structures such as heavy tail or sharp contrast. In this work, we generalize FM to the broader class of location-scale families for handling data inhomogeneity and introduce a novel class of probability paths defined as geodesics on the manifold of probability distributions. We name this approach probabilistic geodesic flow matching to distinguish it from prior geodesic (Riemannian) FM methods defined in input space. We argue that Euclidean OT-based paths are not necessarily optimal in probability space and may limit modeling flexibility. Through synthetic benchmarks and scientific datasets at different scales, we demonstrate that the proposed method more effectively captures complex distributions, leading to improved or comparable performance compared with SOTA geometry-motivated generative models.

Long-reasoning Mixture-of-Experts (MoE) models expose two coupled inference bottlenecks: growing KV caches shift the critical path toward attention, while sparse expert activation causes load imbalance and low hardware utilization. Although Processing-in-Memory (PIM) offers a promising way to mitigate data movement overhead, existing PIM-based accelerators typically optimize attention or FFNs in isolation. We propose SPIMOE, the first co-design framework that exploits hybrid sparsity for efficient MoE inference on heterogeneous PIM architectures. SPIMOE combines adaptive expert routing with block-sparse attention and physical KV-cache eviction, and disaggregates attention and FFNs across SRAM-PIM and HBM-PIM. Static expert mapping and dynamic sub-batch scheduling further balance channel loads and overlap the two paths. Evaluations show that SPIMOE achieves up to $8.35\times$ end-to-end speedup over an NVIDIA A100 GPU and $3.33\times$ speedup in MoE FFN execution over PIMoE, while preserving reasoning accuracy comparable to full-attention baselines.

Cross-site out-of-distribution (OOD) generalization in resting-state functional magnetic resonance imaging (rs-fMRI) often relies on learning task-discriminative representations from full-scan functional connectivity (FC) graphs and promoting invariance across source sites. However, FC graphs are estimated from finite, temporally correlated blood-oxygen-level-dependent (BOLD) sequences. Cross-site agreement therefore does not necessarily imply that predictive evidence remains supported under FC re-estimation within the same scan. In this paper, we propose Brain Network Re-estimation-Informed OOD Learning (BRIO), a framework that uses within-scan FC re-estimation to guide cross-site alignment. BRIO maps fullscan graphs and their re-estimates into consistently indexed connectome factors, enabling comparisons of their predictive contributions. It assesses re-estimation support from changes in these contributions relative to within-class subject variability and class separation. For each source-site pair and class, this task-calibrated support from both sites is combined with predictive relevance to form pairwise qualifications, which determine relative factor weights and overall alignment strength. Leave-one-site-out experiments on four real-world datasets (ABIDE, REST-metaMDD, SRPBS, and ABCD) show that BRIO consistently outperforms competitive baselines, with relative improvements of up to 3.8% in accuracy. These gains also persist under an alternative brain parcellation on ABIDE.

We study the linearized dynamics of the Kolmogorov flow $U^{(0)}=(a\sin x_2,0)$ for the two-dimensional incompressible Navier–Stokes equations with horizontal dissipation $\nu\partial_1^2$. Unlike the fully dissipative case, this anisotropic system admits $U^{(0)}$ as an exact unforced steady state. On each horizontal Fourier mode $k$, the dissipation reduces to the scalar $-\nu k^2$ and commutes with the advection, so that the linearized semigroup factors exactly into $e^{-\nu k^2t}$ times the inviscid Euler group. For $|k|>1$, we prove two-sided bounds showing that the decay rate is exactly $\nu k^2$, uniformly in the shear amplitude $a$; hence no enhanced dissipation occurs. This reflects a fundamental mismatch: the shear transfers enstrophy to high vertical frequencies, which horizontal dissipation does not detect. At the critical modes $|k|=1$, the inviscid group grows like $\sqrt{2at}$, producing a transient amplification of size $(a/e\nu)^{1/2}$ before decay at the rate $\nu$. The horizontally independent modes form an infinite-dimensional undamped kernel. For $0<|k|<1$, the viscous spectrum is an exact translate of the inviscid one, and the mode is linearly unstable if and only if $a\Lambda(k)>\nu k^2$. In particular, when $L>2\pi$, the flow is linearly unstable for all sufficiently large $a$.

Topological signals are dynamical variables supported on higher-order structures such as simplicial or cell complexes. In this work, we investigate the impact of time-delayed interactions on the emergence of global synchronization of topological oscillators, with application to the Stuart-Landau system. We first examine the case where signals are supported on simplexes, or cells, of a given dimension and coupled through the Hodge-Laplace matrix. We derive the Master Stability Function and we prove that for suitable discrete delay values, the stability of the synchronous solution becomes analytically tractable and can be solved by using the Lambert W-function. This analysis yields explicit spectral conditions for Global Topological Synchronization to emerge and shows that admissible delays may either promote or suppress synchronization. We then study delayed interactions between signals supported on simplexes, or cells, of different dimensions coupled by the Dirac operator. Under analogous admissible time delays the variational problem, still related to the Master Stability Function, can again be simplified, however in this case we prove that Global Topological Dirac Synchronization cannot emerge. Numerical simulations on simplicial and cell complexes corroborate and complement these findings.

World Action Models (WAMs) enable future-aware control by jointly modeling actions and environment dynamics. However, iterative diffusion or flow inference incurs substantial denoising latency. Prior inference state offers a natural opportunity for acceleration, yet changing planning contexts, observations, and intermediate representations can quickly render retained state stale. Preserving useful computation therefore requires adapting inference state rather than reusing it as-is. To this end, we present $\mathrm{WAM}{\scriptstyle\mathrm{ACHINE}}$, a training-free framework that accelerates WAM inference by preserving and adapting inference state for efficient and accurate continuation as the control loop evolves. Across closed-loop replans, Trajectory Remapping remaps replan state from the preceding replan to initialize the next replan, reducing redundant trajectory generation. Across denoising steps, Observation Rebinding performs anticipatory inference during action execution and rebinds retained denoising state to the real observation for continuation when consistency checks pass, reducing latency exposed to the control loop. Across Transformer layers, Residual Rescaling selectively rescales retained layer state and refreshes it through full computation of the middle layers when probe checks fail, reducing repeated Transformer computation. Evaluations of three representative WAM architectures on LIBERO and RoboTwin 2.0 show that $\mathrm{WAM}{\scriptstyle\mathrm{ACHINE}}$ achieves 1.47-3.05$\times$ speedups in observation-to-action latency and 2.23-3.27$\times$ speedups in GPU inference time per replan, while preserving 96.69-99.54% of native WAM task success.

Weak interactions at a two-dimensional quadratic band touching (QBT) can generate an exponentially small symmetry-breaking gap, $m\sim e^{-A/V_1}$, that cannot be captured by every finite order of perturbation theory. We show that the singular quantum geometry of the gapped QBT converts this beyond-all-orders scale into an algebraically enhanced response. The quantum metric develops a momentum-space hot spot whose Brillouin-zone integral diverges logarithmically, and therefore grows algebraically when the gap is dynamically generated by interactions. Through the inverse-frequency Souza–Wilkens–Martin optical sum rule, the same amplification appears in the negative-first longitudinal optical moment, even though the ordinary optical conductivity remains $O(e^2/\hbar)$ and its absorption threshold is exponentially small. We establish these results analytically for a massive QBT and verify them microscopically in an interacting kagome lattice model known to develop a spontaneous quantum anomalous Hall mass at its QBT from loop currents order. Our results identify quantum geometry as an asymptotic amplifier of nonperturbative interaction scales.

Leveraging the paradigm of autoregressive diffusion, text-conditioned interactive video world models aim to simulate temporally coherent environments guided by textual instructions. While enabling low-latency, long-duration generation is pivotal for embodied AI and simulation-based planning, current frameworks primarily rely on sliding-window mechanisms to bound computational complexity. However, this approach inherently sacrifices historical context, undermining the long-range interactive capabilities. Conversely, maintaining a full-history cache remains computationally prohibitive and memory-intensive: the quadratic complexity of attention leads to excessive computational overhead, while the linear growth of the KV cache inevitably leads to GPU memory saturation. To overcome these limitations, we propose WorldAttention, a system-oriented attention architecture that achieves high efficiency through the co-design of specialized attention kernels and hierarchical KV cache management. First, we introduce Hybrid Sparse Attention (HSA), which integrates linear global attention supplemented with head-adaptive sparse attention. Additionally, we design a Hierarchical KV Cache (HKV) that organizes historical KV pairs into semantically indexed pages across multi-tier memory, enabling fine-grained retrieval and controlled GPU residency. These two designs are supported by tailored kernels to effectively translate their theoretical efficiency into real-world performance. Extensive experiments on VBench-Long and InterVBench demonstrate that WorldAttention consistently surpasses prior state-of-the-art methods, achieving subject consistency scores of 0.9472 on VBench-Long and 0.9668 on InterVBench, respectively.

Multi-teacher on-policy distillation (MOPD) has emerged as a popular post-training paradigm for integrating specialized capabilities in frontier language models. Existing OPD research has primarily focused on optimizing single-task distillation through objective design, distillation scope, and teacher signal construction, whereas MOPD must aggregate multiple capabilities in shared parameters and address the resulting capability seesaw, in which improving one domain suppresses capabilities acquired from another. Inspired by the distinctive update geometry of OPD, we find that parameter updates from different tasks rapidly concentrate in their respective low-dimensional subspaces during MOPD, providing a direct geometric basis for identifying and controlling cross-task interference. We therefore propose PMOPD (Projection-based Multi-Teacher On-Policy Distillation), which constructs subspace memories from the cumulative parameter displacements of different tasks and projects both gradients and optimizer updates to remove components that interfere with protected task directions. We further develop a lightweight conflict probe to characterize task interactions and guide task ordering, together with a cycling strategy that balances subspace estimation and timely task revisitation. Experiments on representative Code, Reason, and Math tasks show that PMOPD improves every evaluated capability over MOPD, raising the average score across the three tasks by 2.54 points on Qwen2.5-7B and 2.09 points on Llama-3.1-8B. These consistent gains establish geometry-aware optimization as an effective and transferable approach to balanced multi-teacher distillation.

World models learn environment dynamics from interaction experience. These dynamics depend on the current state and actions, as well as on properties that persist across interactions. Yet standard predictive training can reduce error using local evidence alone, without organizing persistent information into reusable context. We introduce SPRII, a training principle that uses relations between interactions as weak supervision for persistent context while retaining the learner's native objective. For example, different trajectories of the same system share persistent properties even when their states and actions differ. SPRII uses such relations to guide context learning without numerical property labels. Two composable components encourage contexts from related interactions to agree (Align) and use one interaction's context to predict another's future (Cross). Our analysis distinguishes three linked questions: what persistent information is accessible in the learned context (Formation), how that context influences a fixed predictor (Use), and whether it reduces task error (Value). Success at one stage does not guarantee success at the next. Controlled experiments show that more reliable relations improve representation organization, but adding a shared-property constraint can reduce access to a property that remains shared. Context substitutions change predictions at fixed model weights, while the benefit from history depends on prediction horizon and readout. Evaluations span thirteen settings, including controlled physical systems, public dynamics tasks, robotic and tactile data, and partner interaction, across multiple learner families. Relative to the corresponding baselines, SPRII yields average gains of over 10% in downstream task performance and over 15% in persistent-property readout. The project page is available at https://persistent-learning-review.netlify.app/interactive.html.

Does repairing an episode make its experience a better memory for the next task? We transfer the same failed source before and after accepted repair to a fixed target, alongside independent execution. Our 3,300 runs cover 100 ThinkingBox pairs and the same 100 APEX pairs with and without source-state inheritance, under eleven conditions. ThinkingBox's Full/Skill/Hybrid correction gains are 44/29/32 percentage points, with corrected performance 25/22/18 points above independence; inference weakens at the task-family level. Yet 12 of Full's 15-point larger correction gap over Skill come from worse uncorrected performance, not better corrected memory. Moreover, 22 of Full's 46 upward transitions restore observed baseline success. Neither APEX regime establishes comparable aggregate correction benefits. Action evidence connects workflow gains with reusable obligations and convention conflicts with source-local choices. Text APEX's accepted execution reaches 52% versus its summary's 40%, without robust global/group-level superiority or an estab- lished advantage over independence. Smaller handoffs reduce input but increase calls. The value of repairing experience is therefore distinct from the value of reusing it: memory updates require both a previous-version reference and a fresh-start reference.

Frozen Earth-observation embeddings are judged almost entirely by spatially blocked cross-validation inside one study region. We show that this number does not predict accuracy in a new region; we show why; and we show the one setting in which such a model does keep working, using a protocol that needs only a linear probe and labels one already has. The testbed is wildfire, with Copernicus burned-area maps of six fires in Greece and Spain and descriptors from the year before each fire, comparing TESSERA and AlphaEarth with ESA WorldCover classes and annual Sentinel-2 index summaries. Inside a fire, the embeddings identify the burned land 0.05 to 0.13 ROC AUC better than the index summaries, and repeated fold allocations, spatial buffers, a block bootstrap, and gradient-boosted trees leave that margin unchanged. On a fire in another region, they lose 0.15 to 0.18 AUC, and the index summaries lose 0.06, so the three end within a few hundredths of each other. The representation is not the cause. Eight labelled blocks from the new region restore the embedding advantage and give a higher AUC than 59,000 labelled pixels from other regions, and the weight vector fitted in one region is nearly orthogonal to the vector fitted in the others, so the part that carries across regions is small and low-dimensional. Forecasting within a region is a different matter. Fitted on a fire that burned in 2023 and applied to a fire twelve kilometres away that burned in 2024, where nothing used postdates the target fire, TESSERA reaches 0.772 AUC and loses 0.04 against a classifier fitted inside the 2024 fire, while classifiers fitted in other regions lose 0.09 to 0.18. A region with one mapped fire can therefore forecast susceptibility for later fires there; a region without one cannot borrow a model from elsewhere, and every evaluation of a frozen embedding should report a held-out region.

It was proved in [3] that on a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities that is invariant under the action of the diffeomorphism group is a multiple of the Fisher–Rao metric. Here we describe all purely covariant tensor fields of arbitrary order on the space of positive densities of a compact manifold with corners which are invariant under the action of the connected component of the diffeomorphism group. Finally, we classify the considerably fewer purely contravariant invariant tensor fields, describe the basic mixed contraction, and indicate the expected form of general invariant tensor fields.

Karlin, Klein, and Oveis Gharan introduced a randomized better-than-$3/2$ approximation algorithm for metric TSP [KKO21] and subsequently established the corresponding improvement in the integrality gap of the subtour-elimination LP [KKO22], with an explicit constant $\varepsilon>1.00000\cdot10^{-36}$. Gurvits, Klein, and Leake subsequently improved the certified saving to $2.18000\cdot10^{-34}$ [GKL24]. In this paper, we obtain a randomized polynomial-time $(3/2-\varepsilon)$-approximation for every fixed $0<\varepsilon<\varepsilon_\star$, where $\varepsilon_\star>2.78621\cdot10^{-18}$, and consequently the subtour-elimination LP has integrality gap at most $3/2-\varepsilon_\star$. The classical worst-case integrality-gap lower bound is $4/3$ [Wil90].

Reinforcement learning (RL) is increasingly used to post-train vision-language-action (VLA) models, yet how RL reshapes these policies remains poorly understood. We find that RL across widely used flow-based VLA models, including $\pi_{0.5}$ and GR00T~N1.5/N1.6, on LIBERO, ManiSkill, MetaWorld, and CALVIN induces substantially lower-rank parameter updates that are highly concentrated in the action expert's Timestep Modules, a small and previously overlooked component. Through systematic module-replacement experiments, we further show that these modules capture a disproportionate share of the performance gains from RL. We then characterize what is encoded in these Timestep Modules. First, we show that RL specializes them to the discrete denoising timesteps used during rollouts, and that this discrete-timestep training underlies the low-rank updates. Second, we find that among their outputs, the shift vector changes most distinctly under RL, and through probing, we show that shift update directions strongly predict task success (ROC-AUC up to $99.6\%$). Third, we find that the geometry of shift updates reflects task relationships, as their pairwise similarity correlates with cross-task transfer patterns. Building on these findings, we show that steering along shift update directions further improves RL-trained policies without additional RL training. Overall, we provide a systematic understanding of how RL reshapes VLA policies by studying how learned signals are encoded in parameter space, offering insights into more efficient and interpretable VLA post-training.

Video temporal grounding (VTG) aims to localize the video interval corresponding to a language query. Recent large vision-language models (LVLMs) show great potential in solving such a multi-modal reasoning task. However, long videos often contain large amounts of redundant information that disturbs LVLMs to mine query-relevant evidence. Instead of dense frame sampling which incurs prohibitive training memory, previous reinforcement learning with verifiable rewards (RLVR) works typically utilize sparse sampling, which makes training feasible but may miss critical evidence. In this paper, we propose a “summarize before grounding” framework (named “SumGround”) for long-video temporal grounding. The key of SumGround is to perform query-guided chunk condensation to aggregate and retrieve query-relevant evidence. Specifically, we split the video into several chunks and perform two-level chunk condensation. First, we introduce query-guided latent summaries, which is represented as KV states of query-guided prompts, to compress redundant visual tokens into compact query-relevant chunk summaries. Furthermore, we design an associative summary retrieval scheme to rank and select chunk summaries that are most likely to contain the event interval. Both query-guided latent summary and associative summary retrieval schemes are enabled by RLVR. To reduce memory consumption, we propose a length-aware gradient gating module to selectively stop gradient back-propagated to visual tokens. Extensive experiments demonstrate that SumGround performs favorably against previous state-of-the-art methods across multiple downstream datasets, with remarkable gains on long videos.

Large language model agents can acquire complex capabilities through multi-step interaction and tool use, but their trajectories can also be illegally collected to dis- till student agents. However, existing watermarking methods either do not fit the structured and interactive nature of agent environments or lack reliable effective- ness across tasks and model architectures. We introduce AuxMark, a behavioral watermarking framework for tracing unauthorized agent distillation. AuxMark dynamically inserts safe, non-essential auxiliary action into teacher trajectories, and stores the associated contexts as private evidence cards. To audit a suspicious student model, AuxMark constructs paired real and fake probes from these cards and applies a card-level sign test. This black-box protocol supports both model- level detection and trace-level attribution. Across three agent benchmarks, two teacher agents, and four student architectures, AuxMark detects all 24 distilled models with zero false positives on 48 clean models. It also preserves task utility and remains effective against data flooding, paraphrasing, truncation, and adaptive cleaning attacks. Our code will be released at this URL.