Papers

This work studies the asymptotic behavior of a class of viscous Hamilton–Jacobi equations with oscillatory periodic potentials, already studied by other authors in the PDE framework, and described in terms of an effective Hamiltonian. A novel variational approach is introduced, based on the classical stochastic control representation involving a Brownian motion, which allows the problem to be reformulated in terms of functionals defined on probability spaces. The core result is the identification of a homogenized Lagrangian obtained via a $\Gamma$-convergence procedure adapted to random processes, where filtrations and Brownian motions are treated as variables. The effective Hamiltonian is then recovered as the Legendre transform of this homogenized Lagrangian. The analysis provides both lower and upper bounds by means of blow-up arguments and the construction of stochastic correctors, yielding a complete characterization of the homogenized limit. This approach allows for a stability result with respect to the addition of some localized defects embedded in the periodic background.

This manuscript aims to advance existing approaches to the abelianization of symplectic quotients. Two such approaches include the imploded cross-sections of Guillemin-Jeffrey-Sjamaar, and the Gelfand-Cetlin abelianizations of the first author and Weitsman. Using our notion of generalized Gelfand-Cetlin data, we generalize the second approach to account for irregular values of the moment map. Connections to symplectic implosion are emphasized throughout this manuscript.

For $d\ge3$, let $\lambda_d$ denote the sharp constant in the nearest-neighbor Hardy inequality on $\mathbb Z^d$ with Euclidean inverse-square weight for functions vanishing at the origin. Recent work established that the continuous Hardy coefficient \[ C_d=\frac{(d-2)^2}{4} \] is sharp in dimensions three and four, while it is not sharp for $d\ge9$. We prove $\lambda_d=C_d$ for the remaining cases $5\le d\le8$. The proof uses reciprocal edge fields and pointwise estimates for the associated vertex weights. The exterior estimates follow from polynomial inequalities, and the weights near the origin are treated by explicit estimates and local corrections.

In this paper we give necessary conditions for 4-class association schemes that are generated by double covers of strongly regular graphs. These conditions are applied to open cases for diameter 4 antipodal distance-regular graphs. Using these conditions we are able to show the nonexistence of four cases in the table of Brouwer, Cohen and Neumeier: $\{20,18,3,1;1,3,18,20\}$, $\{22,21,3,1;1,3,21,22\}$, $\{ 54,50,5,1;,1,5,50,54 \}$, $\{ 170,162,9,1;,1,9,162,170 \}$. More generally, we show there is no distance-regular graph with intersection array $\{k,b_1,b_2,1;1,b_2,b_1,k \}$ where $b_2 \neq 1$ and $\frac{ k b_1 }{4}(1+k+\frac{ k b_1 }{2b_2})$ is odd. Tables are also given for more general 4-class association schemes generated by double covers of strongly regular graphs.

How the brain groups image elements into coherent objects in natural scenes remains unclear. Existing models for grouping in biological vision rely on simplified stimuli with explicit boundaries and cannot explain human behavior in naturalistic settings. We propose a mechanistic framework in which recurrent interactions propagate enhanced neuronal activity within and between cortical areas. The framework links computational principles, neural circuitry and perceptual psychology. Local boundary signals govern early grouping, whereas later stages integrate top-down feedback carrying information about object identity, grouping features across internal edges into coherent object representations. We instantiated this framework as a brain-inspired recurrent neural network trained to group features in natural images. The network learned to propagate enhanced activity across a cued object's representation, mirroring the brain's perceptual grouping mechanisms. The network's dynamics also predicted human reaction times. The framework links cortical dynamics to human vision and generates testable predictions for neuro-physiological and psychophysical experiments.

Most vision-language-action (VLA) models rely on current observations and lose task-relevant evidence once it leaves view, limiting performance on long-horizon, memory-dependent tasks. Existing efforts incorporate compressed historical features or sparse visual keyframes. However, isolated snapshots can leave the policy uncertain about what changed during past interactions and which action should follow. To overcome this limitation, we propose EvoMem-VLA, which constructs state-evolution memory by explicitly encoding and retaining observed changes between historical states. These change representations preserve evidence of interaction outcomes, allowing the policy to track task progress beyond isolated snapshots. Specifically, we introduce conditional delta tokenization to encode ordered frame pairs into directional, source-conditioned delta tokens, each associated with its corresponding state evidence. A shared VLM backbone supports task-adaptive routing: normal long-horizon tasks follow a direct action route, whereas multi-stage tasks use a subtask route that generates an executable subtask as an additional input for action generation. With a single jointly trained policy for each simulation benchmark, EvoMem-VLA achieves success rates of 80.7% on RMBench, 82.0% on RoboMME and 83.8% across four real-world tasks spanning two robot embodiments. These results represent substantial improvements over the previous state of the art in all three evaluation settings.

Recent works augment Vision-Language Models with geometry features from pretrained 3D models, expecting that the geometric signal will boost spatial reasoning. However, we find that simply fusing geometry features and training on standard spatial QA yields only marginal improvements on high-level multi-hop tasks. We attribute this gap to a training-signal problem: standard spatial QA can be largely answered from visual features and language priors, so the geometry pathway receives weak gradients and fails to integrate with the visual features. To provide a training signal that requires geometry, we propose novel-view semantic rendering as an auxiliary training task that requires the model to predict the semantic layout of an unobserved viewpoint, inspired by humans' ability to mentally simulate novel viewpoints during spatial reasoning. This task encourages joint use of both pathways: geometry provides pose-dependent visibility, while vision provides semantic content. Our auxiliary task yields consistent improvements over the geometry-augmented baseline across all three benchmarks (up to +1.6 on VSI-Bench, +2.2 on ReVSI, +2.9 on our 3D-Point-QA dataset) and our full model surpasses prior open-source methods on VSI-Bench and on ReVSI. Project page: https://yuqunw.github.io/Render2Reason/.

Natively training joint video-audio generation models at higher resolutions empowers them to learn richer visual details and sharper motion dynamics. However, full attention incurs quadratic cost and, as resolution increases, spreads attention over increasingly redundant tokens, diluting learning signals for informative content and disrupting pretrained priors. Existing sparse attention methods either target training-free acceleration or overlook the unique structure of joint video-audio data, where cross-modal interactions are inherently concentrated around sound-producing regions. To address this, we propose Prism, a dynamic sparse attention framework for natively training joint video-audio generation models at 2K. In particular, Prism organizes the token sequence into spatiotemporal macro-zones, enabling the attention structure to adapt to local content. For each zone, it estimates local information structure via video feature variance along the channel and feature norms from the audio-to-video cross-attention, jointly capturing how visual content varies directionally and how strongly audio influences each visual region. Based on these signals, Prism dynamically assigns a tailored block shape to each zone, applying finer partitioning along axes of rapid visual content variation and strong audio-visual coupling. This encourages tokens within each block to remain semantically coherent, allowing block-level features to capture both visual content and joint video-audio interaction patterns. Prism further adopts a hybrid block selection strategy to dynamically determine per-query sparsity. Experiments show that Prism achieves 2.5$\times$ training speedup compared to full attention, while surpassing it in generation quality.

A group is an {\it $\SJ$-group} if it admits a general abelian series all of whose terms are subnormal of finite defect in the whole group. We construct a group $G$ which is not an~\hbox{$\SJ$-group}, although every countable subgroup of $G$ is an $\SJ$-group.

Although the advancement of vision-language models (VLMs) has endowed robots with enhanced environmental understanding and task reasoning, a comprehensive evaluation methodology is important to advance the integration of VLMs in robotic navigation and manipulation. However, current benchmarks lack a comprehensive method to evaluate diverse robotic tasks, and evaluation metrics remain relatively constrained, making it difficult to assess the embodied capabilities of VLMs in a thorough and fine-grained manner. To address this issue, we propose RMMBench, an evaluation benchmark that requires robots to understand language instructions and perform long-horizon tasks in continuous spaces. RMMBench seamlessly integrates high- and low-level embodied tasks into a unified framework, constructing a "navigation-manipulation" task suite comprising 70 canonical task scenarios that range from localized manipulation to long-horizon composite navigation. The results reveal that leading VLMs still face major challenges in spatial localization when performing mobile manipulation tasks, and also highlight the necessity of enhancing the spatial perception capability of robots during long-horizon interactions. RMMBench can be accessed at https://mxxq-stack.github.io/rmmbench-project/

Evaluating vision encoders requires metrics that reliably predict their downstream performance in multimodal large language models (MLLMs). Although recent studies have shown that cross-modal metrics can better capture such performance, unimodal metrics remain the dominant choice in practice. In this work, we revisit cross-modal evaluation of vision encoders through large-scale experiments. We identify important limitations in both the experimental design and methodological formulation of prior approaches. After addressing these limitations and introducing simple improvements, we propose RAVEL, a training-free method based on cross-modal nearest-neighbor retrieval. Despite its simplicity, RAVEL achieves state-of-the-art performance across our experiments, outperforming prior methods by a substantial margin. Our results demonstrate that simple cross-modal metrics, when evaluated under a careful and comprehensive setup, can provide a strong basis for evaluating vision encoders for MLLMs.

We prove a complete complexity dichotomy for planar graph homomorphism counting with any fixed symmetric nonnegative matrix of arbitrary finite order, giving an explicit criterion for tractability. We also characterize exactly which fixed positive vertex weights preserve tractability, with both classifications extending from algebraic weights to fixed real weights in a prescribed exact representation. Our proof hinges on an entropy-based continuation argument: maximal logarithmic support identifies distance kernels as maximum-entropy completions, extending their positive definiteness throughout the parameter interval. This enables distance geometry to recover hidden product coordinates even when planar gadgets cannot distinguish colors; counting-hardness arguments then force the factors to be zero-field Boolean Ising interactions. The classification also yields complete tractability criteria for clock models, coupled Ising systems, and planar contractions of stoquastic imaginary-time kernels. All results have been formally verified in Lean 4.

Motion capture data is rarely directly usable, as they typically exhibit missing segments, jitter, drift and contact artifacts. Traditionally, corrupted motions are cleaned by animators through the manual identification of keyframes from noisy motion, subsequent keyframe correction, and interpolation between corrected keyframes to reconstruct coherent motion. While the rise of generative motion models has made automatic cleanup feasible, most approaches operate as black box denoisers with limited controllability, making it difficult to preserve reliable segments or enforce specific user intents. Inspired by animation workflows, we present CleanMDM, a unified multimodal motion cleanup framework that formulates cleanup as masked conditional generation with plug-and-play conditions. This single model supports arbitrary combinations of noisy 3D motion, sparse 2D keyframes, sparse 3D keyframes, and text. This design enables both automatic cleanup without additional user annotation and controllable cleanup under multimodal guidance. To further improve motion realism, we incorporate the Latent Motion Quality Discriminator (LMQD) to better match kinematic distributions and reduce skating, jitter, and interpenetration artifacts, and we apply Mesh-Aware Contact Projection as a test-time optimization step to enhance contact and physical consistency. Experiments across multiple datasets demonstrate that CleanMDM consistently outperforms prior cleanup and generation baselines, and that low cost conditions (text and 2D keyframes) provide reliable controllability gains in multimodal cleanup scenarios.

V. Manuilov introduced the universal Roe algebra, namely the uniform Roe algebra associated with the largest uniformly locally finite coarse structure $\mathrm{Univ}$ on $\mathbb{N}$, together with several variants. We study these algebras through embeddability properties of $\mathrm{C}^*$-algebras. Among other results, we show that the universal Roe algebra admits an embedding from $\prod_n\mathbb{M}_n$, answering a question by Farah. Thus, Ozawa's non-embeddability theorem for $\prod_n\mathbb{M}_n$ in uniform Roe algebras of uniformly locally finite metric spaces does not extend to arbitrary uniformly locally finite coarse spaces. Nevertheless, embeddability properties distinguish the variants introduced by Manuilov and the quasi-local algebra of $\mathrm{Univ}$, apart from the multiplier algebra $M(\mathbb{I})$. As a by-product, we also obtain an operator-norm analogue of Birkhoff's Problem 111: the norm-closed convex hull of permutation operators is exactly the set of doubly substochastic operators. Moreover, we show that every separable $\mathrm{C}^*$-algebra embeds into the quasi-local algebra of $\mathrm{Univ}$. Although we do not know whether the analogous statement holds for the universal Roe algebra, we prove that every separable quasidiagonal $\mathrm{C}^*$-algebra embeds into it, and hence into the reduced $\mathrm{C}^*$-algebra of some étale locally compact second countable groupoid.

Action-conditioned time-series forecasting requires accounting for how future actions and exogenous forcings influence multiple targets through partially observed effects with different delays and persistence. Direct conditioning leaves the evolution and target-specific influence of these effects implicit in the predictor, while static relational graphs specify connections without tracking evolving effects. This motivates representing future-driver influence through structured latent states that evolve over the forecast horizon and route information to individual targets. We introduce BeliefGraph-JEPA, a structured latent world model that factorizes driver influence into typed latent-effect states. These states are rolled forward under future drivers and routed through a graph to target-specific nodes, forming the predictive base of a joint-embedding predictive architecture. A capacity-controlled residual supplements this base with direct driver information. On four multi-target clinical, agricultural, environmental, and industrial systems, the framework outperforms a range of pretrained and supervised known-future-covariate baselines. Matched controls isolate latent dynamics, future rollout, graph routing, and residual capacity; future rollout and graph-first residual routing improve forecasting across all four systems.

Motivated by recent experimental observations by Matsuzawa et al. (2026) of colliding several vortex rings within a water tank, this paper extends a compact trefoil vortex simulation to later times and generates a persistent ==energy spectrum that obeys Kolmogorov scaling, together with other statistics characteristic of fully developed turbulence, including structure function scaling. This temporal extension uses a larger (4pi)3 periodic domain, with the improved compactness being achieved by the use of an algebraic Rosenhead vorticity profile, from which viscosity(nu)-independent finite energy dissipation is generated and pre-reconnection convergence of nu1/4-dependent higher-order vorticity moments. These properties suggest, perhaps for the first time, how decaying Navier-Stokes simulations can generate fully-developed turbulent flow from an unforced initial state that is far from boundaries, thereby suggesting how further simulations at higher values of Re could be harnessed for experimental comparisons. Moreover, the exponents for the energy decay and the integral scale growth, E(t)~(t+t0)-10/7 and and ell(t)~(t+t0)2/7, follow those based upon preservation of the Loitsyanskii integral. On a related question, an integral scale growth rate ell that is close to the experiment rate of ellX~(t+t0)(0.16or1/7)is only obtained if the Fourier modes at the scale of the periodic domain are not considered.

Simulation demonstrations can supplement scarce real-world data for robot policy co-training. However, the value of using data curation to actively select these demonstrations for sim-to-real co-training remains underexplored. Existing curation methods also lack a unified criterion for measuring trajectory-level utility and set-level coverage from closed-loop target behavior. To address these gaps, we present the first systematic study of data curation for sim-to-real robot policy co-training and propose Trajectory-level Utility and set-level Coverage Optimization (TUCO). TUCO uses influence functions to trace how each source demonstration affects target-domain scoring rollouts. Our key insight is that these effects can be decomposed into an overall contribution to target return and variation across rollouts, providing a common closed-loop basis for measuring trajectory utility and set coverage. We further propose a performance-aligned subset optimizer that combines these measures in a unified curation objective to reduce redundancy and select complementary demonstrations. Extensive experiments on RoboMimic and OmniReset establish the value of active simulation data curation for sim-to-real policy co-training and show that TUCO achieves state-of-the-art performance across single-simulator, sim-to-sim, and sim-to-real settings.

We investigate inflationary magnetogenesis with massive vector fields, including charged scalar particle production via the Schwinger effect and its backreaction on the background electric energy density. Initially neglecting the Schwinger effect, we quantize the vector field and solve the equations of motion for transverse and longitudinal modes, computing the energy momentum tensor. We then incorporate the backreaction of the electric energy density and show that the longitudinal energy density is subleading compared to the electric background. Since the electric energy density dominates the magnetic contribution, we can treat the former separately from the perturbative contributions. We adopt this approach when studying particle production via the Schwinger effect, assuming that its backreaction acts only on the background electric energy density. The latter is computed using a classical background electromagnetic field minimally coupled to a quantum complex scalar field. The magnetic and longitudinal components are instead described through quantum fields. In this framework, the Schwinger production affects only the electric energy density, as long as it remains dominant compared to the other components. As a consistency check, we verify that for a null coupling constant we recover the same electric energy density as obtained within the fully quantum electromagnetic description. Finally, we show that for non-null coupling constants Schwinger particle production drastically reduces the electric energy density during the final stages of inflation.

Matrix autoregressive (MAR) models offer a parsimonious framework for modeling matrix-valued time series, yet tools for estimation and inference for their impulse response functions are lacking. We develop asymptotic and bootstrap-based inference for impulse responses of stable MAR($p$) models. We derive the joint asymptotic distribution of the coefficient and covariance estimators, which permits closed-form delta-method standard errors. To address finite-sample bias, we propose ProBAB-MAR, a bias-corrected bootstrap that projects the corrected coefficients back onto the Kronecker parameter space, and prove that it attains asymptotically correct coverage. Monte Carlo simulations show that delta-method intervals undercover in small samples, while ProBAB-MAR achieves near-nominal coverage with intervals considerably narrower than those from an unrestricted VAR. An application to euro area inflation illustrates how shocks transmit across countries and inflation categories.

Recently, it was shown in arXiv:2607.27629 that under a very general condition, a generic family of curved Kakeya sets in $\mathbb{R}^3$ not trivially contained in a hypersurface has Hausdorff dimension strictly greater than 2. In this paper we leverage large language models to give an explicit construction of a family of curves failing the worst compression phenomenon in arXiv:2607.27629, but whose union has Hausdorff dimension and upper box dimension $5/2$. The example shows that there are Kakeya compression phenomena besides the trivial example of concentrating near a hypersurface. This answers a question raised in section 1.9 of arXiv:2607.27629. The models used are ChatGPT 5.6 Sol and ChatGPT 6 Astra.

We study three affine variational quantities built on the affine $L^p$ energy of Lutwak, Yang and Zhang: the affine Poincaré–Sobolev constants $\Lambda^{\mathcal{A}}_{p,q}(\Omega)$ of a bounded open set, the associated affine torsional rigidity, and the affine $p$-capacity of a compact set. We show that ellipsoids are the only extremal sets in their corresponding isoperimetric inequalities, and that the affine capacity of a compact set of positive volume is attained by a potential solving the affine $p$-Laplace equation. We also prove an affine Kohler-Jobin inequality: among sets with prescribed affine torsional rigidity, only ellipsoids minimize $\Lambda^{\mathcal{A}}_{p,q}$. Following the approach of Haddad, Jiménez and Montenegro to affine Sobolev inequalities, our methods rest on the $L_p$ Busemann–Petty centroid inequality. Proving a stability version of it, we obtain quantitative forms of the isoperimetric inequalities for $\Lambda^{\mathcal{A}}_{p,q}$, the affine torsional rigidity and the affine $p$-capacity, together with a stability result for the affine Kohler-Jobin inequality on convex sets.

A central challenge in continual learning is to acquire new knowledge without forgetting what the model has already learned. This challenge appears in language model training when training data comes from various domain-, user-, or task-specific distributions that are encountered unevenly over time. In such settings, successive minibatches are temporally clustered by distribution instead of being sampled i.i.d. from the overall data mixture. Training on temporally clustered data induces a stability-plasticity tradeoff. Adapting the model to the active distribution can improve the model on the active distribution but may lead to a performance degradation on data it previously trained on. We find that this tradeoff intensifies with longer exposure to the same distribution. We therefore ask if the parameter displacement produced by such a sequence (the task vector) should be fully retained or applied partially. We compare applying the full displacement ($\lambda=1$) with partial integration, which scales the task vector by $\lambda$ before applying it to the continuing model and scales the optimizer state by the same coefficient. Across continual pretraining, pretraining from random initialization, supervised post-training, and reinforcement post-training, we find that intermediate values of $\lambda$ often improve average continuing-model performance relative to full integration, particularly after longer same-distribution sequences. In continual-pretraining experiments with both controlled streams and naturally defined adaptation sequences, task-vector scaling outperforms full integration at the matched learning rate, showing that its benefits are not reproduced by learning-rate scaling alone.

Text-to-image diffusion models can generate prohibited content, which motivates concept erasure through machine unlearning. Most erasure methods intervene at the text interface, through prompt modification or localized updates to text-conditioning weights, and they are evaluated by what the model outputs for given prompts. Such evaluation cannot see what the network still encodes. Latent-space auditing, which bypasses text conditioning and probes the denoising network directly, shows that erased concepts remain recoverable from internal representations. We find that this also holds for methods built to be robust against adversarial prompts, and that the problem grows with the number of erased concepts. We propose Auditing-Aware Unlearning for Verifiable Concept Erasure in Diffusion Models (AVCE), a framework that grounds erasure in the model's latent representations. AVCE audits the embedding neighborhood of each concept and condenses the discovered vulnerable directions into an anchor at the weakest geometric point. It edits cross-attention and self-attention projections in closed form at this anchor, then fine-tunes the two pathways with pathway-level auditing losses, using orthogonal gradient projection to consolidate multiple concepts. Experiments on SD v1.5, SDXL, and Flux 1.0 across object, explicit-content, and artistic-style unlearning show that AVCE reduces attack success rates by 5.07x and improves auditing scores by 3.84x over the strongest baseline, while preserving competitive generation quality.

Long-video agents can actively gather question-relevant evidence, but they typically leave a central decision implicit: when has the agent seen enough to answer? We propose CASE, a plug-in termination framework that frames this decision as policy-conditioned sequential stopping. At each causal checkpoint, CASE combines an auxiliary multiple-choice assessment of accumulated evidence with the host agent's execution state. From complete native trajectories, we construct a cost-aware target that compares answering now with stopping later along the same search path, accounting jointly for answer correctness and the full cost of continued reasoning. A lightweight Ridge regressor learns this decision gap and produces STOP/CONTINUE decisions. We evaluate three vision-language models with VideoSeek and AVP. On Video-MME, end-to-end accuracy changes by +0.67 percentage points on average while CASE reduces model-token use by 53.63%. The same frozen policies then transfer zero-shot to LongVideoBench and MLVU, with end-to-end accuracy changes of +3.38 and +4.58 points while saving 58.78% and 51.28% of model tokens, respectively. Across all agent-model-benchmark combinations, CASE attains the highest accuracy-efficiency Pareto-frontier coverage among the compared stopping methods (83.3%) at the selected operating points. Online execution preserves this favorable accuracy-efficiency trade-off and additionally reduces measured runtime by 54.1% on average. CASE provides a plug-in termination framework for long-video reasoning agents, enabling them to decide when further evidence acquisition is no longer worthwhile.

Pull-request review protects software before new code reaches users, helping prevent vulnerabilities that could expose users to attacks. AI agents increasingly perform these reviews and explain which problems need fixing. However, for an attacker submitting vulnerable code, this feedback also reveals what changes may secure approval. Existing PR attacks seek such approval through persuasive text and comments while keeping executable code fixed. This leaves unclear whether an attacker can use the feedback to repair the reported problem while preserving a vulnerability in the revised code. We therefore conduct an empirical study of this threat using AFCRA (Adaptive Feedback-guided Code Revision Attack). To distinguish successful attacks from genuine repairs, we construct AFCRA-Bench from 159 disclosed vulnerabilities, with executable exploits to verify vulnerabilities in code. Across five-round interactions with Sonnet 5 and GPT-5.5 reviewers, AFCRA reaches success rates 2.5x and 12.5x those of the strongest evaluated text- or comment-based attack. Case studies of these successes show how reviewers accept repairs of reported problems while overlooking surviving vulnerabilities. These findings establish feedback-guided code revision as a threat to automated PR review. To address this threat, we derive actionable implications for researchers, AI providers, PR reviewers, and PR authors on securing AI-assisted development.

Autonomous research seeks sustained model improvements through iterative experimentation and feedback. LLM agents show promise in automating machine learning and language-model post-training, but their ability to sustain multimodal improvement remains unclear. We introduce MMPostTrainBench, a benchmark spanning eight tasks in image, audio, video, and joint audio-video understanding and image-grounded software repair. Agents operate from a common base model within fixed budgets, using development feedback before independent evaluation of their submitted models. Evaluation covers target and non-target model outcomes, iterative model improvement and selection, and research integrity. Across all eight tasks, 52.1% of model–task means fall below the base, and evaluated submissions also exhibit non-target regressions. Model performance does not consistently improve across research iterations, and agents do not reliably select the best evaluated candidate for submission; final submissions trail that candidate by up to 5.38 percentage points. Extending autonomous research from text-only to multimodal tasks introduces additional sources of error in perception, cross-modal alignment, and temporal grounding. The observed regressions and selection gaps highlight the need to balance targeted improvements with non-target capability preservation and to retain gains across research iterations. These requirements motivate MMResearch, a multimodal research framework that connects media-grounded evidence to hypotheses and interventions, carries findings across rounds through hierarchical memory, and retains candidates using development evaluation. Added to existing code-agent runtimes, it improves submitted-model accuracy by up to 7.75 percentage points for Claude Opus 4.8 with Claude Code and 2.33 points for GPT-5.6-sol with Codex.

Generative modeling of graph-structured data is crucial for tasks ranging from drug discovery to social network simulation. Among these models, denoising diffusion models have achieved great success in graph generation by learning to progressively reverse a process that adds noise to the original graph. However, the standard noise-prediction approach of diffusion models is suboptimal for graph data. The goal for a graph generative model is to learn the clean graphs' topological properties, such as connectivity and degree distribution. Because a diffusion model that predicts noise does not explicitly learn these topological properties, it is challenging for the model to output graphs with the desired structural statistics. To address this challenge, we introduce Direct Graph Flow Matching (DiGFM), a novel graph transformer model guided by two goals: predict clean graphs and improve sampling efficiency. Distinct from the prevailing diffusion approach, DiGFM employs a continuous flow-matching paradigm and integrates direct graph prediction. Specifically, DiGFM maps the prior noise distribution to the clean graph distribution via a multi-step process: the model repeatedly predicts the underlying clean graph, and a transformation is employed to convert the model output to the velocity vector that points in the direction toward the clean graph distribution. This design enables DiGFM to generate high-quality samples using only 2.5% to 15.6% of the steps required by diffusion-based models, which leads to a 5.3x to 257x speedup in wall-clock inference time. Experiments demonstrate that DiGFM outperforms or matches prior state-of-the-art models across general graph benchmarks and molecular datasets, generating graphs with strong adherence to ground-truth structural statistics at significantly faster inference speeds.

In this paper, we compute the orders of upper triangular symplectic Renner monoids using admissible sets. We obtain both recursive and closed-form formulas for these orders. We then derive their exponential generating functions and establish connections between these functions and the Laguerre polynomials.

While most of the features of the Kitaev honeycomb model are already clarified from the combined ${\mathbb Z}_2$ plaquette and Majorana fermion picture, we show that retrieving the exact quantum many-body form gives a clue to fix the remaining issues on its spin liquid property. We provide an exact two-dimensional tensor network description of a full set of solutions from a random product state, by sequential quantum-number projection and Gutzwiller projection, both expressed as local matrix-product operators of dimension $D=2$. The ground and excited states share the same bond dimension yet exhibit distinct Schmidt spectra, distinguishing their area-law and volume-law entanglement. We demonstrate that the topological entanglement entropy emerges for all eigenstates only after the Gutzwiller projection onto the physical spin Hilbert space, where the gauge constraint removes exactly half of the Schmidt states. This establishes that excited states are likewise topologically ordered. We further show that there exists a projection-induced collapse of the wave function into a single gauge sector in the Parton mean-field states that is known to give a good description of the spin liquids. The demonstrations on the $S=1/2$ kagome and triangular Heisenberg models suggest that the present perspective is applied to a wider class of models hosting ${\mathbb Z}_2$ spin liquids. Our finding visualizes a bulk-boundary correspondence with the Wilson-loop characterization of topological order.

Conversational database interfaces face a critical challenge: users naturally embed queries in conversational noise (greetings, politeness, off-topic remarks), which degrades intent classification accuracy and wastes computational resources. Despite advances in orchestration and retrieval strategies, a fundamental question remains unanswered: which pooling strategy maximizes intent classification accuracy under realistic conversational noise in production language models? This work addresses this gap through 360 controlled experiments spanning four pooling configurations (mean, max, last-token, attention, and FFT-augmented variants) using Llama-3.2-1B-Instruct on BANKING77 and CLINC150 datasets under clean/noisy conditions with ten random seeds. Key findings reveal that attention pooling consistently outperforms alternative strategies under noisy conditions (~+2.6-2.8 F1 over the default), while mean pooling degrades performance by up to ~5 F1 points. Frequency-domain filtering does not produce consistent accuracy improvements and functions primarily as a structural variation rather than an accuracy-enhancing component. These results provide concrete, evidence-based guidance for building noise-robust conversational classifiers: attention pooling is recommended for noisy interfaces, mean pooling should be avoided, and last-token pooling is appropriate for clean-query scenarios.