Papers

Lagrangian Neural Networks (LNNs) learn mechanical systems from trajectory data by parameterizing a scalar Lagrangian and deriving the dynamics through the Euler-Lagrange equations, biasing the model toward motion that respects the variational structure of mechanics. The interactions studied so far have been pairwise-additive, leaving open whether LNNs can recover an irreducible many-body interaction from motion alone. We address this using the Axilrod-Teller triple-dipole interaction, the leading three-body dispersion term, whose dependence on the collective geometry of three particles cannot be represented by any sum of pairwise terms. We prescribe the kinetic energy exactly and learn only the potential, as a function of interparticle distances and angles. Combined with a signal-aware sampling strategy that concentrates training data where the three-body signal is strongest while preserving broad coverage of configuration space, this recovers the interaction from accelerations alone. The learned potential reproduces the radial scaling, angular dependence, and characteristic sign reversal of the Axilrod-Teller interaction, and generates stable trajectories. Embedding it within a pairwise Lennard-Jones potential lets us examine its observability: the three-body term is recovered once its dynamical signature exceeds the residual modeling error, which it does cleanly at amplified coupling but not at the coupling of a real noble gas, bracketing the transition between the two. Finally, symbolic regression on the trained potential, with no assumed functional form, returns the Axilrod-Teller expression with angular numerator, radial law, and coupling constant intact. An LNN with domain-specific structure can thus recover an irreducible three-body interaction from trajectories as a closed-form law, pointing toward learning interaction laws whose structure is not known a priori.

Let $D_{m,n}\subset\C^{m\times n}$ be the union of the zero loci of the maximal minors of a generic $m\times n$ matrix, and let $U_{m,n}$ be its complement. We show that $U_{m,n}\cong\GL_m(\C)\times\Gr(m,n)^\circ$, where $\Gr(m,n)^\circ$ is the open stratum of the Grassmannian on which all Plücker coordinates are nonzero. For $m\in\{2,n-2\}$ this gives closed formulas for the topology of $U_{m,n}$ and recovers results of Yim. Our main result, which is computer-assisted, is that $D_{3,5}$ is not a free divisor. This answers a question of Yim. We determine $\Der(-\log D_{3,5})$ explicitly. It has projective dimension one, and it fails to be free exactly on the matrices of rank at most two. There the failure comes from a non-free transversal arrangement: the ten planes spanned by pairs of five general vectors in $\C^3$. Computations in further cases support the conjecture that $D_{m,n}$ is free only for $m\le 2$ or $n=m+1$.

Threshold and change-plane models provide a useful framework for capturing regime-dependent dynamics, but most existing approaches typically rely on scalar thresholds or linear splitting boundaries. We propose a scalable semiparametric change-plane regression framework that allows the regime boundary to depend nonlinearly on multivariate state variables. Random Fourier features provide a flexible and computationally efficient approximation to the nonlinear boundary function. A two-stage procedure first estimates the induced regime classification using a smooth surrogate and then refits the structural parameters by hard-threshold OLS. We establish convergence of the first-stage regime classification and show that its estimation error is asymptotically negligible for the second-stage refit, yielding oracle equivalence. We further develop a dependent-multiplier bootstrap Sup-Wald test for detecting the existence of regime effects when the boundary is unidentified under the null, and establish its asymptotic validity. Simulations demonstrate accurate regime recovery, near-oracle performance of the proposed estimator, and satisfactory finite-sample behavior of the Sup-Wald test. An application to postwar U.S. unemployment data provides strong evidence of regime dependence, while the estimated nonlinear change plane identifies a distinct stress regime characterized by significant shifts in short-run unemployment dynamics.

Holographic complexity is expected to capture the linear growth of black hole interiors, with quantum corrections ultimately leading to a late-time saturation. We develop a spectral formulation of holographic complexity measures associated with codimension-zero bulk regions in the framework of the complexity=anything proposal. The corresponding generating function of complexity is governed by three-point correlation functions of the density of states, establishing a direct connection between bulk geometric observables and nonperturbative Euclidean spacetime wormholes. We find that the codimension-zero holographic complexity reduces to the sum of two codimension-one contributions and exhibits a universal time evolution, characterized by an exponentially long regime of linear growth followed by saturation at the Heisenberg time. The late-time plateau is a direct result of the spectral level repulsion, a generic feature of quantum chaotic systems, thereby providing a universal mechanism for the saturation of holographic complexity. We also develop a complementary operator interpretation, in which Euclidean wormhole corrections render the semiclassical basis of fixed-complexity states overcomplete. Constructing a complete orthonormal basis then yields well-defined holographic complexity operators that reproduce the same universal time evolution. Our results establish a unified connection among black hole interiors, chaotic spectral statistics, and Euclidean wormholes in quantum gravity.

Recent numerical simulations have shown that black-hole magnetospheres evolve rapidly toward alignment between the magnetic axis and spin axis but the physical origin of this process has remained unclear. We develop an analytic theory of this alignment within resistive relativistic magnetohydrodynamics. Taking the slow-spin Blandford-Znajek monopole solution as the exterior magnetic field, we reduce the induction equation to a relaxation equation for the current-sheet inclination angle. Our analysis shows that alignment results from second-order spin effects in the Blandford-Znajek solution combined with explicit resistive dissipation. We test this prediction using resistive-GRMHD simulations at several spins and resistivities and compare the measured late-time secular decay with the analytic prediction. This alignment timescale hence carries a unique signature which combines plasma dissipation with spacetime rotation.

Prompt optimizers rewrite a prompt to raise one target metric, but prompts also state requirements the metric does not score, such as an output format, citations, or abstention. In a preregistered study, we run GEPA, MIPROv2, and TextGrad on HotpotQA, SQuAD 2.0, and IFEval and count per-item violations of unscored requirements with deterministic checks. By the preregistered criterion, all three optimizers produce regressions, substantially on HotpotQA, where net regression in citation validity reaches 10.7 to 41.6 points while exact match rises by 21 to 34 points. A post-hoc decomposition changes this reading. The optimized prompts elicit reasoning before the required JSON object, and under the 200-token output cap used throughout, 13.9% to 47.0% of responses end before any answer appears. Among parseable outputs, net regression is within 3 points of zero. With a 1,024-token cap, extraction failures disappear, content regression stays below 1 point, and exact match rises further. Two simple gates fail the preregistered criterion. The side effect is narrower than hypothesized: optimized prompts are more accurate and break an explicit output contract, and a lenient target metric does not show the cost.

We formulate perturbative Jackiw-Teitelboim gravity as an ensemble of ordinary one-dimensional Hamiltonians with a confining random potential. The leading profile reproduces the disk density of states, while connected cumulants of a single master field encode the topological expansion. After formulating the cumulant power counting required by the topological expansion, we show that the cumulants reproduce all genus-zero multi-boundary amplitudes $\mathcal Z_{0,n}$. At higher genus, we show that a renormalization scheme can be chosen consistently order by order so that imposing one-boundary polynomiality recursively reproduces the perturbative JT string equation and yields the standard JT one-boundary amplitudes $\mathcal Z_{g,1}$. The framework provides a self-contained finite-$S_0$ quantum dynamics with a discrete spectrum and unitary real time evolution, beyond a mere rewriting of the matrix integral. The same confining dynamics also underlies late-time saturation and the dynamical avoidance of the would-be black hole singularity, as shown in our earlier work.

Distilling long-chain reasoning trajectories from large teacher models provides an effective way to improve the reasoning ability of small language models. However, existing methods typically select a fixed training set before distillation, overlooking that the usefulness of a reasoning example changes as the student evolves. This mismatch becomes especially costly when only a small number of teacher trajectories can be used for training. Besides, examples already mastered provide little new supervision, while examples far beyond the capability of student may be difficult to learn from. Training data should therefore adapt as model capability evolves, yet reliable data selection is difficult when the student is initially weak. To address these challenges, our key idea is to first establish the basic reasoning capability and then adapt the training data to the evolving capability boundary of the student. We propose BoundaryEvo, a two-stage data–model co-evolution framework. In Capability Priming, we directly distill a small set of teacher-generated long reasoning trajectories without using a separate model to judge and filter them, allowing the student to acquire an initial reasoning capability before capability-aware data selection. In Capability-Boundary Co-Evolution, we repeatedly select questions that the current student has not mastered but the expert can reliably solve, and update the training data as the student evolves. With only 1,000 training examples, BoundaryEvo consistently outperforms static and dynamic data selection baselines across 11 reasoning benchmarks, raising the original Qwen3.5-4B accuracy from 62.9 to 75.3 on IMO-AnswerBench and from 26.8 to 46.0 on AMO-Bench. The code and data will be made publicly available.

We investigate the Casimir effect between two parallel wires in $(2+1)D$ Maxwell-Chern-Simons (MCS) electrodynamics under different boundary conditions and separated by a distance $L$. Using a functional approach in which the boundary constraints are implemented by auxiliary fields localized on the wires, we integrate out the gauge field and derive an effective boundary theory whose functional determinant allows us to compute the Casimir energy. We consider perfect electric conductor (PEC), perfect magnetic conductor (PMC), and infinitely permeable (PMC2) boundary conditions. For two PEC wires, we recover the known MCS result and show that it coincides with the result obtained in the Abelian limit of the Curci-Ferrari (CF) model, implying that the Casimir effect in this case probes the photon mass $\mu$ but not its origin. The same energy is obtained for two PMC2 wires. In sharp contrast, the Casimir energy vanishes identically for the covariant PMC condition in MCS theory, both for PMC-PMC and PEC-PMC. Since this cancellation does not occur in the CF model, it could provide a signature of the topological origin of the photon mass in $(2+1)D$. Finally, the PEC-PMC2 case yields a non-vanishing Casimir force and reproduces the known result for a perfectly conducting wire facing an infinitely permeable one. Interestingly enough, we show that for PEC-PMC2, the Casimir force in the MCS theory is smaller than the one of the CF model for any $L,\mu >0$. Our results thus show that, depending on the boundary conditions, the Casimir effect could probe not only the photon mass but also reveal signatures of its origin.

Solving combinatorial optimization problems on near-term quantum computers mainly relies on their quadratic unconstrained binary formulation. Lately, binary polynomial formulations start to take the center stage, having a better scaling with respect to the number of used qubits. However, while quadratic forms are straightforward to implement on quantum circuits, polynomial forms of degree $d$ incur in circuit depth overheads, due to the lack of $d$-qubit gates, for $d\geq 3$, on current hardware. In this paper, we study the problem of designing the shallowest quantum circuit for a given polynomial form. We formulate it as a classical binary linear problem and we prove the NP-completeness of a variant of it. On the algorithmic side, we offer a scalable and performant heuristic method to tackle it, Tempura, as well as faster binary linear problem formulations, which offer computational feasibility while sacrificing optimality. Our performance evaluation shows that the algorithms yield far shorter circuits than the state-of-the-art approaches, and Tempura is mostly comparable with them in terms of runtime.

This paper describes our systems for the Track 1 time-stamped speaker-attributed ASR task of the SmartGlasses Challenge. To handle overlapping speech, background noise and far-field conditions in two-person conversations, we employ SoulX-Transcriber, a multimodal large language model that takes full-length audio as input and generates structured transcriptions. In addition, we investigate the effect of speech frontend processing, including a rule-based Guided Source Separation method and a data-driven speech separation model, both of which improve performance on the validation set. Considering inference stability, our final submission uses the fine-tuned SoulX-Transcriber system, achieving a tcpCER of 6.22 on the test set.

Skeleton-based human action recognition has gained increasing attention due to the stability of skeleton data across diverse environments and advances in motion capture technologies. Following the success of supervised learning approaches, self-supervised learning approaches, particularly contrastive learning ones, have achieved impressive performance. However, they remain vulnerable to adversarial attacks. In this work, we propose a plug-in robustification module via quantization for contrastive learning in self-supervised skeleton-based human action recognition (QCLR), which enhances the robustness of representations against adversarial attacks while preserving their representational capability. Specifically, we employ a dual-level quantization scheme across the encoding pipeline, which breaks the gradient propagation and absorbs small adversarial perturbations within the quantization bins. To mitigate the impact of inevitable quantization error, we further design an attention-guided multi-faceted quantization strategy to maintain the representation quality. Experiments on several benchmark datasets demonstrate that integrating QCLR into a progressive lineage of mainstream contrastive learning models substantially improves robustness against both gradient-based white-box and gradient-free black-box adversarial attacks, while preserving highly competitive classification accuracy.

We study investigative subgraph extraction for Anti-Money Laundering (AML) transaction graphs using the Shortest Paths Network Search Algorithm (SPNSA), which aggregates shortest paths among a small input feed of entities. Since SPNSA is highly sensitive to the feed choice, we evaluate several graph-only feed selection strategies and propose a motif-based coherent feed selection method. Experiments on the IBM-AML benchmark (HI-Small, LI-Small, HI-Medium) and the Elliptic Bitcoin transaction graph show that the proposed strategy yields markedly higher illicit ratios in the extracted subgraph than random and degree-based heuristics on Elliptic and the IBM-AML HI variants, while keeping the output compact.

Let p be an odd prime. We study the Artin-Schreier analogue of Poonen's problem of constructing curves without extra automorphisms. An Artin-Schreier curve carries an unavoidable deck group Cp, so the smallest possible full geometric automorphism group inside the Artin-Schreier locus is Cp. We determine the exact numerical range in which this minimum is attained, for every p-rank. More precisely, for integers r >= 0 and N >= 1, there exists an Artin-Schreier curve X/Fp with g(X) = (p - 1)N/2, gamma(X) = r(p - 1), Aut_Fp(X) is isomorphic to Cp if and only if either r = 0, p does not divide N + 1, N >= 3 and (p,N) not equal to (3, 3), or r >= 1, N >= 2r and (r,N) not equal to (1, 2). All models are defined over the prime field by explicit equations together with elementary choices of auxiliary polynomials, and every excluded admissible case is shown to carry an extra geometric automorphism. The main structural input is the theorem of Valentini and Madan on the uniqueness of the rational subfield of index p outside three exceptional families. We exclude these families by intrinsic arguments: the genus and p-rank in most cases, Nakajima's bound on p-subgroups of automorphism groups of ordinary curves for the ordinary family, and the Lehr-Matignon normal form for isomorphisms of one-point covers for the monomial family.

Vision-language models (VLMs) exhibit complementary capabilities, yet selecting the most suitable expert for a given image-question query remains challenging due to heterogeneous multimodal inputs and varying expert strengths. Existing routing approaches rely on text-based cues or static model profiles, failing to capture fine-grained visual evidence and expert-specific failure patterns. To address this, we propose MHR-Router, a multimodal heterogeneous retrieval-enhanced adaptive routing framework for VLM inference. It accurately dispatches each multimodal query to the most suitable VLM expert via local retrieval evidence. MHR-Router consists of two stages: (1) Multimodal Routing Representation, which fuses frozen multimodal features into a comprehensive query representation; and (2) Heterogeneous Retrieval-Enhanced Adaptive Routing, which retrieves expert-specific success and failure memories as local evidence and employs a shared scorer to adaptively select the optimal expert. Experiments show that MHR-Router effectively achieves heterogeneous modality routing and consistently improves accuracy over traditional baselines.

Memory-augmented assistants retrieve evidence from stored conversations and documents to answer queries. Most embedding-based retrievers compare single-vector representations of queries and memories, even when relevance depends on a small part of the content. Such local evidence can be matched to queries using the contextual token representations already computed by the same embedding models. Our method uses sparse token matching to improve retrieval without additional training. Each query token retrieves a small set of matching tokens across candidate memories. The matching scores are aggregated for each memory and combined with whole-memory similarity to rank memories. An optional low-rank query adapter can be trained with supervision while keeping the encoder and stored memory representations fixed. Our method improves retrieval across eight benchmarks and multiple model families without additional training. Query adaptation further increases the gains to 13.3 and 14.3 percentage points in average Recall@10 and NDCG@10 on Qwen3-Embedding-4B. These retrieval gains translate into higher question-answering accuracy on long-term memory benchmarks.

Set-based language model routing aims to increase the coverage of the event where at least one model answers a query correctly while controlling the number of inference calls made. Existing risk-controlled routing policies bound the all-miss risk (the probability that every model in the selected set fails) by calibrating a single conformal threshold and applying it to a nested family of model sets. Because each model is scored in isolation, these policies ignore the dependence structure of model failures. Models that share training data or architecture tend to fail on the same queries, so two individually strong models can be jointly redundant while a weaker but complementary model covers the queries that the others miss. To account for this dependence, which existing risk-controlled policies ignore, we propose CopRoute, which orders models by how many new queries each one answers correctly beyond those already selected, decides per query how far down that order to go, and then picks the smallest cutoff that still meets the target risk. We show that CopRoute's ordering attains, on the design data, the best guarantee any efficient fixed-ordering algorithm can give for the average number of calls to the first correct model, and that a separate calibration step certifies the all-miss risk of the deployed sets. On RouterBench and RouterEval, CopRoute attains the fewest certified calls on nine of ten datasets at a target risk of 0.05 and on eight of ten at 0.10, making up to 79 percent fewer calls (median 24 percent) than the state-of-the-art risk-controlled policy at the same certified all-miss risk.

Neuronal excitability is commonly modeled using different principles at the cellular and population scales, making it difficult to study how microscopic mechanisms shape macroscopic activity. We introduce a spatiotemporal excitatory-inhibitory (EI) model that unifies these scales through a common mixed-feedback architecture. The model retains the conductance-based circuit structure of Hodgkin-Huxley models and describes intrinsic and synaptic currents through memductances whose temporal and spatial voltage dependence encodes dynamics at the relevant scale. In its minimal form, temporal excitability arises from fast excitatory feedback opposed by slower inhibitory feedback, while spatial excitability arises from short-range excitation opposed by longer-range inhibition, recovering the core lateral-inhibition motif of Amari neural fields. We show that combining these mechanisms gives rise to population excitability in strongly heterogeneous populations. In particular, the model generates population spikes that are localized in both space and time and possess population-level scales distinct from those of individual neuronal spikes, despite substantial cell-to-cell parameter variability. We then show that both intrinsic temporal excitability and spatial synaptic feedback are required for coherent mean-field events and robust spatiotemporal population rhythms. Finally, selective modulation of memductances in a subset of the population tunes the frequency of the population rhythm, illustrating how changes at the cellular scale can shape macroscopic dynamics. By separating circuit architecture from modeling scale, the proposed framework provides a physically interpretable approach to analyzing and designing neuronal excitability across scales.

We classify prime accessible deterministic automata over finite alphabets, both among finite automata and among automata with arbitrary state sets. Every one-state automaton is prime. Over a one-letter alphabet, a finite nontrivial automaton is prime exactly when it is a cycle of prime-power length or a finite chain ending in a fixed state. The unique infinite accessible unary automaton, up to isomorphism, is also prime. Every nontrivial automaton over an alphabet with at least two letters is not prime. Shen proved the finite case; we give a shorter proof. We also characterize a decomposition of the automaton whose states are all finite input words. The reachable product of the quotients by the least right congruences identifying the empty word with nonempty words $p$ and $q$, respectively, is isomorphic to this automaton exactly when $p^r\ne q^s$ for all positive integers $r,s$.

API specifications serve as critical documentation for modern software development, directly impacting integration efficiency and client code generation. While recent advancements have leveraged Large Language Models (LLMs) to generate initial specifications from source code, existing approaches treat this process as a one-time event - overlooking the needs for continuous validation, long-term maintenance, and market-driven evolution of these artifacts. To address this issue, we present Agent4Spec, an autonomous multi-agent framework featuring two distinct pipelines: (1) a validation pipeline that detects and self-corrects OpenAPI syntax errors, and (2) a market analysis pipeline that conducts competitive research, identifies functional gaps against industry leaders, and automatically generates missing API-spec functionalities. We evaluate Agent4Spec on two curated datasets of API specifications spanning both general-purpose and industrial scenarios. Among 9 SOTA LLMs, the top-performer achieves 100% syntax error detection rates and over 95% implementation success for proposed corrections, while securing over 50% adoption rates for suggested endpoint improvements, representing a practical tool for API development.

Post-training has become a key stage for eliciting reasoning capabilities in Video Large Language Models (Video-LLMs). Existing post-training methods mainly follow two paradigms: reinforcement learning (RL) and on-policy distillation (OPD). However, they do not fully exploit visual evidence for effective training. RL supervises the policy with a single trajectory-level reward, which is too coarse-grained for video reasoning: the same response-level advantage is applied to every generated token, disregarding that the tokens of a video response are grounded in the visual stream to very different degrees. OPD provides token-level supervision through output-distribution matching, but lacks direct supervision of the spatiotemporal representations that produce those outputs. We observe across extensive experiments that the same model reasons more accurately when its video view combines global temporal context with question-relevant details. Comparing the same student-generated response under this view and uniform sampling reveals changes in token likelihoods and internal representations, providing a training signal for evidence use. Building on this observation, we propose OWLET, an evidence-privileged RL method that derives training signals from a richer teacher view. This view couples uniform global context with question-conditioned local windows, providing visual evidence without requiring a larger model. To better exploit this privileged visual evidence, OWLET introduces (i) evidence-aware credit redistribution, which compares token likelihoods across the two views and redistributes positive response-level advantages according to their relative evidence support; and (ii) spatiotemporal state alignment, which aligns the two views' hidden states on verifier-accepted responses.

We investigate max-phase isometries on Schatten quasi-classes in the range $0<p<1$. Motivated by the rigidity theory for smooth normed spaces [Results Math. 80 (2025), Article 126], we establish its operator-theoretic counterpart in the quasi-Banach setting. We prove that every surjective max-phase isometry on a finite-dimensional Schatten class is a standard real-linear Schatten isometry multiplied by an even sign-valued function, without any continuity assumption. This extends the scope of the classical Schatten isometry classification [Proc. Edinburgh Math. Soc. 37 (1994), 239–242] to nonlinear mappings preserving only unsigned two-point metric data. Our approach combines support orthogonality, a symmetrized rank-one spectral formula, and a max-profile uniqueness principle. For arbitrary Hilbert spaces, we obtain the corresponding classification on finite-rank operators, while continuity yields the full-space result. We also establish preservation of rank, singular values, and two-sided support orthogonality.

Brambles of constant congestion in directed graphs have interesting structural and algorithmic applications, and it is desirable to find the smallest function $f_c(k)$ such that if a digraph has directed treewidth at least $f_c(k)$, then it contains a bramble of size at least $k$ and congestion at most $c$. By the Directed Grid Theorem of Kawarabayashi and Kreutzer [STOC 2015], such a function $f_c(k)$ exists for every value $c \geq 2$ of the congestion. However, even using the recent improvements due to Hatzel et al. [FOCS 2024], the resulting function is a power tower of height $22$. Recently, Masařík et al. [SIAM J. Discrete Math. 2022] proved that, for congestion $8$, the function $f_8(k)$ can be made polynomial; more precisely, they showed that $f_8(k) = \mathcal{O}(k^{48} \cdot \log^{13} k)$. They asked whether it is possible to decrease the congestion, ideally to $2$, even at the cost of a higher polynomial function. In this work we answer their question affirmatively with the best possible value of the congestion, by proving that $f_2(k) = \mathcal{O}(k^{96}\cdot \log^{23} k)$. We also obtain smaller polynomials for higher congestion, namely $f_4(k) = \mathcal{O}(k^{72} \cdot \log^{21} k)$ and $f_6(k) = \mathcal{O}(k^{66} \cdot \log^{18} k)$. Our results are inspired by the proof for congestion $8$, which we improve by introducing walkages. Walkages allow us to avoid technicalities of the original proof by translating ideas due to Reed and Wood [Eur. J. Comb. 2012] that work for undirected graphs to the directed setting. Our proofs are constructive and naturally yield polynomial-time algorithms to find the brambles assuming a certificate for large directed treewidth is given. Moreover, we discuss algorithmic applications of our results for the Directed Disjoint Paths with Congestion problem, and to half-integral packings of subgraphs with large directed treewidth.

Local projections (LPs) have become a standard tool for estimating dynamic effects in macroeconomics and are typically implemented using ordinary least squares (OLS) for a given lag order. We propose an alternative approach that exploits additional lags as excluded instrumental variables (IVs). Under a finite-order model with martingale-difference shocks, the resulting (optimally weighted) IV estimator is never asymptotically less efficient than OLS and, as we show, can deliver substantial efficiency gains when data are persistent. For the unit-root AR(1) data with i.i.d. errors, our baseline IV estimator (with one overidentifying restriction) has asymptotic variance $2-h^{-1}$, compared with $h$, the asymptotic variance of the OLS lag-augmented estimator in Montiel Olea and Plagborg-Møller (2021), for an integer propagation horizon $h$. We then develop IV-based LP inference that is robust to unknown persistence and moderate local model misspecification, whereas the recursive VAR-based inference is generally not robust to the latter. We also characterize the trade-off between the degree of misspecification and the number of additional lag controls. Through simulations and an empirical application, we demonstrate that the proposed method can yield meaningfully shorter confidence intervals for impulse responses than OLS in finite samples.

GUI grounding, the task of locating the interface element specified by a user instruction, is a fundamental capability of GUI agents. However, existing grounding models remain error-prone, often causing downstream task failures. We systematically evaluate 10 grounding models across five datasets and identify a major error pattern: most incorrect clicks hit non-target interface elements rather than the background, with different models repeatedly selecting the same distractors. Motivated by these findings, we propose ConClick, a contrastive learning framework that teaches models to distinguish the target element from plausible distractors. We construct ConClick-Data, a dataset containing 4,292 challenging target-distractor pairs, and train the model using complementary listwise ranking and pairwise margin objectives. ConClick improves the grounding accuracy of Qwen3-VL-8B from 54.71% to 66.03% on ScreenSpot-Pro, from 83.72% to 86.28% on MMBench-GUI L2, and from 63.33% to 70.20% on OSWorld-G, outperforming prior methods built on the same or similarly sized backbones. We further introduce ReClick, an inference-time strategy that revisits promising regions and compares predictions across competing candidates, yielding an additional 2.96 percentage-point improvement in average accuracy across the three benchmarks. Together, our analysis, dataset, and methods provide both empirical insights and practical tools for building more reliable GUI agents. Data and code are available at https://github.com/zhangruotian/ConClick.

Large language model (LLM) agents are highly vulnerable to memory-poisoning attacks. Existing defenses primarily rely on external modules for either static memory isolation or continuous online auditing, resulting in low memory efficiency and high computational overhead. To address these limitations, inspired by neuroscientific mechanisms that weak reactivation can destabilize memories and induce decay in the absence of reinforcement, we propose an agent-intrinsic training-free memory repair framework, DREAM (Dynamic Reactivation for Engram Attenuation in Memory), that enables selective functional forgetting of poisoned memories. Specifically, DREAM implements a three-stage pipeline: perturbation-induced implicit reactivation to reveal the structural fragility of malicious memories, adaptive anomaly diagnosis based on multi-dimensional activation patterns to detect topological anomalies, and a dynamic memory repair module that selectively suppresses harmful memories while reinforcing benign ones. Extensive experiments across diverse attackers and real-world tasks demonstrate that DREAM reduces attack success rates by over 95% against backdoor poisoning while preserving strong benign utility. DREAM also achieves competitive robustness against injection attacks. In terms of runtime and token consumption, DREAM achieves up to a 2.13$\times$ speedup and a 37.7% reduction in token consumption compared with A-MemGuard. Furthermore, DREAM also achieves a task success rate of 92.96% on poisoned multi-agent systems.

We consider the Navier-Stokes equations in a smooth bounded domain $D\subset \mathbb R^3$. It has been proved in arXiv:2609.08284 that these equations have a unique solution - globally defined in time - when a superlinear noise is introduced and the initial velocity belongs to the space $V$ of divergence-free $H^1_0(D;\mathbb R^3)$-vector fields. Here we show that the same result holds when there is also an additive noise and a deterministic forcing term. Moreover, when the deterministic forcing term is time-independent we prove the existence of at least one invariant measure for this stochastic equation. This is obtained by the Krylov-Bogoliubov method, based on tightness and Feller property in $V$. Finally, we show that the set of invariant measures contains one ergodic invariant measure.

Simulating acid-base equilibria from first principles is a tremendous challenge, as it requires modeling bond-breaking events in a complex hydrogen-bonding environment. The quantum mechanical behavior of the protons is often important, complicating simulations even further. We show that by combining state-of-the-art machine-learning potentials, accelerated sampling of the dissociation process, and an efficient estimation of nuclear quantum corrections it is possible to reliably compute the dissociation constants of different species in water. We demonstrate the transferability of this workflow, applying it successfully to the autoionization of water and to the entire ladder of the aqueous dissociation of phosphoric acid. The definition of the dissociation constant, the choice of order parameters, sampling artifacts and finite-size effects, as well as quantum nuclear effects all play a non-trivial role in determining the outcome of the calculation, so that cutting corners is likely to introduce biases that can only be compensated by fortuitous cancellations of errors.

On-policy distillation (OPD) reveals versatility and convenience during VLM post-training, providing dense supervision for student from teacher. However, we observed an anomaly that the distilled VLM could still answer the questions accurately even when the related visual regions were masked or replaced with noise. Building on this observation, our quantitative and qualitative experiments demonstrate that OPD, which uses the answer as a hint, has failed to teach students to genuinely seek out and rely on visual evidence. Our theoretical analysis suggests that this failure arises from a shortcut enabled by the lack of visual constraints during distillation. To address the issue, we introduce Contrastive Vision On-policy Distillation (CV-OPD), which compares teacher distributions induced by positive and negative crops while conditioning on the same student prefix and augments optimization with a margin-based contrastive constraint, which is modulated with discrepancy gating across token and sample level. Specifically, CV-OPD first introduces a negative teacher unrelated to the answer and designs a Contrastive Divergence Loss (CDL) that constrains the feature distribution of student by contrasting the positive and negative teachers, correcting how the student exploits visual regions. The CV-OPD introduces a Discrepancy Aware Gate (DAG) that uses token-level and sample-level discrepancies to select visually relevant tokens for optimization, directing the student's attention toward visual content. Extensive experiments across a broad range of fine-grained visual benchmarks demonstrate that CV-OPD substantially alleviates shortcut and consistently improves the visual reasoning capabilities of existing VLMs.

Multimodal large language models process the complete visual token sequence, increasing prefill cost even when many tokens are irrelevant to the instruction. Token-wise saliency captures limited inter-token dependence; graph-based selection instead depends on how relations govern importance propagation and ranking. We study support-constrained propagation with node-degree correction. Inspired by sheaf geometry, SheafPrune uses modality-specific maps and a sparse text–visual graph to transfer relevance, then propagates scores on a separate visual graph and corrects them for degree. It retains a hard top-$k$ subset once before the frozen language model. The selector has about $4.5$M parameters and is trained end-to-end through the frozen LLaVA-NeXT-8B backbone using only the language-modeling objective. Explicit retention-ratio conditioning lets one checkpoint serve every budget. Across four backbones, ten benchmarks and seven pruning ratios, with all baselines re-implemented under one protocol, SheafPrune achieves the best retention at $22$ of $28$ backbone–budget settings, with monotonically growing margins in the moderate-to-aggressive regime. On LLaVA-NeXT, retaining $10\%$ of visual tokens yields a $5.15\times$ net prefill speedup and an $84.0\%$ end-to-end FLOPs reduction. Together with component ablations, these results support graph-constrained importance propagation and degree correction as a design for visual token selection across the evaluated backbones and tokenization schemes, improving the trade-off between accuracy retention and inference cost. code:https://github.com/Bob0817912/SheafPrune_ICLR_2027