Papers

One-way network devices, known as data diodes, are used to defend against sophisticated cyberattacks. Partly due to their high cost, data diodes are mostly deployed in nuclear power plants and within the government for handling classified information. Although commercially available data diodes are expensive, a data diode's hardware can assembled from commodity fiber-optic network equipment. However, specialized software is needed to send data through a data diode reliably: the receiving program cannot request retransmission of dropped packets, so packet loss must be minimized and mitigated. First, we developed a minimal program to measure packet loss. We found that most packet loss was caused by the receiving program processing incoming packets too slowly, and that packet loss often occurs in clusters. Also, we discovered ways to minimize packet loss on Linux and macOS without using superuser privileges. Next, we tested three existing open source programs for one-way data transfers: netcat, UDPcast, and lidi. Although these programs were unreliable in their default configurations, we identified reliable configurations for UDPcast and lidi. Finally, we incorporated our findings into pydiode, our cross-platform program for reliable one-way data transfers.

Large language model agents are increasingly deployed for data-intensive work, yet reliable data analysis requires more than general-purpose reasoning and ad hoc tool augmentation. Data Agents, equipped with workflow harnesses, offer a promising paradigm for automating the end-to-end data science lifecycle. This paper examines Data Agents from a harness-centric perspective. First, we introduce a taxonomy of Data Agents and associated data environments, organizing the literature around five functional stages: perception, planning, execution, verification, and repair. Second, we analyze the key technical routes within each stage, identifying 15 distinct approaches ranging from data structure probing to data state reconstruction. Third, we identify four open reliability problems: inactive semantic calibration, missing clarification, missing experience transfer, and the missing verification-repair repository. These problems explain why silent failures can persist even when individual components function correctly, highlighting the need for rigorous workflow harnesses and shared reliability resources. Finally, we summarize the horizontal task families of Data Agents, examine their vertical application settings, and benchmarks for evaluation, while maintaining a companion repository at https://github.com/DEEP-PolyU/Awesome-Data-Agents.

We present MEGATRON, a heterogeneous Edge GenAI System-on-Chip in 28nm FD-SOI CMOS technology combining a non-volatile analog in-memory-computing engine based on a 4Mi-cell phase-change memory (PCM) array with a digital RISC-V-based flexible neural processing unit. MEGATRON demonstrates up to 3.5 TOPS/W using the RISC-V processors and 57.5 TOPS/W with PCiM, at a storage density of 1.52 Mparam/mm${}^2$ with 4-bit effective weight precision.

An exotic linearised theory of superconformal gravity in $D=6, (4,0)$ superspace has been proposed by C.M. Hull. In this note we discuss the bosonic sector of this model in topologically non-trivial spaces. Roughly speaking, Hull's model can be thought of as a square of the $H=dB$ theory, although not all Hull fields can be so presented. We also briefly discuss the form sector of $D=11$ supergravity.

For an integer solution of $y^2=x^3+k$ with $x,y\ge 1$ and $k\ne 0$, the integers $x^3$, $|k|$ and $y^2$ form a triple in which one term is the sum of the other two. When $\gcd(x,y)=1$ this triple is coprime, and the $abc$ conjecture predicts that its quality is asymptotically at most $1$. Following Müller, Taktikos and de Weger, we factor this quality through the product $P=xy|k|$ into the approximation gain $G_a=\log\max(x^3,y^2)/\log P$ and the power gain $G_p=\log P/\log\rad(xy|k|)$, which is at least $1$. We show that the weak form of Hall's conjecture, which asks that $|k|>x^{1/2-\delta}$ for every $\delta>0$ outside finitely many solutions, is equivalent to the asymptotic bound $G_a\le 1$. More generally, for $6/11\le\kappa<6/5$, an asymptotic bound $G_a\le\kappa$ gives $|k|>x^{3/\kappa-5/2-\delta}$ for every $\delta>0$ outside finitely many solutions, and for $3/4\le\kappa<6/5$ the two statements are equivalent. Since the approximation gain never exceeds the quality, an $abc$ inequality with exponent $1\le\kappa<6/5$ gives the same bound for primitive solutions. The case $\kappa=1$ extends to all solutions and recovers the classical implication from the $abc$ conjecture to weak Hall. We also relate small values of $|k|$ to large partial quotients of $\sqrt x$.

Motivated by recent work on conjugacy languages in groups, we introduce a general framework for studying languages of representatives associated to equivalence relations on finitely generated semigroups. After developing this notion in full generality, we particularize it to Green's relations and obtain the corresponding Green languages, which form the central objects of this article. For free inverse monoids, we describe these languages via Munn trees and establish several structural relations among them, including characterizations of the $\mathcal{D}$-, $\mathcal{R}$-, $\mathcal{L}$-, and $\mathcal{H}$-languages. We then investigate the formal language-theoretic complexity of these Green languages. For free inverse monoids of rank at least two, we show that $\mathcal{H}$-Geo is context-free and co-context-free but not regular, while $\mathcal{R}$-Geo, $\mathcal{L}$-Geo, and $\mathcal{D}$-Geo are neither context-free nor co-context-free. In contrast, in the monogenic case, $\mathcal{D}$-Geo is regular and the remaining Green languages are deterministic context-free. We further relate these results to the ShortLex language and the growth of free inverse monoids, proving in particular that $(\text{FIM}_X,X)$ is growth tight. The article concludes with a collection of open problems and directions for future research.

Large Language Models (LLMs) offer a scalable way to simulate survey respondents using demographic profiles and observed reference responses. However, the conventional approach of predicting one question per prompt repeatedly encodes the same context, limits each target to a narrow set of reference responses, and prevents later predictions from using information in earlier answers. Predicting multiple questions in one prompt can reduce these costs, share a broader pool of references, and let later predictions build on earlier ones. This requires forming coherent batches, selecting shared references, and ordering questions and references effectively. We propose Semantically Coherent Batching and Ordering (SCBO), a training-free framework that addresses these challenges. SCBO first uses an LLM to extract compact semantic representations from survey items and filter out template noise. It then groups related questions into batches and builds a shared reference bank using target-specific retrieval and centroid-based completion. Finally, it orders target questions from easy to hard and arranges references according to their semantic alignment with those questions. Experiments on four large-scale survey datasets and four LLMs show that SCBO substantially reduces token consumption and inference time while generally improving prediction accuracy over a non-batched baseline. Code is available at https://anonymous.4open.science/r/SCBO-41D8.

Pretrained robot manipulation policies such as vision-language-action models (VLAs) or world-action models (WAMs) leave interaction-relevant metric geometry implicit. Recent breakthroughs in spatial reconstruction can supply the necessary geometry reliably, but their features describe local shape without stating where it lies with respect to the robot. How best to deliver these features to a pretrained policy remains unresolved. We propose Spatial Grafting, a versatile, lightweight spatial module that binds frozen reconstruction features to metric, robot-relative geometry. Spatial Grafting constructs metric-grounded spatial tokens and injects them into the flow-matching action expert through cross-attention, without modifying the host's perceptual pathway, so the host retains the full benefit of its pretraining. We evaluate it more broadly than any geometry-aware policy we compare against: one graft architecture, with no per-host redesign, on two VLAs and two WAMs, across four simulation benchmarks that span short-horizon manipulation, visual robustness, clutter and long-horizon mobile manipulation, and on three real-robot platforms with single- and dual-arm configurations. On RoboTwin 2.0, a dual-arm manipulation benchmark, the graft improves every host across VLAs and WAMs. Grafted $\pi_{0.5}$ gains 11.3% and 15.6% on clean and randomized scenes, reaching 94.0% and 92.4%, above the strongest published 3D-conditioned policy, WAM4D (93.8% and 89.9%). The margin widens as the horizon lengthens: on tasks from BEHAVIOR-1K, a dual-arm mobile manipulation challenge scored by average task progress, it surpasses the 2025 challenge winner on five of six tasks,by up to 0.47 Q-score, and exceeds a map-conditioned spatial policy on average across the three tasks both report.

Matrix Hilbert series retain local elementary-divisor data that their determinants discard. For locally finite positively graded elementary algebras whose vertex simples are of type $FP_\infty$ and whose matrix Hilbert series is rational, we construct from possibly infinite minimal resolutions a rational Euler matrix and its signed local Smith profile at $x=1$. The profile refines pole-order growth for perfect modules and is invariant under shift-compatible graded Morita and perfect-derived equivalences. Every finite integer profile occurs, while a wholly negative profile forces exponential corner growth. This extends the nonnegative local Smith framework for twisted Calabi–Yau algebras to a setting in which the Euler matrix may itself have poles.

When a VLM answers a visual query, current interpretability tools rely on text rationales, which use a mismatched modality, or on internal read-outs, which originate too early to reflect the final output and require white-box access to the model. We introduce AnswerMap, a training-free, task-agnostic, black-box visual rationale constructed from the output head. The image is cut into K row and K column bands, each shown alone to the frozen model along with the query in the format of a yes/no relevance question. The outer product of the row and column “yes” posteriors gives the query-conditioned spatial map. Crucially, by defining a fixed read-out R (e.g., expectation, maximum) on top of AnswerMap, we can derive continuous outputs like location natively. This bypasses the reliance on discrete text tokens for continuous-output tasks and guarantees an image-dependent answer by construction. However, a rationale can be confabulated, so we validate AnswerMap across four models and three query distributions with two tests: (a) agreement with the model's own generated point and (b) deletion of the map's region. The map lands where the model points (AUC 0.85 against 0.38 for attention), and deleting its region flips 53% of correct answers (against 19% for attention's). Beyond establishing faithfulness, we demonstrate the map's task-agnostic utility through three distinct read-outs: its maximum flags hallucinated objects without generation, its expectation localizes correctly when the model's own pointing fails, and its top-mass region, fed back as a crop, fixes half of the model's wrong answers. AnswerMap thus offers a new lens on VLM interpretability and, through its read-outs, a new output interface for visual tasks beyond text tokens.

Robust and accurate state estimation is fundamental for the reliable operation and monitoring of active distribution networks. Conventional numerical estimators, such as weighted least squares, are computationally slower and often suffer from convergence issues in the presence of sparse measurements affected by non-Gaussian noise. Physics-informed neural networks have recently emerged as a promising alternative by incorporating physical principles through residual-based penalty terms in the objective, which can improve robustness to noise and computational efficiency. However, such penalty-based approaches do not guarantee strict enforcement of physical constraints during inference and provide limited support for principled uncertainty modeling. To address these limitations, we propose a novel Hard-Constrained, Physics-Informed Factor Graph Neural Network (HCP-PINN) that formulates distribution system state estimation as a probabilistic constrained estimation problem on a factor graph. The proposed approach explicitly models non-Gaussian (pseudo-)measurement uncertainty through flexible, closed-form likelihood-based loss functions. It further incorporates a differentiable optimization-based estimation layer that strictly enforces nonlinear equality constraints and measurement consistency, producing physically feasible state estimates during both training and inference. To the best of our knowledge, this is the first PINN-based DSSE framework to combine hard physical constraints with non-Gaussian uncertainty modeling for unbalanced three-phase networks. Numerical experiments demonstrate that the proposed method delivers more accurate and physically consistent state estimates than deep learning benchmarks and numerical estimators, while exhibiting greater robustness to network model errors and improved computational efficiency under realistic measurement scenarios.

An antimagic labelling of a graph G = (V,E) is a bijection from E to {1,2,...,|E|}, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A graph is antimagic if it has an antimagic labelling. Hartsfield and Ringel in 1990 stated the celebrated conjecture: Every connected graph other than K_2 is antimagic. We prove the conjecture for join graphs with at least three vertices.

This paper analyzes the relative efficiency of horizontal and vertical organizational structures modeled as communication networks under limited managerial attention. In this framework, workers receive noisy signals about the state of the world and communicate reports to a decision-maker whose meeting time relatively more constrained. The clarity of each report depends endogenously on meeting lengths and the workers' heterogeneous communication and processing abilities. When workers possess identical communication abilities, the horizontal structure is always optimal because it allows the decision-maker to weight signals optimally without compounding transmission noise. Conversely, when workers have asymmetric communication abilities, the attention constraint of the decision-maker induces a structural switch. Under these constraints, the vertical structure becomes preferred because the decision-maker can delegate the time-intensive task of information aggregation to the superior communicator, balancing the loss from transmission noise against the premium on the decision-maker's scarce time. Under the assumption of homogeneous processing abilities I derive the analytical threshold for the n-worker model.

Time-multiplexed (TDM) photonic reservoirs are usually judged by their scores on a few datasets, which say little about a chip's overall performance, and designed by enumerating candidate circuits and simulating each one, which is inefficient and gives no guarantee of finding a good structure. For a time-unrolled passive linear network with data-modulated gates or sources and a ridge readout, we derive an exact bridge from the task to the prediction risk in three steps. (i) Task features: the finite-shot risk depends on the time series only through finitely many statistics of its training windows and their correlations with the target, selected by the encoding and the optical paths. (ii) Encoding: every output moment is a polynomial in the features of the data-modulated sites, with degree and support bounded by tuples of optical paths. Gate encoding reads the characteristic function and creates interactions across time lags; squeezing encoding reads the moment-generating function and displacement encoding low-order moments, and with quadrature receivers they yield only additive and linear models, respectively, for every topology. (iii) Readout: for homodyne, heterodyne and photon-number receivers the risk closes exactly, and its dependence on the number of shots is an explicit sum over signal-to-noise modes; threshold clicks admit finite-dictionary approximations with certified error. Parts of the network that share no light carry independent states, which a receiver combines only through measurement events that join them. Checks on seven datasets confirm every exact statement to machine precision. The three steps thus yield a useful space of candidate TDM architectures, pruned by exact statements rather than by trial simulation, which can in future guide the selection of TDM chips for target requirements.

Scalable Vector Graphics (SVG) are essential for modern industrial Computer-Aided Design (CAD). However, existing autoregressive SVG generation models are predominantly tailored for artistic creation and struggle to maintain the rigorous geometric fidelity and cross-view spatial alignment required for engineering drawings. To bridge this gap, we introduce DrawingsDreamer, a unified Large Language Model (LLM)-driven framework for multi-view vector-based engineering drawings generation. By formulating the generation of multi-view engineering drawings purely as a sequence modeling task, we eliminate the need of raster image encoders. We propose a Streamlined Representation utilizing hierarchical postfix tokenization, which guides the model to establish local geometric coordinates before assigning semantic boundaries. Optimized via a progressive task-aware curriculum schedule, DrawingsDreamer effectively transitions from localized structural repair to macroscopic generation in a unified model. Extensive experiments demonstrate that our unified model achieves strong performance in both geometric fidelity and syntactic accuracy across diverse conditional and unconditional generation tasks.

Let k be an integer from 1 to n, let f be a positive smooth function on the unit sphere, and consider the normalized flow X_t = -f({nu})|X|^{alpha} sigma_k({kappa}) {nu} + beta X, beta = C_n^k. In the supercritical range alpha > k+1, we prove the flow exists for all time and converges exponentially in C^{infty}, from every smooth strictly convex initial hypersurface enclosing the origin, to the unique smooth strictly convex solution of f(x)r^{alpha} sigma_k({kappa}) = beta u. The convergence is driven by the relative residual p = (log u)_t = beta - f(x)r^{alpha} {sigma}_k({kappa})/u, whose L^{infty} norm is nonincreasing and decays with the explicit exponent beta(alpha-k-1); the residual estimates are proved before, and independently of, the curvature estimates. Existence of a strictly convex solution of the stationary equation in this range, for arbitrary positive angular data, was previously obtained by Bryan-Ivaki-Scheuer through an expanding-type flow started from a barrier; the contribution here is the convergence of the normalized contracting flow from arbitrary initial data, with an explicit exponential rate, together with uniqueness of the limit.

Artificial-intelligence studies using computed tomography (CT) for lung cancer are often broadly labelled "prediction" despite addressing clinically distinct tasks. We systematically mapped CT/low-dose CT (LDCT)-centered lung-cancer AI using five-database retrieval, full-text eligibility assessment, role-aware modality/omics extraction, clinical-task classification, and a Multi-Tier Evidence Graph (MTEG). The final corpus comprised 293 studies (2016-2026): 230 Detection, 8 future Risk-prediction, and 55 Other studies. Clinical variables (96.2%), 3D CT/LDCT (73.0%), and radiomics (63.5%) predominated, whereas external validation (29.0%), calibration (20.5%), decision-curve analysis (13.0%), longitudinal CT (17.7%), and saliency/attribution XAI (21.5%) were less frequent. The MTEG comprised 377 nodes and 3,444 edges; only 31 studies (10.6%) completed the six-tier substantive evidence chain, with greatest attrition at reasoning/explanation. Overall, the literature is detection-dominated, genuine future risk prediction remains uncommon, and complete translational evidence chains are rare.

A Clifford template is a finite ordered family of repeatable Clifford operations, and an instantiation specifies how many times each operation is applied. The Clifford template compilation problem asks how to choose these repetition numbers so that the template realizes a target transformation of Pauli operators. This problem arises, for example, when searching for logical operations in quantum error correction using only Clifford operations permitted by physical or fault-tolerance constraints. Although forward Clifford dynamics is efficiently classically simulable, this inverse problem has sharp complexity transitions. For commuting templates with unrestricted integer exponents, feasibility lies in $\mathrm{NP}\cap\mathrm{BQP}$ and a constructive quantum algorithm returns a particular solution together with the full exponent-relation lattice; already at $k=1$, recovering the repetition number contains finite-field discrete logarithm over $\mathbb{F}_{2^r}^{\times}$. In general, restricting every exponent to $\{0,1\}$ removes the Abelian-group closure and makes feasibility NP-complete for variable $k$, even for exactly commuting CNOT-only operations and X-type Paulis. For commuting self-inverse Clifford actions, both binary feasibility and recovery of one solution are classically polynomial-time solvable, but imposing a bound on the total repetition count is NP-complete, even for CNOT-only operations. These results reveal a rich complexity landscape within Clifford template compilation, spanning classically tractable cases, problems admitting quantum polynomial-time algorithms, and NP-complete variants.

We study optimal dynamic contracts for long-term projects where a risk-averse agent exerts hidden effort to increase the drift of a Brownian process toward a com- pletion threshold. Relative to the first best, the optimal contract slows progress, makes success less likely, induces earlier termination, and narrows project scope. Allowing for costly project resets generates further distortions: resets may be excessive or insufficient depending on the residual effort required afterwards. With endogenous risk taking, optimal incentives introduce penalties for failure and reduce rewards for effort above a critical progress level, resulting in discontinuous and nonmonotonic effort in progress. In the baseline model, the optimal contract can be implemented with linear spot contracts that require no long-term commitment.

We introduce a technological capability scale that ranks civilizations by the control operations they can perform per second. A control operation is defined as setting one binary degree of freedom of matter to a specified value, whatever its previous state. Building on constructor theory, we sort them into construction and its special cases on information media, namely processing, storage and transfer. The index $\Xi = K + B$ adds to the Kardashev index $K$ an efficiency index $B$ of energy per operation, measured from the thermal floor at the microwave background temperature. The Kardashev scale gives the ceiling for resets of thermally random bits with heat radiated into the present sky, and the Barrow scale gives the floor, which for such a reset is the thermal floor at the heat-rejection temperature at every level. Since 1950 the energy per logic operation has fallen 11.7 orders of magnitude, around 5 through miniaturization. Humanity, at $K = 0.73$, computes with CMOS logic gates at $B = -0.78$ in primary energy. We describe the ultimate technology, at $\Xi = 7.58$, which would dissipate the conjectured largest power $c^5/4G$ into an uncharged, non-rotating black hole near its largest mass in de Sitter space.

Long-horizon agents improve solutions through sustained interaction, execution, and task feedback. Scaling studies relate performance to resources and capabilities, yet how existing capabilities shape returns to extended interaction remains less understood. To address this gap, we analyze AutoLab and EdgeBench, two long-horizon benchmarks. We find that starting performance and subsequent growth are associated with different capabilities: within a task category, similar early scores can precede different later gains. To formalize this finding, we model capability-time scaling with category-specific logistic power laws shared across models. Fitted to early trajectories, these curves extrapolate the observed models' category-average scores to later computation. However, rising average scores mask narrowing improvement opportunities: later gains concentrate among fewer improving models. High final scores and continued improvement also have distinct capability profiles. Predicted mean gains estimate each model's fraction of improving tasks; averaging these estimates forecasts the average share of improving models. These uneven returns motivate deciding whether a specific run should continue. We therefore derive a continuation policy to save time and compute with limited score loss. The policy conditions growth predictions on the run's observed progress and weighs immediate and delayed gains against computation costs. In replay with training and price calibration based on other models' histories, the policy saves roughly one-third of full-run time, with relative score losses of 2.4% on AutoLab individual runs and 3.3% on EdgeBench published mean curves. Our repository is available at https://github.com/Chihaya-Anon-chan/long-horizon-scaling.

Weighted ultrametric embedding with outliers asks for a minimum weight set of points whose deletion makes the remaining metric an ultrametric, equivalently, leaves no triple with a unique largest distance. We give a deterministic $5/2$-approximation using $O(n^5)$ arithmetic and comparison operations, improving the previous factor $3$ for arbitrary nonnegative vertex weights. Approximating the problem within any factor strictly below $2$ is UGC-hard.

Agentic AI systems increasingly act via tools, memory, delegation, and external services. Existing observability and provenance mechanisms can reconstruct events post hoc, but they rarely show, at the time of the record, whether each policy-relevant action was checked by the intended control before execution. This leaves a trust-observability gap for continuous monitoring, detection, and response: later assurance may rest on evidence that is incomplete, privacy-leaking, mutable, or detached from the policy context that governed the event. What's missing in the literature is contemporaneous, policy-bound evidence that the intended control was evaluated under the policy in force at the time. We introduce ProofWeave, a record-time chain-of-evidence concept for agentic AI assurance. At each policy-relevant action boundary, ProofWeave generates a privacy-minimised and integrity-anchored evidence transaction that binds (i) agent intent or action, (ii) control response, and (iii) a policy-at-time snapshot. Each transaction is committed to an append-only ledger and materialised into a derived proof graph. A bounded Weaver Agent translates policy intent into proof obligations, while deterministic validators check evidence completeness, privacy minimisation, policy binding, and integrity. In the minimal scenario, an agent attempts to transmit a secret to an unapproved external sink. The audit compares a logs-only correlation baseline with ProofWeave across verdict latency, join ambiguity, privacy exposure, tamper detection, and resistance to graph-only proof injection. ProofWeave reduces candidate bindings per verdict from up to `10,201` to one, validation operations from up to `10,201` to approximately `26`, and assurance evidence storage from `0.79`M̃iB to `0.15`M̃iB per project.

Large language model (LLM) agents face critical privacy risks when acting as delegates in human-agent-human communication. To prevent such breaches, agents must understand users' social relationships and adhere to context-dependent social information disclosure boundaries. Current studies on agent memory privacy focus on instantaneous interactions, leaving the long-term relational disclosure problem unexplored. In this paper, we propose EP-Mem, an Elastic Privacy Memory architecture that reframes privacy as user-owned boundary control across social roles. EP-Mem introduces (1) token-level memory driven by user-configurable a privacy policy that stratifies persons and events, combining domain-level default circulation rules with fact-level whitelist/blacklist exceptions; and (2) a pluggable sidecar with a privacy engine that aligns disclosure controls with memory across summary, detail, and boundary granularities, enforced throughout generation, storage, and retrieval. We construct EP-Bench, to our knowledge the first long-term multi-party benchmark with cross-session correlated events for policy-conditioned relational disclosure. Experiments show that EP-Mem achieves 94.0% privacy classification accuracy, improves disclosure-permission judgment from 22% to 68%, and reduces privacy leakage by 75.6%, while maintaining retrieval performance and cross-benchmark generalization.

Visual-token compression is effective for improving the efficiency of vision-language models, but under extreme compression budgets, token pruning can break visual grounding while learned resamplers increase parameter count, attention cost, and training complexity. We revisit compression through a token parameterization lens, separating (i) basis transformation and structured truncation (retained subspace/compressibility) from (ii) coordinate organization (optimization and cross-modal alignment). This view yields two coupled objectives, compressibility and learnability, which we formalize as unified functionals. Guided by these objectives, we design Braco, a lightweight four-step coder that combines transform-basis truncation, input-independent basis-coordinate embeddings, budget-dependent orthogonal re-parameterization, and learned spatial residual tokens from lightweight pooling. Experiments show that Braco forms the favorable empirical accuracy-efficiency frontier under $23\times$–$64\times$ compression and remains competitive at $144\times$, reaching 95.2% accuracy while reducing prefill FLOPs by 84.2%–86.7% relative to the uncompressed upper bound. Against prior methods, Braco matches or improves accuracy while achieving up to approximately 36% end-to-end speedup and using $16.6\times$/$78.8\times$ lower compressor latency/FLOPs.

We propose NUDGE (Nudge Update via Differentiable GEometry), a training-free obstacle-avoidance procedure that can be incorporated in any robot policy based on diffusion or flow matching, including diffusion policies and vision-language-action models. Our work injects gradients from a signed distance field, a function returning each point's distance to the nearest obstacle, into the policy at inference time to steer it away from obstacles. It supports any common action parameterization, from absolute or relative joint poses to end-effector poses, through a differentiable joint-trajectory decoder. Experiments show that NUDGE preserves the policy's task distribution and runs reactively in real time.

The complex spacing ratio is the complex displacement from a reference eigenvalue to its nearest neighbor divided by the corresponding displacement to its next-to-nearest neighbor. Its statistics provide a useful diagnostic of spectral correlations and nonintegrability in open quantum systems. Here, starting from the exact joint eigenvalue probability densities, we derive finite-$N$ complex-spacing-ratio distributions for the Gaussian ensembles of non-Hermitian random matrices in classes AI$^{\dag}$ and AII$^{\dag}$, realized by complex symmetric and complex self-dual random matrices, respectively. In class AII$^{\dag}$, we obtain an exact algebraic expression for arbitrary $N$ and explicitly evaluate the distributions and representative moments for $N=3, 4, 5, 6$. In class AI$^{\dag}$, although the joint density retains a noncompact integral over nonunitary eigenvector degrees of freedom, we analytically derive a normalized one-dimensional integral representation for $N=3$ and determine the asymptotic behavior, including a logarithmic correction to the cubic level repulsion and a nonanalytic contribution to the angular density. We further confirm these analytical results through direct numerical diagonalization of non-Hermitian random matrices.

We settle in the negative the longstanding question whether every Bézout domain is an elementary divisor domain by constructing a Bézout domain over which an explicit $2\times 2$ matrix has no Smith normal form. The obstruction is topological and is detected by the Möbius line bundle.

Latent test-time scaling improves reasoning by refining hidden states during inference, but existing methods typically apply a single scalar reward to all editable latent tokens. For multimodal large language models, this global update ignores that generated tokens play different roles: some are sensitive to visual evidence, while others correspond to uncertain reasoning decisions. We present Token-Disentangled Latent Test-Time Scaling, an inference-time framework that makes latent refinement token-role-aware. Starting from an initial generated trajectory, we optimize a short hidden-state prefix while routing perception-side visual feedback to image-sensitive tokens and reasoning feedback to high-entropy tokens. Tokens selected by neither route are constrained by an anchor regularizer. Across both perception and reasoning benchmarks on Qwen2.5-VL-7B and InternVL3.5-8B, our method lifts macro accuracy over CoT by +2.57 and +1.51 respectively, and outperforms strong output-space test-time scaling baselines under matched decoded-candidate budgets. Code is available at https://github.com/Qwen-Applications/TD-LTTS.

Plug-and-Play methods are among the state-of-the-art approaches for image reconstruction, but they do not scale well with the image size. We propose a multiresolution block-coordinate Plug-and-Play algorithm that decomposes the image into wavelet blocks and applies a block-wise denoiser network to only a subset of blocks at each iteration, selected through a stochastic Gauss-Southwell-inspired activation rule. Numerical results on deblurring show that the proposed method outperforms the standard Plug-and-Play in different degradation regimes, and in particular the adaptive rule dynamically adjusts to the degradation regime to match the optimal activation rule in every context.