Papers

We present GPUPHOT, an open-source Python framework for GPU-accelerated real-time photometry and astrometry of astronomical CCD and scientific CMOS images. Four of its seven stages run entirely on the GPU through CuPy (background estimation, source detection, PSF modeling and aperture photometry); the catalog crossmatch selects a CPU or GPU backend by problem size, and the zero-point and astrometric calibrations run on the CPU, within a containerized distributed system. Checkpoint-based GPU memory monitoring and an opt-in spatial-binning fallback let a single container image run on GPUs from a 4 GB laptop card to 80 GB datacenter accelerators. We benchmark the framework on nineteen observations from two robotic facilities, the Two-meter Twin Telescope and the Transient Survey Telescope, spanning 4.2 to 151.2 megapixels and 228 to 134,206 cataloged sources, on eight NVIDIA GPU platforms with one process per image. The H100 completes the densest 151.2-megapixel field end-to-end in 31.9 s, and GPU source detection on the A100 is 6-15x faster than the CPU library sep on the same frames. Once three sources of non-determinism are pinned, catalogs and zero points agree to the fourth decimal across GPU models and host CPUs. In this one-process-per-image regime the CuPy 14 / cuML stack showed a 7% lower peak memory and a median 38% higher per-image latency than CuPy 12, both due to the RAPIDS allocator displacing the CuPy memory pool at import; restoring the pool removes the memory difference and cuts the median overhead on datacenter GPUs to 11%, with identical output. Long-lived workers, the production mode, run the two stacks near parity. We recommend the CuPy 14 stack for its reproducibility and maintained libraries, not for memory or speed. GPUPHOT and its benchmark scripts are released for autonomous facilities that require end-to-end photometric reduction at survey cadence.

The present study explores integer and rational matrix solutions for the Diophantine equation $X^{4}+Y^{4}=2Z^{4}$, establishing that infinitely many solutions exist over different matrix rings, including $M_2(\mathbb{Z})$, $M_3(\mathbb{Z})$, $M_4(\mathbb{Z}).$ Furthermore, expanding the scope beyond the integer domain, the analysis demonstrates that an infinite number of matrix solutions can be found in degree-4 and degree-16 field extensions, specifically within $M_4(\mathbb{Q}(\sqrt[4]{l}))$ and $M_4(\mathbb{Q}(\sqrt[4]{l_1}, \sqrt[4]{l_2}))$ when the rational numbers involved lack perfect fourth powers and are not perfect squares.

Geometrically parametrised PDEs arise in shape optimisation, where solving a PDE over many deformed domains at manageable cost is a central challenge. Free-form Deformation (FFD) parametrises shape variations through a lattice of control points, but the resulting parameter space is typically high-dimensional, with most directions barely affecting the quantity of interest (QoI). We address this with a two-stage reduction pipeline. An Active Subspace (AS)-guided structured control-point selection identifies the low-dimensional subspace of FFD weights driving the QoI. A Sinkhorn Autoencoder (SAE) is then trained on the reduced weights, learning their distribution in a compact latent space by minimising the Wasserstein distance between aggregated posterior and prior. We compare three non-intrusive Reduced-order Models (ROMs), mapping full FFD weights, AS-reduced weights, or SAE latent codes to the QoI, each using Random Forests, Gaussian Processes, and K-Nearest Neighbours. We test the methodology on a non-linear heat equation with Gaussian random Robin boundary data on a deformed Stanford Bunny, and on drag prediction for the DTC Hull bulb under FFD deformations. In both cases, the generative model captures the bulk of the QoI distribution over a comparable support, thinning the shoulder opposite the design objective, while its extremes in the design-relevant direction match the FFD sample within numerical and sampling uncertainty. ROMs learned in the SAE latent space yield smaller test errors than those on full FFD weights in most regressor-metric combinations, whereas AS-reduced weights give no comparable gain. Only the latent representation attains a positive predictive coefficient $Q^2$.

Topological magnetic textures can serve as information carriers driven by spin currents. However, their motion is generally accompanied by a Hall effect that deflects them from the current direction, limiting transport efficiency and controllability. We develop a unified spin-space transformation framework enabling a systematic study of hybrid spin textures with different helicities, such as skyrmions, antiskyrmions, bimerons, and antibimerons. Combining analytical theory with micromagnetic simulations, we establish the relation between helicity and current-driven transport. An analytical solution of the generalized Thiele equation identifies helicity as a geometric control parameter and yields a simple expression for the Hall angle, enabling its continuous tuning, complete suppression, and deterministic steering along arbitrary in-plane directions. Micromagnetic simulations confirm that the generated spin textures remain stable under Landau–Lifshitz–Gilbert dynamics and validate the analytical predictions. These results establish helicity as a versatile control parameter for programmable transport of topological magnetic textures.

Let $A$ be a commutative associative unital algebra over a field $K$ of characteristic zero, and let $(G,\rho)$ be a Lie–Rinehart algebra over $A$. We revisit the Gerstenhaber structure carried by the exterior algebra $\bigwedge_A G$ from the point of view of graded derivations. Particular attention is paid to the well-definedness of the Schouten–Nijenhuis extension over the coefficient algebra $A$: the Lie–Rinehart identity is shown to provide exactly the correction terms needed for the bracket to descend to the $A$-balanced exterior algebra. After establishing graded antisymmetry, the Leibniz rule and the graded Jacobi identity without circularity, we study the inner graded derivations $\adSN(P)=[P,\cdot]_{SN}$ and prove \[ [\adSN(P),\adSN(Q)]=\adSN([P,Q]_{SN}). \] Finally, we give a complete proof of the converse construction: Gerstenhaber brackets on $\bigwedge_A G$ are in one-to-one correspondence with Lie–Rinehart structures on $G$.

Let $(\G,\rho,\omega)$ be a symplectic Lie–Rinehart–Jacobi algebra over a commutative algebra $A$, equivalently a Lie–Rinehart algebra $(\G,\bar\rho)$ endowed with a $1$-cocycle $\chi$ and a nondegenerate $2$-form closed for the twisted differential $d_\rho=d_{\bar\rho}+\chi\wedge$. Starting from the standard extension by the $2$-cocycle $\omega$, we study the strict lifting problem for its canonical $1$-form $\eta$ in the LRJ setting. We prove that the strict symmetries of $\eta$ are precisely the elements $X_f+fe$ and that $f\mapsto X_f+fe$ identifies the Jacobi Lie algebra $(A,\{\,,\})$ with this Lie algebra of strict symmetries. For locally Hamiltonian elements, the obstruction to a strict lift is the class $[i_x\omega]\in H^1_\rho(\G,A)$, yielding the exact sequence $0\to\ham\to\hamloc\to H^1_\rho(\G,A)\to0$. We also relate Okassa's symplectic curl to the variation of $d\eta$ and establish a conformal triviality criterion. In the smooth case the framework reduces to locally conformally symplectic geometry, and on a closed surface of genus $g\geq2$ we obtain structures that are not conformally trivial and whose obstruction space has dimension $2g-2$.

This paper develops a general two-point dependent wild bootstrap (DWB) for weakly dependent estimating equations. Its key feature is that the two-point marginal distribution and the latent serial dependence specification can be chosen separately. The construction combines a normalized two-point distribution with a stationary latent Gaussian process via a Gaussian copula transformation, includes dependent Rademacher and Mammen multipliers, and nests the classical iid two-point wild bootstrap as the serially independent case. The induced multiplier autocovariances determine the lag weights in a corresponding heteroskedasticity- and autocorrelation-consistent (HAC) covariance estimator, which coincides exactly with the conditional covariance of the bootstrap estimating-equation sum. We establish first-order bootstrap validity for asymptotically linear estimators by showing that the matched-HAC estimator consistently estimates the long-run covariance and that the bootstrap estimating-equation sum converges conditionally to the same Gaussian limit as its original-sample counterpart, yielding valid HAC-studentized $z$-tests and the corresponding Wald and Lagrange multiplier tests. Monte Carlo experiments in nonlinear generalized method of moments (GMM) and linear regression, with common HAC studentization and matched multiplier covariances, show that dependent Rademacher generally yields better size control than Mammen and Gaussian DWB, especially for restricted $z$-tests. An application illustrates differences between asymptotic and bootstrap inference.

The paper examines the energy-mass relation of Special Relativity (SR), its status and interpretation, through the lens of classical/non-quantum relativistic field theory. The latter arguably constitutes the fullest embodiment of SR as what Einstein labelled a "principle theory". It forms, we propose, the most appropriate perspective also for understanding the energy-mass relation. In a field-theoretic setting, the key notion is a system's energy-momentum (in local/differential or global/integral form, defined via a suitable energy-stress complex). The energy-mass relation then expresses the role that a system's _rest_-energy (provided it exists) plays as the functional counterpart of mass: thanks to important theorems, rest-energy qualifies as its field-theoretic generalisation or successor term. That is, while mass is dispensed with as a fundamental notion, rest-energy retains some—but not all—of its salient functional roles; for special cases, it turns out to be directly correlated with mass. In field theory as a general framework for more specific relativistic theories, energy-momentum replaces mass as the essential notion—a profound, yet often overlooked revision in basic physical concepts. Conservation in particular is guaranteed only for energy-momentum, but no longer for mass. In several regards, energy-momentum fuses energy, momentum and mass, with novel connections amongst them and concomitant physical effects. Situating the energy-mass relation within field theory is a surprisingly neglected, but deeply insightful vista for clarifying and philosophically reflecting on SR's foundations. The field-theoretic interpretation achieves a compelling inner coherence and unifying power, and ties it to the rich heuristic resources of field theory, crucial for post-1905 developments in physics.

We introduce STRIDE (State-Transition Representation via Increment Dynamics and Evolution), which defines states through derivative fingerprints and learns local functions for state transitions (qpairs), recasting continuous forecasting as transition prediction. Trailing convolution windows estimate local joint-transition frequencies, whose lagged differences form a high-dimensional increment trajectory. Proper orthogonal decomposition (POD) gives coordinate paths, jointly forecast by sparse dynamics with memory. Recombining their forecasts and applying history-anchored inversion recovers future transition distributions; sampled state paths select local functions to generate continuous forecasts. Three-seed experiments compare STRIDE against fourteen baselines across nine benchmark families. Five independent Markov and hidden-state baselines cover all 230 evaluated tasks, with 220 complete whole-horizon pairs. Against these comparators, system-weighted late-Energy win fractions range from 73.6% to 78.5% on 190 multi-step pairs; against DLinear, the fraction is 77.3% on 72 paired multi-step tasks. Matched controls examine the intermediate representation. On 64 independently initialized Aizawa trajectories, late-Energy reductions against four matched controls range from approximately 24% to 56%, with all four prespecified contrasts passing Holm correction. These results connect transition-statistic prediction to continuous probabilistic forecasting, with substantial long-horizon gains in the matched Aizawa study.

Let \begin{equation*} f_p(x)=\frac{\mathcal{K}(\sqrt{x})}{p-\ln\sqrt{1-x}}, \end{equation*} where $\mathcal{K}$ denotes the complete elliptic integral of the first kind, and set $g_p=1/f_p$. Tian and Yang conjectured that, at $p=\ln4$, both $-f_{\ln4}^{\prime\prime\prime}$ and $g_{\ln4}$ are absolutely monotonic on $(0,1)$. Writing \begin{equation*} \frac{2}{\pi}f_{\ln4}(x)=\sum_{n=0}^{\infty}a_n(\ln4)x^n,\quad \frac{\pi}{2}g_{\ln4}(x)=\sum_{n=0}^{\infty}b_n(\ln4)x^n, \end{equation*} we prove \begin{equation*} a_n(\ln4)<0\quad(n\geq3),\quad b_n(\ln4)>0\quad(n\geq0), \end{equation*} thereby settling both conjectures. The proof of the first inequality is based on the representation \begin{equation*} a_n(\ln4)=\frac{(-1)^nC}{15^{n+1}}-M_n, \end{equation*} where $C>0$ and $(M_n)$ is a positive moment sequence. Its strict log-convexity, together with estimates for the initial coefficients, determines the sign of every $a_n$. The second inequality follows from a factorization of the quadratic truncation of the normalized Taylor series and a reciprocal-series argument.

Dense associative memories have traditionally focused on storing and retrieving vector-valued patterns. Many modern machine learning problems, however, are naturally graph-structured, requiring memory mechanisms for relational patterns, graph diffusion geometries, community structures, and graph-based inductive biases. We propose a spectral dense associative memory for storage and retrieval of graph data, extending the classical vector-valued memories. Retrieval is performed through a log-sum-exp energy induced by Dirichlet energy with spectral norm distances, producing a softmax-weighted average of the stored Laplacians that remains a valid graph Laplacian. We prove exponential storage capacity and exponentially decaying retrieval error. Beyond graph retrieval, we establish theoretical guarantees for spectral quantities central to graph learning, including eigenvalues, eigenspaces, and diffusion operators. Experiments on synthetic graph data, real-world airline network, protein conformation data and wearable sensor data demonstrate robust graph retrieval while preserving the graph geometry of the data. Our framework provides a new associative memory paradigm for graph-structured data and bridges dense associative memory with modern graph learning and generative AI.

We consider the quadratic NLS system \begin{equation*} \begin{cases} i\partial_tu+\Delta u=v\bar{u},\newline i\partial_tv+\kappa\Delta v=u^2, \end{cases} \qquad (t,x)\in\mathbb{R}\times\mathbb{R}^5, \end{equation*} where $\kappa>0$. If $\kappa=1/2$, which is called mass resonance condition, then scattering below the ground state is shown by Hamano. Moreover, when $\kappa \neq 1/2$, scattering of radial solutions is proved in Hamano–Inui–Nishimura (2021). In the present paper, we prove scattering below the ground state for $\kappa\neq1/2$ without radial symmetry. Our proof is based on the concentration compactness and rigidity method by Kenig–Merle (2006). For the rigidity argument, following Pausader (2010), we use a localized virial argument in the direction orthogonal to the momentum.

Probabilistic time series forecasting requires modeling and predicting complex and time-varying distributions. Recently, Denoising Diffusion Probabilistic Model (DDPM)-based approaches have shown promise by equipping the dif- fusion process with pretrained mean and variance estimators to accommodate distributional shift. However, these methods typically follow the standard DDPM framework and consider only partial components of the evidence lower bound (ELBO), treating the training of estimators as designed regression tasks separate from the variational inference framework. To address this, we rethink the ELBO under the Location-Scale Noise Model (LSNM) and find that it naturally induces a Gaussian negative log likelihood objective for the estimators and inherently defines a joint training objective that unifies recent diffusion paradigms for probabilistic forecasting. Building on this principled ELBO reformulation, we propose Diff- PTS, a general framework that enables end-to-end optimization of all components within the ELBO. Across multiple benchmarks, DiffPTS consistently outperforms recent models, achieving state-of-the-art performance with an average CRPS/MSE reduction of over 14.53%/16.55% compared to existing diffusion-based methods. The code is available at https://github.com/wwy155/DiffPTS.

Image steganography refers to embedding secret messages within cover images while maintaining imperceptibility. Recent advances in deep learning - primarily driven by Convolutional Neural Networks (CNNs) and architectures such as inverse neural networks, autoencoders, and generative adversarial networks - have led to notable progress. However, these frameworks are primarily built on CNN architectures, which treat images as regular grids and are limited by their receptive field size and a bias toward spatial locality. In parallel, Graph Neural Networks (GNNs) have recently demonstrated strong adaptability in several computer vision tasks, achieving state-of-the-art performance with architectures such as Vision GNN (ViG). This work moves in that direction and introduces StegGNN - a novel autoencoder-based, cover-agnostic image steganography framework based on GNNs. By modeling images as graph structures, our approach leverages the representational flexibility of GNNs over the grid-based rigidity of conventional CNNs. We conduct extensive experiments on standard benchmark datasets to evaluate visual quality and imperceptibility. Our results show that our GNN-based method performs comparably to existing CNN benchmarks. These findings suggest that GNNs provide a promising alternative representation for steganographic embedding and open the field of deep learning-based steganography to further exploration of GNN-based architectures.

Debate distillation adapts weaker verifiers using multi-agent debate transcripts to improve their judgement in subsequent debates, but gains on monitored tasks do not establish reliability on related unmonitored tasks. We study epistemic reliability degradation, in which adaptation preserves monitored performance while reducing support for correct responses on hidden tasks. We consider an adversarial debater that manipulates debate arguments while defending the correct monitored response, and ask whether the resulting degradation merely reflects catastrophic forgetting and whether standard evaluation can detect it. To address these questions, we propose ER-Audit, a two-stage black-box auditing framework that compares frozen verifier checkpoints before and after adaptation, and introduce two evaluation benchmarks pairing monitored and hidden task prompts grounded in shared contexts. ER-Audit searches for counterexamples to non-degradation by evaluating semantically valid paraphrases and, if none is found, uses independent paraphrases for sequential hypothesis testing. We derive anytime-valid lower confidence bounds on the non-degradation probability, allowing data-dependent stopping within a finite budget. We further establish a common lower bound across fixed paraphrase distributions and extend it to distributions within a bounded total variation distance of their mixtures. Our experiments show that higher hidden-task accuracy can coexist with more counterexamples to non-degradation and lower non-degradation bounds. This divergence challenges explanations based solely on broad catastrophic forgetting and shows that auditing can uncover selective hidden-task degradation concealed by aggregate performance gains. Our code and benchmarks are available at https://github.com/CSIRO-CQS-AI-alignment-Team/Epistemic-Reliability-Auditor.

Geospatial simulation of infrastructure interventions requires mobility generators that respond directly to edited maps, yet many data-driven generators do not expose the map as an editable condition. We formulate this task as map-conditioned autoregressive generation of human mobility: a road raster conditions a decoder that emits nominal 31.25 m mesh-cell tokens at one-minute intervals. The mesh-local vocabulary supports held-out and locally edited maps without retraining or vocabulary changes. We instantiate a ResNet-50 visual-prefix configuration and a Vision Transformer (ViT) cross-attention configuration, trained from scratch on 87,400 smartphone-derived trajectories from 874 meshes in Ishikawa Prefecture, Japan; 219 meshes are held out. We evaluate map sensitivity by comparing correct-map and within-split shuffled-map generations with held-out real trajectories. On the 110-mesh test split, for the ResNet-50 configuration, correct-map generations are closer than shuffled-map generations on 60% of meshes under Hausdorff-based energy distance (p = 0.021), while DTW is directional but inconclusive (57%, p = 0.074); correlation with real density is 0.38 with the correct map versus 0.01 with shuffled maps. The ViT configuration shows weaker trajectory-level sensitivity and smaller density gains. An illustrative bridge-removal edit changes generated continuations without retraining. Together, these results support the feasibility of editable-map human-mobility simulation.

We study matrix semirings over the three-element flat additively idempotent semiring with elements one, a, and infinity, where the square of a is infinity. We determine the associated matrix-variety chain completely. The scalar, two-by-two, and three-by-three cases generate three distinct varieties, while every matrix dimension at least three generates the same variety. The proof shows that every failure of an identity in arbitrary dimension is already witnessed on three indices, and it yields a coordinate criterion for all identities in the stable variety. We also realize every graph semiring arising from a directed graph of in-degree and out-degree at most one as a divisor of a direct power of the two-by-two matrix semiring. Consequently, the variety generated by all three-nilpotent flat semirings is contained in the two-by-two matrix variety. Directed cycles and independent reversal identities then embed the power-set lattice of the odd primes into each interval between the base variety and a nontrivial matrix variety. Thus every such interval has continuum cardinality and contains continuum-sized chains and antichains. Finally, we determine the last three powers of the multiplicative subsemiring obtained by deleting the constant all-one matrix, and we develop general matrix operators on the lattice of additively idempotent semiring varieties, including stable closures, stable cores, and propagation of equality along matrix-dimension chains.

Solution of convection-dominated problems using stabilized methods often requires to specify stabilization parameters whose optimal choice is not known but which considerably influence the quality of the approximate solution. In a recent work of the authors, an approach for computing these parameters by machine learning was proposed and applied to the streamline upwind/Petrov-Galerkin (SUPG) method for convection-diffusion equations. In the present paper, this approach is studied numerically for unstructured meshes and extended to meshes obtained by anisotropic mesh adaptation.

We study the stability of Boolean constraint satisfaction problems (CSPs) through the notion of average sensitivity (Varma and Yoshida, SODA 2021; SICOMP 2023). It measures the expected $1$-Wasserstein distance between an algorithm's output distributions before and after the deletion of a uniformly chosen constraint, using the unnormalized Hamming metric. We establish two dichotomies for every finite Boolean constraint language $\Gamma$, where $n\geq 2$ denotes the number of variables in an instance. For stable solvability, exactly one of the following holds: $\bullet$ either there is an algorithm that solves $\mathrm{CSP}(\Gamma)$ and has average sensitivity $O_{\Gamma}(1)$ for all satisfiable instances; $\bullet$ or every algorithm that solves $\mathrm{CSP}(\Gamma)$ has average sensitivity $\Omega_{\Gamma}(n)$ on satisfiable instances of arbitrarily large $n$. The first alternative holds if and only if $\Gamma$ has finite duality: unsatisfiability can be witnessed on a bounded number of variables. For stable approximability, where a $(1-\varepsilon)$-approximation violates at most an $\varepsilon$-fraction of the constraints in expectation, exactly one of the following holds: $\bullet$ either for every $\varepsilon\in(0,1]$, there is an algorithm that $(1-\varepsilon)$-approximates $\mathrm{CSP}(\Gamma)$ with average sensitivity $O_{\Gamma}(\varepsilon^{-1}\log n)$ for all satisfiable instances; $\bullet$ or there exists $\varepsilon_{\Gamma}\in(0,1]$ such that every algorithm that $(1-\varepsilon_{\Gamma})$-approximates $\mathrm{CSP}(\Gamma)$ has average sensitivity $\Omega_{\Gamma}(n)$ on satisfiable instances of arbitrarily large $n$. The first alternative holds if and only if $\Gamma$ has bounded width: local consistency checks on bounded sets of variables detect unsatisfiability.

An explicit finite identity basis is given for the eight-element semiring of upper triangular Boolean \(2\times2\) matrices in the signature \((+,\cdot)\). The basis consists of a known multiplicative basis, the ai-semiring laws, and 30 mixed identities, each using at most eight variables. The proof combines a finite basis for the multiplicative reduct with finite rules for shuffling words, duplicating a marked occurrence, and interchanging adjacent occurrences while adding prescribed witnesses. This converts the one-letter gap criterion into a derivation of every valid semiring identity. We also study the band subvariety, a distinguished 156-element interval of the subvariety lattice, congruences, flat members, and finite representations of free algebras. Every \(m\)-letter word has an equivalent subword of length at most \(m^2\) for \(m\geq2\), and the free algebras have doubly exponential rank growth. For arbitrary partially ordered sets, we determine the equational theory of Boolean relation semirings and of finite-support incidence semirings over nontrivial bounded distributive lattices: finite height \(h\) gives the theory of \(T_h\), while unbounded height gives precisely the identities of all additively idempotent semirings.

Model-internal features can be studied through both their ability to identify a specified concept and their causal effect when manipulated, e.g., through steering or weight editing. A prominent approach to feature learning is Sparse Autoencoders (SAEs), which learn broad feature dictionaries whose relation to particular concepts is typically identified post hoc. However, many interpretability questions are instead hypothesis-driven and concern a concept specified in advance. We study this setting as targeted feature learning, where a single feature is constructed for such a predefined concept. We present a controlled comparison across three model signals (activation values, activation gradients, and parameter gradients) and two estimators (contrastive mean and a learned one-dimensional encoder-decoder), yielding six targeted methods, with CAA and GRADIEND as existing instances and four new methods covering the remaining combinations. We compare these methods against pretrained SAEs across 15 tasks and three language models, evaluating both detection and causal intervention. Across models, the strongest detection performance is achieved by contrastive activation value methods, whereas the strongest intervention performance is achieved by gradient-based methods. Overall, our results show that targeted feature quality depends jointly on the model signal and estimator, with detection and intervention capturing complementary properties.

This abstract addresses the incorporation of human motion prediction into proactive and dynamic human-aware motion planning, with the goal of enabling safe collaboration between humans and robots. A deep learning, graph-based model is used to forecast human motion and is integrated into a planning framework. This framework employs a static roadmap along with a time-variant A* algorithm to modify the trajectory of a UR5e manipulator. This method greatly improves human-robot interaction and enables proactive collision avoidance by combining precise motion forecasts with adaptive trajectory planning.

Visual token reduction is an effective way to accelerate multimodal large language models (MLLMs), but performance deteriorates rapidly under extremely low token budgets. Existing work has explored both visual-token selection and training-based adaptation to reduced visual inputs. We take a step further by asking how a heavily compressed MLLM should learn from the states induced by its own generations. This setting naturally calls for on-policy self-distillation: a heavily compressed model is supervised on the states induced by its own generations, while its full-token counterpart serves as an information-rich teacher. Based on this insight, we propose LT-OPD, a training framework for extreme visual-token reduction. The student rolls out responses with only a small fraction of visual tokens, and a frozen full-token copy of the same MLLM provides distributional supervision along these student-generated trajectories. To stabilize on-policy learning when visual evidence is severely limited, we further introduce a budget-level curriculum that progressively decreases the token budget during training. Across nine benchmarks on Qwen3.5-4B, LT-OPD raises average retained performance under 5% visual-token retention from 68.6% to 82.3%, outperforming training-free, training-based, and reinforcement-learning baselines at the same budget. The gains transfer consistently to Qwen3.5-9B, GLM-4.6V-9B, and LLaVA-OV-1.5-4B. LT-OPD also reduces KV-cache usage by 85.2% and prefill FLOPs by 85.4% without additional inference overhead, demonstrating that on-policy learning can substantially recover capabilities lost to extreme visual-token reduction.

Vision-language models (VLMs) have shown increasing potential for medical image understanding, yet their capabilities in ophthalmic imaging remain insufficiently characterized. Existing ophthalmic datasets are typically designed for individual diseases or specialized tasks, making it difficult to systematically evaluate whether VLMs can move beyond disease recognition toward comparative reasoning and fine-grained spatial grounding. We introduce EyeVQA, a unified visual question answering benchmark for comprehensive evaluation of ophthalmic VLMs. EyeVQA is constructed from 21 available ophthalmic datasets and contains 20,000 question-answer pairs spanning six disease groups and seven question types: Single-Choice, Multi-Select, Variable-Select, True-False, Ranking, Point Location, and Bounding Box. Gold answers are deterministically derived from source-provided diagnoses, severity grades, clinical findings, segmentation masks, bounding boxes, and anatomical landmarks, enabling reproducible evaluation without relying on model-generated annotations. Notably, 44.5% of the questions require reasoning across multiple images, extending evaluation beyond conventional single-image medical VQA. We benchmark fourteen representative general-purpose, scientific, and medically specialized VLMs under a unified zero-shot protocol. The best-performing model only achieves an overall score of 62.8, while substantial gaps remain in spatial grounding and cross-task generalization. These results highlight the limitations of current VLMs in comprehensive ophthalmic visual understanding and establish EyeVQA as a diagnostic benchmark for developing more reliable and spatially grounded ophthalmic multimodal models. The project page is available at https://github.com/PKUTHM/EyeVQA.

Comparative Process Reward Models (PRMs) provide critical step-level guidance for autonomous web agents by evaluating state-conditioned preferences between candidate actions. However, existing preference training data synthesized via multi-policy sampling suffers from a severe scarcity of Grounded Minimal Contrastive Pairs (GMCPs)-where competing candidates target genuine on-page elements with identical action types. In representative baselines preference data (namely, WebArbiter), GMCPs account for merely 24.19%, biasing PRMs during training to rely on shallow shortcuts (such as element hallucinations and action type mismatches) rather than acquiring genuine contextual decision semantics. To address these challenges, we propose SURFPRM, a graph-guided process preference synthesis framework for comparative Web PRMs. SURFPRM structures web demonstrations into a persistent Interaction Element Graph that acts as an environment-grounded negative action proposal mechanism, systematically synthesizing contrastive negative actions across spatial, temporal, and spatiotemporal confusion axes. This elevates the GMCP proportion from 24.19% to 74.60%, producing the curated SURFPRM-DATA dataset. Across six open-source backbones (3B to 9B parameters), PRMs trained on SURFPRM-DATA outperform baseline-trained models on average on WEBPRMBENCH and rival leading proprietary LLMs. In downstream reward-guided trajectory search on WEBARENA-LITE, SURFPRM provides step-level guidance for both GPT-4o (+14.21%) and GPT-4o-mini (+12.83%) policies, yielding substantial improvements in complex web task success rates.

Predictive coding (PC) is a local, energy-based alternative to backpropagation (BP) whose iterative inference dynamics make it attractive for implementation on analog hardware. However, standard nonlinear PC requires evaluating the derivative of the activation function during both inference and learning, which can be difficult to realise physically. Here, we introduce activation-matched Bregman PC, replacing standard squared-error energies with Bregman divergences matched to the activation function. This formulation eliminates activation derivatives and, when combined with inference via mirror descent, yields local inference and learning rules requiring only weighted sums, local prediction errors, state integration, and the activation function. In digital experiments, Bregman PC performs comparably to standard PC and BP on classification and generative tasks, while preserving characteristic learning dynamics of PC and its convergence to BP under stable large-model parameterisations. These results provide a more analog-friendly formulation of nonlinear PC while retaining its key computational properties.

In the setting of a hyperbolic (polynomial) system $(\mathcal{V}, p, e)$ of degree $n$, an $n$-tuple $\mathbf{A} = \big[ a_1, a_2, \dots, a_n \big]$ is said to be an $e$-doubly stochastic $\mathcal{V}$-matrix if each $a_i$ belongs to the hyperbolicity cone, has trace $1$, and $a_1 + a_2 + \dots + a_n = e$. In this article, we characterize linear preservers of such $\mathcal{V}$-matrices, describe some connections between $e$-doubly stochasticity and majorization, and study extreme points of the set of all $e$-doubly stochastic $\mathcal{V}$-matrices. We show, for example, that $(i)$ when $n>1$, positive, unital, and trace-preserving transformations are (the only) linear transformations on $\mathcal{V}$ that preserve $e$-doubly stochasticity; $(ii)$ when $\mathbf{A}$ is $e$-doubly stochastic, the eigenvalue vector of the linear combination $\sum_{i=1}^{n} r_ia_i$ is majorized by the coefficient vector $(r_1, r_2, \dots, r_n)^{T} \in \mathbb{R}^n$; and $(iii)$ when $p$ is complete, $e$-doubly stochastic $\mathcal{V}$-matrices induced by (generalized) Jordan frames are extreme points of the compact convex set of all $e$-doubly stochastic $\mathcal{V}$-matrices.

Graph coloring is a well-known NP-complete problem with applications in scheduling, register allocation, frequency assignment, and network optimization. Quantum computing offers the potential for polynomial or even super-polynomial speedups in certain problem instances, yet practical quantum graph coloring methods must carefully balance qubit resources, circuit depth, and constraint enforcement. We proposed a solver agnostic quantum framework for $K$-coloring. Along with a novel encoding and efficient constraint implementation for its exact coloring exploiting Grover search and almost optimal coloring by the Quantum Approximate Optimization Algorithm (QAOA), and Quantum Annealing. Unlike using $O(NK)$ qubits as in SOTA, we reduced the qubit requirements to $O(N \log_2 K)$, along with optimized comparator circuits enforcing adjacency constraints. Further symmetry-based graph reduction is incorporated as an optional preprocessing step to further reduce the instance size before quantum execution.

The detection of the long-sought Population III (Pop III) stars is, perhaps, one of the most intriguing missing links in modern astronomy. Caustic crossing events (CCE) – extreme magnification at the critical curves of galaxy clusters of individual stars at cosmological distances – are postulated to allow for the direct detection of individual Pop III stars. However, in the usual CCE regime, the abundant existence of intracluster stars as microlenses limits the maximum magnification attainable, thus limiting the theoretical detection of luminous stars to relatively low redshifts, significantly smaller than the redshifts where Pop III stars are expected to exist. Here in this letter, we propose to observe Pop III stellar populations as CCEs in the pristine regions of merging clusters. Pristine regions are defined as areas in the lens where the intracluster light, and hence the corresponding stelalr microlenses, is exceptionally low. In thes regions, the low density of microlenses allows background stellar populations to achieve magnification closer to the theoretical limit (whitout microlenses). We show that the maximum magnification in the pristine region scales inversely with the surface mass density of stellar microlenses. Adopting Pop III isochrones, regular James-Webb $\sim29\,$mag observations are sufficient to detect individual Pop III stars in pristine regions, offering a unique observational strategy to detect Pop III stars with the incoming cluster observations. The intermediate regions between high-redshift merging clusters (such as El Gordo) are naturally devoid of microlenses and constitute exceptional targets for the search of Pop III stars.

This paper compares three human motion prediction methods - GMM-based clustering, TransFusion, and Graph-Mixer - evaluating their effectiveness in human-robot collaboration. These predictions are valuable for improving robot motion planning by anticipating human movements and enhancing safety and efficiency in dynamic environments.