arXiv:2602.18690v2 Announce Type: replace-cross
Abstract: Humans rehearse possible futures offline, as in mental practice and perhaps dreaming, suggesting that world models may support task learning away from the environment. Standard machine learning world models compress visual input into latent vectors, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world models: architectures that preserve sensory topology, so physics prediction becomes geometric propagation rather than abstract state transition. We implement this idea with motor-gated neural fields, where activity evolves through local lateral connectivity and motor commands multiplicatively modulate specific channels. Across three experiments, the same architecture learns ballistic prediction without ``teleporting,'' improves a catching policy offline by propagating task error through a frozen learned world model, and develops body-selective motor channels without body labels. These results provide preliminary evidence that physical prediction, offline task learning, and body-linked representation share a common computational substrate: action-conditional prediction within a spatial map.
Science Journals
arXiv:2605.18106v3 Announce Type: replace-cross
Abstract: A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants operate inherently coordinate-wise, rendering them unable to respect the equivariance structures of the parameter space. We address this disparity by introducing a symmetry-compatible principle for optimizer design: the gradient update rule should be equivariant under the symmetry group acting on the corresponding weight block. Following this principle, we first provide a unified perspective on bi-orthogonally equivariant updates for general matrix layers, as employed by stochastic spectral descent, Muon, Scion, and polar gradient methods. More importantly, by moving from orthogonal groups to permutation and shared-shift symmetries, we derive symmetry-compatible optimizers for parameter blocks whose symmetries differ from those of general matrix layers: embedding and LM head matrices, SwiGLU MLP projections, and MoE router matrices. These constructions include one-sided spectral, row-norm, hybrid row-norm/spectral, row-aware, column-aware, centered row-norm, and left-spectral updates. They yield an end-to-end layerwise optimizer stack in which each major matrix-valued parameter class is assigned an update whose equivariance matches its symmetry group. We corroborate this principle through pre-training experiments on dense and sparse MoE language models, including Qwen3-0.6B-style, Gemma 3 1B-style, OLMoE-1B-7B-style, and downsized gpt-oss architectures. Across these experiments, symmetry-compatible update rules consistently improve final validation loss, reduce load imbalance in sparse MoE models, and in several cases improve training stability over the corresponding AdamW updates.
arXiv:2605.11607v2 Announce Type: replace-cross
Abstract: Probabilistic partial least squares (PPLS) is a central likelihood-based model for two-view learning when one needs both interpretable latent factors and calibrated uncertainty. Building on the identifiable parameterization of Bouhaddani et al.\ (2018), existing fitting pipelines still face two practical bottlenecks: noise--signal coupling under joint EM/ECM updates and nontrivial handling of orthogonality constraints. Following the fixed-noise scalar-likelihood protocol, we develop an end-to-end framework that combines noise pre-estimation, constrained likelihood optimization, and prediction calibration in one pipeline. We estimate the observation noise from the low-eigenvalue noise subspace and enforce orthogonality through exact Stiefel-manifold optimization. The noise-subspace estimator attains a signal-strength-independent leading finite-sample rate and matches a minimax lower bound, whereas a full-spectrum noise estimator carries a deterministic bias under the same model. We further extend the framework to sub-Gaussian settings via optional Gaussianization and provide closed-form standard errors through a block-structured Fisher analysis. Across synthetic high-noise settings and two multi-omics benchmarks (TCGA-BRCA and PBMC CITE-seq), the method achieves near-nominal coverage without post-hoc recalibration, reaches Ridge-level point accuracy on TCGA-BRCA at rank $r=3$, matches or exceeds PO2PLS on cross-view prediction while providing native calibrated uncertainty, and improves stability of parameter recovery.
arXiv:2605.26704v2 Announce Type: replace
Abstract: Epidemic forecasting faces a fundamental challenge: human behavior dynamically responds to disease spread, creating feedback loops that induce distribution shifts at policy intervention points. This renders data-driven models unreliable under distribution shift. We propose \textbf{SL-BiLEM} (Structured Learnable Behavior-in-the-Loop Epidemic Model), leveraging physical constraints as regularization for robust extrapolation. The framework decomposes effective transmission as $\beta_{\text{eff}}(t,g) = \beta_0(g) \times m_{\text{policy}}(t) \times m_{\text{media}}(t) \times m_{\text{comp}}(t,g)$, where monotonicity, smoothness, and bounded-jump constraints on the learned compliance function maintain predictive validity under novel policy regimes. Beyond forecasting, SL-BiLEM enables counterfactual analysis for intervention decision support. We validate forecasting on three real-world datasets (cruise ship, school influenza, and school-district COVID-19 surveillance) and evaluate counterfactual recovery on synthetic benchmarks with known ground truth. SL-BiLEM demonstrates: (1) 76\% improvement over neural-mechanistic baselines, with only 53\% OOD degradation versus 1142\% for neural baselines under policy-induced shift; (2) 100\% bootstrap CI coverage across 27 synthetic counterfactual experiments; and (3) Treatment Effect Accuracy exceeding 0.85. These results establish SL-BiLEM as an interpretable tool for public health decision-makers seeking accurate prediction and principled intervention planning.
arXiv:2605.26366v3 Announce Type: replace
Abstract: Recent studies on hallucination detection have shown that hallucination-related signals are more strongly encoded in intermediate layers than in the final layer of large language models (LLMs). Although a growing body of work has sought to exploit this property for hallucination detection, how to automate the selection of high-performing layers remains underexplored, and principled methods for this purpose are still lacking. To address this gap, we first propose several hypotheses for why such signals emerge in intermediate layers and evaluate corresponding criteria for automatic layer selection across diverse LLM architectures, scales, and tasks, covering both question answering and summarization hallucination detection benchmarks. However, we find that none of these criteria consistently delivers satisfactory performance. We therefore propose a new selection criterion, First Effective Peak of Intrinsic Dimension (FEPoID), which consistently identify optimal or near-optimal layers and outperforms both the aforementioned criteria and existing hallucination detection baselines. FEPoID is training-free and incurs negligible computational overhead. In addition, we study the generation behaviors of LLMs and introduce a simple yet effective truncation strategy, which further amplifies hallucination-related signals and substantially improves overall detection performance. Code is publicly available at https://github.com/DesoloYw/Automatic-Layer-Selection-for-Hallucination-Detection.git
arXiv:2501.17377v4 Announce Type: replace
Abstract: Deep Reinforcement Learning (DRL) has emerged as a promising approach for solving Combinatorial Optimization (CO) problems, such as the 3D Bin Packing Problem (3D-BPP), Traveling Salesman Problem (TSP), or Vehicle Routing Problem (VRP), but these neural solvers often exhibit brittleness when facing distribution shifts. To address this issue, we uncover the Satisficing Generalization Edge, which we validate both theoretically and experimentally: identifying a set of promising actions is inherently more generalizable than selecting the single optimal action. To exploit this property, we propose Adaptive Selection After Proposal (ASAP), a generic framework that decomposes the decision-making process into two distinct phases: a proposal policy that acts as a robust filter, and a selection policy as an adaptable decision maker. This architecture enables a highly effective online adaptation strategy where the selection policy can be rapidly fine-tuned on a new distribution. Concretely, we introduce a two-phase training framework enhanced by Model-Agnostic Meta-Learning (MAML) to prime the model for fast adaptation. Extensive experiments on 3D-BPP, TSP, and CVRP demonstrate that ASAP improves the generalization capability of state-of-the-art baselines and achieves superior online adaptation on out-of-distribution instances.
arXiv:2603.05691v3 Announce Type: replace
Abstract: It is increasingly common in machine learning to use learned models to label data and then employ such data to train more capable models. The phenomenon of weak-to-strong generalization exemplifies the advantage of this two-stage procedure: a strong student is trained on imperfect labels obtained from a weak teacher, and yet the strong student outperforms the weak teacher. In this paper, we show that the potential improvement is substantial, in the sense that it affects the scaling law followed by the test error. Specifically, we consider students and teachers trained via random feature ridge regression (RFRR). Our main technical contribution is to derive a deterministic equivalent for the excess test error of the student trained on labels obtained via the teacher. Via this deterministic equivalent, we then identify regimes in which the scaling law of the student improves upon that of the teacher, unveiling that the improvement can be achieved both in bias-dominated and variance-dominated settings. Strikingly, the student may attain the minimax optimal rate regardless of the scaling law of the teacher -- in fact, when the test error of the teacher does not even decay with the sample size.
arXiv:2603.05406v2 Announce Type: replace
Abstract: The Optimal Morse Matching (OMM) problem asks for a discrete gradient vector field on a simplicial complex that minimizes the number of critical simplices. It is NP-hard and has been studied extensively in heuristic, approximation, and parameterized complexity settings. Parameterized by treewidth $k$, OMM has long been known to be solvable on triangulations of $3$-manifolds in $2^{O(k^2)} n^{O(1)}$ time and in FPT time for triangulations of arbitrary manifolds, but the exact dependence on $k$ has remained an open question. We resolve this by giving a new $2^{O(k \log k)} n$-time algorithm for any finite regular CW complex, and show that no $2^{o(k \log k)} n^{O(1)}$-time algorithm exists unless the Exponential Time Hypothesis (ETH) fails.
arXiv:2606.03982v1 Announce Type: new
Abstract: Quantities with measurement units, such as 110 cm and 1.2 m, require language models (LMs) to combine a numeral with a symbolic unit scale. Here, we study how LMs compare such quantities in controlled settings spanning several unit systems. We find that accuracy degrades near the comparison boundary, where small changes in value determine the correct answer. The resulting errors are systematic: linear surrogate models predict LM preferences from numerical-difference and unit-scale-difference cues, and causal interventions on subspaces aligned with these variables shift model's output. The results suggest that LMs compare quantities through a bag of heuristics over numerals and units, rather than first converting both expressions to an exact shared-scale representation.
arXiv:2605.20731v2 Announce Type: replace
Abstract: Text-to-image models now generate graphic design at production scale, yet their supervision still comes primarily from photo-style preference datasets with a single overall verdict per comparison. Designers evaluate designs along several distinct axes (e.g., typography, layout, color harmony) that a single preference label collapses. We release \emph{TASTE} \textit{(Typography, Aesthetics, Spatial, Tone, Etc.)}, a multi-dimensional preference dataset in which two disjoint cohorts of five professional designers each ranked outputs from four current text-to-image models across nine criteria along with per-image hallucination flags. We pair the dataset with two contributions. First, a criterion-agnostic signal-validation framework based on Kendall's $\tau$, majority-vote probability, and Condorcet cycles against exact iid-uniform nulls; the analysis reveals significant but moderate designer agreement, with every TASTE criterion rejecting the random-rater null. Second, we benchmark preference models on TASTE and find that off-the-shelf VLM judges and dedicated T2I scorers fail to reach majority agreement with the designer panel, while a small MLP head trained directly on TASTE substantially narrows the gap to the single-rater ceiling, setting a baseline for future TASTE-trained preference models.
arXiv:2606.03989v1 Announce Type: new
Abstract: Images composed of 2D pixel arrays are the standard input to computer vision algorithms, yet many underlying computations can be distributed across pixels. Transmitting raw, redundant, and noisy pixel data off the sensor remains inefficient, motivating a shift toward focal-plane sensor-processors that perform a significant part of the computation directly within each pixel. We envision pixels synthesizing higher-level signals locally, reducing downstream load, and providing richer inputs for higher-level vision tasks.
We propose a fully parallelizable form of visual odometry and depth estimation across pixels, where sensor-processors exchange information through Gaussian Belief Propagation (GBP) to achieve consensus about camera motion and infer depth from per-pixel photometric observations and a surface normal prior. To maintain geometric stability during optimization, we introduce a keyframe-like anchoring mechanism that regulates the effective baseline between frames, enabling consistent motion and depth updates. Our method is evaluated on realistic datasets, demonstrating the feasibility of GBP-based pixel-level distributed odometry and depth estimation with keyframe anchoring on-sensor. Project Page: https://www.shinjeongkim.com/pixvod/
arXiv:2606.03980v1 Announce Type: new
Abstract: Reward models (RMs) provide critical feedback signals for LLM post-training, notably in reinforced fine-tuning (RFT) and reinforcement learning (RL) pipelines. However, current reward evaluation relies on heterogeneous criteria such as rule-based verifiers, ground-truth references, procedural checklists, and complex rubrics, where a unified mechanism to integrate all types of evidence remains unexplored. To this end, we propose Skill Reward Model (Skill-RM), a unified framework that reformulates reward modeling as the execution of a reusable Reward-Evaluation Skill. By treating reward computation as a structured agentic task, Skill-RM provides a consistent interface to orchestrate heterogeneous resources, dynamically selecting and aggregating evidence tailored to the specific requirements of each input. This approach enables the reward model to move beyond static evaluation, ensuring consistency and transparency across diverse tasks. Extensive experiments on reward benchmarks and downstream applications, including best-of-N selection and reinforcement learning, demonstrate that Skill-RM consistently outperforms traditional judge baselines. Our findings suggest that Skill-RM not only provides a unified solution for reward modeling but also achieves superior performance through the strategic and dynamic orchestration of evidence. The code is at https://github.com/Qwen-Applications/Skill-RM.
arXiv:2512.22914v2 Announce Type: replace
Abstract: In the context of distributed fusion estimation, directly transmitting local estimates to the fusion center may cause a privacy leakage concerning exogenous inputs. Thus, it is crucial to protect exogenous inputs against full eavesdropping while achieving distributed fusion estimation. To address this issue, a noise injection strategy is provided by injecting mutually independent noises into the local estimates transmitted to the fusion center. To determine the covariance matrices of the injected noises, a constrained minimization problem is constructed by minimizing the sum of mean square errors of the local estimates while ensuring ({\epsilon}, {\delta})-differential privacy. Suffering from the non-convexity of the minimization problem, an approach of relaxation is proposed, which efficiently solves the minimization problem without sacrificing differential privacy level. Then, a differentially private distributed fusion estimation algorithm based on the covariance intersection approach is developed. Further, by introducing a feedback mechanism, the fusion estimation accuracy is enhanced on the premise of the same ({\epsilon}, {\delta})-differential privacy. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed algorithms, and the trade-off between differential privacy level and fusion estimation accuracy.
arXiv:2605.20402v3 Announce Type: replace
Abstract: MXFP4 arithmetic can dramatically accelerate reinforcement learning (RL) post-training of large language models (LLMs), yet the quantization error introduces severe accuracy degradation. Existing work treats the quantization error as a monolithic noise term, missing the distinct mechanisms upon interpreting how quantization error damages training. We prove an exact three-way decomposition of quantization error and show how each component dominates a distinct RL training pathway. Our theoretical and empirical analysis decomposes the MXFP4 quantization error into three additive components: "scale bias" from power-of-two rounding, "deadzone truncation" from zeroing small values, and "grid noise" from rounding to the nearest 4-bit grid. Each component dominates a distinct RL failure mode: scale bias accumulates multiplicatively through the backward pass, affecting gradient accuracy; deadzone truncation degrades rollout quality; and grid noise raises the policy's entropy. We combine corrections that are RL failure mode-targeted but not component-exclusive: Macro-block scaling to reduce scale bias, Outlier Fallback recovers deadzone entries, but also partially reduces scale bias induced error, and Adaptive Quantization Noise (AQN) for controlling the policy entropy. On Qwen2.5-3B dense and Qwen3-30B-A3B-Base mixture-of-experts model, the targeted corrections recover BF16 accuracy to within 0.7% and exceed BF16 by +1.0% respectively.
arXiv:2511.13020v2 Announce Type: replace
Abstract: Although hyperspectral imaging offers unparalleled non-invasive physiological insight, its bulky hardware, slow acquisition, and regulatory burden severely limit its clinical availability. A natural workaround is to reconstruct hyperspectral information from ubiquitous RGB or CASSI measurements. However, existing paradigms, developed for object-centric scenes, rely on reflectance-based feature alignment, assuming that spectral similarity preserves semantic meaning. This assumption breaks down in physiological imaging, where visually similar RGB responses may arise from distinct and entangled physiological states. This mismatch motivates a shift from reflectance alignment to physiology-aware representation learning, grounded in shared light-matter interaction principles -- a shift that introduces fundamental challenges from cross-channel semantic shifts (C1) and irreversible information loss in RGB-based acquisition (C2). We therefore design PHASE, a physiology-aware hyperspectral reconstruction paradigm that fundamentally redefines object-to-human transfer by disentangling cross-channel physiological semantics via Physiological Channel Reinterpretation and restricting reconstruction to physiologically plausible solutions through Physiologically Constrained Alignment. Under two source-to-target transfer protocols, PHASE consistently outperforms state-of-the-art methods by up to +2.20 SSIM and -3.06 in SAM with merely 1.5% labeled supervision.
arXiv:2601.18627v2 Announce Type: replace-cross
Abstract: Cross-correlations between 21cm observations and galaxy surveys provide a powerful probe of reionization by providing robustness against foreground contamination while linking ionization morphology to galaxies. We quantified the constraining power of 21cm galaxy cross-power spectra for inferring the neutral hydrogen fraction, $x_\mathrm{HI}(z),$ and mean overdensity, $\langle 1+\delta_\mathrm{HI} \rangle(z)$, exploring dependence on the field of view; redshift precision, $\sigma_z$; and minimum halo mass, $M_\mathrm{h,min}$. We employed our simulation-based inference framework EoRFlow for likelihood-free parameter estimation. Mock observations include thermal noise for 100h of SKA-Low with foreground avoidance and realistic galaxy-survey effects. For a fiducial survey ($\mathrm{FOV}=100\,\mathrm{deg}^2$, $\sigma_z=0.001$, $M_\mathrm{h,min}=10^{11}\mathrm{M}_\odot$), cross-power spectra yield unbiased constraints with posterior volumes (PVs) of $\sim$10% relative to priors. Cross-power measurements reduce the PV by 20-30% versus 21cm auto-power alone. With foreground avoidance, spectroscopic redshift precision is essential; photometric redshifts render cross-correlations uninformative. Notably, cross-power spectra constrain ionizing source properties, the escape fraction $f_\mathrm{esc,}$ and the star formation efficiency $f_*$, which remain degenerate in auto-power (PV >60%). Tight constraints require either deep surveys detecting faint galaxies ($M_\mathrm{h,min} \sim 10^{10}\mathrm{M}_\odot$) with moderate foregrounds (PV~11%) or conservative mass limits with optimistic foreground removal (PV~19%). 21cm galaxy cross-correlations enhance morphology constraints beyond auto-power while enabling previously inaccessible source property constraints. Realizing full potential requires precise redshifts and either faint galaxy detection limits or improved 21cm foreground cleaning.
arXiv:2603.05290v2 Announce Type: replace
Abstract: Large language models (LLMs) achieve promising performance, yet their ability to reason remains poorly understood. Existing evaluations largely emphasize task-level accuracy, often conflating pattern matching with reasoning capability. We present X-RAY, an explainable reasoning analysis system that maps the LLM reasoning capability using calibrated, formally verified probes. We model reasoning capability as a function of extractable \textit{structure}, operationalized through formal properties such as constraint interaction, reasoning depth, and solution-space geometry. X-Ray generates probes via formal tools with controlled structural variations, enabling precise isolation of incremental structural information through formal calibration and verification. We evaluate state-of-the-art LLMs on problems ranging from junior-level to advanced in mathematics, physics, and chemistry. Our analysis reveals a systematic asymmetry in LLM reasoning: models are relatively robust to constraint refinement, where additional conditions shrink an existing solution space, but degrade sharply under solution-space restructuring, where modifications alter the underlying structural form of the solution manifold. Moreover, calibrated formal probes differentiate models that appear indistinguishable on standard benchmarks and reveal failure modes that are structurally interpretable rather than opaque. Beyond evaluation, our framework is contamination-free and supports the training and testing of reasoning models.
arXiv:2603.04956v2 Announce Type: replace
Abstract: This paper considers the problem of converting a given dense linear layer to low precision. The tradeoff between compressed length and output discrepancy is analyzed information theoretically (IT). It is shown that a popular GPTQ algorithm may have an arbitrarily large gap to the IT limit. To alleviate this problem, a novel algorithm, termed ``WaterSIC'', is proposed and is shown to be within a rate gap of 0.255 bits to the IT limit, uniformly over all possible covariance matrices of input activations. The key innovation of WaterSIC's is to allocate different quantization rates to different columns (in-features) of the weight matrix, mimicking the classical IT solution known as "waterfilling". Applying WaterSIC to the Llama and Qwen family of LLMs establishes new state-of-the-art performance for all quantization rates from 1 to 4 bits. Our code is available at https://github.com/egorlifar/watersic.
arXiv:2603.01576v3 Announce Type: replace
Abstract: Geo-Foundation Models (GFMs) have been evaluated across diverse Earth observation task including multiple domains and have demonstrated strong potential of producing reliable maps even with sparse labels. However, benchmarking GFMs for Cryosphere applications has remained limited, primarily due to the lack of suitable evaluation datasets. To address this gap, we introduce \textbf{Cryo-Bench}, a benchmark compiled to evaluate GFM performance across key Cryospheric components. Cryo-Bench includes debris-covered glaciers, glacial lakes, sea ice, and calving fronts, spanning multiple sensors and broad geographic regions. We evaluate 14 GFMs alongside UNet and ViT baselines to assess their advantages, limitations, and optimal usage strategies. With a frozen encoder, UNet achieves the highest average mIoU of \textbf{66.38}, followed by TerraMind at \textbf{64.02} across five evluation dataset included in Cryo-Bench. In the few-shot setting (10\% input data), GFMs such as DOFA and TerraMind outperform UNet, achieving mIoU scores of \textbf{59.53}, \textbf{56.62}, and \textbf{56.60}, respectively, comapred to U-Net's 56.60. When fully finetuning GFMs, we observe inconsistent performance across datasets and models. However, tuning learning rate along with finetuning substantially improves GFM performance. For example, evaluation on two representative datasets (GLID and CaFFe) shows an average relative improvement of \textbf{12.77\%}. Despite having minimal Cryosphere representation in their pretraining data, GFMs exhibit notable domain adaptation capabilities and produce meaningful results across tasks. Based on our findings, We recommend encoder fine-tuning with hyperparameter optimization optimization to achieve the best possible performance, while using frozen encoders when users need quick results without extensive experimentation.(\href{https://github.com/Sk-2103/Cryo-Bench}{GitHub}).
arXiv:2511.12085v3 Announce Type: replace
Abstract: Phishing and related cyber threats are becoming increasingly sophisticated, with email-based phishing remaining the most persistent attack vector. These attacks exploit human vulnerabilities to deliver malware or gain unauthorized access to sensitive information. Transformer-based models enhance phishing detection through robust contextual language understanding; yet they are often regarded as black boxes due to a lack of interpretability. Moreover, recent AI-enabled attacks further undermine model resilience. To address these challenges, this work proposes a lightweight phishing detection framework based on DistilBERT, a lightweight Transformer model. Robustness to embedding-level perturbations and character-level input noise is enhanced through gradient-based adversarial training using the Fast Gradient Method (FGM), combined with stochastic character-level perturbations. To improve transparency, three prominent Explainable AI (XAI) methods, LIME (Local Interpretable Model-agnostic Explanations), SHAP (SHapley Additive exPlanations), and IG (Integrated Gradients), are integrated to interpret model decision-making. A structured rule-based prompt combines model predictions and XAI features to guide Flan-T5-Small in generating plain-language, evidence-based explanations. Experimental results demonstrate that the proposed framework outperforms a standard DistilBERT-based detection model trained without robustness enhancements in terms of accuracy and resilience. This integrated approach helps bridge the gap between model reliability and user trust, advancing transparent phishing detection.
arXiv:2601.04120v2 Announce Type: replace-cross
Abstract: Optimal control of obstacle problems arises in a wide range of applications and is computationally challenging due to its nonsmoothness, nonlinearity, and bilevel structure. Classical numerical approaches rely on mesh-based discretization and typically require solving a sequence of costly subproblems. In this work, we propose a single-loop bilevel deep learning method, which is mesh-free, scalable to high-dimensional and complex domains, and avoids repeated solution of discretized subproblems. The method employs constraint-embedding neural networks to approximate the state and control and preserves the bilevel structure. To train the neural networks efficiently, we propose a Single-Loop Stochastic First-Order Bilevel Algorithm (S2-FOBA), which eliminates nested optimization and does not rely on restrictive lower-level uniqueness assumptions. We analyze the convergence behavior of S2-FOBA under mild assumptions. Numerical experiments on benchmark examples, including distributed and obstacle control problems with regular and irregular obstacles on complex domains, demonstrate that the proposed method achieves satisfactory accuracy while reducing computational cost compared to classical numerical methods.
arXiv:2509.17531v2 Announce Type: replace
Abstract: We introduce a two-level hybrid restricted additive Schwarz (RAS) preconditioner for heterogeneous steady-state convection-diffusion equations at high P\'{e}clet numbers. Our construction builds on the multiscale spectral generalized finite element method (MS-GFEM), wherein the coarse space is spanned by locally optimal basis functions obtained from local generalized eigenproblems on operator-harmonic spaces. Extending the theory of Ma (2025) to convection-diffusion problems in conservation form, we establish exponential convergence of the MS-GFEM approximation with respect to the dimension of the local approximation space. Rewriting MS-GFEM as a RAS-type iteration, we show for coercive problems that this exponential convergence property is inherited by the RAS-type iterative method (at least in the continuous setting). Employed as a preconditioner within the generalized minimal residual method (GMRES), the resulting method requires only a few iterations for high accuracy even with low-dimensional coarse spaces.
Through extensive numerical experiments on problems with high-contrast diffusion and non-divergence-free, rotating velocity fields, we demonstrate robustness with respect to the grid P\'{e}clet number and the number of subdomains (tested up to $10^5$ subdomains), while coarse-space dimensions remain small as grid P\'{e}clet numbers increase. By adapting the coarse space and oversampling size, we are able to achieve arbitrarily fast convergence of preconditioned GMRES. As an extension, for which we do not have theory yet, we show effectiveness of the method even for indefinite problems and in the vanishing-diffusion limit.
arXiv:2606.03978v1 Announce Type: new
Abstract: This study presents the first clinical integration and experimental demonstration of a nozzle-mounted Compton camera prompt gamma imaging (PGI) system for in vivo proton range verification. Four position-sensitive solid-state Compton camera modules, each containing four cadmium zinc telluride (CdZnTe) detector crystals, were integrated into a modified range shifter mounted directly on the treatment nozzle of a clinical proton therapy gantry. This compact fixed-geometry configuration maintained alignment with the proton beam axis throughout irradiation and enabled stable synchronized data acquisition during pencil-beam scanning delivery. The system was evaluated under realistic clinical proton beam delivery conditions using single-energy and spread-out Bragg peak (SOBP) irradiations at gantry angles of 90{\deg} and 270{\deg}, delivered doses of 2 Gy and 7.5 Gy, and controlled distal range shifts of up to 10 mm. Prompt gamma events were reconstructed into three-dimensional emission distributions using a physics-based Compton scatter reconstruction framework. The system operated reliably during all irradiations and produced reproducible prompt-gamma localization across repeated measurements. Reconstructed emission distributions remained geometrically consistent across gantry angles and demonstrated sensitivity to controlled distal range perturbations, with measurable upstream shifts of the emission hotspot corresponding to reduced proton penetration depth. These results demonstrate the feasibility of a clinically integrated nozzle-mounted quad-camera Compton PGI system for detecting millimeter-scale proton range variations during beam delivery and represent an important step toward clinically deployable prompt gamma-based in vivo treatment verification in proton therapy.
arXiv:2606.03975v1 Announce Type: new
Abstract: In the 1960s, Fisher, Kasteleyn and Temperley designed an ingenious algorithm for computing the partition function of the dimer model, or equivalently, for counting perfect matchings in edge-weighted planar graphs (Philos. Mag. 1961; J. Mathematical Phys. 1963). This FKT algorithm later became the foundation for Valiant's holographic algorithms (FOCS 2004; SIAM J. Comput. 2008), which motivated the study of counting problems under the Holant framework. Combined with an algorithm by Yuster (FOCS 2008), the FKT algorithm allows us to count edge-weighted perfect matchings in planar $n$-vertex graphs with $\tilde{O}(n^{\omega/2})$ arithmetic operations, where $\omega<2.372$ is the matrix multiplication exponent.
We prove a corresponding lower bound: Over algebraic circuits and other sufficiently strong computational models, perfect matchings in edge-weighted $n$-vertex planar graphs $G$ cannot be counted in $O(n^{\omega/2-\epsilon})$ arithmetic operations. This confirms the optimality of Yuster's algorithm. Our bound holds even when $G$ is an edge-weighted square grid.
arXiv:2606.02461v2 Announce Type: replace
Abstract: Language agents spend substantial inference time solving individual tasks, yet the experience acquired in one episode is often underutilized in future episodes. Continual learning expects an agent to accumulate reusable experience across a stream of tasks, improve over time, and avoid interference from irrelevant experiences. Unfortunately, existing benchmarks struggle to evaluate continual learning in language agents rigorously. Most efforts focus on retrieval and reasoning over long-context conversations or documents, while recent lifelong-adaptation benchmarks often rely on naive task streams with limited analysis of cross-task relationships, making it difficult to understand what an agent learns and reuses over time. This paper presents an evaluation framework AgentCL for continual learning in agents, centered on controlled task streams and metrics for transfer gains. AgentCL constructs compositional streams where earlier sub-solutions, evidence, or workflows are intentionally reusable in later tasks, and contrasts them with naive streams where such reusability is not guaranteed. We use the benchmark to evaluate non-parametric memory designs for continual learning. To diagnose how memory design choices affect continual learning, we develop MemProbe, a probing method that stores interactions, insights, and skills, while filtering unreliable experiences during consolidation. Empirical analysis across coding, deep research, and language understanding/reasoning tasks shows that naive streams offer limited ability to distinguish memory designs, whereas controlled streams more clearly distinguish their plasticity. Meanwhile, naive and held-out settings often yield limited gains and can expose memory-induced degradation. These results highlight the need for stronger memory designs that balance plasticity and stable reuse.