arXiv:2605.18654v1 Announce Type: new Abstract: A fraud scorer needs to answer in under 2 ms. The best tabular foundation models (TFMs) take 151-1,275 ms on GPU. We close this gap by distilling the TFM offline into an XGBoost or CatBoost student that runs natively on CPU. The central obstacle is specific to in-context learning (ICL) teachers: they leak labels when scoring their own training set, so the soft targets collapse to near-one-hot vectors with no inter-class structure left to distill. Stratified out-of-fold (OOF) teacher labeling prevents this. Across 153 classification datasets drawn from TALENT, OpenML-CC18, TabZilla, and TabArena, distilling TabICLv2 into XGBoost gives 0.882 macro-mean AUC (96.5% of teacher AUC) at 1.9 ms on CPU, a 38x to 860x speedup across teacher-student pairs with a statistically significant edge over a tuned CatBoost baseline (Wilcoxon p = 0.0008; 51% win rate). Four further findings: teacher rank transfers exactly to student rank; gains concentrate on low-dimensional data (< 21 features: +0.011 over CatBoost vs. >21 features: +0.001); multi-teacher averaging helps MLP students (+0.006, p = 0.003) but adds less than 0.001 for tree students; and on high-dimensional tasks where the teacher itself trails CatBoost, distillation makes things worse rather than better. The full pipeline is open-sourced as part of the TabTune library.
Science Journals
arXiv:2605.18670v1 Announce Type: new Abstract: Risk-limiting audits (RLAs) are post-election auditing procedures that rigorously guarantee a specified maximum probability that an incorrect electoral outcome will not be detected. Aside from ready access to physical ballots, known RLAs require a software-independent accounting of the sizes of each ballot batch, called a ballot manifest. While typical electoral procedures automatically provide rough estimates for batch sizes, even slight inaccuracies (commensurate with the margin of the contest under audit) completely invalidate conventional RLAs (Lindeman et al., EVT 2012). Thus, establishing a sufficiently accurate manifest often requires handling every ballot and can be the dominant cost of conducting the RLA. We propose two new risk-limiting techniques: 1) A statistical mechanism for ensuring that the batch sizes reported by an untrusted tabulation are, in fact, an accurate manifest; this effectively bootstraps from a rough manifest to an accurate one with sublinear effort. 2) We propose a new class of RLAs called direct ballot selection. This method reverses the traditional comparison procedure and compares uniformly selected ballots against their cast vote records, requiring a new statistical test for identifier duplication but efficiently supporting elections without in order identifiers. These techniques reduce the complexity of RLAs across many elections. Our two main findings are as follows: 1) The time to create a manifest can be drastically reduced with a modest increase in the number of ballots sampled in the audit. At a 3% margin and a large population, there is a reduction in the overall audit time of at least an order of magnitude across methods. 2) Direct ballot selection improves over state-of-the-art polling for small margins. For Connecticut (29th in population) at a 1% margin, it beats Minerva (Security 2022) by 55% in ballot sample complexity.
arXiv:2605.17424v1 Announce Type: new Abstract: This paper presents an optimization framework for Spatial Packaging of Interconnected Systems with Physical Interactions (SPI2) that addresses the geometric challenges of three-dimensional component placement and routing. While SPI2 generally includes physical interactions, this study isolates the spatial optimization aspect to evaluate placement and routing performance independently. The framework integrates the Maximal Disjoint Ball Decomposition (MDBD) for geometric abstraction with a hybrid optimization strategy that combines stochastic initialization and gradient-based refinement with interior point optimization. It is formulated to handle the nonlinear, non-convex, and continuous characteristics of spatially coupled design problems. The proposed framework is evaluated against a use case from prior SPI2 research and tested with a newly introduced benchmark that enables verifiable assessment of optimization performance. Results indicate that the presented method achieves more than a 10% improvement over existing SPI2 implementations and converges to spatially analytical optima across various benchmark scenarios. Benchmark experiments show solution accuracy of 0.6-2% relative to the ground truth.
arXiv:2605.18004v1 Announce Type: new Abstract: Randomized linear algebra (RLA) algorithms are a modern class of numerical linear algebra techniques that play an essential role in scientific computing and machine learning, with broad and growing adoption. However, their discovery remains mostly a manual process that requires deep expert knowledge and inspiration. While Reinforcement Learning (RL) offers a pathway to automation, standard approaches struggle with sparse reward landscapes and vast search spaces inherent to high-performing RLA algorithms. In this paper, we present RL4RLA, a general RL framework that automates the discovery of interpretable, symbolic RLA algorithms. Unlike black-box approaches, our method builds explicit algorithms from basic linear algebra primitives, ensuring verifiable and implementable representations. To enable efficient discovery, we introduce: (1) a numerical curriculum that progressively increments problem difficulty to encode inductive bias specific to the RLA domain; (2) Monte Carlo Graph Search, which optimizes exploration by identifying and merging equivalent partial algorithms. We demonstrate that RL4RLA rediscovers state-of-the-art methods, including sketch-and-precondition solvers, Randomized Kaczmarz, and Newton Sketch, and can be targeted to produce algorithms optimized for specific trade-offs between accuracy, speed, and stability. Code is available at https://github.com/Tim-Xiong/RL4RLA.
arXiv:2510.16046v3 Announce Type: replace Abstract: We present CARDIO-Affect, a complex-systems theoretical framework for long-term emotional dynamics in bounded social groups, with explicit uncertainty quantification at every layer. Long-period naturalistic emotion in stable small groups exhibits hallmarks of complex systems -- multi-stable attractors, weak chaos, long-range memory, and sparse heterogeneous coupling -- invisible to conventional short-clip facial-emotion analysis. CARDIO-Affect treats individual emotion as a multi-stable nonlinear stochastic dynamical system and group emotion as a sparsely-coupled network with emergent macrostates, formalised through six propositions and four pillars: (i) statistical mechanics with neural-parameterised Hamiltonian SDE over asymmetric potentials; (ii) information geometry on a 45-dimensional Fisher-Rao manifold; (iii) topological data analysis for invariant trajectory signatures; (iv) HRV-inspired Emotional Variability Analytics (EVA) decomposing each person-day into multi-scale time/frequency/nonlinear measures. We validate on the first 30.1-month longitudinal in-the-wild facial-emotion corpus (companion: arXiv:2510.15221) by discovering three falsifiable paradoxes: Sparse-Contagion (R_0=0.36, density 2.7%, 8 BH-FDR edges), Asymmetric-Persistence (negative dwell 5.85x positive, 1.77D potential gap), and Crisis-Inversion (Shanghai 2022 lockdown naive d=-0.40 collapses to permutation-p=0.94 under BSTS + synthetic-control). On synthetic benchmarks, CARDIO-EBM v2 matches asymptotically optimal Granger on linear VAR data (Class A AUROC 0.984+/-0.012 vs Granger 0.997+/-0.001, 5 seeds) but fails on tanh-coupled nonlinear data (Class B AUROC 0.490 vs Granger 0.796), a documented limitation of the linear mask-self estimator. We release framework code and the full reproduction pipeline.
arXiv:2510.23641v2 Announce Type: replace Abstract: Transformers are very effective in capturing both global and local correlations within high-energy particle collisions, but they present deployment challenges in high-data-throughput environments, such as the CERN LHC. The quadratic complexity of transformer models demands substantial resources and increases latency during inference. In order to address these issues, we introduce the Spatially Aware Linear Transformer (SAL-T), a physics-inspired enhancement of the linformer architecture that maintains linear attention. Our method incorporates spatially aware partitioning of particles based on kinematic features, thereby computing attention between regions of physical significance. Additionally, we employ convolutional layers to capture local correlations, informed by insights from jet physics. In addition to outperforming the standard linformer in jet classification tasks, SAL-T also achieves classification results comparable to full-attention transformers, while using considerably fewer resources with lower latency during inference. Experiments on a generic point cloud classification dataset (ModelNet10) further confirm this trend. Our code is available at https://github.com/aaronw5/SAL-T4HEP.
arXiv:2511.08704v2 Announce Type: replace Abstract: This paper investigates the scaling properties of autoregressive next-pixel prediction, a simple, end-to-end yet under-explored framework for unified vision models. Starting with images at resolutions of 32x32, we train a family of Transformers using IsoFlops profiles across compute budgets up to 7e19 FLOPs and evaluate three distinct target metrics: next-pixel prediction objective, ImageNet classification accuracy, and generation-based completion measured by Fr'echet Distance. First, optimal scaling strategy is critically task-dependent. At a fixed resolution of 32x32 alone, the optimal scaling properties for image classification and image generation diverge, where generation optimal setup requires the data size grow three to five times faster than for the classification optimal setup. Second, as image resolution increases, the optimal scaling strategy indicates that the model size must grow much faster than data size. Surprisingly, by projecting our findings, we discover that the primary bottleneck is compute rather than the amount of training data. As compute continues to grow four to five times annually, we forecast the feasibility of pixel-by-pixel modeling of images within the next five years.
arXiv:2512.08089v2 Announce Type: replace Abstract: Real-time, energy-efficient inference on edge devices is essential for graph classification across a range of applications. Hyperdimensional Computing (HDC) is a brain-inspired computing paradigm that encodes input features into low-precision, high-dimensional vectors with simple element-wise operations, making it well-suited for resource-constrained edge platforms. Recent work enhances HDC accuracy for graph classification via Nystr\"om kernel approximations. Edge acceleration of such methods faces several challenges: (i) redundancy among (landmark) samples selected via uniform sampling, (ii) storing the Nystr\"om projection matrix under limited on-chip memory, (iii) expensive, contention-prone codebook lookups, and (iv) load imbalance due to irregular sparsity in SpMV. To address these challenges, we propose HyperX, the first end-to-end FPGA accelerator for Nystr\"om-based HDC graph classification at the edge. HyperX integrates four key optimizations: (i) a hybrid landmark selection strategy combining uniform sampling with determinantal point processes (DPPs) to reduce redundancy while improving accuracy; (ii) a streaming architecture for Nystr\"om projection matrix maximizing external memory bandwidth utilization; (iii) a minimal-perfect-hash lookup engine enabling $O(1)$ key-to-index mapping; and (iv) sparsity-aware SpMV engines with static load balancing. Implemented on an AMD Zynq UltraScale+ (ZCU104) FPGA, HyperX achieves $6.85\times$ ($4.32\times$) speedup and $169\times$ ($314\times$) energy efficiency gains over optimized CPU (GPU) baselines, while improving classification accuracy by $3.4\%$ on average across TUDataset benchmarks, a widely used standard for graph classification.
arXiv:2605.17989v1 Announce Type: new Abstract: Retrieval-Augmented Generation (RAG) improves factual grounding in large language models but suffers from substantial latency due to synchronous retrieval. While recent work explores asynchronous retrieval, existing approaches rely on heuristic coordination between retrieval and generation and assume stable information demands during decoding that often break in complex, multi-domain settings. In this paper, we propose an advanced asynchronous retrieval framework that enables predictive prefetching aligned with evolving information needs. The framework explicitly predicts when retrieval should be triggered and what information should be retrieved using three components, a retrieval predictor, a context monitor, and a query generator, by exploiting semantic precursors in generation dynamics that emerge several tokens before uncertainty becomes critical. Experiments on multiple benchmarks demonstrate up to 43.5% end-to-end latency reduction and 62.4% improvement in time-to-first-token, while maintaining answer quality comparable to synchronous RAG baselines.
arXiv:2602.02236v4 Announce Type: replace Abstract: We study online fine-tuning of pretrained control policies for autonomous driving using Real-Time Recurrent Reinforcement Learning (RTRRL), a memory-efficient algorithm that updates policy parameters at every time step without backpropagation through time. We extend RTRRL to support LrcSSM, a recently proposed nonlinear diagonal state-space model, and combine offline behavioral cloning with online RTRRL fine-tuning to adapt policies to distribution shifts at deployment. We validate the approach in the CarRacing simulation and on a 1:10-scale RoboRacer platform equipped with an event camera, where a pretrained policy is fine-tuned online during real-world line-following. To our knowledge, this is the first demonstration of online RL fine-tuning with event-camera observations on standard (non-spiking) hardware in closed-loop control. LrcSSM-based policies improve fastest and most consistently across both settings.
arXiv:2605.17423v1 Announce Type: new Abstract: We study series-level cinematic remaking, a long-horizon video-to-video generation problem that localizes full episodes or films via stylization or actor replacement while strictly preserving narrative structure, motion choreography, and character identity across hundreds of shots. Existing video generation and editing pipelines often break down in this regime due to compounding identity drift, background mutation, and semantic erosion under large camera motions and viewpoint changes. We propose Soap2Soap, a multi-agent framework that enforces long-term language-visual consistency through a Dual-Bridge Consistency mechanism: a scene-aware JSON screenplay serving as a persistent semantic backbone, and dynamically allocated visual reference anchors at both scene and shot levels. To suppress drift before video synthesis, we introduce batch keyframe consistency, jointly generating multiple keyframes in a shared latent context via a grid-based formulation. A closed-loop verification agent further audits identity, stability, and alignment to trigger selective regeneration. Experiments on SoapBench demonstrate strong improvements over commercial video generation APIs in long-term consistency and narrative fidelity.
arXiv:2605.17381v1 Announce Type: new Abstract: Large detectors are often monitored at the channel level (drift time, collected charge, and hit maps), which validates hardware but not tracking performance. A wire-by-wire tracking efficiency diagnostic is presented for the Belle~II Central Drift Chamber~(CDC). The method is directly analogous to the extrapolation-based efficiency measurement standard in resistive-plate-chamber~(RPC) stacks developed for the India-based Neutrino Observatory~(INO). A reference track (helix) is extrapolated to each wire layer; the fraction of crossings that contain an associated hit defines the per-wire efficiency. Implemented in the Belle~II Data Quality Monitoring~(DQM) framework and validated on Monte Carlo simulation with controlled dead-wire conditions, the method reveals localised tracking failures that are invisible to conventional channel-level diagnostics. The resulting plots provide direct feedback for run selection, operations, and long-term ageing studies.
arXiv:2605.08925v2 Announce Type: replace Abstract: Interactive segmentation allows efficient label generation by leveraging user-provided clicks to progressively refine predictions, which is critical when fully supervised labels are costly or generalization to unseen classes is needed. Existing 3D interactive methods are limited: most operate sequentially, predicting only one object per iteration with binary masks, while several recent approaches depend on 2D foundation models and camera alignment to bridge the 2D-3D gap. To address these limitations, we propose a novel interactive segmentation framework that operates directly on sparse, randomly downsampled 3D points and processes multiple object clicks in a single forward pass. Our framework consists of a point Transformer-based encoder and a hierarchical mask decoder, which integrates multi-level crop-and-merge operations conditioned on learnable semantic embeddings. Unlike prior interactive approaches that require repeated model updates after each manually corrective click, our method jointly reasons over all click queries, modeling inter-instance relationships and refining both spatial masks and semantic predictions through spatial and semantic embeddings. Extensive experiments demonstrate that our model improves the mIoU metric by over 20 percent compared to strong baselines and achieves 8-10 percent gains under cross-dataset evaluation for a one-click per instance setting, often requiring only a single click per object. Our approach provides a generalizable and efficient solution for interactive 3D instance segmentation, particularly suitable for real-time applications such as robotic manipulation, navigation, and rapid 3D semantic annotation.
arXiv:2605.17396v1 Announce Type: new Abstract: In this paper, we present exact exponential algorithms for computing branchwidth that are fast both in theory and in practice. The running times of these algorithms are single-exponential in the number of vertices. Our basic algorithm is based on a conceptually simple recurrence on vertex sets and computes the branchwidth of an $n$-vertex hypergraph in time $\mathcal{O}^*(4^n)$. This is the first single-exponential time algorithm for hypergraphs. We have two algorithms tailored specifically for graphs. The first algorithm runs in time $\mathcal{O}(3.293^n)$, improving upon the previously best-known running time of $\mathcal{O}(3.4652^n)$ [Fomin-Mazoit-Todinca, DAM 2009]. Moreover, our computational experiment shows that it overwhelmingly outperforms state-of-the-art practical algorithms for computing branchwidth. The second algorithm is a candidate for a theoretical improvement: we conjecture that it runs in time $\mathcal{O}(c^n)$ for some constant $c$ that is smaller than 3.293. In practice, it performs significantly better on some instances that are hard for the first algorithm.
arXiv:2605.09395v2 Announce Type: replace Abstract: In this paper, we propose the first VL$\underline{\textbf{M}}$ $\underline{\textbf{a}}$gentic $\underline{\textbf{r}}$easoning framework for few-$\underline{\textbf{s}}$hot multimodal $\underline{\textbf{T}}$ime $\underline{\textbf{S}}$eries $\underline{\textbf{C}}$lassification ($\textbf{MarsTSC}$), which introduces a self-evolving knowledge bank as a dynamic context iteratively refined via reflective agentic reasoning. The framework comprises three collaborative roles: i) Generator conducts reliable classification via reasoning; ii) Reflector diagnoses the root causes of reasoning errors to yield discriminative insights targeting the temporal features overlooked by Generator; iii) Modifier applies verified updates to the knowledge bank to prevent context collapse. We further introduce a test-time update strategy to enable cautious, continuous knowledge bank refinement to mitigate few-shot bias and distribution shift. Extensive experiments across 12 mainstream time series benchmarks demonstrate that $\textbf{MarsTSC}$ delivers substantial and consistent performance gains across 6 VLM backbones, outperforming both classical and foundation model-based time series baselines under few-shot conditions, while producing interpretable rationales that ground each classification decision in human-readable feature evidence.
arXiv:2605.11617v2 Announce Type: replace Abstract: Streaming decision trees are natural candidates for open-world continual learning, as they perform local updates, enjoy bounded memory, and static decision boundaries. Despite these, they still fail in online class-incremental learning due to two coupled miscalibrations: (i) their split criterion grows unreliable as the class count K expands, and (ii) the absence of knowledge transfer at split time. Both failures share a common root: the range of Information Gain intrinsically scales with log2 K. Consequently, any Hoeffding-style confidence radius derived from it must inevitably grow with the class count, making a K-independent split criterion structurally impossible, taking away the potential benefits of applying streaming decision trees to continual learning. To fix this issue, we present MIST (McDiarmid Incremental Streaming Tree), which resolves both failures through three integrated components: (i) a tight, K-independent McDiarmid confidence radius for Gini splitting that acts as a structural regulariser; (ii) a Bayesian inheritance protocol that projects parent statistics to child nodes via truncated-Gaussian moments, with variance reduction guarantees strongest precisely when splitting is most conservative; and (iii) per-leaf KLL quantile sketches that support both continuous threshold evaluation and geometry-adaptive leaf prediction from a single data structure. On standard and stress-test tabular streams, MIST is competitive with global parametric methods on near-Gaussian benchmarks and uniquely robust on non-Gaussian geometry where SOTA benchmarks collapse.
arXiv:2605.17506v1 Announce Type: new Abstract: A fundamental difficulty in all-in-one blind image restoration is that degradation is usually treated as an implicit factor hidden in degraded-to-clean mapping, rather than as an explicit object that can be measured and manipulated. This limitation becomes more pronounced under mixed, compound, or unseen degradation conditions, where degradation effects are hard to assign to predefined labels or task-specific parameters. We propose the Degradation Frequency Curve (DFC), a structured spectral representation that quantifies degradation responses by measuring band-wise residual-to-degraded energy ratios in the frequency domain. DFC converts visually entangled and hard-to-describe degradation effects into a measurable degradation coordinate space. Moreover, DFC can be adaptively decomposed into band-wise spectral tokens, allowing local degradation responses to be represented as reusable restoration priors. Based on this representation, we develop the DFC-guided Image Restorer (DFC-IR), a token-conditioned multi-scale framework that progressively estimates DFCs from intermediate restorations and uses the resulting spectral tokens to guide degradation-aware restoration in a coarse-to-fine manner. Extensive experiments on standard, composite, unseen, and real-world degradation benchmarks show that DFC provides an effective representation basis for all-in-one restoration, leading to state-of-the-art performance and improved generalization under complex degradation profiles.
arXiv:2605.17626v1 Announce Type: new Abstract: Test-time scaling is an important mechanism for improving large language models, especially on tasks with deterministic verifiers. Code translation is a canonical example: the source program constrains valid outputs, while compilers, type check- ers, and behavioral checks provide exact pass/fail feedback. Existing approaches typically apply these verifiers only after generation, which is inefficient because early errors corrupt the autoregressive context and are rarely corrected later. We introduce Decoding Time Verification (DTV), a framework that treats structural boundaries as meta steps for verifier-guided decoding. DTV interleaves generation with verifier calls under a state-machine controller that enforces valid prefixes, using structural-boundary checks and structure-aware rollback to prevent error propagation while reducing wasted tokens. We evaluate DTV on C-to-Rust and JavaScript-to-TypeScript translation. Using Qwen3-4B as the primary generator under matched token budgets, DTV improves pass rates from 72.3% to 82.0% on C-to-Rust and from 33.3% to 46.0% on JavaScript-to-TypeScript relative to matched self-refinement baselines, while using fewer tokens per case; the same trend largely transfers to Gemma-4-E4B. In the evaluated cost-matched grid, DTV achieves a more favorable pass-rate-cost tradeoff than post-hoc verification or sampling-based scaling. These results show that verifier-guided decoding is an effective use of inference-time compute for code translation.
arXiv:2605.17691v1 Announce Type: new Abstract: Automating the classification of negative treatment in legal precedent is a critical yet nuanced NLP task where misclassification carries significant risk. To address the shortcomings of standard accuracy, this paper introduces a more robust evaluation framework. We benchmark modern Large Language Models on a new, expert-annotated dataset of 239 real-world legal citations and propose a novel Average Severity Error metric to better measure the practical impact of classification errors. Our experiments reveal a performance split. Google's Gemini 2.5 Flash achieved the highest accuracy on a high-level classification task (79.1%), while OpenAI's GPT-5-mini was the top performer on the more complex fine-grained schema (67.7%). This work establishes a crucial baseline, provides a new context-rich dataset, and introduces an evaluation metric tailored to the demands of this complex legal reasoning task.
arXiv:2605.17879v1 Announce Type: new Abstract: Training frontier-scale foundation models involves coordinating tens of thousands of GPUs over multi-month runs, where even minor performance degradations can accumulate into substantial efficiency losses. Existing health-check mechanisms, such as NCCL tests or GPU burn-in, primarily focus on functional correctness and often fail to detect fail-slow behaviors that silently degrade system performance. In this paper, we present Guard, a scalable system for detecting stragglers and ensuring node health in large-scale training clusters. Guard combines lightweight online performance monitoring during training with an offline node-sweep mechanism that systematically evaluates and qualifies nodes before they participate in production workloads. This design enables Guard to detect both acute failures and long-running fail-slow behaviors that traditional diagnostics cannot capture. Deployed on large-scale foundation model pretraining workloads, Guard improves mean FLOPs utilization by up to 1.7x, reduces run-to-run training step variance from 20% to 1%, increases mean time to failure (MTTF), and significantly reduces operational and debugging overhead. These results demonstrate that proactive straggler detection and systematic node qualification are critical for maintaining stable and efficient large-scale training.
arXiv:2605.17886v1 Announce Type: new Abstract: This tutorial presents cooperative and noncooperative game-theoretic frameworks for modeling, learning, and control in socio-technical systems, where human behavior, incentives, institutions, and social interactions are coupled with cyber-physical and networked infrastructures. The paper reviews strategic, dynamic, cooperative, matching, learning, and feedback-control approaches for analyzing how local decision-making, adaptation, and strategic interactions shape collective system outcomes. The tutorial further develops feedback-learning and incentive-design perspectives that connect equilibrium analysis with adaptation, distributed control, and mechanism design under information and coordination constraints. We also examine resilience and security challenges arising from adversarial behavior, misinformation, disruptions, and cascading failures in interconnected socio-technical networks. Finally, we discuss emerging research directions at the intersection of game theory, control, learning, and network science for resilient and adaptive socio-technical systems.
arXiv:2605.17894v1 Announce Type: new Abstract: While agentic AI and its core multimodal large language models (MLLMs) have demonstrated remarkable promise in language and visual reasoning across domains ranging from daily life to advanced scientific research, a profound gap remains between artificial and human intelligence. Despite the integration of powerful tools and advanced MLLMs, state-of-the-art AI agents frequently fail at foundational, seemingly simple tasks that a child can resolve with ease. Inspired by the Wechsler Intelligence Scale for Children (WISC), we introduce ChildAgentEval, the first psychometrically grounded interactive benchmark for evaluating cognitive age alignment in MLLM-based agents. ChildAgentEval systematically compares the reasoning performance of various MLLM-based interactive agents against age-specific human developmental stages, exposing where current agentic AI systems can and cannot simulate age-specific cognitive behavior.
arXiv:2605.18564v1 Announce Type: new Abstract: Free-particle Green's function plays a central role in the theoretical description of electron scattering and autoionization processes in quantum physics and chemistry. Recently, Gaussian basis set approaches have become increasingly important in applications to unbound and metastable electronic states. However, the practical use of such methods has been limited by the lack of efficient and compact analytical expressions for matrix elements of the free-particle Green's function in Gaussian-based representations. Here we present a novel, general analytical framework for the evaluation of one- and two-center matrix elements of the free-particle Green's function over spherical Gaussian basis functions and plane-wave-modulated spherical Gaussians. The derivation is based on the Fourier transform of Gaussian functions together with the addition theorem of harmonic polynomials, leading to compact closed-form expressions and efficient recurrence relations. We also analyze the asymptotic behavior of the free-particle Green's function matrix elements, which is essential in the description of low-energy continuum electrons using finite Gaussian basis sets.
arXiv:2605.12012v2 Announce Type: replace Abstract: Public-sector legal departments in the Netherlands face acute staff shortages, increased case volumes, and increased pressure to meet regulatory compliance. This paper presents LegalCheck, a novel system that addresses these challenges by automating the drafting of objection response letters through a combination of Retrieval-Augmented Generation (RAG) and Context-Augmented Generation (CAG). Using a large language model (LLM) alongside curated legal knowledge bases, LegalCheck performs retrieval of relevant laws and precedents, and uses controlled prompting to incorporate both external knowledge and case-specific details into a coherent draft. An expert-in-the-loop review ensures that each generated letter is legally sound and contextually appropriate. In a real-world deployment within the Municipality of Amsterdam, LegalCheck produced near-final advice letters in minutes rather than hours, while maintaining high legal consistency and factual accuracy. The output is based on actual regulations and prior cases, providing explainable outputs that captured the vast majority of required legal reasoning (often 80\% to 100\% of essential content). Legal professionals found that the system reduced their workload and ensured a consistent application of legal standards, without replacing human judgment. These results demonstrate substantial efficiency gains, improved legal consistency, and positive user acceptance. More broadly, this work illustrates how responsible AI can be deployed in the legal domain by augmenting LLMs with domain knowledge and governance mechanisms.
arXiv:2605.17918v1 Announce Type: new Abstract: Domain transfer (DT) maps source to target distributions and supports tasks such as unsupervised image-to-image translation, single-cell analysis, and cross-platform medical imaging. However, DT is fundamentally ill-posed: push-forward mappings are generally non-identifiable, as measure-preserving automorphisms (MPAs) preserve marginals while altering cross-domain correspondences, leading to content-misaligned translation. Recent work shows that MPAs can be eliminated by jointly transferring multiple corresponding source/target conditional distributions, but supervision signals labeling such conditionals are not always available in practice. We develop an alternative route to DT identifiability. Under a structural sparsity condition on the Jacobian support pattern, we show that distribution matching together with a single paired anchor sample suffices to identify the ground-truth transfer -- requiring substantially less supervision than prior approaches. To enable practical high-dimensional learning, we further propose an efficient Jacobian sparsity regularizer based on randomized masked finite differences, yielding a scalable surrogate without explicit Jacobian evaluation. Empirical results on synthetic and real-world DT tasks validate the theory.