arXiv:2405.06415v2 Announce Type: replace-cross Abstract: While metric and similarity learning has been extensively studied from several theoretical perspectives, a rigorous understanding of its generalization performance is still lacking. In this paper, we investigate the generalization behavior of metric and similarity learning by exploiting the specific structure of the true metric (i.e., the target function). In particular, by deriving the explicit form of the true metric for metric and similarity learning with the hinge loss, we construct a structured deep ReLU neural network as an approximation of the true metric, whose approximation ability depends on the network complexity. Here, the network complexity is characterized by the network depth, the number of nonzero weights, and the number of computational units. Based on the hypothesis space consisting of such structured deep ReLU networks, we establish excess risk bounds for metric and similarity learning by carefully controlling both the approximation error and the estimation error. An explicit excess risk rate is derived by choosing the proper capacity of the constructed hypothesis space. To the best of our knowledge, this is the first generalization analysis that provides explicit excess risk bounds for metric and similarity learning. In addition, we investigate properties of the true metric for metric and similarity learning under more general loss functions. Experiments show that the proposed model is empirically competitive and better captures the underlying similarity structure.
Science Journals
arXiv:2605.17633v1 Announce Type: new Abstract: The Segment Anything Model (SAM) achieves strong open-vocabulary segmentation, but its ViT-based image encoders dominate inference latency and memory. Existing activation compression methods, such as token merging, reduce the token length to process, yet introduce non-trivial runtime overhead and encounter catastrophic quality drop under high compression. Other methods applying Sparse Attention focus on attention alone, leaving the MLP fully dense and capping achievable speedup. We propose SparseSAM, a (i) training-free structured sparsification framework that jointly accelerates attention and MLP layers while preserving token identity. SparseSAM introduces (ii) Stripe-Sort Attention, which uses a deterministic Z-order permutation to transform dense attention into static hardware-friendly sparse patterns, eliminating dynamic masking overhead. SparseSAM further introduces a (iii) Residual-Consistency MLP that routes only informative tokens through the MLP while propagating remaining tokens through the residual pathway. Across four segmentation benchmarks, SparseSAM loses only 0.004 mIoU at a 0.4 density and 0.021 mIoU at 0.3, a 2.10x reduction in accuracy loss versus token merging advances, while achieving 2x faster inference and 2.8x memory reduction.
arXiv:2605.17629v1 Announce Type: new Abstract: Integrated sensing and communication (ISAC) is considered to be a promising technology for future wireless systems due to its ability to provide communication and sensing services using shared hardware and spectrum resources. Moreover, the introduction of recently developed pinching antennas (PAs) and movable antennas (MAs) has the potential to further improve the performance gains of ISAC. Therefore, our goal is to study the optimization of the sum-rate for an ISAC system equipped with PAs and MAs, capable of satisfying minimal sensing requirements. To achieve it, we derive a closed-form solution for the optimal sensing receive combiner, and show that it is determined by other optimization variables. For these other variables (i.e., the positions of the transmit PAs, the positions of the users' MAs, the communication precoding matrices, and the sensing transmit beamformer), we propose a deep learning (DL) network that finds their optimal values. To train the network in an unsupervised manner, we formulate a loss function consisting of the objective function, as well as the penalty terms related to the constraints for the PAs and MAs positions. Simulation results show that using PAs and MAs in ISAC systems provides a larger sum-rate compared to ISAC systems with only fixed antennas, and that this performance advantage is increased with the maximum transmit power. Furthermore, we demonstrate that the communication performance of the considered system is a bit more affected by the sensing signal-to-interference-plus-noise ratio (SINR) threshold compared to the sensing performance.
arXiv:2605.17854v1 Announce Type: new Abstract: Conventional approaches to learning on graphs involve message passing along existing (i.e., positive) edges to update node features. However, these approaches often disregard the potentially valuable information contained in the absence (i.e., negative) of edges. Here, we theoretically analyze the value of negative edges in graph representations and prove that in settings of low label rates, high homophily, and high edge density, access to negative edges provides significant information gain over using only positive edges. Motivated by this insight, we introduce Contrastive Message Passing (CMP), a general message passing architecture that enable graph neural network layers to reason over positive and negative edges. By imposing soft positive semidefinite constraints on the learnable weights, our approach differentially applies similarity-preserving transformations to positively connected nodes and dissimilarity-inducing transformations to negatively connected nodes. Over simulated and real datasets in varying data regimes, CMP consistently outperforms baselines in low-label settings when negative edges are informative.
arXiv:2605.17898v1 Announce Type: new Abstract: Gaussian process (GP) inference in Python is dominated by libraries such as GPyTorch and GPflow, which are built on deep-learning frameworks and inherit their dispatch overhead and dependency footprint. We present LightGP, a dependency-free C++17 library for GP regression with Python bindings, supporting Apple Metal and NVIDIA CUDA backends alongside tuned CPU paths via Apple Accelerate and OpenBLAS. LightGP provides four inference paths -- exact Cholesky, matrix-free conjugate gradients, sparse variational free energy, and structured kernel interpolation with FFT -- covering problems from $N{=}100$ to $N{=}500{,}000$. On an Apple M4, LightGP CPU is 2.6--8.7$\times$ faster than GPyTorch CPU for exact GP and ${\sim}1.5\times$ faster for sparse GP at every scale tested. On an NVIDIA RTX~3060, LightGP CUDA is 2.3--6.7$\times$ faster than GPyTorch CUDA for exact GP up to $N{=}2{,}048$, with GPyTorch closing the gap at $N{=}4{,}096$. A fused matrix-free kernel-vector product on Metal achieves 32$\times$ over the explicit path at $N{=}20{,}000$ with $O(N)$ memory, and an FFT-accelerated SKI matvec via Accelerate vDSP runs in sub-millisecond time at $N{=}200{,}000$. LightGP compiles as a single static library with zero external dependencies and is installable via \texttt{pip install lightgp
arXiv:2605.17426v1 Announce Type: new Abstract: We propose a framework for predicting the effects of mobility introduction measures using a human-flow digital twin. This digital twin incorporates a multi-agent simulator that can represent how visitors choose destinations depending on factors such as their current location and the attractiveness of spots. We extract data on how visitors selected destinations with respect to measured pre-intervention human-flow data, inter-spot distances, spot attractiveness, and travel volumes, and use these data to train each agent's decision model of this simulator. The trained decision model is a function that takes a visitor's current state and surrounding environmental information as input and outputs which spot the visitor will move toward next. By expressing mobility introduction measures as changes to inter-point distances or to spot attractiveness, the framework can reproduce human flows with mobility introduction in the multi-agent simulator and thereby quantify effects such as changes in visitor counts and circulation. We evaluated the proposed method using human-flow data measured with and without introducing mobility within Wakayama Castle Park in Japan. When reproducing flows with mobility introduction using a multi-layer perceptron decision model, the cosine similarity of the spatial population distribution exceeded 0.7, confirming that the approach can replicate the flow changes caused by the mobility introduction.
arXiv:2605.18008v1 Announce Type: new Abstract: Uncertainty quantification (UQ) is critical for safety-critical domains like healthcare, yet it is rarely evaluated under realistic out-of-distribution (OOD) conditions. Here, we assessed predictive performance and uncertainty reliability for deep learning-based blood pressure (BP) estimation from photoplethysmography (PPG) signals under both in-distribution (ID) and OOD settings. Using an XResNet1D-50 trained on PulseDB and tested on four external datasets, we compared deep ensembles (DE) and Monte Carlo dropout (MCD) with Gaussian negative log-likelihood (GNLL) and mean squared error (MSE) losses, optionally followed by post-hoc recalibration via conformal prediction (CP), temperature scaling (TS), and isotonic regression (IR). The key findings of our study are as follows: (1) DE provides stronger predictive robustness under domain shift than MCD, an advantage that becomes clear primarily under external shift. (2) Recalibrated GNLL-based methods yield the best uncertainty calibration (e.g., GNLL+DE+CP for systolic blood pressure (SBP), GNLL+DE+TS for diastolic blood pressure (DBP)), while MSE-based uncertainty requires recalibration to become practically useful. (3) Across settings, CP and TS offer the most consistent gains, with IR remaining competitive in several cases. Overall, our results identify DE-based methods as most robust for predictive performance under domain shift, GNLL as strongest for native UQ, and recalibration as essential for making MSE-based uncertainty practical. These findings highlight the need to jointly assess predictive accuracy and calibration on external data for trustworthy cuffless BP estimation
arXiv:2605.18176v1 Announce Type: new Abstract: This report presents MARS, short for Multimodal Agentic Reasoning with Source selection, our system for the CASTLE Challenge at EgoVis 2026. Participants must answer 185 closed-form questions over the CASTLE 2024 dataset. In contrast to prior single-video egocentric benchmarks, CASTLE requires reasoning over four days of activity, 15 synchronized perspectives, official transcripts, and multiple auxiliary modalities, including personal photos, auxiliary videos, gaze, thermal imagery, and heartrate measurements. MARS therefore treats the task as an agentic evidence-selection problem over multimodal sources rather than a purely text-only pipeline. MARS first follows the official CASTLE directory organization to build evidence memories from two primary sources, videos and transcripts, and four auxiliary sources, gaze, heartrate, photos, and thermal imagery. Long videos are converted into captions and DeepSeek-based summaries only because CASTLE videos are too long to fit directly into the model context for every question; this step compresses temporal evidence while keeping photos and other auxiliary media available as source-specific evidence. At inference time, a GPT-5.4 decision agent repeatedly chooses whether to continue reasoning, request a specific missing modality, produce an answer, or fall back to a random option when the evidence remains insufficient. The resulting system achieved second place on the final CASTLE Challenge leaderboard. Our codes are available at https://github.com/Hyu-Zhang/MARS.
arXiv:2605.10919v2 Announce Type: replace Abstract: Motivated by DNA data storage, we study the expected number of coded symbols drawn from a linear code until a desired information symbol can be decoded - the random access expectation. We focus on generator matrices with a type of symmetry, conjectured in prior work to be optimal, which we call fully symmetric. We point out an equivalence between binary fully symmetric codes and LT codes. Using this observation, we analyze the random access expectation of binary fully symmetric codes under a peeling decoder, in the large blocklength limit. Under these assumptions, the random access expectation, normalized by the number of information symbols, is at least $\pi/4 \approx 0.7854$, while a value of $\approx 0.7869$ is achievable.
arXiv:2605.18199v1 Announce Type: new Abstract: The rapid growth of tabular datasets in data lakes, data spaces, and open data portals makes effective dataset search essential for reuse and analysis. Existing search systems rely mainly on metadata, which is often incomplete or low quality, especially for tables whose meaning depends on both schema and cell values. Recent advances in Large Language Models (LLMs) enable richer, content-based representations of tables. However, prior LLM-based retrieval methods have focused on Table Question Answering, where the goal is to select a single table to answer a question, rather than retrieve and rank relevant datasets. We propose PIPER, a content-driven retrieval method for tabular datasets that uses table profiles and LLM-generated queries embedded for dense retrieval. Designed for dataset search in poor-metadata settings, PIPER outperforms both classical metadata-based baselines and strong TableQA retrieval methods, demonstrating the value of LLM-based content modeling for tabular dataset search.
arXiv:2605.18244v1 Announce Type: new Abstract: Double-slit diffraction studies with photons or massive particles rank among the most beautiful experiments in physics. In particular, measurements at very low intensities demonstrate the particle-wave duality and the coherent superposition of states very clearly. In this paper, low-intensity double-slit experiments in the time domain are presented measuring the spectral distribution of synchrotron light from a single relativistic electron in a storage ring. In two consecutive radiation sources (so-called undulators) with a magnetic detour between them, electrons emit two temporally separated light pulses leading to a spectrum with interference fringes, very much like the angular distribution of light behind two spatially separated slits. Independent experiments at two synchrotron light sources (DELTA in Germany and UVSOR-III in Japan) directly demonstrate that the spectral distribution of accumulated synchrotron light from a single electron is essentially the same as the spectrum from a beam of many electrons. While the latter is usually explained as interference between electromagnetic waves from the two undulators, the single-electron experiments demonstrate that coherent photon emission is delocalized over several meters and the accumulated spectral distribution exhibits a deterministic interference pattern at small wavelengths. The experiments presented here were conducted with near-ultraviolet light to avoid an elaborate in-vacuum setup, but the very wide spectral range of synchrotron radiation, from infrared light to X-rays, enables access to regimes not available in laser-based quantum optics experiments.
arXiv:2605.17809v1 Announce Type: new Abstract: This research addresses the challenges inherent in developing Artificial Intelligence (AI) applications, particularly those leveraging Large Language Models (LLMs). While AI vendors provide Application Programming Interfaces (APIs) and Software Development Kits (SDKs) to facilitate developer interaction, the former often requires intricate manual request construction, and the latter can lead to significant vendor lock-in. Furthermore, existing model abstraction frameworks, though mitigating vendor dependency, introduce an additional layer of complexity and potential security concerns. To reconcile these conflicting factors, the study introduces PuppyChatter, a novel software framework designed to preserve the intuitive simplicity of vendor-specific SDKs while simultaneously adhering to the vendor-neutrality principles characteristic of model abstraction, thereby offering a more streamlined and flexible development paradigm.
arXiv:2605.18273v1 Announce Type: new Abstract: The hydroelastic response of free floating viscoelastic covers is measured using Faraday waves on the surface of a vertically oscillated fluid layer. We systematically vary the thickness $d$ of the covers to investigate its effect on the hydroelastic dispersion relation, the damping and the isotropy of the waves. Compared to bare fluids, the wave patterns are disordered. Various methods are explored to define and analyze the wavelengths, the isotropy, and shape of the waves. We find a significant difference between the measurements and the theoretical dispersion relation. Over all thicknesses $d$, this is explained by an increase in the in-plane membrane tension, which scales with $d^{3/2}$. Covering waves also has a large efect on their damping. Only for thin covers ($d = 20\: \mu{\rm m}$) the onset amplitude (and thus the damping) can be explained by dissipation in the bulk and in the boundary layer of the water beneath the cover. The same was found for bare water due to the presence of an immobile surface layer. Lastly, we find a large effect of the membrane on the ampitude of the waves, which we attribute to nonlinear wave interaction.
arXiv:2605.10408v2 Announce Type: replace Abstract: Testing robots requires assessing whether they perform their intended tasks correctly, dependably, and with high quality, a challenge known as the test oracle problem in software testing. Traditionally, this assessment relies on task-specific symbolic oracles for task correctness and on human manual evaluation of robot behavior, which is time-consuming, subjective, and error-prone. To address this, we propose VISOR, a Vision-Language Model (VLM)-based approach for automated test oracle assessment that eliminates the need of expensive human evaluations. VISOR performs automated evaluation of task correctness and quality, addressing the limitations of existing symbolic test oracles, which are task-specific and provide pass/fail judgments without explicitly quantifying task quality. Given the inherent uncertainty in VLMs, VISOR also explicitly quantifies its own uncertainty during test assessments. We evaluated VISOR using two VLMs, i.e., GPT and Gemini, across four robotic tasks on over 1,000 videos. Results show that Gemini achieves higher recall while GPT achieves higher precision. However, both models show low correlation between uncertainty and correctness, which prevents using uncertainty as a correctness predictor.
arXiv:2605.18288v1 Announce Type: new Abstract: Unsupervised fine-grained image hashing aims to learn compact binary codes that preserve subtle visual differences among highly similar instances without manual annotations. However, most existing methods neglect collision resistance, leading to identical hash codes for slightly semantically different samples. In this paper, we propose Collision-Resistant Single-Pass Self-Supervised Semantic Hashing (CS3H), a collision-resistant framework that directly optimizes Hamming-space similarity via a single-pass normalized Hamming distance loss to produce well-separated binary representations. We further introduce a collision-sensitive attention module to emphasize rare and discriminative local patterns, reducing hash collisions and improving fine-grained discrimination. Experiments on multiple benchmarks show that CS3H consistently outperforms state-of-the-art methods in retrieval accuracy while achieving superior collision resistance with minimal computational overhead.
arXiv:2605.18309v1 Announce Type: new Abstract: Although Large Language Models (LLMs) achieve strong alignment through supervised fine-tuning and reinforcement learning from human feedback, the alignment is often fragile under subsequent fine-tuning. Existing explanations either attribute alignment fragility to gradient geometry or characterize it as a distributional shift in model outputs, yet few provide a unified account that bridges parameter-space learning dynamics with function-space alignment behavior during fine-tuning. In this work, we introduce a tractable alignment score and derive its closed-form update during fine-tuning, yielding a unified framework for alignment dynamics. Our analysis decomposes alignment updates into two competing components: a \textbf{\color{red!60!black} Rebound Force}, governed jointly by the current alignment state and the narrowness of model distribution, and a \textbf{\color{green!60!black} Driving Force}, determined by how the training distribution aligns with outcome-conditioned posteriors over aligned and non-aligned completions. This decomposition explains why prior alignment can be reversed by later fine-tuning and why narrower posterior structure strengthens such reversal. Moreover, our framework predicts a \textbf{Rehearsal Priming Effect}: prior alignment leaves a latent posterior imprint that amplifies the effective Driving Force upon re-exposure, leading to faster re-alignment. We validate these predictions across safety alignment, emergent misalignment, and sentiment settings, demonstrating consistent alignment reversal and accelerated re-alignment under re-exposure. In addition, controlled experiments in safety alignment confirm the predicted dependence of rebound strength on posterior narrowness. Together, these results provide a unified dynamical perspective on how alignment is disrupted and reactivated during LLM fine-tuning.
arXiv:2605.18013v1 Announce Type: new Abstract: Segment Anything Model 2 (SAM 2) serves as a core foundation model in the field of video segmentation. Building upon the original SAM model, it introduces a memory bank mechanism and demonstrates outstanding performance in tasks such as semi-supervised video object segmentation and tracking anything. However, the complex computational characteristics of SAM 2's multi-stage image encoder and memory module have raised the barrier to the model's deployment in practical applications. To address this issue, we propose TinySAM 2, a lightweight video segmentation model that balances performance and efficiency. First, a memory quality management mechanism is introduced to select and retain high-informative historical frames as the memory. In addition, a joint-spatial-temporal token compression is proposed that reduces the memory storage and computational cost. Specifically, average pooling is employed to first compress redundancy tokens in the spatial domain. In the temporal domain, informative tokens are selected across frames in the memory bank based on token-level similarity measurement. Besides, we take RepViT as the lightweight image encoder, which further reduces the model parameters. Extensive experiments on challenging datasets such as DAVIS and SA-V demonstrate that TinySAM 2 achieves 90% of the performance of SAM 2.1, with only 7% memory tokens and 3% training data. This study effectively alleviates the bottlenecks in parameter count, computational load, and deployment costs associated with SAM 2, providing a resource-efficient solution for the widespread application of video segmentation models on devices.
Agents for Experiments, Experiments for Agents: A Design Grammar for AI-Enabled Experimental Science
arXiv:2605.17746v1 Announce Type: new Abstract: AI systems are becoming active participants in organizational and knowledge work. They increasingly interact with humans, coordinate workflows, and operate in multi-agent arrangements. Understanding their effects therefore requires more than measuring output accuracy; it requires evidence about mechanisms, delegation, feedback, and control. Experiments remain central to this task, but they also face a recursive challenge: we need experiments for agents to study these arrangements, and we may need agents for experiments to help search the expanding space of possible designs. Yet experimental conditions for human-AI and agentic workflows are still largely specified in prose, making them difficult to compare, reuse, or audit. We frame this as a problem of workflow representation, traceability, and governance in AI-enabled knowledge production. We introduce SEED (Structural Encoding for Experimental Discovery), a framework that represents experimental conditions as typed actor-flow graphs. SEED supports three design functions: describing conditions as interaction structures, evaluating structural novelty relative to encoded prior designs, and generating candidate designs under feasibility and governance constraints. We report a lightweight empirical feasibility test that compares graph-blind and SEEDguided generation in a medical-triage design task. In this diagnostic contrast, SEED-guided candidate designs show clearer actor-flow changes, assumptions, and governance checks, supporting the feasibility of the grammar as a design aid. The commentary closes by identifying governance tensions around novelty, replication, validity, diversity of inquiry, and accountability.
arXiv:2605.16017v1 Announce Type: new Abstract: In this paper, we present CT-AGD (Curvature-Tuned Accelerated Gradient Descent), an optimization method for non-convex optimization problems in deep learning training tasks. CT-AGD is a general boosting procedure that accelerates first-order methods by explicitly capturing the local curvature using finite-difference quotients, and the development of heuristics aimed at mitigating noise and bias introduced by stochastic mini-batch training. CT-AGD has a comparable storage and computational overhead as adaptive gradient methods such as Adam. Our extensive experiments demonstrate that CT-AGD achieves the same level of accuracy as the baseline first-order methods, yet reduces the required training epochs by 33% on average.
arXiv:2605.16012v1 Announce Type: cross Abstract: BEDT-TTF-based organic conductors host a number of ground states, tuned by electron repulsion from Mott and charge ordered insulators to superconductors. Knowing charge distribution on the molecular sites in the insulating state of these materials is a key to understanding the origin of these ground states. We survey and discuss the C=C stretching modes in BEDT-TTF based molecular conductors. These molecular vibrations are extremely crucial in characterization of charge-ordered insulators, and are recently linked to superconductivity in some compounds. Focusing on the known examples of BEDT-TTF$^{+0.5}$ salts, we analyse the reliability of the C=C stretching modes for the determination of charge ordering and absolute site charge. Considering the charge-ordered states, a prominent shift in frequency of 141 cm$^{-1}$ per elementary charge $e$ for $\nu_{27}(b_{1u})$ and 98 cm$^{-1}$$e$ for $\nu_2$($a_g$) can be clearly realised, however, the distribution resulting from different compounds span over 20 cm$^{-1}$. For nominal BEDT-TTF$^{+0.5}$ compounds, the distribution of the resonance also extends around 20 cm$^{-1}$, yielding an unexpected large uncertainty of $\Delta\rho~\approx~(~\pm~0.045)e$, which is presumably due to the influence of small differences in the structure. This highlights the limitations of charge-frequency relations to detect small deviations in absolute charge values on molecular lattice sites, and emphasises on the use of the relations to estimate charge-ordering, rather than absolute site charge.
arXiv:2605.16149v1 Announce Type: new Abstract: Space plasmas are generally characterized by non-Maxwellian distributions with suprathermal populations, as routinely revealed by in situ observations. Such departures from standard Maxwellian distributions can be understood as signatures of quasiequilibrium states, in which the distribution of the medium can be expressed as a continuous superposition of Maxwellian distributions, namely through superstatistics. Here, we construct macroscopic relations linking fluxes to their associated driving forces in such plasmas, where superstatistical effects enter the picture through the transport coefficients. After comparing the resulting superstatistical distributions with observed electron distributions in the solar wind, we turn to the kinetic response of quasiequilibrium plasmas and derive the corresponding transport coefficients, including the electric and thermal conductivities, the mobility, and the diffusion coefficient. We further extend the analysis to viscous plasmas and compute the shear and bulk viscosity coefficients. Overall, quasiequilibrium effects are found to systematically enhance the transport coefficients relative to their Maxwellian values. We quantify this enhancement for the three main universality classes of superstatistics, which are the most commonly encountered in experimental and observational situations, and interpret it as a consequence of the increased population of energetic particles in the non-Maxwellian tails.
arXiv:2605.16067v1 Announce Type: new Abstract: We propose a variational quantum classifier operating on high dimensional deep representations via amplitude encoding, stabilized by a learnable classical pre encoding layer.By combining normalized amplitude embeddings with bounded quantum observables, the resulting model induces a structured and smooth hypothesis class with controlled sensitivity to input variations. Model reliability is assessed using SAFE-AI metrics derived from the Cramer von Mises divergence, enabling consistent evaluation across accuracy, robustness, and explainability dimensions. Empirical results show that the proposed quantum model provides competitive predictive performance compared with strong classical baselines while exhibiting a more balanced SAFE reliability profile, with improved robustness to noise and stability under structured feature removal. These findings suggest that variational quantum circuits offer a principled mechanism for stability oriented SAFE learning in safety critical settings.
arXiv:2605.15793v1 Announce Type: new Abstract: Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientific machine learning. However, the inherent complexity and structural diversity of PDE solution operators make multi-PDE pre-training fundamentally challenging. Existing methods mainly address this by increasing model capacity, while leaving the target solution operators unchanged. Inspired by classical numerical analysis, we instead propose to transform complex and diverse solution operators into simpler, better-aligned forms that are easier to model jointly. Since the optimal transformation varies across PDE types, it must be adaptive and input-dependent, allowing a single neural operator to approximate an entire family of operators. We instantiate this idea as AOT-POT (adaptive operator-transformation for pre-training operator transformer), which expands hidden representations into multiple parallel streams, adaptively aggregates and redistributes them before and after each sub-layer, and mixes streams through Sinkhorn-projected doubly stochastic matrices for stable training. These mechanisms together reshape diverse solution operators into a unified form that can be effectively modeled by a single architecture. Empirically, AOT-POT achieves state-of-the-art performance on 12 PDE benchmarks with only 3\% additional parameters, reducing relative L2 error by up to 77.6\% (40.9\% on average). Fine-tuning AOT-POT further reduces L2 error by up to 92\% on in-domain PDEs and 89\% on out-of-domain PDEs (unseen types during pre-training), demonstrating that adaptive operator transformation is an effective and complementary direction for advancing PDE foundation models beyond simply scaling model capacity.
arXiv:2605.16052v1 Announce Type: new Abstract: Recent advances in large language models (LLMs) have significantly enhanced automated legal reasoning. Yet, it remains unclear whether their performance reflects genuine legal reasoning ability or artifacts of data contamination. We present a comprehensive empirical study of tax law reasoning approaches and implement a contamination detection protocol to rigorously assess LLM reliability. We show that performance can be inflated by contamination. Building on this analysis, we conduct a systematic evaluation, comparing monolithic LLMs with hybrid systems that translate statutory text into formal representations and delegate inference to symbolic solvers. We build a novel test suite designed to probe generalization to unseen documents via case and rule variations. Our findings indicate that legal reasoning is inherently compositional and that neuro-symbolic frameworks offer a more reliable and robust foundation for legal AI, as well as improved generalization to unobserved situations.
arXiv:2509.21663v2 Announce Type: replace Abstract: Neurosymbolic integration (NeSy) blends neural-network learning with symbolic reasoning. The field can be split between methods injecting hand-crafted rules into neural models, and methods inducing symbolic rules from data. We introduce Logic of Hypotheses (LoH), a novel language that unifies these strands, enabling the flexible integration of data-driven rule learning with symbolic priors and expert knowledge. LoH extends propositional logic syntax with a choice operator, which has learnable parameters and selects a subformula from a pool of options. Using fuzzy logic, formulas in LoH can be directly compiled into a differentiable computational graph, so the optimal choices can be learned via backpropagation. This framework subsumes some existing NeSy models, while adding the possibility of arbitrary degrees of knowledge specification. Moreover, the use of G\"odel fuzzy logic and the recently developed G\"odel trick yields models that can be discretized to hard Boolean-valued functions without any loss in performance. We provide experimental analysis on such models, showing strong results on tabular data and on two NeSy tasks with a perceptual component.