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01.
arXiv (CS.CV) 2026-06-16

Active Reference Acquisition in Few-Shot Font Generation

Few-shot font generation aims to synthesize the remaining glyphs of a font given one or a few reference glyphs while preserving stylistic consistency, thereby supporting font designers in efficiently completing a typeface. Existing methods primarily focus on improving generation quality given a fixed reference set. However, when the current reference glyphs are insufficient to represent the target style, few-shot font generation may fail to produce satisfactory results. In practical scenarios, additional reference glyphs can often be obtained from the designer when necessary. Accordingly, we propose a new framework, Active Reference Acquisition in Few-Shot Font Generation, in which the model sequentially decides which character to acquire next as an additional reference. Furthermore, we propose a reference part-coverage-based acquisition function to efficiently query the designer. Motivated by the observation that font styles are well characterized by local structural parts, we represent each glyph using a histogram of local features and select query characters that maximize the expected part coverage of the reference set. By prioritizing characters that contain parts not yet covered by the current references, the proposed method progressively expands the diversity of visual parts in the reference set. As a result, generation quality is improved with fewer queries. Experiments on the Google Fonts dataset demonstrate that the proposed method achieves higher generation quality than random querying and reference-agnostic baselines. The code is available at https://github.com/matsuo-shinnosuke/ActiveRef-FontGen.

03.
arXiv (CS.LG) 2026-06-19

Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representations

arXiv:2606.19375v1 Announce Type: new Abstract: Identifying anisotropic yield functions remains challenging since yielding is not directly observed in full-field mechanical measurements, directional calibration can require many loading directions, and selecting an appropriate analytical form is nontrivial. This study proposes a physics-informed framework for discovering yield functions from full-field displacement data and reaction force data, without stress observations, plastic strain measurements, direct yield surface data, or a prescribed parametric yield function. The framework identifies the yield function as a mechanically constrained constitutive component inside elastoplastic stress integration, rather than through direct stress-space supervision. The yield function is represented by a convex neural network that enforces convexity and positive homogeneity of degree one while imposing the assumed tension-compression symmetry, and this neural yield function is trained with a differentiable stress update and a physics-informed force equilibrium loss across multiple loading cases. The proposed framework is validated using finite element (FE) benchmark studies with von Mises, Hill 1948, and Yld2000-2d yield functions, assessing yield contour agreement, displacement-noise sensitivity, identifiability through plastically active stress states, epistemic uncertainty, and polynomial-surrogate deployment. This study provides a mechanics-constrained pathway for discovering anisotropic yield functions from displacement and force data while keeping the identified component within the structure of elastoplastic stress integration.

04.
arXiv (CS.AI) 2026-06-12

Bag of Dims: Training-Free Mechanistic Interpretability via Dimension-Level Sign Patterns

arXiv:2606.12629v1 Announce Type: cross Abstract: We show that the standard basis of transformer hidden states already provides a training-free, architecture-general feature basis. Individual dimensions encode semantic content via their signs and confidence via their magnitudes, functioning as independent binary registers. We validate this Bag of Dims framework across three model families (Qwen 3.5-4B, Gemma 3-4B, Mistral 7B) through four progressive experiments. Sign patterns alone carry predictive content: replacing all magnitudes with unity achieves 72-93% top-5 next-token accuracy through the LM head, and pure Hamming scoring without any decoder reaches 80-90% top-4096. These sign patterns organize into semantic features: using a single-token type cache (one forward pass per vocabulary token, no context), we discover 175 categories via per-dimension sign consistency (mean AUC 0.80) from 50 anchors with zero training. A trained probe adds only +0.018 AUC and converges to axis-aligned weights, confirming negligible cross-dimension structure. This structure extends to attention: all 175 categories remain discoverable in K and V projections. On the write side, static FFN weight inspection links 20% of features to individual writer neurons (>0.70 agreement; random controls: 0%), with top-200 neuron coalitions achieving >0.70 agreement on 99.9% of prototypes via majority vote. Fully unsupervised discovery (random seeds, no labels) scales to 1500 features at 100% yield and 99% sparsity across all three models, with pairwise MI of 0.0014 bits confirming low inter-dimension coupling. These results establish that the standard basis already suffices for feature reading throughout the transformer compute pathway, requiring no training, no optimization, and no GPU-days beyond a single forward pass per vocabulary token.

05.
arXiv (CS.CL) 2026-06-16

ArFake: A Robust Framework for Multi-Dialect Arabic Speech Spoofing Detection Benchmark

With the rise of generative text-to-speech models, distinguishing between real and synthetic speech has become challenging, especially for Arabic that have received limited research attention. Most spoof detection efforts have focused on English, leaving a significant gap for Arabic and its many dialects. In this work, we introduce the first multi-dialect Arabic spoofed speech dataset. To evaluate the difficulty of the synthesized audio from each model and determine which produces the most challenging samples, we aimed to guide the construction of our final dataset either by merging audios from multiple models or by selecting the best-performing model, we conducted an evaluation pipeline that included training classifiers using two approaches: modern embedding-based methods combined with classifier heads; classical machine learning algorithms applied to MFCC features; and the RawNet2 architecture. The pipeline further incorporated the calculation of Mean Opinion Score based on human ratings, as well as processing both original and synthesized datasets through an Automatic Speech Recognition model to measure the Word Error Rate. Our results demonstrate that FishSpeech outperforms other TTS models in Arabic voice cloning on the Casablanca corpus, producing more realistic and challenging synthetic speech samples. However, relying on a single TTS for dataset creation may limit generalizability.

06.
arXiv (quant-ph) 2026-06-15

Quantum Entanglement of Bethe States

arXiv:2606.14140v1 Announce Type: cross Abstract: We investigate the quantum entanglement of Bethe states across a family of integrable spin chains, including the XXX$_{\frac{1}{2}}$ model, its higher-spin generalizations (XXX$_s$), and the non-compact $SL(2,\mathbb{R})$ chain. For on-shell eigenstates, we perform a comprehensive scan of the bipartite entanglement entropy across the entire spectrum of finite chains with periodic boundary conditions, and identify the Bethe solutions that minimize and maximize the entanglement. These extremal solutions follow systematic, spin-dependent patterns in the Bethe quantum numbers. In the XXX$_{\frac{1}{2}}$ spin chain, for the antiferromagnetic chain, the state with minimal entropy always coincides with the lowest-energy state (the ground state) within a given fixed-magnon sector. For the higher-spin XXX$_s$ model, however, the lowest-entropy state is not always identical to the ground state, and can even be the state of highest energy. By contrast, the Bethe roots that maximize entropy exhibit considerably more intricate structure. Our analysis further reveals how special Bethe root configurations, such as singular and strange solutions, affect entanglement, and it uncovers characteristic entanglement features in the non-compact $SL(2,\mathbb{R})$ chain that are absent from compact spin chains. For off-shell Bethe states, we develop an optimization algorithm that extremizes the entanglement entropy over rapidity distributions, enabling us to explore the maximum entanglement achievable by a Bethe state without imposing the Bethe ansatz equations.

07.
bioRxiv (Bioinfo) 2026-06-16

Super Learner Ensemble Modeling of CPTAC Proteomic Data for Survival Prediction in Head and Neck Squamous Cell Carcinoma

Survival analysis in head and neck squamous cell carcinoma (HNSCC) is traditionally performed using Cox proportional hazards models, alongside some exploration into black-box machine learning methods. The Super Learner (SL) algorithm addresses this model selection dilemma by combining diverse candidate algorithms into a weighted ensemble to perform comparably to the best candidate method. This study evaluates the performance of SL in HNSCC. Proteomic features as well as clinical covariates from 96 CPTAC HNSCC samples were modeled with three candidate algorithms (Cox LASSO, Cox Ridge, and Random Survival Forest) as well as the ensemble SL method. Models were optimized via Uno's time-dependent Concordance Index (C-index) and tested at 1- and 3-year time horizons using 2000 bootstrap resamples. The Cox Ridge regression model achieved the highest predictive accuracy among the four total methods. However, the SL demonstrated stable performance over both time horizons (1-year C-index: 0.985; 3-year C-index: 0.960). Variable importance analysis of the Cox Ridge model successfully identified malignant proteins (ATR, MAML1, MIEN1) alongside novel potential prognostic indicators (ZNF800, KERA). This analysis emphasizes the statistical necessity for larger cohorts for ensemble learning, while providing a benchmark of proteomic indicators in HNSCC.

08.
arXiv (CS.AI) 2026-06-19

Dual-Agent Framework for Cross-Model Verified Translation of Natural-Language Protocols into Robotic Laboratory Platform

arXiv:2606.20120v1 Announce Type: cross Abstract: Biological experiment protocols are written in natural language, whereas automation systems rely on predefined control commands, creating a semantic gap that limits autonomous execution. Microplate-based automatic experiments are particularly challenging due to the need to simultaneously control well mapping, sample-reagent combinations, replicate placement, and parallel dispensing. This study proposes an agent-based protocol translation framework that converts natural-language microplate-based protocols into executable control commands for a robotic laboratory platform. A Parser Agent formalizes the natural-language protocol into a structured representation, and a rule-based mapping engine deterministically incorporates the operational constraints of the robotic laboratory platform to generate device-level control commands. A heterogeneous LLM Validation Agent verifies completeness, parameter accuracy, and execution order, and triggers a self-correction loop with structured feedback when errors are detected. A sweep involving 7 Parsers and 3 Validators on randomly selected ELISA protocols evaluates how model scale and Validator type affect translation accuracy and pass rates under cross-model verification. The accuracy-latency trade-off is further verified by comparing the rule-based mapping of the proposed framework with LLM end-to-end direct mapping. Finally, Bradford assay-based protein quantification using a microplate was demonstrated on a robotic laboratory platform, validating end-to-end autonomous execution from natural-language protocols to real-world experiments. The proposed framework provides a flexible approach to narrowing the semantic gap between natural-language protocols and microplate-based self-driving laboratories.

09.
arXiv (CS.AI) 2026-06-15

DiffusionBlocks: Block-wise Neural Network Training via Diffusion Interpretation

arXiv:2506.14202v4 Announce Type: replace-cross Abstract: End-to-end backpropagation requires storing activations throughout all layers, creating memory bottlenecks that limit model scalability. Existing block-wise training methods offer means to alleviate this problem, but they rely on ad-hoc local objectives and remain largely unexplored beyond classification tasks. We propose $DiffusionBlocks$, a principled framework for transforming transformer-based networks into genuinely independent trainable blocks that maintain competitive performance with end-to-end training. Our key insight leverages the fact that residual connections naturally correspond to updates in a dynamical system. With minimal modifications to this system, we can convert the updates to those of a denoising process, where each block can be learned independently by leveraging the score matching objective. This independence enables training with gradients for only one block at a time, thereby reducing memory requirements in proportion to the number of blocks. Our experiments on a range of transformer architectures (vision, diffusion, autoregressive, recurrent-depth, and masked diffusion) demonstrate that DiffusionBlocks training matches the performance of end-to-end training while enabling scalable block-wise training on practical tasks beyond small-scale classification. DiffusionBlocks provides a theoretically grounded approach that successfully scales to modern generative tasks across diverse architectures. Code is available at https://github.com/SakanaAI/DiffusionBlocks .

10.
arXiv (CS.CV) 2026-06-11

Semantic search for 100M+ galaxy images using AI-generated captions

Finding scientifically interesting phenomena through slow manual labeling campaigns severely limits our ability to explore the billions of galaxy images produced by telescopes. In this work, we develop a pipeline to create a semantic search engine from completely unlabeled image data. Our method leverages Vision-Language Models (VLMs) to generate descriptions for galaxy images, then contrastively aligns a pre-trained astronomy foundation model with these embedded descriptions to produce searchable embeddings at scale. We find that current VLMs provide descriptions that are sufficiently informative to train a semantic search model that outperforms direct image similarity search. Our model, AION-Search, achieves state-of-the-art zero-shot performance on finding rare phenomena despite training on randomly selected images with no deliberate curation for rare cases. Furthermore, we introduce a VLM-based re-ranking method that nearly doubles the recall for our most challenging targets in the top-100 results. For the first time, AION-Search enables flexible semantic search for over 100 million galaxy images, enabling discovery from previously infeasible searches, including the identification of 36 new extragalactic stellar stream candidates. More broadly, our work provides an approach for making large, unlabeled scientific image archives semantically searchable, expanding data exploration capabilities in fields from Earth observation to microscopy. The code, data, and app are publicly available at https://github.com/NolanKoblischke/AION-Search

11.
arXiv (CS.CV) 2026-06-16

When the Past Matters: FlashBack Memory for Precipitation Nowcasting

Accurate precipitation nowcasting is crucial for disaster mitigation and socio-economic planning, yet existing methods often struggle with false alarms, missed events, and long range dependency modeling at high spatiotemporal resolution. To address these challenges, we propose FlashBack Memory (FB), a module that dynamically retrieves key historical states and integrates them via an adaptive fusion gate, enhancing the spatiotemporal representation capability of recurrent-based models. We incorporate FB into PredRNN, PredRNNpp, MIM, MotionRNN, and PredRNN-V2, and evaluate on CIKM2017, Shanghai2020, and SEVIR datasets. Experimental results demonstrate that FB significantly improves MSE, MAE, SSIM, and CSI metrics, particularly for high-intensity rainfall and long-sequence predictions, while reducing false alarms and missed events and enhancing temporal consistency and spatial localization. The proposed method provides a general and efficient memory enhancement mechanism, improving the overall performance of recurrent-based precipitation nowcasting models.

12.
arXiv (math.PR) 2026-06-11

Hilbert space embeddings of independence tests and interaction measures of several variables

arXiv:2411.08653v2 Announce Type: replace-cross Abstract: We present a unified theoretical framework for kernel-based measures of dependence on product spaces. Building on the ideas underlying distance covariance, distance multivariance, and the Hilbert-Schmidt Independence Criterion (HSIC), we define a new family of kernels on an $n$-fold Cartesian product, termed positive definite independent of order $k$ (PDI$_{k}$ kernels). These kernels extend the concepts of positive definite and conditionally negative definite kernels to higher orders and provide the foundation for generalized independence and interaction tests, such as the generalized Lancaster interaction of order $k$ ($\Lambda_{k}^{n}$), and the Streitberg interaction ($\Sigma$). Our analysis focuses on the continuous setting, where we prove a Kernel Mean Embedding Theorem for PDI$_{k}$ kernels and establish the corresponding integrability restrictions. Based on these results, we characterize how the Kronecker products of PDI kernels behave.

13.
arXiv (CS.CV) 2026-06-19

Cinematic Compositing Using Character-Environment-Harmonized Video Generation Models

Cinematic compositing aims to integrate green-screen characters into novel environments while maintaining physical and photometric realism. Previous methods often fail to capture the complex bidirectional interactions between characters and their surroundings, which we characterize as Character-to-Environment (C2E) physical interaction and Environment-to-Character (E2C) lighting harmonization. To address this, we propose an end-to-end video diffusion framework that jointly models C2E and E2C interactions, specifically handling the challenges of interactive props. Our approach introduces a tri-mask-guided architecture with RGB-D joint denoising to ensure physically consistent interactions among the character, props, and environment. We further develop an efficient prior-driven data curation pipeline to construct high-quality relighting pairs without expensive rendering. Finally, a reference-conditioned mechanism enables controllable environment synthesis and precise prop replacement. Extensive experiments demonstrate that our framework significantly outperforms existing methods in cinematic-quality dynamic video compositing.

14.
arXiv (CS.CV) 2026-06-11

Towards Conditional Feature Alignment for Cross-Domain Counting

Object counting models often degrade under cross-domain deployment because density composition varies across domains and is itself task-relevant. Standard feature alignment methods tend to suppress such variation by encouraging global domain invariance, which can be harmful when source and target domains contain different proportions of background, sparse foreground, and dense foreground. We propose Conditional Feature Alignment (CFA), a cross-domain counting framework that aligns representations within label-induced conditions rather than across full marginal feature distributions. Given density annotations or pseudo-density predictions, CFA constructs foreground/background or density-level conditions and aligns only features belonging to matching conditions. We formalise this idea through a conditional divergence perspective, showing that conditional alignment removes within-condition discrepancy while preserving condition-marginal density shift. For unsupervised domain adaptation, CFA estimates source conditions from annotations and target conditions from detached pseudo-density maps, then performs condition-wise adversarial alignment with full-image consistency regularisation. For source-domain generalisation, we instantiate the same principle with MPCount by enforcing condition-wise memory-consistency between generated source-domain views. Experiments on crowd and cell counting benchmarks show competitive or improved performance across diverse UDA and DG settings. For example, on JHU-CROWD++ FH$\rightarrow$SN, CFA-DG reduces MAE/RMSE from MPCount's 216.3/421.4 to 90.5/169.9, indicating that condition-wise alignment is especially effective under large weather- and density-induced shifts. These results suggest that condition-wise alignment is a promising design principle for domain-adaptive counting.

15.
arXiv (quant-ph) 2026-06-12

Quasi-local Edge Mode in XXX Spin Chain/Circuit with Interaction Boundary Defect

arXiv:2603.17835v2 Announce Type: replace-cross Abstract: We study the Heisenberg spin-1/2 model on a semi-infinite chain - or, equivalently, a trotterized unitary SU(2) symmetric six-vertex quantum circuit - with a boundary defect where the interaction between the two spins nearest the edge differs from that in the bulk. For sufficiently strong boundary interaction we explicitly construct a conserved operator quasi-localized near the boundary using a matrix-product ansatz. This quasi-local edge mode leads to non-decaying boundary correlation functions, corresponding to a nonzero boundary Drude weight. The correlation length of the edge mode diverges at a finite critical value of the boundary interaction, signaling a transition to ergodic boundary dynamics for subcritical interactions.

16.
arXiv (CS.LG) 2026-06-19

Bioacoustic Geolocation: Species Sounds as Geographic Signals

arXiv:2505.18726v3 Announce Type: replace-cross Abstract: Can we determine someone's geographic location solely from the sounds they hear? Are acoustic signals enough to localize within a country, state, or even city? In this work, we tackle the challenge of global-scale audio geolocation, with a particular focus on wildlife and natural sounds. We posit that bioacoustic signals contain informative geolocation cues because of well-defined geographic ranges of species. To test this hypothesis, we benchmark image geolocation and soundscape mapping methods, design oracles and species-centric baselines, and propose a hybrid approach that combines species range prediction with retrieval-based geolocation. We further ask whether geolocation improves with species-diverse recordings and spatiotemporal aggregation across neighboring samples. Finally, we extend our study to multimodal geolocation with case studies from movies that combine both audio and visual content. Our results highlight the potential of incorporating bioacoustic signals into geospatial tasks, motivating future work on species recognition and audio geolocation.

17.
arXiv (CS.CV) 2026-06-17

UoU: A Universal Fingerprint Foundation Model Based on Large-Scale Unsupervised Learning

Fingerprint recognition is still dominated by task-specific pipelines, where enhancement, structural parsing, alignment, and matching are optimized in isolation. Although effective in narrow settings, this design limits representation reuse across sensors, qualities, and downstream applications. We therefore present UoU, short for ``a Universal fingerprint foundation model based on large-scale Unsupervised learning,'' which reframes fingerprint feature extraction as a domain-specific foundation-model problem. UoU is organized around a multi-level representation hierarchy spanning image restoration, structural fields, semantic tokens, point-level biometric entities, and compact global descriptors. Its training recipe combines a supervised cold start on precise annotations, large-scale weakly supervised refinement, and large-scale unsupervised consolidation, with the latter two stages iterated during large-scale training so that weak supervision broadens semantic coverage while unsupervised learning stabilizes correspondences, invariances, and representation geometry. Rather than treating fingerprint imagery as generic texture, UoU exploits domain-specific symmetries and intermediate structure, including orientation flow, periodic ridge patterns, sparse biometric entities, and spatial equivariance. The framework is intentionally architecture-agnostic: while the present study includes an initial transformer-based structured-prediction instantiation, the broader design supports multi-task learning, scalable model configurations, and downstream specialization for matching, alignment, enhancement, registration, and related fingerprint applications. This paper presents the technical motivation, system design, and validation protocol of UoU, and part of the baseline implementation is publicly available at https://github.com/XiongjunGuan/UoU.

18.
arXiv (quant-ph) 2026-06-11

PHASE: Pauli Hierarchical Assembly on Subdivided Elements for Quantum-Compatible Operator Synthesis

arXiv:2606.11478v1 Announce Type: new Abstract: Efficiently decomposing finite element stiffness matrices into the Pauli basis is challenging due to the exponential growth of Pauli strings with problem size. A naive Pauli expansion requires $\Theta(8^{\lceil \log_2 N \rceil})$ operations, where $N$ denotes the number of degrees of freedom, rendering direct decomposition infeasible for large systems. Existing approaches exploit algebraic sparsity or operator structure but do not incorporate the geometric organization intrinsic to finite element discretizations, and consequently exhibit poor scaling for stiffness matrices. To address this problem, we introduce PHASE, a hierarchical, geometry-aware Pauli decomposition algorithm that leverages recursive mesh partitioning to organize element contributions across multiple spatial scales. PHASE employs a hybrid strategy that combines full- and reduced-space Tensorized Pauli Decomposition with Fast Walsh-Hadamard Transform-based aggregation to assemble global Pauli coefficients efficiently. We show that this approach yields a dimension-dependent reduction in the exponential scaling exponent of Pauli assembly asymptotic complexity relative to existing methods, reducing the cost from $2^{2{\lceil \log_2 N \rceil}}$ to $2^{\gamma_d{\lceil \log_2 N \rceil}}$ with $\gamma_d < 2$ under standard mesh regularity and balanced partition assumptions. These results substantially improve the feasibility of quantum-compatible operator synthesis for large-scale finite element models.

19.
arXiv (CS.CV) 2026-06-12

Bridging Modal Isolation in Interleaved Thinking: Supervising Modality Transitions via Stepwise Reinforcement

Interleaved thinking, where a unified multimodal model alternates between textual reasoning and visual generation, has shown promise on spatial and physical tasks. However, in complex long-chain scenarios, we identify a fundamental failure mode: generated images diverge from the textual context while subsequent text ignores the visual evidence, causing the two modalities to alternate without genuinely informing each other. We term this Modal Isolation and attribute it to compounding information loss at modality boundaries. We decompose each reasoning cycle into atomic operations and define modality transition loss, quantifying cross-modal hallucination (text-to-image) and visual utilization deficit (image-to-text) at each boundary. We propose MoTiF (Modality Tiransition Fidelity), a two-stage training framework that directly optimizes these transitions: Reflective SFT trains the model to detect and recover from erroneous visual outputs; Flow-GRPO improves image generation fidelity via reinforcement learning. All training signals in MoTiF derive from transition-level fidelity rather than end-task accuracy. Across four visual puzzle benchmarks, this transition-level supervision substantially improves both cross-modal coherence and final task accuracy. The results demonstrate that effective interleaved reasoning requires explicit structural supervision at modality boundaries, not merely scaling or end-task optimization.

20.
arXiv (CS.CV) 2026-06-12

VietFashion: Benchmarking Sketch-Text Composed Image Retrieval for Cultural Outfits

Cultural garments pose a unique challenge for visual retrieval systems, as their identity often depends on subtle structural and symbolic details that are poorly captured by standard AI models. We introduce VietFashion, a new benchmark for sketch-text composed image retrieval centered on the Ao Dai, a traditional Vietnamese garment. VietFashion enables designers and researchers to retrieve culturally meaningful outfits using a combination of hand-drawn sketches, which convey garment structure, and textual descriptions, which encode cultural semantics. The dataset is initialized with 650 sketches and expanded using generative models to produce over 21,000 photorealistic images with aligned captions. Textual prompts that describe detailed outfit attributes, which are extracted from fashion magazines to ensure authenticity and diversity. To better reflect the inherent ambiguity of design intent, VietFashion adopts a multi-target retrieval setting, where a single query may correspond to multiple valid results. We establish standardized evaluation protocols and benchmark state-of-the-art composed image retrieval methods. Experimental results reveal significant performance gaps in modeling fine-grained cultural semantics and multi-modal composition, positioning VietFashion as a challenging benchmark for fine-grained fashion retrieval. The dataset is publicly available at: https://hng0303.github.io/VietFashion.

21.
arXiv (CS.LG) 2026-06-15

A Unified Framework for Structured Flow Modeling: From Representation to Verification and Model Discovery

arXiv:2605.18250v3 Announce Type: replace-cross Abstract: Many dynamical systems can be described in terms of structured flows combining source/sink behavior, cyclic dynamics, and topology-constrained transport. These features arise across a wide range of physical, engineered, and data-driven systems. The objective of this work is to establish a unified perspective on such systems, to identify modeling approaches that balance expressivity, interpretability, computational complexity, and data requirements, and to investigate how highly expressive models can be used to uncover the dominant mechanisms underlying observed dynamics. Starting from the Helmholtz-Hodge decomposition of continuous vector fields, we review the recently proposed Graph Vector Field (GVF) framework and its discrete representation on simplicial complexes. We then introduce a hierarchy of alternative approaches, including parametric conditional models, linear graph dynamical systems, and reduced Hodge representations. Finally, we propose a verification and validation methodology based on benchmark datasets from well-understood physical systems and on systematic model-reduction and ablation studies. The resulting family of structured-flow models within a common framework, ranging from low-dimensional parametric representations to full GVF formulations, supports a diagnostic methodology in which gradient, curl, harmonic, and topological contributions are systematically assessed through ablation studies. This process enables the identification of dominant mechanisms underlying the observed dynamics and guides the construction of simplified models tailored to the available data and operational constraints. By separating structural verification, behavioral verification, and domain-specific validation, the proposed approach provides a foundation for scalable and interpretable analysis of complex dynamical systems across multiple application domains.

22.
arXiv (CS.CL) 2026-06-12

Beyond Uniform Tokens: Adaptive Compression for Time Series Language Models

Large language models (LLMs) have enabled time series (TS) analysis by jointly modeling numerical observations and textual context through a shared token interface. However, TS tokens and prompt tokens exhibit fundamentally different information structures, making uniform token processing inefficient. In this paper, we study token efficiency in TS language modeling from an asymmetric-token perspective. We show that TS tokens have highly uneven spectral contributions, where many tokens share redundant frequency patterns while a small subset preserves critical temporal evidence. We also observe that prompt-token influence attenuates with model depth, suggesting that full prompt retention across all layers is unnecessary. Based on these findings, we develop an adaptive token budgeting framework that compresses TS tokens via frequency-domain structure and progressively reduces prompt tokens across layers. Experiments across forecasting, classification, imputation, and anomaly detection demonstrate up to 7.68$\times$ inference acceleration and performance gains in 78\% of evaluated settings, showing the effectiveness of asymmetric token compression for scalable TS foundation models.

23.
arXiv (quant-ph) 2026-06-17

Closest Accessible Symmetry reduction: a tool for Hamiltonian interpolation analysis

arXiv:2606.18161v1 Announce Type: new Abstract: We introduce a framework for analysing the spectrum of Hamiltonian interpolations without heavily relying on discretising the interpolation parameter. The method is based on the concept of accessible symmetries: a problem-class-dependent family of certifiable reflections that induce bipartitions of the Hilbert space. At each step, the interpolation Hamiltonian is projected onto the sectors of the accessible symmetry that is closest to being satisfied, yielding a hierarchy of weakly coupled pseudo-eigenspaces together with explicit residual couplings between them. We show that this representation captures qualitative signatures of quantum phase transitions, provides estimates of their location, and offers insights into their nature. The quality of the approximation is controlled by the compatibility between the accessible symmetry family and the problem instance. Although motivated in spirit by adiabatic quantum computation, our approach applies more broadly to the study of Hamiltonian phase diagrams, providing a new perspective on the spectral reorganisation of many-body quantum systems.

24.
arXiv (CS.AI) 2026-06-11

MPC-Patch-Bench: Security-Aware LLM Code Patch for Multi-Party Computation

arXiv:2606.11416v1 Announce Type: cross Abstract: Repository-level benchmarks for evaluating Large Language Model (LLM) code repair on Secure Multi-Party Computation (MPC) software do not yet exist, and directly transplanting general-purpose benchmarks such as SWE-bench fails on three structural fronts: (i) MPC repositories are dominated by generic Python infrastructure rather than cryptographic logic; (ii) high-value MPC fixes lack the standardized tests rigid extraction pipelines require; and (iii) standard fail-to-pass evaluation is insufficient for code that must also be cryptographically safe. MPC is increasingly deployed for privacy-preserving machine learning, biomedical collaboration, and secure analytics. Existing MPC-specific code-synthesis efforts cover only operator-level or single-framework tasks; evaluating LLM agents on real repository-level MPC repair instead demands MPC-aware data curation and a verifier matched to the security and numerical-fidelity guarantees MPC programs must obey neither of which existing benchmarks provide. We introduce MPC-Patch-Bench, a repository-level benchmark organised around two frameworks. (1)The Data Curation Framework combines a domain-specific curation agent that filters raw pull requests through three cryptographic layers with a human-AI completion engine that synthesizes missing problem statements and Fail-to-Pass/Pass-to-Pass tests, yielding 205 fully verified instances. (2)The MPC Verifier provides dedicated security and numerical-fidelity checks via dynamic differential testing against plaintext oracles and MPC-specific static analysis rules that flag unsafe reveals, insecure arithmetic, and illegal public/private casts. The strongest evaluated LLM functionally resolves only 22.9% of MPC-Patch-Bench tasks; the MPC Verifier further reduces verified resolution to 17.1%, with up to 40% of functionally-passing patches rejected for cryptographic or numerical-fidelity violations.