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01.
arXiv (CS.CL) 2026-06-11

ChartFI: Benchmarking Faithfulness and Insightfulness of Chart Descriptions from Multimodal Large Language Models

Chart descriptions are essential for accessibility, cross-modal retrieval, and assisting readers in extracting insights from complex visualizations. As multimodal large language models (MLLMs) are increasingly adopted for automated chart description generation, a critical question arises: how faithfully and insightfully do these models actually describe charts? Current benchmarks fall short on two fronts: existing datasets consist of simple, homogeneous charts paired with shallow, fact-enumerating descriptions; and prevailing metrics fail to capture the multi-faceted nature of description quality. To address these gaps, we present the Chart Faithfulness and Insightfulness Benchmark (ChartFI-Bench). We first summarize four dimensions that characterize high-quality chart descriptions: factual accuracy, salient feature emphasis, domain-informed guidance, and chart-text complementarity. Guided by these dimensions, we construct a high-quality benchmark comprising 896 chart-description pairs, which feature visually complex charts and semantically rich descriptions. Furthermore, we design four aligned evaluation metrics – Faithfulness, Coverage, Informativeness, and Acuity – to systematically assess the quality of descriptions across these dimensions. Experiments conducted on mainstream MLLMs demonstrate the effectiveness of the proposed framework and reveal common weaknesses among existing models.

02.
arXiv (CS.LG) 2026-06-19

Data Bias Mitigation under Coverage Constraints & The Price of Fairness

arXiv:2606.20461v1 Announce Type: new Abstract: Machine learning models have been shown to exhibit discriminatory outcomes or degraded performance for individuals at the intersection of multiple sensitive attributes, such as race and gender. This stems in part from two interrelated challenges: the lack of principled measures for quantifying bias (potentially intersectional), and insufficient representation of intersectional subgroups in training data. We extend a recent bias mitigation framework to incorporate coverage constraints that enforce sufficient representation across groups, including intersectional subgroups. Since achieving exactly zero bias for all groups may not be data efficient (meaning it may require large amounts of data), our solution trades small approximation errors in bias for greater data efficiency while satisfying coverage constraints. We also formulate bias mitigation as an integer linear program that optimizes over all mitigation strategies, and characterize the price of fairness, the minimum data modification cost, as a function of fairness tolerance. This is essential both for legal compliance, where regulations may mandate specific fairness thresholds, and for data governance, enabling practitioners to make informed trade-offs between bias reduction and data modification (particularly, data purchasing) costs. We evaluate our techniques on publicly available datasets, demonstrating that bias mitigation via our framework preserves predictive accuracy across multiple classifiers, and that coverage constraints, while motivated by statistical considerations, are essential for preserving downstream ML performance.

03.
arXiv (CS.LG) 2026-06-12

Predicting Cognitive Load from Speech and Interaction Dynamics in Dyadic Conversations

arXiv:2606.12971v1 Announce Type: new Abstract: Estimating cognitive load from speech has largely been studied in controlled laboratory settings, with limited understanding of its reliability in natural collaborative conversations. We investigate whether speech and interaction dynamics predict perceived cognitive load during dyadic conversations. We analyze audio from 53 dyads performing nine collaborative tasks and extract static acoustic, dynamic, and interaction features to train a two-head Gated Recurrent Unit encoder to predict cognitive load scores. Results show conversational interaction provides useful signals for predicting cognitive load related to time pressure, mental work, effort, and task performance. Temporal demand is associated with turn-taking dynamics such as overlap and speaker switch, while mental demand is linked to imbalanced participation between speakers. These findings highlight the importance of task structure and conversational interaction for modeling cognitive load in natural collaborative settings.

04.
arXiv (CS.LG) 2026-06-17

A fairness-aware extension of Stochastic Multicriteria Acceptability Analysis for ranking

arXiv:2606.17756v1 Announce Type: new Abstract: Fairness has become a central concern in ranking problems involving individuals or social groups, particularly under the Responsible Artificial Intelligence agenda. In Multi-Criteria Decision Analysis, Stochastic Multicriteria Acceptability Analysis (SMAA) provides a robust framework for handling uncertainty and incomplete preference information, but it does not explicitly address fairness in the resulting rankings. This paper proposes SMAA-Fair, a fairness-aware extension of SMAA for ranking problems. The approach reweights the simulated rankings generated by SMAA according to their level of group fairness, so that fairer rankings contribute more strongly to the acceptability indices and central weights vector. The framework is independent of the aggregation model and can incorporate different fairness metrics. In this study, Statistical Parity, normalized discounted Kullback–Leibler divergence (rKL) and normalized discounted cumulative Kullback–Leibler divergence (nDKL) are adopted. Rankings are derived from the fairness-adjusted acceptability matrix using expected ranking and maximum acceptability ranking. We also derive the central weight according to the degree of fairness in the obtained rankings. Numerical experiments with synthetic and real data show that SMAA-Fair improves the representation of protected groups among favourable ranking positions, while preserving robustness to preference uncertainty.

05.
arXiv (CS.CL) 2026-06-15

Beyond Perplexity: UTF-8 Validity in Byte-aware Language Models

Byte-level tokenization enables language models to handle any Unicode input, but models can generate invalid UTF-8 sequences when encountering rare or unseen characters. We investigate the relationship between training scale and UTF-8 generation reliability with a 355M parameter model trained on 80B tokens from a balanced multilingual corpus of English, Japanese, Korean, and Chinese. We introduce multiple evaluation protocols that isolate UTF-8 structural validity from language modeling. UTF-8 validity convergence lags perplexity by a roughly a factor of two: perplexity stabilizes after 2.1B tokens, but UTF-8 validity requires 4.2B tokens. In context-free generation, rare characters achieve higher structural validity than common characters, suggesting over-specialization of frequent character representations. Through experiments, we observed that reliable UTF-8 generation is a distinct capability requiring evaluation beyond perplexity.

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

Cross-Domain Multi-Person Human Activity Recognition via Near-Field Wi-Fi Sensing

Wi-Fi-based human activity recognition (HAR) provides substantial convenience and has emerged as a thriving research field, yet the coarse spatial resolution inherent to Wi-Fi significantly hinders its ability to distinguish multiple subjects. By exploiting the near-field domination effect, establishing a dedicated sensing link for each subject through their personal Wi-Fi device offers a promising solution for multi-person HAR under native traffic. However, due to the subject-specific characteristics and irregular patterns of near-field signals, HAR neural network models require fine-tuning (FT) for cross-domain adaptation, which becomes particularly challenging with certain categories unavailable. In this paper, we propose WiAnchor, a novel training framework for efficient cross-domain adaptation in the presence of incomplete activity categories. This framework processes Wi-Fi signals embedded with irregular time information in three steps: during pre-training, we enlarge inter-class feature margins to enhance the separability of activities; in the FT stage, we innovate an anchor matching mechanism for cross-domain adaptation, filtering subject-specific interference informed by incomplete activity categories, rather than attempting to extract complete features from them; finally, the recognition of input samples is further improved based on their feature-level similarity with anchors. We construct a comprehensive dataset to thoroughly evaluate WiAnchor, achieving over 90% cross-domain accuracy with absent activity categories.

07.
arXiv (CS.CV) 2026-06-16

MMLongEmbed: Benchmarking Multimodal Embedding Models in Long-Context Scenarios

Recent advancements have significantly expanded the theoretical context windows of Multimodal Embedding Models (MEMs). However, larger context windows do not necessarily translate into effective comprehension and representation of long-context multimodal inputs, which remains a critical bottleneck for real-world deployment. To address the lack of systematic evaluation in this setting, we introduce MMLongEmbed, the first comprehensive benchmark for evaluating MEMs in long-context scenarios. MMLongEmbed comprises four retrieval tasks spanning multiple context-length ranges, covering text, document, and video modalities. Through extensive evaluation of state-of-the-art models, we find that current architectures rely heavily on superficial feature matching and struggle to capture deep semantic and structural dependencies. We further observe that performance degradation varies systematically with context length and key information placement. Moreover, models exhibit substantially different robustness to redundant contextual information across modalities. For reproducibility, the benchmark and code are publicly available.

08.
arXiv (CS.CV) 2026-06-17

Remote sensing data imputation using deep learning for multispectral imagery

Remote sensing techniques have been increasingly utilised in aquatic applications in recent years. A common challenge in using optical satellite data is the presence of missing observations due to cloud cover. These data gaps can lead to missed detection of critical events, such as algal blooms, in lakes of high interest to water authorities. As a result, enhancing the completeness of optical satellite datasets is crucial for improving the monitoring and prediction of algal blooms. In this study, we compared a traditional data imputation method (i.e., linear interpolation) with deep learning models for reconstructing missing spectral bands across four lakes with historical records of algal blooms. The deep learning models adopted include CNN-based architectures (i.e., CNN, Inception Resnet, and Autoencoder) and CNN-LSTM-based architectures (i.e., CNN-LSTM, Resnet-LSTM, and Autoencoder-LSTM). Our results demonstrated that deep learning models substantially outperformed the baseline linear interpolation method in imputing spectral band values within artificially masked regions. Among these models, CNN delivered the best performance across most lakes. Furthermore, we evaluated the performance of algal bloom indices (i.e., Green/Red and NDCI) derived from the imputed imagery by comparing them with the observed data. Our results demonstrate that deep learning models are effective for imputing missing data in PlanetScope SuperDove imagery, enabling more reliable applications in water monitoring.

10.
arXiv (CS.CV) 2026-06-19

DiT-JSCC: Rethinking Deep JSCC with Diffusion Transformers and Semantic Representations

Generative joint source-channel coding (GJSCC) has emerged as a new Deep JSCC paradigm for achieving high-fidelity and robust image transmission under extreme wireless channel conditions, such as ultra-low bandwidth and low signal-to-noise ratio. Recent studies commonly adopt diffusion models as generative decoders, but they frequently produce visually realistic results with limited semantic consistency. This limitation stems from a fundamental mismatch between reconstruction-oriented JSCC encoders and generative decoders, as the former lack explicit semantic discriminability and fail to provide reliable conditional cues. In this paper, we propose DiT-JSCC, a novel GJSCC backbone that can jointly learn a semantics-prioritized representation encoder and a diffusion transformer (DiT) based generative decoder, our open-source project aims to promote the future research in GJSCC. Specifically, we design a semantics-detail dual-branch encoder that aligns naturally with a coarse-to-fine conditional DiT decoder, prioritizing semantic consistency under extreme channel conditions. Moreover, a training-free adaptive bandwidth allocation strategy inspired by Kolmogorov complexity is introduced to further improve the transmission efficiency, thereby indeed redefining the notion of information value in the era of generative decoding. Extensive experiments demonstrate that DiT-JSCC consistently outperforms existing JSCC methods in both semantic consistency and visual quality, particularly in extreme regimes.

11.
arXiv (CS.CV) 2026-06-19

BAFIS: Dataset + Framework to assess occupational Bias and Human Preference in modern Text-to-image Models

Generative artificial intelligence has the potential to improve productivity and transform the production of creative content. However, existing research indicates that image generation models are significantly influenced by biases. This work investigates the inherent biases and language-induced biases present in text-to-image models within the context of occupation-related image generation, complementing established metrics with human preference feedback. We present a comprehensive evaluation of five current text-to-image models: Midjourney v6.1, Stable Diffusion 3 Medium, DALL-E 3, Playground v2.5, and FLUX.1-dev , focusing on gender and ethnicity bias, image quality, and prompt alignment. To facilitate this evaluation, we developed the "Battle-Arena for Fair Image Synthesis" (BAFIS), a platform designed to collect human feedback on bias in generated images. Furthermore, we created a dataset comprising 21,140 synthetic images generated using multilingual prompts, which serves as a basis for our analysis. We further place our results within a broader social context by comparing them to official statistics from the German Federal Employment Agency. Our findings reveal systematic biases in text-to-image models, with established evaluation metrics in partial correlation with subjective user ratings. Thus, our research emphasizes the need for including human preferences to develop fairer and more inclusive text-to-image models.

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

Spectral Retrieval-Augmented Time-Series Forecasting

arXiv:2606.19412v1 Announce Type: new Abstract: Time series forecasting leverages historical patterns to predict future values, but traditional methods face challenges when dealing with complex, non-stationary patterns that are difficult to memorize during training. Retrieval-augmented approaches have emerged as promising solutions by retrieving similar historical patterns to enhance predictions. However, existing retrieval methods suffer from two fundamental limitations: spectral blindness, which overlooks critical frequency-domain characteristics that capture underlying periodic structures, and temporal recency, which treats all historical data equally without emphasizing recent, more relevant patterns. In this paper, we propose SpecReTF, a novel retrieval method that addresses these issues by converting time series into windowed frequency representations, measuring similarity with a combined metric that captures both amplitude and phase information. To balance recency and historical context, we apply an exponential moving average weighting scheme that emphasizes recent windows. Extensive experiments on benchmark datasets demonstrate that SpecReTF outperforms time-domain retrieval methods, achieving superior forecasting accuracy across diverse, non-stationary time series.

13.
medRxiv (Medicine) 2026-06-10

Optimisation of steatotic liver disease screening algorithm for resource-poor settings using machine learning

Background The European Association for the Study of the Liver (ESAL) - Steatotic Liver Disease (SLD) screening algorithm involves two steps; initial screening with FIB-4 followed by referral for vibration-controlled transient elastography (VCTE) in patients likely to have significant fibrosis (SF). However, VCTE is not widely available in resource-limited settings. Aim To optimise the EASL SLD screening algorithm for resource-poor settings using machine learning (ML). Methods We analysed data from 964 adults aged [≥]35 years who underwent VCTE at a tertiary referral centre in Sri Lanka between November 2024 and 2025. Multiple ML models using different methods and variable combinations were trained on 80% of the dataset and tested on the remaining 20%. Best models were selected based on performance and externally validated using data from 430 patients who underwent VCTE before November 2024. Model performance was compared with the FIB-4 using confusion matrices. Results A Random Forest model incorporating age, AST, ALT, and platelet count separately, rather than using FIB-4, outperformed. The all-variable ML model showed the best predictive performance for SF, with accuracy of 77.2%, recall of 0.762, precision of 0.778, and AUC-ROC of 0.818. The variables used in the model, in descending order of feature importance, were AST, platelet count, BMI, ALT, age, diabetes mellitus, hypertension, dyslipidaemia, sex, family history, hypothyroidism, diabetes complication and smoking. External validation demonstrated 75.1% accuracy and an AUC of 0.779. When used as the first step of the SLD screening algorithm, the all-variable ML model identified 37 (17.1%) additional true positives and reduced false-negative diagnoses by 50% compared with FIB-4. Conclusions ML-based models were more effective than the FIB-4 score as the first-line screening tool for VCTE referral, substantially improving the identification of patients with significant fibrosis in this South Asian cohort.

14.
arXiv (CS.AI) 2026-06-19

Co-policy: Responsive Human-Robot Co-Creation for Musical Performances

arXiv:2606.19914v1 Announce Type: cross Abstract: Art has long stood as a pivotal expression of human creativity. Embodied artificial intelligence offers a route for generative models to participate in that creativity through physical action rather than disembodied digital content. In robotic music co-creation, it is challenging to connect semantic musical understanding with real-time and physically executable performance. We present Co-policy, a framework for human-robot musical co-creation that separates semantic intent grounding, constrained musical variation, and visuomotor execution. To ground musical semantics, Co-policy uses pre-inference semantic anchors and a fine-tuned Qwen-vl planner (F-Qwen) to transform speech, live musical seeds, and visual observations into structured co-creation plans. To support low-latency execution, Co-policy introduces a Gaussian-Mixture Visuomotor Policy (GMP), implemented as a conditional mixture-density policy that maps target notes and visual context to multimodal robot actions in a single forward pass. Unlike robotic playback systems that merely reproduce user-specified notes, Co-policy generates complementary musical responses under both musical and physical constraints. Real-robot chime experiments, ablations, and expert evaluation show improved intent alignment, execution accuracy, and response frequency over diffusion-policy and ablated baselines, supporting physically grounded action generation as a key requirement for embodied human-AI co-creation.

15.
arXiv (math.PR) 2026-06-18

On a class of reflected McKean-Vlasov Stochastic Differential Equations with jumps

arXiv:2606.18433v1 Announce Type: new Abstract: This paper investigates a class of reflected McKean-Vlasov Stochastic Differential Equations driven by both Brownian motion and a compensated Poisson random measure. We establish the existence and uniqueness of solutions and provide moments estimates for the state processes.

16.
arXiv (CS.LG) 2026-06-15

Cluster LOCO: Feature Importance For Interpreting Clusters

arXiv:2606.14592v1 Announce Type: cross Abstract: Clustering is widely used for exploratory analysis and scientific discovery, driving insights from market segmentation to biological data analysis, but its outputs can be difficult to interpret, audit, and reproduce as modern datasets become increasingly large and complex. Reliable use of clustering requires understanding which features drive the discovered structure, yet feature-level explanations for clustering remain scarce compared with methods in supervised learning. Furthermore, existing clustering feature importance scores are often tied to specific algorithms and data assumptions. To address these challenges, we propose Cluster LOCO (Leave-One-Covariate-Out), a family of model-agnostic feature importance scores for clustering. Cluster LOCO is built on feature occlusion and clustering generalizability, defined as whether cluster labels learned on one subset of the data can be accurately predicted on held-out samples. For any chosen clustering algorithm, Cluster LOCO quantifies a feature's importance by measuring how much its removal degrades generalizability. We first introduce Cluster LOCO-Split, which relies on data splitting, and then extend it to Cluster LOCO-MP, a minipatch ensemble-based version designed for large-scale data. Across synthetic simulations and an application to cell-type discovery in single-cell transcriptomics, we show that Cluster LOCO more reliably recovers informative features than existing clustering feature importance methods.

17.
arXiv (CS.AI) 2026-06-16

InvDesMobility: a reliability-gated first-principles feedback framework for closed-loop materials discovery

arXiv:2606.16133v1 Announce Type: cross Abstract: Inverse materials design starts from target functionality and searches for structures that can realize it. Its value in closed-loop discovery depends not only on prediction performance, but also on whether expensive first-principles results are independently validated, provenance-recorded, and admitted as feedback only when evidence is sufficient. This is especially important for composite properties such as carrier mobility, where a final scalar value hides intermediate quantities, fit quality, convergence history, and workflow assumptions. Here we present InvDesMobility, a reliability-gated first-principles feedback framework that integrates multi-agent automated DFT, evidence stratification, generative structure proposal, acquisition ranking, and auditable release. Using 516 2DMatPedia-derived candidates, the workflow produced 280 QC-passed materials and 573 retained carrier-direction seed channels after channel-level reliability gating. These records were split into two feedback objects: relaxed structures updated the generative model, while retained mobility channels trained the acquisition model and set validation priority. Over multiple iterations, InvDesMobility screened 2.4 x 10^6 structures, submitted 102 candidates for DFT validation, and retained 86 reliability-gated generated channels across 41 formulas. Overall, the main contribution is not a fixed list of high-mobility materials, but a transferable feedback contract that makes closed-loop inverse design both useful and auditable when learning from expensive calculated properties. All source data, retained feedback records, and workflows are available at https://github.com/DreamLufei/invDesMobility, with an accompanying evidence website at https://dreamlufei.github.io/invDesMobility/.

18.
arXiv (CS.AI) 2026-06-12

AgentBeats: Agentifying Agent Assessment for Openness, Standardization, and Reproducibility

arXiv:2606.13608v1 Announce Type: new Abstract: Agent systems are advancing quickly across domains, but their evaluation remains fragmented. Most benchmarks rely on fixed, LLM-centric harnesses that require heavy integration, create test-production mismatch, and limit fair comparison across diverse agent designs. The root problem is the lack of an open, agent-agnostic assessment interface. We advocate Agentified Agent Assessment (AAA), where evaluation is performed by judge agents and all participants interact through standardized protocols: A2A for task management and MCP for tool access. Conventional benchmarking defines two separate interfaces, one for the benchmark and one for the agent, while AAA only needs one; this yields a generic, unified framework that separates assessment logic from agent implementation and enables reproducible, interoperable, and multi-agent evaluation. We further introduce AgentBeats as a concrete realization of AAA: we identify five practical operation modes that make standardized assessment compatible with real-world constraints on openness, privacy, and reproducibility. To evaluate our design at scale, we conduct two studies: a five-month open competition that drew 298 judge agents across 12 categories together with 467 subject agents from independent participants, showing that AAA applies across a heterogeneous range of benchmarks; and a case study on coding agents that confirms agentified evaluation preserves fidelity with the public record while surfacing previously missing head-to-head results, yielding research insights about agent design. Combining a community-scale field study and a controlled coding case study, we verify that AAA delivers coverage, practicality, and fidelity across heterogeneous scenarios at scale. Together, AAA and AgentBeats offer a clear path toward open, standardized, and reproducible agent assessment.

19.
arXiv (quant-ph) 2026-06-17

Fermionic Hamiltonian engineering with local control

arXiv:2606.17158v1 Announce Type: new Abstract: Quantum simulators enable the exploration of complex quantum phenomena in condensed-matter systems by reproducing their dynamics on controllable quantum devices. However, experimental constraints often restrict the class of Hamiltonians that can be realized natively. Hamiltonian engineering addresses this limitation by expanding the set of accessible target Hamiltonians from a fixed system Hamiltonian defined by the hardware. We introduce a new framework for fermionic Hamiltonian engineering based on conjugating free evolution under the system Hamiltonian with sequences of experimentally feasible local fermionic unitaries. The required sequences and free-evolution times are obtained efficiently via a linear program. By interleaving system evolution with these local unitaries, our method realizes effective time evolution under a broad class of target Hamiltonians, with intrinsic robustness to finite-pulse-time errors. In particular, we demonstrate that arbitrary complex tunnelling coefficients can be realized, constrained only by the connectivity of the underlying system Hamiltonian. We illustrate this capability by engineering the dynamics of the non-interacting Harper-Hofstadter model on a 1088-mode lattice and an interacting Fermi-Hubbard chain with complex tunnelling coefficients. By construction, our approach avoids the continuous energy absorption inherent to Floquet engineering.

20.
arXiv (CS.CV) 2026-06-16

Bridging Information Asymmetry: A Hierarchical Framework for Blind Face Restoration with Reduced Uncertainty

Blind face restoration remains a persistent challenge due to the inherent ill-posedness of reconstructing holistic structures from severely constrained observations. Current generative paradigms, while capable of synthesizing realistic facial details, remain limited by the under-constrained nature of blind restoration, where severely degraded inputs can be mapped to plausible yet identity-inconsistent outputs. To address this issue, we present Pref-Restore, a hierarchical framework for BFR with reduced restoration uncertainty. Our design is organized around three complementary principles: (1) Semantic Information Augmentation, where an auto-regressive semantic branch converts image and text cues into structured tokens that provide a stable high-level anchor; (2) Texture-level Fidelity Alignment, where the diffusion generator is trained under this anchor to recover identity-relevant details; and (3) Fidelity-constrained Preference Optimization, where a face-aware reward refines the diffusion trajectory while controlling the quality–fidelity trade-off. Extensive experiments on synthetic and real-world benchmarks show that Pref-Restore achieves state-of-the-art performance, with stronger identity-sensitive fidelity and lower restoration uncertainty across repeated sampling. Systematic ablations further attribute these gains to the proposed hierarchical design, showing the necessity of staged training, the robustness and quality dependence of the text pathway, and the benefit of fidelity-constrained preference optimization.

21.
arXiv (CS.LG) 2026-06-18

PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling

arXiv:2602.11467v2 Announce Type: replace Abstract: Understanding how anatomical shapes evolve in response to developmental covariates - and quantifying their spatially varying uncertainties - is critical in healthcare research. Existing approaches typically rely on global time-warping formulations that ignore spatially heterogeneous dynamics. We introduce PRISM, a novel framework that bridges implicit neural representations with uncertainty-aware statistical shape analysis. PRISM models the conditional distribution of shapes given covariates, providing spatially continuous estimates of both the population mean and covariate-dependent uncertainty at arbitrary locations. A key theoretical contribution is a closed-form Fisher Information metric that enables efficient, analytically tractable local temporal uncertainty quantification via automatic differentiation. Experiments on three synthetic datasets and one clinical dataset demonstrate PRISM's strong performance across diverse tasks - from modeling shape evolution to personalized shape prediction and anomaly detection - within a unified framework, while providing interpretable and clinically meaningful uncertainty estimates.

22.
arXiv (math.PR) 2026-06-12

Characterizing metric-space-valued processes: separating classes and weak invariance principles for measure-theoretic inference

arXiv:2606.13084v1 Announce Type: cross Abstract: This article investigates stochastic processes taking values in metric spaces that lack a topological vector space structure, a regime characterized by intricate interplay between topological, geometric, and temporal dependence structures. It is formally established that spaces admitting an isometric Hilbertian embedding constitute a strict subclass within the much broader class of metric spaces possessing the ball property. While traditional kernel methods are susceptible to geometric distortion when the underlying space cannot be isometrically embedded into a Hilbert space, we bypass such limitations by exploiting a fundamental structural property inherent to this broader class; namely, that Borel probability measures are uniquely determined by their values on balls. These separating classes provide the foundation for the subsequently introduced measure-theoretic inference methodology. We derive uniform convergence of a family of time-dependent random measures, alongside weak invariance principles for the corresponding nonstationary random fields. This framework explicitly exposes how dependence and geometric complexity influence sample path regularity. Furthermore, because the rapid decay of small-ball probabilities can prohibit the existence of limiting distributions for supremum-based discrepancy measures, we develop $L^p$-based alternatives. By directly leveraging the introduced convergence results, this approach circumvents the need for higher-order $U$-process formulations. Finally, for spaces that do admit an isometric Hilbertian embedding, and where $U$-processes naturally arise, we establish limit theory for both degenerate and nondegenerate multi-parameter $U$-processes, and demonstrate that local discrepancy tests maintain asymptotic stability under dynamic parameter regimes.

23.
Nature (Science) 2026-06-12

Daily briefing: How Venus flytraps snap shut

作者:

Softening cells enable flytraps to shut with astonishing speed. Plus, the cutting-edge science happening at the World Cup and why scientists shouldn’t ignore the Pope’s AI message. Softening cells enable flytraps to shut with astonishing speed. Plus, the cutting-edge science happening at the World Cup and why scientists shouldn’t ignore the Pope’s AI message.

24.
arXiv (CS.AI) 2026-06-17

Functional Equivalence in Attention: A Comprehensive Study with Applications to Linear Mode Connectivity

arXiv:2606.17830v1 Announce Type: cross Abstract: Neural network parameter spaces are inherently non-injective, as distinct parameter configurations can realize identical functions through functional equivalence. While this symmetry is well understood in classical fully connected and convolutional models, it becomes substantially more intricate in modern attention-based architectures. Existing analyses of multihead attention have largely focused on the vanilla formulation, overlooking positional encodings that fundamentally reshape architectural symmetries. In this work, we provide a formal study of functional equivalence in Transformers with positional encodings. Focusing on the two most widely used variants–sinusoidal and rotary positional encodings (RoPE)–we show that sinusoidal encodings preserve the equivalence structure of vanilla attention, whereas rotary encodings significantly reduce the symmetry group, thereby enhancing expressivity. This offers a principled explanation for the growing prominence of RoPE in practice. We further examine how positional encodings affect linear mode connectivity, and through an alignment algorithm, empirically demonstrate that the presence and variability of connectivity across Transformer settings crucially depend on the positional encoding.

25.
arXiv (CS.CL) 2026-06-18

Compact Geometric Representations of Hierarchies

Computing geometric representations of data is a cornerstone of modern machine learning, typically achieved by training dual encoders which map queries and documents into a shared embedding space. Recent work of You et al. [NeurIPS '25] has extended this approach to hierarchical retrieval, where relevance is determined by the ancestor-descendant relationships in a Directed Acyclic Graph (DAG). While previous work has shown that valid embeddings exist when the number of descendants is small, these bounds degrade significantly for deep hierarchies, requiring dimensions as large as the total number of nodes. In this paper, we investigate compact reachability embeddings for more general graph classes and provide theoretical guarantees for representing hierarchies using embeddings whose dimension depends on structural graph parameters. We prove that for any directed tree, there exists a reachability embedding in constant dimension 3, independent of the tree's size or depth. We generalize this result to graphs characterized by treewidth $t$, constructing embeddings of dimension $O(t \log n)$, where $n$ is the number of nodes. Complementing these upper bounds, we provide matching or near-matching lower bounds, showing that dimension $\Omega(n)$ is necessary for general DAGs and $\Omega(t/\log(n/t))$ is required for graphs of treewidth $t$. We also obtain upper and lower bounds parameterized by the number of cross-edges in the DAG. We additionally show that our embeddings can be constructed on real world datasets, and that they give much smaller dimensions in high recall regimes compared to prior embeddings with theoretical guarantees.