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01.
bioRxiv (Bioinfo) 2026-06-19

OmniPath Metabo: chemical structures, interactions and mechanisms to study the metabolome

Mechanistic and functional analysis of omics data largely relies on the incorporation of prior knowledge; however, connecting metabolomics data and knowledge is a major methodological challenge. This is largely driven by the diverse prior knowledge being fragmented across many databases requiring the merging of different database records across chemical structures, identifiers, and varying levels of structural specificity. Hence, this limits mechanistic interpretation and functional characterisation of the metabolome. Here, we present OmniPath Metabo, a comprehensive, harmonized, metabolome-centric database covering metabolites, lipids, food-derived compounds, and small molecule drugs, along with their associated receptors, transporters, enzymes, reactions, allosteric regulators, and disease associations. OmniPath Metabo harmonizes attributes using controlled vocabularies and ontologies, structures and built-in cheminformatics to map identifiers and track ambiguity. OmniPath Metabo is built directly from 40+ original resources and is freely accessible via an interactive web app and API at metabo.omnipathdb.org. OmniPath Metabo enables dynamic, context-specific construction of subnetworks to serve dedicated purposes, such as cell-cell communication or integrated multi-omics metabolite-driven regulation, connecting reactions, allosteric regulation, metabolite-receptor and metabolite-transporter interactions. Combining it with the over 170 other resources in OmniPath, it can be used for integrated networks of signaling, gene regulation, and metabolism. We showcase the application of OmniPath Metabo by analysing publicly available metabolomics data of lung cancer cell lines and metabolic footprints to mutational patterns. In summary, OmniPath Metabo transforms fragmented resources into a harmonised prior knowledge framework for a mechanistic and functional analysis of the metabolome.

02.
arXiv (CS.AI) 2026-06-12

The AI Legal Specialist: A Juridically Autonomous Professional Profile for AI Governance

arXiv:2606.12415v1 Announce Type: cross Abstract: The rapid global expansion of artificial intelligence regulation has generated, across multiple jurisdictions, a demand for legal expertise dedicated to AI that the market has addressed in a fragmented manner. Data protection officers extend their remit beyond data protection law; privacy lawyers reposition themselves toward AI; compliance officers add AI chapters to their existing manuals. This paper argues that none of these adaptive responses adequately covers the professional space opened by the emerging global AI regulatory landscape, of which the EU Artificial Intelligence Act (Regulation (EU) 2024/1689) is the most comprehensive instance, alongside the Council of Europe Framework Convention on AI, the United States executive and sectoral framework, and analogous initiatives in the United Kingdom, Canada, Brazil, China, Japan, Singapore, and beyond. A distinct professional profile is required: the AI Legal Specialist, conceived as a jurist – understood broadly to encompass any professional with advanced legal training – operating at the intersection of legal interpretation and AI governance. The profile is juridically autonomous: it derives its existence from the structure of regulatory obligations generated wherever AI is subject to substantive regulation, rather than from any technical standard or the extension of adjacent roles. The paper provides a juridically grounded definition of the profile, argues for its autonomy from adjacent figures and international standards, proposes a reference competence architecture aligned with the European e-Competence Framework (e-CF, EN 16234-1) as a methodological choice, and articulates the conditions for its operational measurement through key performance indicators. The contribution is intended as a foundation for international standardization of the profile and as a reference for practice, curricula, and adoption across jurisdictions.

03.
arXiv (CS.LG) 2026-06-11

Urban Heat MiniCubes: An AI-Ready dataset for urban heat research

arXiv:2606.11534v1 Announce Type: cross Abstract: Urban heat is amplified by impermeable surfaces and heterogeneous built environments, yet street-level variability remains difficult to quantify because multi-sensor observations are rarely available in consistent, analysis-ready form at the necessary spatiotemporal scales. We present "Urban Heat MiniCubes," a publicly available, FAIR-oriented dataset designed for machine learning applications in urban heat research. The dataset provides harmonized 90 x 90 km gridded data cubes for 48 cities in the Western Hemisphere spanning 2022-2023, with variables reprojected and collocated to a common grid to reduce preprocessing (e.g., reprojection, resampling, and spatiotemporal alignment). Urban Heat MiniCubes includes two complementary modalities: (i) higher-spatial-resolution, lower-frequency observations from Landsat 8/9 (e.g., surface reflectances) and Sentinel-1 (e.g., synthetic aperture radar backscatter), and (ii) higher-temporal-frequency, coarser observations from GOES-R (e.g., longwave infrared brightness temperatures) and a microwave land surface temperature product. We document variables and metadata and provide technical assessment using inter-variable analyses and autoencoder-based reconstruction-error summaries across pixel classes (e.g., water and cloud). Potential use cases and limitations are also discussed.

04.
arXiv (CS.CL) 2026-06-15

A Computational Audit of Demographic Association Encoding in ClinicalBERT Language Predictions

Transformer-based clinical language models are increasingly integrated into high-stakes clinical decision support pipelines, yet the computational mechanisms through which demographic associations encoded in medical documentation propagate into model probability distributions remain empirically underspecified. We present a systematic computational audit of representational bias in ClinicalBERT (Alsentzer et al., 2019), a BERT-based model pretrained on MIMIC-III discharge summaries, employing two complementary probing methodologies: Log Probability Bias Analysis (LPBA), which quantifies demographic descriptor-induced shifts in masked token probability distributions across behavioral and evaluative semantic categories, and Masked Language Model-based analysis (MLM), which probes internal representational structure for demographic agency attribution encoding across 98 real clinical sentence templates and eight intersectional race-gender combinations. Corpus frequency analysis operationalizes the distinction between statistical disparity and bias amplification by benchmarking model outputs against empirical term frequencies in the MIMIC-III training corpus. Of 32 statistically significant findings, 65.6% contradict observed corpus distributions, rising to 80% for Black patients and 87.5% for agency attribution under MLM probing, providing direct empirical evidence that representational bias in ClinicalBERT operates predominantly through model-internal amplification rather than training data inheritance. Keywords: natural language processing, clinical documentation, algorithmic auditing, representational bias, health equity 1

05.
arXiv (CS.AI) 2026-06-12

When Does Delegation Beat Majority? A Delegation-Based Aggregator for Multi-Sample LLM Inference

arXiv:2606.08098v2 Announce Type: replace Abstract: Majority voting over sampled answers is the dominant unsupervised aggregator for multi-sample LLM inference. In this paper, we show a delegation-based aggregator (Propagational Proxy Voting, PPV; Sakai et al., 2025) yields an unsupervised consensus rule that beats majority on MMLU-Pro by +1.5 pp overall and +2.24 pp on the non-trivial subset (paired McNemar p ~ 1.0e-14, n = 8,099). Majority discards two signals that every sample carries: within-group letter entropy and between-group reasoning geometry. PPV exposes per-voter levers that consume exactly these two signals: When (how much weight a voter keeps on its own pick) and Whom (how it splits the remainder across peers). We drive When with letter entropy and Whom with per-question-centered embedding cosine. Our method needs no gold labels and no auxiliary training: per-question, we partition 128 sampled generations into 16 groups, compute each group's letter-level semantic entropy and reasoning embedding centroid, and feed both into a stochastic delegation matrix whose stationary distribution selects the consensus answer. We walk through an example in which PPV overturns a clear 10-6 majority for the wrong letter: the 10-voter majority cluster is geometrically incoherent (mean within-cluster cosine -0.02) while the 6-voter minority is tight (+0.26), so propagated delegation mass concentrates on the minority's answer even though entropy alone would keep the majority ahead. We further report delegation strategies with negative results that constrain the design space for unsupervised LLM aggregation. No within-question ensemble of confidence modes closes the oracle gap.

06.
arXiv (CS.AI) 2026-06-25

Compositional Behavioral Semantics for State Abstraction in Reinforcement Learning

arXiv:2606.25357v1 Announce Type: cross Abstract: State abstraction plays a key role in scaling reinforcement learning to complex but structured systems. In studying such systems, a wide range of behavioral structures have been studied in reinforcement learning, including value functions, invariants, bisimulation relations, and behavioral metrics. However, a general principle for determining what structures are provably preserved under state abstraction is still lacking. In this paper, we present a unified framework for defining and analyzing behavioral structures in reinforcement learning. Our framework provides a compositional way to specify behavioral semantics based on local, one-step descriptions of system dynamics. Using this framework, we establish results showing how behavioral structures can be safely transferred between abstract and concrete systems. We further show how to construct quantitative metrics from logical behavioral semantics with soundness guarantees. Together, these results provide a principled foundation for reasoning about behaviors under state abstraction in reinforcement learning and offer reusable definition and proof principles for a broad class of behavioral structures in reinforcement learning.

07.
arXiv (CS.LG) 2026-06-19

Algebraic Dead Directions in LayerNorm Transformers: A Forward-Pass-Only Diagnostic at LLM Scale

arXiv:2606.19491v1 Announce Type: new Abstract: Pretrained transformers sit near singular minima of the loss, where the Fisher information metric degenerates along dead directions: directions in parameter space along which the directional Fisher vanishes. Locating such a direction normally needs a forward pass and an eigendecomposition of activations, or a sampling-based complexity estimate; none returns a direction computable from the network's parameters alone. We give one, for LayerNorm transformers. The inverse-scale direction $\gamma^{-1}/\|\gamma^{-1}\|$ of the LayerNorm affine is an exact algebraic kernel of the post-final-norm centred activation covariance, for any input distribution, and induces a corresponding dead direction in parameter space. It is read from the LN scale parameter alone, with no forward or backward pass and no eigensolve: the cheapest dead-direction read, specific to LayerNorm. We test it on $14$ pretrained transformers ($9$ LayerNorm, $5$ RMSNorm; $160$M-$35$B; language and vision objectives). At random initialisation the predicted direction matches the measured bottom singular direction (one forward pass, direct SVD) to four decimal places on $9/9$ LayerNorm models, and is correctly absent on $5/5$ RMSNorm models, which lack the mean-subtraction projector that creates it. On the trained checkpoint the covariance eigenvalue along this direction deepens by ${\sim}10^3\times$ and further dead directions open; the random-init-to-trained gap is a one-forward-pass, per-checkpoint readout of singular structure along the predicted coordinate. Two consequences follow in closed form: the residual stream's smallest singular value is preserved block-to-block on $13/14$ transformers measured on their own input distribution, the one exception (Gemma$4$-$31$B) a genuine dead direction the same read pinpoints; and the kernel direction's presence classifies a transformer's normalisation from the parameters alone.

08.
arXiv (CS.AI) 2026-06-18

scGTN: Deep Siamese Graph Transformer Network for Single-cell RNA Sequencing Clustering

arXiv:2606.18672v1 Announce Type: cross Abstract: Single-cell RNA sequencing (scRNA-seq) serves a pivotal role in characterizing gene expression at the cellular level, enabling the identification of cell types and advancing the understanding of cellular heterogeneity. Despite the significant progress in scRNA-seq data clustering, we argue that current methods always ignore the sparsity and noise, as well as the complex intercellular structural information inherent in scRNA-seq data. Toward this end, in this paper, we propose a novel single-cell RNA-seq clustering framework via deep Siamese Graph Transformer Network (termed scGTN), which explicitly integrates gene expression profile and intercellular structural dependencies for cell clustering. In particular, we formulate scRNA-seq data as a graph and construct two augmented graph views that serve as dual views to capture complementary intercellular information. Then, a Siamese graph transformer network is employed to explicitly incorporate shortest-path information and node-wise distances for capturing richer structural relationships between cells. Finally, we employ an optimal transport strategy to guide the cell clustering in a self-supervised manner. Extensive experiments on multiple benchmark scRNA-seq datasets demonstrate that our scGTN consistently outperforms existing methods. Our code is available at https://github.com/W-RMSL/scGTN.

09.
arXiv (quant-ph) 2026-06-16

Entanglement-Rank Duality in Quadratic Phase Quantum States

arXiv:2605.05167v2 Announce Type: replace Abstract: Absolutely maximally entangled (AME) states are fundamental resources in quantum information theory, yet their construction and certification remain a nontrivial problem. Within the family of quadratic phase quantum states, defined by symmetric matrices $P$ over finite fields $\mathbb{F}_{p^m}$, we show that the Rank-Purity Duality $\operatorname{Tr}(\rho_S^2) = |\mathbb{F}|^{-\operatorname{rk}_{\mathbb{F}}(P_{S,\bar{S}})}$ follows from additive character orthogonality and holds over all $\mathbb{F}_{p^m}$, yielding a polynomial-time AME certification criterion. For square-free dimensions $d = p_1\cdots p_r$, the Chinese Remainder Theorem induces a prime-field factorisation. This implies additivity of Rényi-2 entropy and yields sharp obstruction criteria that rule out cases such as $\operatorname{AME}(4,6)$ and constrain the open case $\operatorname{AME}(8,6)$. As a proof of concept, we construct an explicit $\operatorname{AME}(17,10001)$ state, certified across all $65{,}535$ bipartitions, demonstrating that the framework scales to large systems and previously inaccessible local dimensions.

10.
medRxiv (Medicine) 2026-06-23

Social networks and their association with quality of life among older adults in rural Burkina Faso

Objective: This study aimed to identify the types of social networks present among older adults in a rural, low-income country setting and describe their association with quality of life (QoL). Methods: A population-representative, cross-sectional survey was conducted in 60 villages around Nouna in Burkina Faso from July to August 2021. Data were collected from resident adults aged 40 years and older. Variables captured were sociodemographic status; social network characteristics (using the Practitioner Assessment of Network Typology (PANT)); quality of life (using the EuroHIS-8 tool); presence of non-communicable diseases, mental health conditions, and disability. Additionally, social networks were broadly categorised as aggregated integrated and aggregated less-integrated groups. Social network types and the groups were described separately, and a multivariable linear regression model was used to understand the association between social network types and QoL, adjusted for sociodemographic and morbidity factors. Results: Among the 2390 respondents, median age was 55 yrs (IQR: 47-64 yrs) and 55.8% were female. Locally Integrated (35.4%) or Family Dependent (30.3%) were the most common PANT social network types, followed by a mixed group (having characteristics of two or more social network types) (30.5%). Private Restricted (2.1%), Locally Self-Contained (1.2%), and Wider Community-Focussed (0.4%) types were uncommon. Adults with aggregated integrated network groups (36.1%) and aggregated less-integrated group (36.0%) were near equal, while others were non-aggregable. Although Wider Community-Focused type showed a significantly better QoL ({beta}= 8.69, 95%CI: 4.10 to 13.27), the association between social networks and QoL were subdued when controlled for morbidity factors, and hence no significant associations were observed between other types or the aggregated groups. Conclusion: Although having integrated social networks lead to a better QoL, morbidity has a greater effect on the QoL among older adults in Nouna and hence, investing more on improving the physical and mental health needs appears more beneficial.

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

ToolSelf: Unifying Task Execution and Self-Reconfiguration via Tool-Driven Emergent Adaptation

arXiv:2602.07883v4 Announce Type: replace Abstract: LLM-powered agentic systems excel at complex long-horizon tasks, but remain constrained by static configurations fixed before execution. Such rigidity forces a trade-off between domain-specific performance and cross-task generalization: strong priors and compact tool spaces aid specialization but weaken transfer, while task-agnostic workflows and broad action spaces expand coverage but dilute guidance. Existing pre-execution optimization, planner-worker orchestration, and configuration patching fall short of resolving this tension, as they decouple adaptation from execution, causing information loss, fragmented optimization, and ambiguous credit assignment. We propose ToolSelf, a tool-driven runtime self-reconfiguration paradigm that abstracts configuration updates as a standardized tool interface and unifies execution and adaptation within one policy's action space. The execution agent can dynamically update sub-goals, strategies, toolboxes, context, and context-management modes based on task progress and feedback. We further introduce Configuration-Aware Two-stage Training (CAT), which combines rejection sampling fine-tuning with trajectory-level KTO reinforcement learning to internalize self-reconfiguration. Across diverse benchmarks, zero-shot ToolSelf rivals task-specialized agents; after CAT training, ToolSelf gains 28.8 points over the static-configuration baseline on average, illuminating a path toward emergent adaptivity that obviates manually injected guidance. The code is available at https://github.com/lian-tian-mo-zun/ToolSelf.

12.
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.

13.
arXiv (CS.AI) 2026-06-16

Bayesian Inference and Decision Audits for Public Archives of Frontier AI Evaluations

作者:

arXiv:2606.17005v1 Announce Type: new Abstract: Public AI evaluations are often read as terminal leaderboards, yet the underlying evidence is a selective time series shaped by reporting rules, benchmark revisions, and missingness. Repeated public archives for LiveBench and Open LLM Leaderboard v2 serve as the primary longitudinal record; LMArena provides a preference stress test; and GAIA and tau-bench contribute limited agentic pilots. Together, these archives instantiate a Bayesian inference problem: under a fixed reporting convention, one constructed terminal-only example over $1{,}000$ systems is compatible with two pre-terminal histories, yielding times of $23.03$ or $75.13$ to reach within $0.05$ of the ceiling under the same terminal-tail model. In synthetic posterior comparisons, action-facing diagnostics differ across observation regimes. The candidate selection-aware frontier model fails synthetic recovery, objective-archive prediction, preference transfer, and uncertainty calibration; correspondingly, fixed audit gates reject its stronger claims. An archive-and-adjudication protocol reconstructs public evaluation histories, isolates a verified timing boundary, and falsifies unsupported frontier claims.

14.
arXiv (CS.AI) 2026-06-12

Existence Precedes Value: Joint Modeling of Observational Existence and Evolving States in Time Series Forecasting

arXiv:2606.13571v1 Announce Type: cross Abstract: Real-world time series are often highly incomplete and irregular due to sensor dormancy, transmission delays, and event-driven sampling, making reliable forecasting fundamentally challenging. Existing methods have evolved from impute-then-forecast pipelines to continuous-time models such as Neural ODEs and continuous-time graph networks. While these approaches improve the modeling of historical irregularity, they still rely on an implicit oracle assumption at inference time: the timestamps of future valid observations are presumed to be known in advance. This assumption limits practical relevance, since in many real systems the more fundamental question is not only what the future value will be, but also whether a valid observation will occur at all. In this paper, we propose Timeflies, a unified framework that reformulates forecasting as a joint problem of future observability inference and value estimation. To explicitly model the interaction between observation dynamics and state evolution, Timeflies adopts an observation stream and a value stream, coupled through three dedicated modules for reliability-aware embedding, observation-guided dependency modeling, and joint prediction. We further construct Shadow, a benchmark that combines natural missingness from public datasets with real-world industrial data, and introduce the Observation-Value Joint Entropy (OVJE) metric to comprehensively evaluate this coupled predictability. Extensive experiments show that Timeflies consistently outperforms existing methods, highlighting the importance of explicitly modeling future observability in time series forecasting with missing values. Code and dataset are available in https://github.com/ant-intl/Timeflies.

15.
arXiv (CS.CL) 2026-06-24

Removing Noise, not Finding Gold: Quality Filtering for Large-Scale Pretraining

Large-scale models are pretrained on massive web-crawled datasets containing documents of mixed quality, making data filtering essential. A popular method is Classifier-based Quality Filtering (CQF), which trains a binary classifier to distinguish between pretraining data and a small, high-quality set. It assigns each pretraining document a quality score defined as the classifier's score and retains only the top-scoring ones. We provide an in-depth analysis of CQF. We show that while CQF improves downstream task performance, it does not necessarily enhance language modeling on the high-quality dataset. We explain this paradox by the fact that CQF implicitly filters the high-quality dataset as well. We further compare the behavior of models trained with CQF to those trained on synthetic data of increasing quality, obtained via random token permutations, and find starkly different trends. Our results challenge the view that CQF captures a meaningful notion of data quality.

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

Federated Causal Inference from Multi-Site Observational Data via Propensity Score Aggregation

arXiv:2505.17961v4 Announce Type: replace-cross Abstract: Causal inference typically assumes centralized access to individual-level data. Yet, in practice, data are often decentralized across multiple sites, making centralization infeasible due to privacy, logistical, or legal constraints. We address this problem by estimating the Average Treatment Effect (ATE) from decentralized observational data via a Federated Learning (FL) approach, allowing inference through the exchange of aggregate statistics rather than individual-level data. We propose a novel method to estimate propensity scores via a federated weighted average of local scores using Membership Weights (MW), defined as probabilities of site membership conditional on covariates. MW can be flexibly estimated with parametric or non-parametric classification models using standard FL algorithms. The resulting propensity scores are used to construct Federated Inverse Propensity Weighting (Fed-IPW) and Augmented IPW (Fed-AIPW) estimators. In contrast to meta-analysis methods, which fail when any site violates positivity, our approach exploits heterogeneity in treatment assignment across sites to improve overlap. We show that Fed-IPW and Fed-AIPW perform well under site-level heterogeneity in sample sizes, treatment mechanisms, and covariate distributions. Theoretical analysis and experiments on simulated and real-world data demonstrate clear advantages over meta-analysis and related approaches.

17.
arXiv (CS.LG) 2026-06-19

Distributionally Robust Set Representation Learning Under Inference-Time Element Corruption

arXiv:2605.30089v2 Announce Type: replace Abstract: Standard Set Representation Learning methods typically excel on curated data but often overlook the challenge of inference-time element corruption. This refers to scenarios where deployed models encounter element-level degradations, such as outliers or missing components, that may distort set representation and degrade performance. We propose SW-DRSO, a distributionally robust optimization framework tailored for sets. Rather than minimizing loss solely on observed training data, SW-DRSO optimizes a tractable surrogate of the worst-case expected loss over a family of plausible inference-time variations. We introduce a barycentric adversary that approximates the intractable search over corrupted sets by a differentiable training-time optimization over simplex weights. Extensive experiments across four tasks demonstrate that SW-DRSO effectively enhances robustness against corruption while maintaining high overall performance.

18.
arXiv (CS.CV) 2026-06-19

RC-GeoCP: Geometric Consensus for Radar-Camera Collaborative Perception

Collaborative perception (CP) enhances scene understanding through multi-agent information sharing. While LiDAR-centric systems offer precise geometry, high costs and performance degradation in adverse weather necessitate multi-modal alternatives. Despite dense visual semantics and robust spatial measurements, the synergy between cameras and 4D radar remains underexplored in collaborative settings. This work introduces RC-GeoCP, the first framework to explore the fusion of 4D radar and images in CP. To resolve misalignment caused by depth ambiguity and spatial dispersion across agents, RC-GeoCP establishes a radar-anchored geometric consensus. Specifically, Geometric Structure Rectification (GSR) aligns visual semantics with geometry derived from radar to generate spatially grounded, geometry-consistent representations. Uncertainty-Aware Communication (UAC) formulates selective transmission as a conditional entropy reduction process to prioritize informative features based on inter-agent disagreement. Finally, the Consensus-Driven Assembler (CDA) aggregates multi-agent information via shared geometric anchors to form a globally coherent representation. We establish the first unified radar-camera CP benchmark on V2X-Radar and V2X-R, demonstrating state-of-the-art performance with significantly reduced communication overhead. Code will be released soon.

19.
arXiv (CS.CL) 2026-06-25

Continual Knowledge Updating in LLM Systems: Learning Through Multi-Timescale Memory Dynamics

LLMs are trained once, then deployed into a world that never stops changing. External memory compensates for this, but most systems manage it explicitly rather than letting it adapt on its own. Biological memory works differently: coupled multi-timescale dynamics make new associations immediately usable, strengthen what repetition confirms, and let the rest fade. We argue that external memory should follow a similar principle. In Memini, this view takes the form of an associative memory that organizes knowledge as a directed graph. Each edge carries two coupled internal variables, one fast and one slow, following the Benna-Fusi model of synaptic consolidation. From this coupling, episodic sensitivity, gradual consolidation, and selective forgetting are expected to emerge as facets of a single mechanism, reframing external memory as a learning substrate that reorganizes through its own dynamics. This workshop article describes an early-stage conceptual design without experimental evaluation.

20.
arXiv (math.PR) 2026-06-24

Negative index, matchings, and nonnegative eigenvalues of tridiagonal stochastic matrices

arXiv:2606.21122v2 Announce Type: replace Abstract: We study negative eigenvalues of $n\times n$ stochastic matrices whose off-diagonal support is constrained by a sparse graph. The main tool is a matching-based inertia principle: if $G$ is bipartite with matching number $\mu(G)$, $S$ is a real symmetric matrix supported on $G$ with nonnegative diagonal entries and whose negative index (i.e. number of negative eigenvalues counted with their multiplicities) is denoted by $\nu_{-}(S) $, then \[ \nu_{-}(S)\leq \mu(G). \] In particular, every $n\times n$ nonnegative tridiagonal stochastic matrix $P$ satisfies $ \nu_{-}(P)\leq \left\lfloor \frac{n}{2}\right\rfloor. $ Consequently, after ordering the eigenvalues of $P$ in the decreasing order, we have $ \lambda_{\lceil n/2\rceil}(P)\geq0, \ and hence \ \lambda_2(P)\geq0, \mbox{ for } n\geq3. $ This gives an all-dimensional strengthening of the previously known $4\times4$ tridiagonal stochastic result. Next, we show that this tridiagonal bound is sharp in every dimension in both reducible and irreducible cases. Finally, we explore some possible extension and raise some open questions.

21.
arXiv (quant-ph) 2026-06-16

Worst-case depth hierarchy for shallow quantum circuits

arXiv:2606.16425v1 Announce Type: new Abstract: Circuit depth is a central resource in complexity theory. While bounded-depth classical circuits admit well-understood hierarchy theorems, the internal structure of constant-depth quantum computation remains comparatively unexplored. We prove an explicit depth hierarchy theorem for $\mathsf{QNC}^0$. For each $d\ge 12$, we construct a family of two-round interactive problems on which no depth-$(d-1)$ quantum circuit can achieve near-perfect success, regardless of gate set, circuit size, or ancillary qubits. In contrast, we prove that our construction admits realizations by simple bounded fan-in quantum circuits of depth larger than $d$ by a small constant factor. Moreover, all bounded fan-in classical circuits of sublogarithmic depth (in the input size) fail to achieve perfect success on these tasks for every $d$, yielding a hierarchy of problems that show unconditional quantum advantage of $\mathsf{QNC}^0$ over $\mathsf{NC}^0$. A key obstacle is the scarcity of lower bound techniques for quantum circuits. To address this, we develop methods to analyze how depth affects a circuit's ability to realize nonlocal correlations amongst its output qubits in a fine-grained manner. Our approach exploits the correspondence between constraint systems and nonlocal games, translating group-theoretic constructions into rigid operator-valued constraint systems and then into non-local games. In particular, we construct constraint systems whose unique faithful operator-valued solutions require every perfect strategy, and every near-perfect strategy to a fixed precision, to implement multi-controlled phase operations. This reduces to a nonlocal unitary-synthesis problem, yielding depth lower bounds for both shallow quantum and classical circuits. These results show that increasing depth strictly increases computational power within $\mathsf{QNC}^0$, establishing a genuinely quantum hierarchy.

22.
arXiv (quant-ph) 2026-06-15

Tamed Feynman-Kac diffusion processes: Killing-branching intertwine

arXiv:2605.07824v2 Announce Type: replace-cross Abstract: Relaxation to equilibrium of a drifted Brownian motion is quantified by a transition probability density function, whose main (multiplicative) entry is an inferred Feynman-Kac kernel of the Schr\"{o}dinger semigroup operator. Although seemingly devoid of a natural probabilistic significance (except for its explicit path integral definition), the pertinent kernel relaxes to equilibrium as well. The implicit Feynman-Kac potential ${\cal{V}}(x)$, continuous, confining and bounded from below, may take negative values. If positive, ${\cal{V}}(x)$ can be interpreted as the killing rate of the decaying diffusion process. In case of relaxing F-K kernels the killing effects are tamed (often overcompensated). The taming inavoidably appears in conjunction with the existence of the negativity subdomains of ${\cal{V}}(x)$ in $R$. If locally ${\cal{V}}(x) < 0$, its sign inversion $- {\cal{V}}(x)$ can be interpreted as the branching (cloning, alternatively bifurcation) rate in the course of the other wise free random motion. The arising killed diffusion processes with branching, we interpret as the possible path-wise background of tamed (relaxing) Feynman-Kac diffusions. We present acomputer-assisted path-wise arguments, towards a consistency of the killing/branching taming scenario, for a number of nonlinear model systems in one space dimension. Special attention is paid to Feynman-Kac potential shapes in the double well form, where an analytic access to eigenvalues and eigenfunctions is scarce. Throughout the paper the dynamics refers to the positive real time. Since the Newton-type equations of motion for admissible classical trajectories have a Euclidean form (due to the sign inverted force term), we give a brief resume of a couple of their explicit solutions, without recourse to the Euclidean time intuitions, and the instanton lore of related quantum model systems.

23.
arXiv (CS.CL) 2026-06-16

daVinci-kernel: Co-Evolving Skill Selection, Summarization, and Utilization via RL for GPU Kernel Optimization

GPU kernel optimization represents a paradigm where functional correctness is assumed and execution efficiency is the objective. We present daVinci-kernel, a reinforcement learning framework that couples skill discovery with skill exploitation through a dynamically evolving skill library. daVinci-kernel jointly trains three agents sharing one LLM backbone: a Skill Selection Agent that retrieves relevant techniques via BM25 and LLM reranking, a Policy Agent that generates multi-turn CUDA/Triton kernels conditioned on selected skills, and a Skill Summary Agent that distills successful rollouts into reusable skills. Candidate skills are added only after execution-based verification confirms reproducible speedups. All three agents share a single LLM backbone, are initialized via a structured SFT cold start on diversity-filtered data, and are then jointly optimized end-to-end with multi-turn REINFORCE and per-agent advantage estimation. On KernelBench, daVinci-kernel-14B achieves 37.2%, 70.6%, and 32.2% on Level 1, Level 2, and Level 3 under the Fast$_1$ threshold, outperforming the strongest prior RL-trained model, Dr.Kernel-14B.

24.
arXiv (CS.LG) 2026-06-19

EFIQA: Explainable Fundus Image Quality Assessment via Anatomical Priors

arXiv:2606.20108v1 Announce Type: cross Abstract: Image quality control is vital for a wide range of downstream applications. Deep learning-based image quality assessment methods typically train classifiers on dataset-specific quality labels, inheriting two limitations: (1) generalization is tied to the labeling criteria of the training set and (2) these methods cannot provide spatial feedback on where the quality is degraded, lacking explainability. In this work, we propose EFIQA, a framework that requires no quality-related supervision and produces spatial quality maps by design. Rather than learning ``what is degradation" from human-annotated labels, EFIQA learns ``what should be there" by leveraging anatomical priors. For fundus photography, we instantiate this as a two-stage approach, by first training an unsupervised anomaly detector via masked anatomical inpainting to identify regions of missing vasculature, and then distilling this prior knowledge into a shallow adapter mapping features of a frozen foundation model to precise quality maps. External-dataset evaluation demonstrates that this label-free approach with minimal adaptation achieves better performance and explainability compared with supervised methods across benchmarks with different quality criteria, highlighting its potential for real-world applications.

25.
arXiv (CS.LG) 2026-06-16

Towards a Unified Generative Model for Scarce Time Series with Domain Experts

arXiv:2606.15172v1 Announce Type: new Abstract: Synthesizing realistic time series with generative models has wide-ranging applications in real-world scenarios. Despite recent progress, most existing methods are trained under the assumption of abundant training data, which substantially limits their effectiveness in data-scarce settings. In this paper, we propose TimeMoDE, a novel framework that integrates Diffusion Transformers with Mixture-of-Experts to exploit both domain adaptability and diffusion-stage awareness for time series generation under data scarcity. It is pre-trained on a large-scale collection of multi-domain datasets to extract domain-agnostic temporal representations and domain-specific information benefiting generalization during fine-tuning. We propose Domain Prompts to condition expert assignment for indistinguishable noised tokens, mitigating the limitations of capturing inter-dataset relationships. Moreover, we incorporate diffusion timestep signals to equip the experts with awareness of time series degradation variations, facilitating adaptive calibrate to stage-dependent denoising requirements. Extensive experiments demonstrate that TimeMoDE outperforms existing methods under diverse low-data settings. It establishes an innovative paradigm for advanced time series few-shot generation.