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

Learning New Tasks via Reusable Skills: Skill-Compositional Experts for Embodied Continual Learning

Embodied Continual Learning (ECL) aims to enable robots to continually acquire new manipulation tasks while retaining previously learned behaviors under closed-loop control. Compared with conventional continual learning, ECL suffers from more severe catastrophic forgetting. Feature drift accumulated under closed-loop control progressively propagates through sequential decision-making, leading to degradation of previously learned behaviors. A key challenge in ECL lies in structured skill reuse across continually evolving tasks, since existing methods primarily focus on skill learning without explicitly organizing them for coherent task execution. To address this issue, we propose SCE, a Skill-Compositional Experts framework for ECL. SCE builds a skill base via Compositional Skill Grounding (CSG), which decomposes task demonstrations into reusable skills. Based on this, Dual Execution-and-Transition Experts (DETE) enable new task learning through skill composition, where one branch ensures skill execution and the other supports transitions between skills for coherent behavior. Experiments on LIBERO benchmarks and real-world manipulation tasks demonstrate that SCE consistently improves retention and overall task performance. Further feature drift analyses and ablation studies verify the effectiveness of our method. Project website: https://eqcy.github.io/sce/.

02.
arXiv (CS.AI) 2026-06-15

When Should Agent Trust Be Conditional? Characterizing and Attacking Skill-Conditional Reputation in Agent Swarms

arXiv:2606.14200v1 Announce Type: new Abstract: Open platforms increasingly route tasks among heterogeneous LLM agents–differing in base model, scaffold, and tool stack–whose competence varies sharply by skill: an agent excellent at one skill may be useless at another. The standard reputation approach summarizes each agent by a single global trust score, but that scalar is the wrong object here, because routing every task to the globally most-trusted agent leaves the value of specialization unclaimed. We study skill-conditional trust R(i | k)–the trust to place in agent i for a task requiring skill k, rather than one score per agent–and pose three falsifiable questions: when is conditioning worth it, how much cross-skill evidence should be borrowed, and whether that borrowing is safe. A controlled phase-diagram analysis answers the first two: conditional trust wins only in a specific regime–high agent heterogeneity, sparse per-skill evidence, and correlated skills–and the coupling strength beta that buys this data efficiency is dual-use, because the same cross-skill borrowing is also a laundering channel. On a public benchmark of 14 genuinely heterogeneous AppWorld agents, real pools land inside the beneficial regime–a small but genuine gain, with the per-skill best agent genuinely changing across skills. We then show that an attacker with cheap evidence in one skill and none in a target skill hijacks the conditional router, driving routing regret from 0 to 0.94 on a pool our zero-cost Conditional Information Value Test (CIVT) rates GREEN–while the ungated trust verdict it contaminates reads -0.06 instead of the honest +0.19. A zero-evidence gate bounds the attack but does not eliminate it; we characterize the residual cost under an explicit budget. We do not claim Sybil-resistance–we quantify the trade-off.

03.
arXiv (math.PR) 2026-06-16

The Winner Takes It All

arXiv:2606.16885v1 Announce Type: cross Abstract: The winner-takes-all (WTA) process takes place on an arbitrary graph. There is an agent on each vertex of the graph, and active agents at neighboring vertices play games. In each game, a randomly chosen agent wins, while the loser is eliminated from subsequent games. The games are played at random times; each game finishes instantaneously, and the games cease when each active agent has only losers among its neighbors. On the one-dimensional lattice, the fraction of winners in the final state is $e^{-1}$, and we also determine the fractions $w_j$ of winners who won $j=0, 1, 2$ games. For the WTA process on a segment, we determine statistics of the total number of winners (the average, the variance, and all higher cumulants), the probabilities of reaching the final state with the minimum or maximum number of winners, and establish the behavior near the boundaries. For infinite regular trees with vertices of degree $d$, i.e., Bethe lattices with coordination number $d$, the fraction of winners is $(2/d)^{d/(d-2)}$.

04.
arXiv (CS.CV) 2026-06-16

GraphWorld: Long-Horizon Planning with World Models for End-to-End Autonomous Driving

End-to-end autonomous driving has made significant progress by unifying perception, prediction, and planning within a single learning framework, achieving strong performance in short-horizon decision making. However, most existing E2E-AD methods remain confined to short-horizon planning and lack the ability to model long-term temporal dependencies, which severely limits their generalization and security in complex and highly interactive driving scenarios. In this work, we propose GraphWorld, an E2E-AD framework that explicitly enhances long-horizon planning through latent world modeling. We introduce an Ego-Centric Interaction Graph, which adaptively models critical neighboring agents based on spatial proximity, and propagates relational context to planning queries via cross-node cross-attention. We present a World-State-Conditioned Planning that learns ego-centric latent world representations by modeling interactions between an ego vehicle and surrounding agents. This latent world state captures key interaction dynamics and safety-relevant semantics, and serves as a conditioning signal to guide long-horizon, safety-aware trajectory planning. Extensive experiments on Bench2Drive, NAVSIMv1/2, and nuScenes demonstrate that GraphWorld significantly reduces collision rates and improves long-horizon planning performance, validating its effectiveness in complex driving environments.

05.
arXiv (quant-ph) 2026-06-19

Attosecond Path Qubits in High-Harmonic Generation: Classical Dephasing and Trace-Out Decoherence

arXiv:2606.20372v1 Announce Type: cross Abstract: High-harmonic generation (HHG) is governed by interference between electron trajectories. We propose that the dominant short and long trajectories define an experimentally addressable two-level subsystem: an attosecond path qubit (APQ). We formulate a trajectory-resolved density matrix to identify two distinct coherence-loss mechanisms: classical dephasing from ensemble averaging and quantum decoherence arising from the trace-out of unobserved degrees of freedom. By investigating shot-to-shot fluctuations and unresolved transverse momentum, we demonstrate that while dephasing suppresses coherence through averaging, the ``trace-out'' channel produces mixed states even for fixed driving parameters. We explore how these mechanisms modify APQ purity and show that mode selection and conditioning provide operational routes to isolate them. These results establish a reduced-state framework for diagnosing coherence loss in HHG and for engineering trajectory-based quantum states in attosecond interferometry.

07.
arXiv (quant-ph) 2026-06-11

Lowest order Carleman linearization for low Reynolds long-term behaviour of fluid flow simulations

arXiv:2605.23380v2 Announce Type: replace Abstract: It is shown that the lowest (second) order truncation of the Carleman linearization of the fluid equations (C2) recovers the late stage of the evolution, namely the steady-state solution, although to a decreasing degree of accuracy at increasing Reynolds number. This asymptotic property is first proved analytically for the decaying logistic with external forcing and then shown to hold to a significant degree of accuracy also for the more complex case of two-dimensional Kolmogorov-like fluid flow at low Reynolds numbers, below $Re \sim 10$. This time-asymptotic property may open interesting prospects for the quantum simulation of low-Reynolds steady-state fluid flows.

08.
medRxiv (Medicine) 2026-06-17

High burden of subclinical TB in Africa revealed from a postmortem cohort.

Tuberculosis (TB) is increasingly recognised as a spectrum of infection and disease, yet the prevalence of viable, asymptomatic Mycobacterium tuberculosis (M.tb) infection remains uncertain. Subclinical Tuberculosis (scTB), defined as microbiologically confirmed M.tb infection in the absence of recognised symptoms, is under detected by symptom, sputum and imaging-based approaches. We conducted postmortem examinations of 94 adults who died from non-infectious causes, none of whom were clinically suspected of TB or reported TB related symptoms prior to death. Lung and extrapulmonary tissues were cultured for M.tb. Viable M.tb was confirmed in six individuals, corresponding to a prevalence of 6.4% (95% CI: 2.4 to 13.4%). These findings provide direct tissue-based evidence that viable, asymptomatic M.tb infection can persist beyond the reach of conventional clinical detection. Our data suggest that a biologically active reservoir of infection may exist undetected within high-burden settings, with implications for surveillance strategies aimed at TB elimination.

09.
arXiv (CS.CV) 2026-06-16

Towards Next-Generation Healthcare: A Survey of Medical Embodied AI for Perception, Decision-Making, and Action

Foundation models have demonstrated impressive performance in enhancing healthcare efficiency across a wide range of medical applications. Nevertheless, their limited ability to perceive, understand, and interact with the physical world significantly constrains their effectiveness in real-world clinical workflows, where safety-critical decision-making and physical execution are tightly coupled. Recently, embodied artificial intelligence (AI) has emerged as a promising physical-interactive paradigm for intelligent healthcare, enabling agents to operate in complex medical environments. As research in this area rapidly expands, understanding how intelligent agents function as integrated, end-to-end systems in clinical environments becomes increasingly critical. However, existing surveys on medical embodied AI largely emphasize individual aspects or functional components, lacking a unified system-level organization of the field. To support and consolidate recent advances, we systematically survey the core components of medical embodied AI, with a particular emphasis on the coordinated integration of perception, decision-making, and action. We further review representative medical applications and relevant datasets, and we analyze the major challenges encountered in real-world clinical practice. Finally, we discuss key directions for future research in this rapidly evolving field. The associated project can be found at https://github.com/VMVLab/Medical_Embodied_AI_Paper_List.

10.
bioRxiv (Bioinfo) 2026-06-18

Bayesian modeling of longitudinal metatranscriptomes of broiler meat spoilage microbiomes shows shared predictive signature associated with spoilage at refrigerated temperatures

Microbial spoilage of packaged meat is driven by complex microbial succession and related metabolic activity, yet conventional shelf-life assessment is mainly based on shelf-life studies relying on culturing and sensory analysis. In routine quality assurance, results are obtained retrospectively, and they are only indirectly linked to the metabolic activity related to sensory deterioration. Functional, time informative approaches that capture the active metabolic state of the spoilage microbiome and predict the rate of spoilage are lacking. We developed a censoring-aware Gaussian process (CAGP) framework to model longitudinal pathway expression profiles from broiler meat metatranscriptomes collected over consecutive storage days at 4 or 6{degrees}C. Samples were annotated using odor-based sensory scores defining fresh, early-spoilage, and late-spoilage phases. Because observed zeros in pathway-level data may reflect non-detection rather than true absence, the model treats low values as left-censored observations below a detection threshold while estimating smooth temporal trajectories with uncertainty. In leave-one-out prediction within the 4{degrees}C time series, predicted sampling days differed from the true days by an average of 0.43 days, and predicted spoilage phases agreed with the sensory classification. Trajectories learned at 4{degrees}C also transferred to an independent 6{degrees}C time series at the spoilage-phase level, suggesting that shared functional spoilage programs are preserved despite temperature-dependent changes in spoilage rate. Cross-entropy ranking further identified pathway modules carrying time- and phase-informative signals across temperatures. Overall, this framework provides a probabilistic approach for linking metatranscriptomic functional dynamics to sensory spoilage progression, supporting shelf-life assessment beyond retrospective microbial enumeration.

11.
arXiv (CS.LG) 2026-06-12

An Empirical Study on Predictive Maintenance for Component X in Heavy-Duty Scania Trucks

arXiv:2606.12486v1 Announce Type: new Abstract: Condition-based Predictive Maintenance (PdM) for truck fleets has gained momentum in recent years. This maintenance strategy aims to minimize unplanned downtimes and reduce costs by monitoring the health status of vehicles and taking proactive action based on their condition. However, the implementation of condition-based PdM systems is challenging due to the large volume of data generated by the trucks, the inherent complexity of detecting failures through sensor data and the difficulties in finding cost-effective trade-offs in the solution's implementation. In this paper, we define and validate a condition-based PdM methodology built on the assumption that the wear-and-tear state of the monitored component can be represented as a monotonically non-decreasing time series. It involves selecting only the most recent observations from the time series and transforming them into a tabular format for classification using machine learning (ML) models designed for tabular data. Our results indicate that the proposed methodology reduces costs on the Scania Component X dataset compared to current state-of-the-art (SOTA) approaches, while also simplifying the modeling process through AutoML.

12.
arXiv (CS.LG) 2026-06-16

DemoDiffusion: One-Shot Human Imitation using pre-trained Diffusion Policy

arXiv:2506.20668v3 Announce Type: replace-cross Abstract: We propose DemoDiffusion, a simple method for enabling robots to perform manipulation tasks by imitating a single human demonstration, without requiring task-specific training or paired human-robot data. Our approach is based on two insights. First, the hand motion in a human demonstration provides a useful prior for the robot's end-effector trajectory, which we can convert into a rough open-loop robot motion trajectory via kinematic retargeting. Second, while this retargeted motion captures the overall structure of the task, it may not align well with plausible robot actions in-context. To address this, we leverage a pre-trained generalist diffusion policy to modify the trajectory, ensuring it both follows the human motion and remains within the distribution of plausible robot actions. Unlike approaches based on online reinforcement learning or paired human-robot data, our method enables robust adaptation to new tasks and scenes with minimal effort. In real-world experiments across 8 diverse manipulation tasks, DemoDiffusion achieves 83.8\% average success rate, compared to 13.8\% for the pre-trained policy and 52.5\% for kinematic retargeting, succeeding even on tasks where the pre-trained generalist policy fails entirely. Project page: https://demodiffusion.github.io/

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

Attention is Just Another Name for Coupling?: A Fast-Slow ODE Perspective on Hierarchical Pretraining

arXiv:2606.16730v1 Announce Type: cross Abstract: Causal self-attention is a coupling mechanism: each token's hidden state is updated by a learned mixture of preceding tokens at the same timescale. This paper asks whether a second, temporally slower coupling-a slow sub-system operating on a temporally-downsampled view of the sequence and fed back into the fast path through a zero-initialised gate-complements it. The question is framed in the language of singularly perturbed ordinary differential equations (ODEs), where the fast variable $x$ evolves at the token rate, the slow variable $y$ evolves at one update per $P$ tokens, and the timescale ratio $\varepsilon = 1/P$ is enforced structurally by causal block-mean pooling. The paper instantiates the fast-slow ODE formalism as a concrete neural network: a fast path of standard causal attention over $T$ tokens, a slow path of full attention over $T/P$ pooled tokens ($P^2 \times$ cheaper per layer), and a zero-initialised additive gate. In addition, under a linear-generator assumption on the fast dynamics, we prove that the equilibrium manifold $x = \phi(y)$ is exactly the master-equation (ME) stationary distribution $p_{\mathrm{st}}(y)$; in that regime a learned MLP $\phi_\theta(y)$ is a variational approximation of it (the trained block is not a generator, so this identity is the structured limit, not a claim about the network as trained). Empirically, at $500$k tokens the coupling is neutral – the gate stays closed and the coupled and frozen ablations are within run-to-run noise – at a wall-clock cost comparable to a dense baseline. The contribution is the precise, gap-marked mapping itself, not a performance gain.

14.
arXiv (CS.LG) 2026-06-16

Prediction of Runtime Parameters of Parallel Chemistry Applications via Active and Generative Learning

arXiv:2606.16226v1 Announce Type: new Abstract: In this work, we develop two main Machine Learning based approaches to predict the runtime parameters of highly scalable parallel chemistry computations.These approaches employ active and generative learning together with the empirically determined gradient boosted regression tree models chosen among a rich suite of machine learning models. When evaluated on Coupled-Cluster with Singles and Doubles computations, our models achieve a mean absolute error percentage (MAPE) as low as 0.023 and a coefficient of determination as high as 99.9%. Furthermore, when combined with active learning to mitigate the lack of large amounts of training data, our models score a MAPE about 0.2 with 20-25% of the original dataset.

15.
arXiv (CS.AI) 2026-06-18

Optimizing Lithium Production Decisions under Geological, Demand, and Pricing Uncertainties: A POMDP Framework for Multi-Objective Decision Making

arXiv:2606.18598v1 Announce Type: new Abstract: Decision making in lithium production is challenging, whether from an investor's perspective or a strategic production standpoint. Determining which mines to open and when to open them involves not only geological and price uncertainties, but also complexities around the choice of extraction method, from direct lithium extraction to hard rock mining. Prior work explored models of this problem and different methods to optimize mining decisions; these models did not account for uncertainty in pricing, uncertainty in demand, or different mining technologies to extract lithium. Incorporating different pricing models and extraction technology into these models enables more robust strategies for determining not only when and where to open a mine, but also which method of production to pursue. We frame the problem as a partially observable Markov decision process (POMDP) and solve using belief state planning methods to get optimal decision making. In our study, we show that POMDP solvers outperform human inspired heuristics by dynamically adapting to shifting lithium price regimes (static, linear, exponential, and stochastic) through belief state planning and explicit uncertainty management. By optimally sequencing exploration, production, and technology choice, the framework achieves higher demand fulfillment and more balanced economic environmental outcomes over the projects lifetime in all different pricing and deposit scenarios.

16.
arXiv (CS.LG) 2026-06-18

Stochastic Thermodynamics and SDE-based Generative Models

作者:

arXiv:2606.18290v1 Announce Type: cross Abstract: SDE-based generative models, including diffusion models and the Schrödinger bridge, have found broad applications in signal processing tasks such as speech enhancement, image restoration, and time-series generation. This note presents a modeling framework for such models within the context of stochastic thermodynamics. The main results of this note are trajectory-level definitions of work, heat, and entropy production, along with a generalized Jarzynski identity and a second-law-like inequality. The proposed framework extends the original Jarzynski setup to accommodate time-dependent bath temperature and nonconservative driving forces. This thermodynamic perspective may deepen our understanding of diffusion models and the Schrödinger bridge from a nonequilibrium statistical mechanics viewpoint.

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

TACOMORE: Exploring a replicable prompting protocol for LLM-assisted corpus analysis

As corpus linguistics continues to scale, researchers are facing a growing methodological bottleneck: while computational tools can easily count billions of words, the qualitative interpretation of these data remains a slow and labor-intensive human task. Large Language Models (LLMs) offer a promising way to automate this process, yet their integration into the field is often hindered by concerns over black-box unpredictability and a lack of replicability. This study introduces TACOMORE, a structured prompting framework designed to transform ad-hoc AI interactions into a standardized linguistic protocol. Built upon four foundational principles (Task, Context, Model, and Replicability), the framework guides LLMs to move beyond generic probability prediction to anchoring their reasoning in the specific co-occurrence patterns of a target corpus. We applied this framework to three core corpus tasks, i.e., the analysis of keywords, collocates, and concordances, using an open corpus of COVID-19 research abstracts. After testing three LLMs, we found that while structured prompting improves accuracy and replicability, inherent limitations regarding hallucination persist. This research offers a critical lens into the role of LLMs in corpus linguistics, highlighting their potential as complementary tools while emphasizing the irreplaceable role of human validation.

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

Depth-Width tradeoffs in Algorithmic Reasoning of Graph Tasks with Transformers

Transformers have revolutionized the field of machine learning. In particular, they can be used to solve complex algorithmic problems, including graph-based tasks. In such algorithmic tasks a key question is what is the minimal size of a transformer that can implement the task. Recent work has begun to explore this problem for graph-based tasks, showing that for sub-linear embedding dimension (i.e., model width) logarithmic depth suffices. However, an open question, which we address here, is what happens if width is allowed to grow linearly, while depth is kept fixed. Here we analyze this setting, and provide the surprising result that with linear width, constant depth suffices for solving a host of graph-based problems. This suggests that a moderate increase in width can allow much shallower models, which are advantageous in terms of inference and train time. For other problems, we show that quadratic width is required. Our results demonstrate the complex and intriguing landscape of transformer implementations of graph-based algorithms. We empirically investigate these trade-offs between the relative powers of depth and width and find tasks where wider models have the same accuracy as deep models, while having much faster train and inference time due to parallelizable hardware.

19.
Nature (Science) 2026-06-10

Daily briefing: Ancient ground squirrels ate like ‘zombies of the Pleistocene’

作者:

Evidence from fossilized poo reveals the diverse diet of ancient ground squirrels. Plus, the science behind the peptide craze and our innate tendency to wander anticlockwise. Evidence from fossilized poo reveals the diverse diet of ancient ground squirrels. Plus, the science behind the peptide craze and our innate tendency to wander anticlockwise.

20.
arXiv (CS.AI) 2026-06-18

Analysing drivers and interdependencies in European electricity markets using XAI

arXiv:2606.19118v1 Announce Type: new Abstract: Electricity markets are inherently complex systems characterised by strong nonlinearities, high-dimensional interactions, and increasing interdependence across regions. While deep neural networks (DNNs) have demonstrated strong predictive capabilities for electricity prices, their lack of interpretability limits their usefulness for understanding the underlying drivers of price formation. This paper addresses this gap by combining DNN models with explainable artificial intelligence (XAI) techniques to analyse the determinants of electricity prices across 39 European bidding zones. We employ SHAP (SHapley Additive exPlanations) to quantify feature contributions and apply and extend SSHAP, an aggregation framework to improve interpretability in high-dimensional settings. The analysis identifies that renewable energy sources, particularly solar, play a disproportionately important role in price formation despite their lower share in total power generation. Gas prices remain a dominant and consistent driver across electricity markets, while interconnections significantly shape price dynamics, highlighting the strong interdependence of European electricity systems. In addition, a synthetic EU-wide electricity market is constructed to explore the counterfactual scenario of a fully integrated market with a single price.

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

RankGraph-2: Lifecycle Co-Design for Billion-Node Graph Learning in Recommendation

arXiv:2606.18379v1 Announce Type: cross Abstract: Graph-based retrieval at billion-node scale requires jointly solving three tightly coupled problems – graph construction, representation learning, and real-time serving – yet existing work addresses each in isolation. We present RankGraph-2, a framework deployed at Meta that co-designs all three lifecycle stages for similarity-based retrieval (U2U2I and U2I2I), where each stage's requirements shape the others. Serving requires a co-learned cluster index to avoid expensive online KNN – this pushes index co-training into the training objective. Training benefits from the observation that similarity-based retrieval tolerates pre-computed neighborhoods, eliminating online graph infrastructure – this requires construction to produce self-contained data. Construction must also support hour-level refresh for item coverage. Acting on these cascading requirements, RankGraph-2 reduces hundreds of trillions of edges to hundreds of billions via subsampling with popularity bias correction, pre-computes multi-hop neighborhoods via personalized PageRank, and co-learns a residual-quantization cluster index that reduces serving computational cost by 83%. This lifecycle co-design enables a simple architecture to achieve 3.8 x higher recall than a GAT + Deep Graph Infomax model on a bipartite graph and 2.1 x higher than PyTorch-BigGraph on item retrieval. RankGraph-2 delivers up to +0.96% CTR and +2.75% CVR, and has powered 20+ retrieval launches across major surfaces.

23.
bioRxiv (Bioinfo) 2026-06-18

pykarambola: Minkowski tensor morphometry of 3D structures

Three-dimensional biological morphologies encode functional and physiological state, yet the directional, orientational, and topological properties of these shapes are rarely captured by morphometric tools available for bioimage analysis. Minkowski tensors are mathematically rigorous tensor-valued measures that encode surface curvature and directionality for objects of arbitrary topology, with tensor eigensystems that directly quantify elongation axes and anisotropy. A C++ implementation, karambola, computes Minkowski tensors for triangulated surfaces but is inaccessible within Python-based bioimage workflows. Here we present pykarambola, a pip installable Python package that accepts NumPy arrays and standard mesh formats and returns Minkowski tensors, including derived anisotropy and orientation quantities. A high-level label-image API converts 3D integer arrays into per-object Minkowski tensors in a single call, making pykarambola directly compatible with the output of widely used segmentation tools. An optional Cython extension accelerates graph-traversal steps of mesh initialization for large-scale analyses. Benchmarked on 1,584 adrenal gland meshes, pykarambola reproduces all 121 C++ karambola output features to near-floating-point agreement and, in the pure-Python build, is 2.8x faster at 28^3 and 1.5x faster at 64^3 voxel resolution, with speedups primarily attributable to karambola's sequential per-object file I/O. pykarambola is freely available as an open-source software package.

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

On the Variance of Temporal Difference Learning and its Reduction Using Control Variates

arXiv:2606.20357v1 Announce Type: new Abstract: We analyze the variance of temporal difference (TD) learning using the phased setting with tabular representation, and show that one of the mechanisms behind its ability to reduce variance is by effectively aggregating over a larger number of independent trajectories. Based on this insight, we demonstrate that (1) the variance of TD is asymptotically bounded from above by Monte Carlo (MC) estimators, and (2) shorter horizon updates incurs less variance for a fixed number of samples. Beyond TD, we show that Direct Advantage Estimation (DAE), a method for estimating the advantage function, can be seen as a type of regression-adjusted control variate, which achieves a tighter bound on the variance compared to TD in the large-sample limit. Finally, we numerically illustrate the behaviors of these estimators with carefully designed environments.

25.
arXiv (quant-ph) 2026-06-15

Compact graphs and quantum automorphisms

arXiv:2606.13928v1 Announce Type: new Abstract: Compact graphs are graphs for which the fractional automorphism polytope has no genuinely fractional vertices. This paper proposes a quantum analogue of this idea by evaluating the fundamental magic unitary of the quantum automorphism group on states, which we show to produce a closed convex set of doubly stochastic matrices sitting between the classical automorphism polytope and the full fractional automorphism polytope. Our main result is that the natural quantum analogue of compactness is classical, that is, a quantum compact graph is classically compact. We also relate this set to the quantum orbital algebra and obtain a hierarchy of classical and quantum compactness pseudo notions. The framework recovers familiar consequences of compactness through commutants and suggests quantum analogues of generous transitivity and distance-transitivity. We also isolate examples and open problems indicating where quantum symmetries may strictly refine the classical compactness theory.