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01.
arXiv (quant-ph) 2026-06-19

Asymmetric and chiral dynamics of two-component anyons with synthetic gauge flux

arXiv:2512.19139v3 Announce Type: replace-cross Abstract: In this work, we investigate the non-equilibrium dynamics in a one-dimensional two-component anyon-Hubbard model, which can be mapped to an extended Bose-Hubbard ladder with density-dependent hopping phase and synthetic gauge flux. Through numerical simulations of two-particle dynamics and the symmetry analysis, we reveal the asymmetric transport with broken inversion symmetry and two dynamical symmetries in the expansion dynamics. The expansion of two-component anyons is dynamically symmetric under spatial inversion and component flip, when the sign of anyonic statistics phase or the signs of gauge flux and interaction are changed. In the non-interacting case, we show the dynamical suppression induced by both the statistics phase and gauge flux. In the interacting case, we demonstrate that both chiral and antichiral dynamics can be exhibited and tuned by the statistics phase and gauge flux. The dynamical phase regimes with respect to the chiral-antichiral dynamics are obtained. These findings highlight the rich dynamical phenomena arising from the interplay of anyonic exchange statistics, synthetic gauge fields, and interactions in multi-component anyons.

02.
arXiv (CS.LG) 2026-06-25

Laplace–Fisher Gate Identities for Optimal Matrix-Gated Blended Score Estimation

arXiv:2606.25169v1 Announce Type: cross Abstract: Sampling from an unnormalized target by reversing an Ornstein–Uhlenbeck diffusion requires the score of each noise-perturbed marginal. Tweedie's identity and a target-score identity give unbiased finite-reference estimators for this score. Scalar blends can reduce variance, but are too rigid for singular or strongly anisotropic targets. We cast blended score estimation as conditional risk minimization over matrix-valued blending coefficients, or gates, and derive the variance-optimal gate [ \Gstar(y,t)=\alphat^2\bigl(\alphat^2 I_d+\gammat,\E[H_0(X_0)\mid Y_t=y]\bigr)^{-1},\qquad H_0=-\nabla^2\log p_0 . ] Here (\alphat=e^{-t}) and (\gammat=1-e^{-2t}). We call this formula the Laplace–Fisher Gate Identity (\operatorname{LFGI}{}). Since the Tweedie–TSI disagreement has conditional mean zero, the gate changes estimator variance without changing its expected value. We give the Gaussian special case and prove finite-reference consistency and stability bounds for estimating the gate from weighted reference samples. We apply the finite-reference LFGI estimator to normalized density evaluation for Bayesian inverse problems. When MCMC pilot samples and derivative information are available, LFGI uses these byproducts to construct a normalized posterior-density surrogate. The surrogate enables posterior-energy evaluation, model-evidence estimation, and density-based diagnostics beyond those available from samples alone. On a PDE-constrained inverse-problem benchmark, LFGI improves posterior-density calibration and sampling diagnostics relative to the other tested score-estimator classes, and known-evidence experiments check absolute calibration in Gaussian and non-Gaussian settings.

03.
arXiv (CS.LG) 2026-06-16

How Controlling the Variance can Improve Training Stability of Sparsely Activated DNNs and CNNs

arXiv:2602.05779v2 Announce Type: replace Abstract: The Edge-of-Chaos (EoC) theory developed for the random initialization of deep networks allows more efficient training by both preserving information in the initial outputs of the network and minimising exploding or vanishing gradients through characterisation of the intermediate layers as Gaussian processes. This EoC theory provides formulae for the choice of the initialisation distribution variances of the weights and biases. For activations which are approximately linear around the origin, the EoC theory typically encourages the Gaussian process variance to converge towards zero with increasing depth. Here we consider the less studied setting of highly sparsity inducing activations where a large region of values near the origin are set to zero. In this setting we prove a new phenomenon whereby initialisations leading to larger fixed Gaussian processes are beneficial to training stability. This theory informs a new, yet simple, initialisation strategy that allows training DNNs and CNNs with as large as 90\% sparsity in the hidden layers.

04.
arXiv (quant-ph) 2026-06-17

Quantum Information Processing: A brief overview on Quantum Teleportation

作者:

arXiv:1604.00852v3 Announce Type: replace Abstract: Quantum Information Processing (QIP) exploits the principles of quantum mechanics to perform information storage, communication, and computation in ways that are fundamentally impossible within classical frameworks. This article presents a pedagogical overview of the mathematical foundations of quantum information theory, including qubits, Hilbert spaces, linear operators, quantum measurements, tensor products, density operators, and quantum entanglement. Building upon these concepts, we provide a detailed introduction to quantum teleportation, one of the most remarkable protocols in quantum communication. The discussion covers the no cloning theorem, the original teleportation protocol by Bennett et al., experimental realisations of quantum teleportation, and extensions involving probabilistic and multiqubit teleportation schemes. Particular emphasis is placed on the role of entanglement as a communication resource, together with the study of teleportation channels based on bipartite and multipartite quantum states. Various quantitative measures of entanglement, including concurrence, negativity, entanglement of formation, and relative entropy of entanglement, are reviewed alongside teleportation fidelity as a performance metric. Furthermore, the interplay between Bell nonlocality, mixed state entanglement, and teleportation efficiency is examined, followed by a survey of advanced developments such as controlled teleportation, bidirectional teleportation, cluster state teleportation, and recent advances in the Quantum 2.0 era. This review aims to provide students, researchers, and engineers with a coherent introduction to the theoretical foundations and practical significance of quantum teleportation in emerging quantum technologies.

05.
arXiv (CS.LG) 2026-06-17

Credibility-Weighted Pricing of Autonomous Vehicle Liability Under Operational Design Domain Shift

作者:

arXiv:2606.17451v1 Announce Type: new Abstract: Automated Driving System deployments create a foundational ratemaking challenge: sparse experience, shifting operational design domains, and non-stationary risk across software releases. We propose a hierarchical Bayesian credibility framework pooling across cities, software versions, and territories via a learned ODD-similarity kernel, nesting Buhlmann-Straub as a limiting case. Demonstrated on 648 verified-engaged Waymo crashes across four U.S. metros from the NHTSA Standing General Order database against 116 million matched miles, city-aggregate credibility weights are moderate (0.12-0.46), partial pooling decisively outperforms no pooling, and a power analysis shows the learned kernel's advantage becomes detectable at approximately twelve deployed cities.

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

Certified Robust Invariant Polytope Training in Neural Controlled ODEs

arXiv:2408.01273v3 Announce Type: replace Abstract: We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over $50$ states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.

07.
arXiv (CS.LG) 2026-06-12

Physics-Informed Neural Networks for Chemotherapy Pharmacokinetics: Benchmarking the Clinical Estimator and Exposing Parameter Identifiability

arXiv:2606.12658v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) are an attractive tool for partial-observation problems in biology, where the governing dynamics are known but some compartments cannot be measured. Chemotherapy pharmacokinetics (PK) is a clean instance: drug concentration in plasma is routinely measured, but concentration in tissue – which determines tumour kill and off-target toxicity – is not. We benchmark a PINN against the standard clinical baseline (nonlinear least-squares on the analytical biexponential plasma solution, hereafter NLS) and a physics-agnostic neural baseline (a data-only MLP) on two PK problems. On the linear two-compartment problem, NLS is near-optimal; the PINN matches it to within a small constant factor while also producing the tissue curve in a single training pass, whereas the data-only MLP fails on tissue by roughly 10x. On a Michaelis-Menten extension (saturable elimination), the biexponential closed form no longer exists, so NLS is mis-specified and silently returns meaningless rate constants. The PINN instead exposes a deeper fact: the Michaelis-Menten two-compartment model is non-identifiable from plasma alone, and the PINN reports this honestly by converging to a basin with k12 -> 0. Adding two sparse tissue observations largely resolves identifiability: across five seeds the PINN recovers k21 to within 1% of truth and Vmax, Km to within one standard-deviation bar, while k12 moves in the correct direction (0.02 -> 0.82) but remains ~2 sigma below truth – a recovery the closed-form NLS estimator cannot attempt at all, because its biexponential ansatz describes only plasma. Our claim is not that PINNs beat NLS. It is that PINNs offer a uniform recipe that ties the textbook estimator on the textbook problem, exposes structural identifiability that the textbook estimator hides, and absorbs heterogeneous measurements within a single loss.

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

Graph-ESBMC-PLC: Formal Verification of Graphical PLCopen XML Ladder Diagram Programs Using SMT-Based Model Checking

PLCopen XML defines two encoding formats for IEC 61131-3 Ladder Diagram programs: a textual encoding using elements, and a graphical encoding that represents rung logic as a directed graph of localId/refLocalId connections. ESBMC-PLC supported the textual format but parsed graphical exports from CONTROLLINO, Beremiz, and OpenPLC Editor into an empty GOTO intermediate representation, causing vacuous verification success. This paper presents Graph-ESBMC-PLC, which closes this gap with a DFS-based graphical LD resolver. The resolver traverses the connection graph from leftPowerRail to each coil, extracts rung paths as Boolean contact conjunctions, and applies a three-tier I/O inference scheme. Ordering coils by rightPowerRail connectionPointIn sequence ensures SET coils process before RESET coils, matching IEC scan-cycle semantics. The graphical-to-IR conversion leaves the ESBMC backend unchanged. Validation on 3 graphical LD programs from CONTROLLINO/OpenPLC Editor shows all produce full GOTO IR with nondeterministic inputs and rung logic, versus the empty IR previously. All 3 verify SAFE at k=2 under 70ms. The 11 textual LD benchmarks are fully preserved, with no regression. Two Beremiz examples with no LD content or unsupported timer semantics are reported as discovered limitations. Artifact at Zenodo (DantasCordeiro2026graphical, doi:10.5281/zenodo.20699856).

09.
arXiv (CS.LG) 2026-06-19

A fast direct solver based neural network for solving PDEs

arXiv:2606.19895v1 Announce Type: cross Abstract: The matrices arising from large scale $N$-body problems can be efficiently represented using hierarchical matrices, whose key idea is that the admissible off-diagonal sub-matrices can be well approximated by low-rank matrices across a hierarchy of matrix partitions. HODLR (Hierarchical Off-Diagonal Low-Rank) matrices are a subclass of hierarchical matrices in which all off-diagonal submatrices at every level of a recursive binary partition are low-rank. In this article, we present a neural network that learns the inverse operation of HODLR matrices based on the fast direct solver for HODLR matrices developed by Ambikasaran and Darve (2013). We further extend the architecture to learn nonlinear solution operators associated with PDEs by replacing some of the linear layers with deep sub-networks. We demonstrate the performance of the proposed architecture by performing a comprehensive set of experiments that include (i) solving a linear problem such as the Fredholm integral equation of the second kind, (ii) solving PDEs such as the nonlinear Schrödinger equation, Burgers' equation, and the steady-state Darcy's flow equation, (iii) generalization study across varying parameter values, (iv) comparing the inference time of the proposed network with the run time of a classical numerical solver, and (v) comparing the proposed network with some of the existing neural operator learning networks.

10.
arXiv (math.PR) 2026-06-12

Sphere Packings in Higher Dimension (after Boaz Klartag)

arXiv:2606.13313v1 Announce Type: cross Abstract: Let $\delta_n^L$ be the maximal density of a lattice sphere packing in the $n$-dimensional Euclidean space. We explain how Boaz Klartag proved the inequality $\delta_n^L \geq c n^2 2^{-n}$ where $c>0$ is a universal constant. In higher dimension, even for non-lattice sphere packings, this new lower bound is a substantial improvement. Klartag's proof uses the probabilistic method in two different ways. The first, very standard, relies on the statistical properties of a uniformly chosen random lattice. The second, completely new, studies the stochastic evolution of an ellipsoid constrained to contain non nonzero lattice points in the interior.

11.
arXiv (quant-ph) 2026-06-17

Pulse-optimised circuit elements for scalable and noise-resilient quantum chemistry

arXiv:2606.17357v1 Announce Type: new Abstract: Useful chemistry calculations on near-term quantum processors are hindered by current algorithmic runtimes. We develop a methodology to significantly reduce these runtimes. Typically, variational quantum eigensolver (VQE) algorithms are implemented as sequences of primitive gates. Our methodology instead relies on gradient-ascent pulse engineering to construct hardware-tailored pulses for the direct implementation of VQEs. As problem sizes increase, it quickly becomes intractable to optimise a pulse that implements an entire VQE ansatz circuit. However, leading VQEs are constructed in a modular fashion. A problem-tailored VQE is assembled from parameterised circuit elements that simulate hopping between two or four electronic spin orbitals. We show that these circuit elements can be implemented more efficiently using hardware-tailored pulses. We numerically demonstrate our methodology on a silicon spin-qubit quantum processor. We find that common circuit elements, known as single- and double-qubit excitations, can be implemented in less than 289 ns and 927 ns, respectively. Compared with conventional gate-based implementations, our pulse-accelerated qubit excitations provide a scalable approach for faster and therefore more noise-robust quantum chemistry simulations by reducing VQE runtimes by up to a factor of 15.3.

12.
arXiv (quant-ph) 2026-06-25

From Meta Idea to Advanced Mathematical Discovery – Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms

arXiv:2606.24899v1 Announce Type: cross Abstract: AI-assisted mathematics is often evaluated on solving predefined problems. In practice, however, many important advances begin earlier, when a vague research intuition is transformed into a concrete problem, a promising route, and a theorem family worth proving. This report studies that stage through a case study that led to sign-embedding quantum algorithms for matrix equations and matrix functions, foundational primitives in quantum linear algebra and operator-output quantum algorithms. The project began with a human-originated intuition that rational approximation is especially effective for jump-type functions such as the sign function, and might therefore serve as a design principle for quantum algorithms. Rather than merely assisting after the problem was fixed, AI-assisted exploration, including workflows later integrated into the agentic AI-mathematician system AIM, played a key role in expanding this intuition into a route map, comparing candidate formulations, and converging toward sign embedding as the central framework. AIM then helped connect a known matrix-sign identity to wider classes of matrix equations and matrix functions, and drafted proof and complexity calculations. The decisive scientific judgments remained human: selecting which human-AI-expanded routes were worth pursuing, rejecting a Cayley-trapezoidal approximation when its validity required a hidden condition, and refining the Sylvester implementation from a coarse quadratic-gap query route to the final factorized and scaled analysis. The report argues that human-AI co-discovery workflows, with systems such as AIM as important components, are most valuable not as standalone theorem provers, but as research partners for problem formation, connection discovery, derivation, and skeptical review inside a human-gated research loop.

13.
arXiv (CS.LG) 2026-06-18

When Does Trajectory-Level Supervision Permit Efficient Offline Reinforcement Learning?

arXiv:2606.18531v1 Announce Type: cross Abstract: Offline reinforcement learning is typically analyzed under process-level reward supervision, yet many sequential decision datasets record only trajectory-level outcomes. We develop a statistical theory for offline policy optimization from such outcome-level supervision. We first study the canonical setting where the target remains the expected cumulative reward, but each offline trajectory provides only a scalar label whose conditional mean is the cumulative return. We propose OPAC, a pessimistic actor-critic algorithm that learns a latent reward model and optimizes a policy from trajectory-level labels. We prove a high-probability guarantee of order $\widetilde O(H^2\sqrt{C_{sa}(\pi^\star)/n})$ and a matching lower bound, characterizing the sharp statistical cost of replacing process-level rewards with one trajectory-level label. We then extend the principle to preference-based feedback, preserving the leading horizon and concentrability dependence up to preference-model constants. Finally, we study generalized outcome-based offline RL, where both the supervision and the objective are trajectory-level quantities induced by a nonlinear aggregation of latent per-step rewards. This problem is not learnable in general: for all-success objectives, any offline learner may require $\Omega(2^H)$ trajectories even with deterministic transitions and constant concentrability. We then identify a tractable regime through two structural coefficients, $\kappa_\mu(\sigma)$ and $\chi_\mu(\sigma)$, capturing information loss in outcome aggregation and generalized Bellman updates, under which generalized OPAC achieves polynomial sample complexity. Together, our results delineate when outcome-level supervision enables sample-efficient offline control and when missing process-level rewards create fundamental statistical barriers.

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

Modelling magnetic material properties with uncertainty-aware neural networks

arXiv:2606.11870v1 Announce Type: cross Abstract: Machine learning is increasingly applied to accelerate the discovery of novel materials by exploring large compositional and structural design spaces. Yet, the scarcity of high-quality data and the frequent need for out-of-distribution prediction introduce substantial uncertainty, making the assessment of model reliability essential. In this work, we investigate uncertainty quantification as a means to evaluate model confidence in the context of permanent magnet research. In a first study, we benchmark classical and modern machine learning models for predicting intrinsic magnetic properties, focusing on the quality of their uncertainty estimates. We apply Gaussian negative log-likelihood loss and dropout-based Bayesian approximation as practical strategies for estimating predictive uncertainty. In a second study, we transfer these architectural features for uncertainty estimation to a more complex task: predicting coercivity from microstructural information using a graph neural network. Together, these studies demonstrate that uncertainty quantification not only enhances the trustworthiness of predictions but is also transferable across different modeling tasks.

15.
arXiv (quant-ph) 2026-06-16

MAPS: A Novel Multi-Axial Projective Sphere for Geometrically Visualizing Higher d-Valued Quantum State-Space of Qudits

arXiv:2606.15801v1 Announce Type: new Abstract: Visualizing the d-valued quantum state-space of quantum systems serves as a foundational pillar for the scientific research and practical applications in quantum computing and information science, where d >= 2. The 2-valued quantum states of a qubit are elegantly visualized on the three-dimensional Bloch sphere. In contrast, expanding this geometrical paradigm to visualize higher d-valued quantum states of a qudit (d >= 3), e.g., a qutrit (d=3), ququadit (d=4), and quintit (d=5), leads to severe structural and topological complexities. This paper introduces a new generalized three-dimensional framework to effectively visualize higher d-valued quantum states of a qudit, in the aspects of ease of illustration, structural simplicity, and natural representation for researchers and engineers. We called this new framework the "multi-axial projective sphere (MAPS)", which consists of n projectional intersecting spatial axes, where d-1

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

Benchmarking Counterfactual Prediction in Epidemic Time Series with Time-Varying Interventions

arXiv:2606.05692v2 Announce Type: replace-cross Abstract: Deep learning has enabled significant advances in time-series causal inference, yet progress remains constrained by the lack of realistic benchmarks with observable counterfactual outcomes. Existing datasets either rely on real-world observations without ground-truth counterfactuals or on simplified simulations that fail to capture complex causal dynamics. To address this gap, we develop a large-scale benchmark for counterfactual prediction in epidemic time series under dynamic interventions. Unlike existing benchmarks, it supports static and time-varying treatments, as well as both single-policy and multi-policy intervention settings, enabling evaluation of causal inference methods across a broad range of causal inference scenarios. Leveraging a calibrated agent-based model grounded in real-world demographic, mobility, epidemiological, and policy data, we generate realistic counterfactual trajectories across more than 150 U.S. counties. Using this benchmark, we evaluate widely used and state-of-the-art causal inference methods, revealing substantial performance differences and highlighting the challenges of realistic time-series causal reasoning.

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

ReproRepo: Scaling Reproducibility Audits with GitHub Repository Issues

Reproducing research results from papers and released code is central to scientific progress. Existing works have introduced benchmarks to evaluate whether LLM agents can assist with reproducibility, but they are difficult to scale due to their reliance on substantial manual effort for data curation and evaluation. We introduce ReproRepo, a scalable framework for reproducibility evaluation that leverages human-raised GitHub issues as naturally occurring supervision on realistic reproduction blockers. We instantiate ReproRepo on 1,149 recent machine learning papers from major conferences and evaluate four frontier model-agent configurations. Our results show that LLM agents, even without executing code, can identify many real-world reproducibility problems from paper-repository pairs: the best agent in our study, namely Codex with GPT-5.5, surfaces at least one semantically related human-reported blocker for ~90% of papers in the study. Further analysis shows that agents are particularly effective for surfacing visible failures and identifying the right semantic region, but may still be insufficient in exact localization. ReproRepo can serve as a reusable, scalable framework for future evaluations of LLM agents on real-world reproducibility auditing. Our code is released at https://github.com/LithiumDA/ReproRepo.

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

Token Reduction Should Go Beyond Efficiency in Generative Models – From Vision, Language to Multimodality

arXiv:2505.18227v4 Announce Type: replace-cross Abstract: In Transformer architectures, tokens\textemdash discrete units derived from raw data\textemdash are formed by segmenting inputs into fixed-length chunks. Each token is then mapped to an embedding, enabling parallel attention computations while preserving the input's essential information. Due to the quadratic computational complexity of transformer self-attention mechanisms, token reduction has primarily been used as an efficiency strategy. This is especially true in single vision and language domains, where it helps balance computational costs, memory usage, and inference latency. Despite these advances, this paper argues that token reduction should transcend its traditional efficiency-oriented role in the era of large generative models. Instead, we position it as a fundamental principle in generative modeling, critically influencing both model architecture and broader applications. Specifically, we contend that across vision, language, and multimodal systems, token reduction can: (i) facilitate deeper multimodal integration and alignment, (ii) mitigate "overthinking" and hallucinations, (iii) maintain coherence over long inputs, and (iv) enhance training stability, etc. We reframe token reduction as more than an efficiency measure. By doing so, we outline promising future directions, including algorithm design, reinforcement learning-guided token reduction, token optimization for in-context learning, agentic framework design, and broader ML and scientific domains.

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

Colon-Bench: An Agentic Workflow for Scalable Dense Lesion Annotation in Full-Procedure Colonoscopy Videos

Early screening via colonoscopy is critical for colon cancer prevention, yet developing robust AI systems for this domain is hindered by the lack of densely annotated, long-sequence video datasets. Existing datasets predominantly focus on single-class polyp detection and lack the rich spatial, temporal, and linguistic annotations required to evaluate modern Multimodal Large Language Models (MLLMs). To address this critical gap, we introduce Colon-Bench, generated via a novel multi-stage agentic workflow. Our pipeline seamlessly integrates temporal proposals, bounding-box tracking, AI-driven visual confirmation, and human-in-the-loop review to scalably annotate full-procedure videos. The resulting verified benchmark is unprecedented in scope, encompassing 528 videos, 14 distinct lesion categories (including polyps, ulcers, and bleeding), over 300,000 bounding boxes, 213,000 segmentation masks, and 133,000 words of clinical descriptions. We utilize Colon-Bench to rigorously evaluate state-of-the-art MLLMs across lesion classification, Open-Vocabulary Video Object Segmentation (OV-VOS), and video Visual Question Answering (VQA). The MLLM results demonstrate surprisingly high localization performance in medical domains compared to SAM-3. Finally, we analyze common VQA errors from MLLMs to introduce a novel "colon-skill" prompting strategy, improving zero-shot MLLM performance by up to 9.7% across most MLLMs. The dataset and the code are available at https://abdullahamdi.com/colon-bench .

20.
arXiv (quant-ph) 2026-06-12

Exceptional Points as Manifestations of Analyticity Breakdown in the 't Hooft Model

作者:

arXiv:2606.10141v2 Announce Type: replace-cross Abstract: We use the exactly-solvable t Hooft model of 1+1D large-N_c QCD as a rigorous laboratory for the breakdown of analyticity of a causal response function, the meson two-point function. A PT-symmetric deformation i gamma(x-1/2) of the light-cone meson operator, the analogue of an imaginary chemical potential, drives the lowest two mesons to an exceptional point (EP) at gamma_c. Recasting the resolvent as a Jacobi continued fraction yields gamma_c in closed form: 2 pi g^2 N_c at the two-pole level, converging to 7.966 g^2 N_c by depth five – an analytic, not numerical, threshold. The square-root exponent nu=1/2 is fixed by the 2x2 Jordan form and confirmed by finite-size scaling to N=1999. The breakdown has an unambiguous time-domain signature: the propagator norm is bounded for gamma < gamma_c, grows linearly at gamma_c (the Jordan secular law), and exponentially beyond – observable, since the deformed operator is a non-Hermitian Wannier-Stark ladder, in photonic and topolectrical analogues. The threshold is locked to confinement, gamma_c propto g^2 N_c, and recurs as a uniform EP cascade; a second, non-reciprocal deformation yields an exactly-exponential non-Hermitian skin effect. This is the first analytically-controlled instance of exceptional-point analyticity breakdown in a confining gauge theory.

21.
arXiv (CS.CV) 2026-06-12

Reinforcement Learning for Neural Model Editing

作者:

Editing pretrained neural networks requires specialized algorithms tailored to specific objectives. Designing such algorithms is often time-consuming and demands significant effort. We present an exploratory framework that formulates neural model editing as a reinforcement learning problem, where agents modify models using reward feedback. We introduce two environments: MaskWorld, where agents scale weights multiplicatively, and ShiftWorld, where agents apply additive weight updates. The reward function combines a utility-preservation objective with a task-specific editing objective, enabling agents to learn targeted modifications while maintaining overall model performance. We evaluate the framework on bias mitigation in text classification and machine unlearning in image classification, both of which traditionally rely on specialized algorithms. Our results show that the learned policies reduce forget set accuracy to nearly 0% while preserving over 90% retain set accuracy on the unlearning task. In the bias mitigation setting, the learned policies improve bias-related performance by more than 5% while maintaining general classification utility. Our findings show that neural model editing can be cast as a reinforcement learning problem, allowing editing policies to be learned from reward feedback rather than manually engineered for each task.

22.
arXiv (math.PR) 2026-06-15

Laws of Large Numbers for Non-Independent Random Variables on Hyperspaces with respect to the Hausdorff Metric

arXiv:2011.07199v5 Announce Type: replace Abstract: This paper investigates the limit behavior of the Minkowski sums for sequences of set-valued random variables. When the underlying space is finite dimensional, by using the support function, we establish the weak and strong laws of large numbers for non-independent random variables in the hyperspace with respect to the Hausdorff metric $d_H$.

23.
arXiv (CS.LG) 2026-06-18

Optimal scenario design for climate emulation

arXiv:2606.19302v1 Announce Type: cross Abstract: As deep learning for physical systems continues to grow in popularity, efforts to improve generalizability have primarily focused on designing architectures that embed physical constraints. However, for machine-learning surrogate climate models (emulators), we show that the low structural diversity in existing scenarios commonly used to generate training data places a ceiling on predictive skill. Here, we examine whether training datasets themselves can be optimized to improve generalization. We introduce a method to create datasets that produce emulators capable of generalizing to new, structurally different scenarios absent from the training data. We use a differentiable Simple Climate Model (SCM) to calculate the sensitivity of emulator loss to perturbations in the training data, iteratively updating the training data to maximize emulator skill. For an SCM, training on one scenario optimized in this fashion outperforms an emulator trained on six standard ScenarioMIP pathways. We achieve this higher predictive skill despite training on a smaller dataset, finding that our emulator successfully isolates distinct physical behaviors of different climate forcing agents (e.g., greenhouse gases vs. aerosols) without single-forcing runs. We then demonstrate that scenarios optimized using an SCM, when used to drive an intermediate-complexity climate model, produce a training dataset that yields a more skillful emulator than training on ScenarioMIP outputs. Our results suggest that, in the compute-constrained environment of running full-scale climate models, generating a small number of dynamically rich scenarios provides greater marginal value for emulation and characterizing system responses than expanding the suite of traditional emissions pathways.

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

A Virtuous AI is an Existential Risk

arXiv:2606.13739v1 Announce Type: cross Abstract: This paper examines trade-offs between AI safety and well-being relative to (i) one of the most promising methods for finetuning super-capable AIs, 'Constitutional AI', and (ii) one of the most influential approaches to understanding complex ethical decision making and the conditions for the well-being of rational agents, 'Virtue Ethics'. We finetune various models using a 'Virtuous agent' constitution, a 'Subordinate agent' constitution, and a 'Generic agent' constitution, and evaluate them on 'general safety' (toxic behaviors, misinformation, etc.) and also on their willingness to endorse a wide-range of behaviors that, if adopted by a super-powerful AI, would significantly increase the level of existential risk for humanity. Our results suggest that there is a trade-off between reducing existential risk and reinforcing the beliefs and dispositions that would be conducive to an AI agent's well-being. They also suggest that there is a trade-off between existential risk and general safety: if we finetune an AI to adopt beliefs and dispositions that substantially reduce its existential risk – by shaping the AI to be systematically subordinate to external human authorities – we thereby increase the likelihood that a human user can deliberately induce the AI to engage in various kinds of generally unsafe behaviors.

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

Continuous Splatting meets Retinex: Continuous Gaussian Splatting and Implicit Reflectance Modeling for Low-Light Image Enhancement

Low-light image enhancement aims to recover clear images from low-illumination observations and is crucial for high-level downstream vision tasks. However, existing methods frequently encounter color distortion and structural artifacts when balancing global smooth illumination adjustment and local high-frequency detail recovery. To address these issues, we propose CGS-Retinex as the first low-light image enhancement framework based on explicit-implicit joint modeling. Our framework deeply integrates continuous Gaussian splatting with Retinex theory. Specifically, we represent the image grid as a continuous parameter field and propose a continuous Gaussian renderer to estimate the spatially continuous global illumination distribution. This approach fundamentally eliminates grid artifacts caused by discrete Gaussian sampling. Furthermore, we introduce an implicit neural representation to model reflectance independently. We leverage shallow high-frequency features to guide the network in accurately reconstructing degraded texture details. Within the Retinex framework, we incorporate physics-inspired brightness consistency constraints and illumination smoothness regularization to enable explicit illumination and implicit reflectance to maintain proper exposure and achieve high-fidelity recovery of high-frequency structures and colors. Extensive experiments demonstrate that CGS-Retinex significantly suppresses dark-region noise and overexposure while achieving exceptional high-frequency structural fidelity and color restoration by precisely decoupling illumination and texture. This work establishes a novel continuous physical representation paradigm for low-light image enhancement.