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

Understanding, Detecting, and Repairing Real-World In-Context-Learning-Based Text-to-SQL Errors

Large language models (LLMs) have been adopted for text-to-SQL tasks, utilizing their in-context learning (ICL) capability to translate natural language questions into SQL queries. However, such a technique faces correctness problems. In this paper, we conduct the first comprehensive study of text-to-SQL errors of ICL-based techniques. Our study covers four representative ICL-based techniques, five basic repairing methods, two benchmarks, and two LLM settings. We find that text-to-SQL errors are widespread and summarize 27 error types of 7 categories. We also find that existing repairing attempts have limited correctness improvement while having high computational overhead and many mis-repairs. Based on these findings, we propose MapleDoctor, a novel text-to-SQL error detection and repairing framework. The evaluation demonstrates that MapleDoctor outperforms existing solutions by repairing 13.8% more queries with a negligible number of mis-repairs and reducing 67.4% repair latency. The artifact is publicly available at GitHub.

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

Mask, Sample, Revise: A Revisable CTMC Inference Stack for Guided Discrete Flow Matching Text-to-Speech

arXiv:2606.13989v1 Announce Type: cross Abstract: Recent alignment-free non-autoregressive (NAR) text-to-speech (TTS) models formulate synthesis as a conditional infilling task, bypassing explicit duration predictors and external aligners. When speech is represented with neural codec tokens, the infilling problem becomes discrete, making Discrete Flow Matching (DFM), a Continuous-Time Markov Chain (CTMC) framework for discrete generation, a natural fit. However, inference-time control for stable low-step conditional infilling remains underexplored. We propose Mask, Sample, Revise, an inference-time CTMC stack for alignment-free DFM-TTS. The stack combines predictor-free guidance to strengthen text conditioning, prompt-matched conditional coupling to align the probability path with the acoustic prompt, and SC-ReMask, a schedule-constrained remasking mechanism that introduces token-to-mask transitions so early de-masking decisions can be revised. These components require no post-hoc fine-tuning and operate in a single tau-leaping sampler. Controlled ablations show that this stack improves intelligibility and robustness in the low-NFE prompted setting, outperforming unguided and guidance-only samplers with substantially more steps.

03.
arXiv (math.PR) 2026-06-12

Sub-Riemannian spectral distance

arXiv:2606.12804v1 Announce Type: cross Abstract: We study eigenvalues and eigenfunctions of the ``div-grad type" sub-Laplacian with respect to Popp's volume on a compact equiregular sub-Riemannian manifold $M$. Since Popp's volume is canonically determined by the sub-Riemannian structure of $M$, the spetra of the sub-Laplacian carry geometric meanings. In this paper, we first embed $M$ into the Hilbert space of square-summable sequences using eigenfunctions and then define a spectral distance between two compact equiregular sub-Riemannian manifolds. Our result is a sub-Riemannian analogue of Berard-Besson-Gallot's classical work in the Riemannian case.

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

From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

arXiv:2503.05598v2 Announce Type: replace-cross Abstract: This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet, PCANet, and the Fourier Neural Operator, highlighting their underlying representations, computational structures, and comparative performance. These architectures are demonstrated on three canonical PDE problems: the Poisson equation, a linear elasticity problem, and a hyperelasticity problem. To make the presentation self-contained, key foundational topics are introduced, including finite-dimensional representations of function spaces, singular-value decomposition, and sampling from infinite-dimensional function spaces. Beyond forward modeling, the review discusses the use of neural operators as surrogate models within a Bayesian inverse-problem framework, including prior specification, forward-map approximation, and posterior computation. The performance of the three neural-operator architectures is evaluated on in-distribution samples, out-of-distribution samples, and Bayesian inference tasks. The review also discusses challenges related to prediction accuracy and generalization, outlining emerging strategies such as residual-based error correction and multi-level training. The review concludes by positioning neural operators within broader scientific-computing workflows and by identifying directions for reliable, scalable operator learning.

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

A Comprehensive Survey of Medical Image Segmentation: Challenges, Benchmarks, and Beyond

Medical image segmentation plays a critical role in clinical diagnostics, treatment planning, disease monitoring, and neurological disorder identification. This article presents a comprehensive review of its systematic development, covering widely used public datasets, representative methods built on the U-Net, Transformer, and SAM architectures, and key evaluation metrics with their differences, followed by an analysis of major challenges from multiple perspectives. Unlike surveys that focus on a single model family or a specific clinical application, this review organizes U-Net-, Transformer-, and SAM-based methods within a unified analytical framework, with a particular focus on their effectiveness in improving segmentation accuracy and efficiency. This work aims to guide future research and support clinical translation of medical image segmentation, with all related resources publicly available in our GitHub repository: https://github.com/andrew-pengyu/Awsome_MedSeg/tree/main.

06.
medRxiv (Medicine) 2026-06-24

INCREASED REMOVAL SIGNALS ON ERYTHROCYTES OF ANEMIC CANCER PATIENTS

BACKGROUND: Anemia is a negative factor in cancer, influencing the prognosis, quality of life and financial situation of cancer patients. Recent studies have shown that anemia in cancer is provoked by augmented erythrocyte removal. OBJECTIVE: In this study we sought to investigate the molecular bases for erythrocyte removal in cancer patients with anemia. In particular, we explored the levels of erythrocyte CD47, lactadherin, calreticulin and MCP1. METHODS: Thirty five anemic cancer patients (25 women, aged 66.4 +/-11.35 years old) and twelve healthy non-anemic controls (8 men, aged 61.1+/-9.98 years old) participated in our study. Red blood cells were isolated throug multiple centrifugations, and were lysed with the use of Triton-X 100. The levels of CD47, lactadherin, calreticulin and monocyte chemoattrractant protein 1 were determined by ELISA. RESULTS: Erythrocytes of anemic cancer patients display reduced CD47 (p

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

Folded Transport MCMC: Eliminating Label Switching by Sampling on a Fundamental Domain

作者:

arXiv:2606.04307v2 Announce Type: replace Abstract: In Bayesian mixture models and other exchangeable-component models, the posterior is invariant under permutation of component labels, creating m! equivalent modes-the label-switching problem. Standard MCMC methods either mix poorly across these modes or rely on post-hoc relabelling that cannot guarantee the sampler has converged. We propose Folded Transport MCMC (FolT-MCMC), which eliminates label switching before sampling by restricting the Markov chain to a fundamental domain-a sorted or reflected subspace containing exactly one representative from each symmetric mode. The proposal is a learned normalising flow whose density is symmetrised over the group orbits, ensuring correct targeting on the reduced space. We show that this construction preserves a computable convergence diagnostic based on the oscillation of the log-density ratio, and that the diagnostic becomes sharper on the fundamental domain whenever the original-space flow under-covers one or more symmetric modes. Experiments on Gaussian mixtures (d=2-20), label-switching targets (up to 24 equivalent modes), a standard Bayesian three-component mixture posterior, and real accelerometer data from a supertall building show improvement ratios of 2x to 145x, with the folded diagnostic stable across dimensions while the unfolded diagnostic collapses.

08.
Nature Medicine 2026-06-25

<b>HPV vaccination linked to dramatic reduction in cervical cancer deaths</b>

A new study examines the impact of the national HPV vaccination program in England, initiated almost two decades ago — showing huge declines in cervical cancer mortality among young women. A new study examines the impact of the national HPV vaccination program in England, initiated almost two decades ago — showing huge declines in cervical cancer mortality among young women.

09.
arXiv (CS.CL) 2026-06-17

DICE: Diffusion Large Language Models Excel at Generating CUDA Kernels

Diffusion large language models (dLLMs) have emerged as a compelling alternative to autoregressive (AR) LLMs, owing to their capacity for parallel token generation. This paradigm is particularly well-suited for code generation, where holistic structural planning and non-sequential refinement are critical. Despite this potential, tailoring dLLMs for CUDA kernel generation remains challenging, obstructed not only by the high specialization but also by the severe lack of high-quality training data. To address these challenges, we construct CuKe, an augmented supervised fine-tuning dataset optimized for high-performance CUDA kernels. On top of it, we propose a bi-phase curated reinforcement learning (BiC-RL) framework consisting of a CUDA kernel infilling stage and an end-to-end CUDA kernel generation stage. Leveraging this training framework, we introduce DICE, a series of diffusion large language models designed for CUDA kernel generation, spanning three parameter scales, 1.7B, 4B, and 8B. Extensive experiments on KernelBench demonstrate that DICE significantly outperforms both autoregressive and diffusion LLMs of comparable scale, establishing a new state-of-the-art for CUDA kernel generation.

10.
arXiv (CS.AI) 2026-06-17

Transformer-Based Warm-Starting for Feasible and Optimal Terminal Approach to Tumbling Objects with Space Manipulators

arXiv:2606.17317v1 Announce Type: cross Abstract: Real-time trajectory generation for on-orbit robotic servicing is challenging due to the nonlinear coupling between spacecraft bus motion, manipulator dynamics, visibility cone, and trajectory-level safety constraints. This paper studies learning-based warm-starting for sequential convex programming (SCP) in the terminal approach of a space manipulator toward a tumbling target. The proposed framework decomposes the problem into a system center-of-mass translational planning stage and a coupled attitude–manipulator torque-allocation stage, and applies a causal transformer warm-start to the latter, which constitutes the dominant computational bottleneck. Linear and flow matching action decoders are compared under different action-chunking and training dataset sizes, and the resulting warm-starts are evaluated under both cost-optimal and feasibility projection using SCP. Across 300 held-out scenarios, the learned warm-start reduces the second-stage SCP iteration count by up to 28% and the runtime by 23% while preserving the final control-cost distribution. When the learned warm-starts are used for nonconvex feasibility projection, they nearly halve the runtime relative to cost-optimal SCP, while avoiding the catastrophic high-cost tail behavior observed when initialized heuristically. These results indicate that sequence-model warm-starts can improve both the computational efficiency and trajectory robustness of optimization-based terminal guidance for space manipulation.

11.
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.

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

SegmentAnyTreeV2: Scaling Transformer-Based Tree Instance Segmentation Across Sensors, Platforms, and Forests

We present SegmentAnyTreeV2, a sensor- and platform-agnostic framework for semantic and instance segmentation of forest point clouds. The model combines a serialization-based Point Transformer v3 backbone with a lightweight semantic head and a tree-focused cross-attention mask decoder. Semantic predictions restrict instance decoding to tree-class voxels, while instance-aware query initialization, one-to-many seed supervision, and asymmetric mask scoring improve separation in dense and structurally complex stands. We further introduce FOR-instance v3, an expanded benchmark comprising 427 scenes and 26,496 annotated trees across diverse biomes, forest structures, and LiDAR platforms. On the FOR-instanceV2 test split, SegmentAnyTreeV2 achieves 90.5% precision, 80.2% recall, 85.0% F1, 90.7% coverage, and 87.6% semantic mIoU, outperforming previous learning-based methods in both instance detection and mask completeness. Zero-shot evaluation on independent sites further demonstrates strong cross-domain generalization.

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

Neural Bayesian Anomaly Mitigation: A Robust Loss that Doubles as an Unsupervised Contamination Classifier

arXiv:2606.16524v1 Announce Type: new Abstract: Engineered robust losses such as Huber, Student-$t$, and generalised cross-entropy make supervised models tolerant of contamination but cannot answer which observations are corrupted. We introduce Neural Bayesian Anomaly Mitigation (NBAM), a general-purpose drop-in loss derived from a Bayesian latent-switch mixture model: the marginal likelihood defines a robust supervised loss, and the associated posterior defines an unsupervised contamination classifier. Like Huber or Student-$t$, NBAM can replace the standard training loss in any supervised pipeline; unlike them, it additionally learns a structured contamination model and returns a calibrated per-sample contamination posterior. A learned input-dependent prior $\pi_\phi(x)$ captures the spatial locality of contamination, so that samples near known corruptions are more likely to be flagged, while an Occam penalty emerges automatically and regularises against over-flagging. On CIFAR-10 with asymmetric label contamination, NBAM recovers the structure of the corruption process without supervision: the contamination posterior separates clean from corrupted samples, and the learned anomaly head identifies the direction of every label-flip pair. Alongside these capabilities, NBAM outperforms the four robust-loss baselines considered here at contamination rates 0.2-0.6.

14.
arXiv (CS.CL) 2026-06-17

Atlas: Orchestrating Heterogeneous Models and Tools for Multi-Domain Complex Reasoning

The integration of large language models (LLMs) with external tools has significantly expanded the capabilities of AI agents. However, as the diversity of both LLMs and tools increases, selecting the optimal model-tool combination becomes a high-dimensional optimization challenge. Existing approaches often rely on a single model or fixed tool-calling logic, failing to exploit the performance variations across heterogeneous model-tool pairs. In this paper, we present ATLAS (Adaptive Tool-LLM Alignment and Synergistic Invocation), a dual-path framework for dynamic tool usage in cross-domain complex reasoning. ATLAS operates via a dual-path approach: (1) training-free cluster-based routing that exploits empirical priors for domain-specific alignment, and (2) RL-based multi-step routing that explores autonomous trajectories for out-of-distribution generalization. Extensive experiments across 15 benchmarks demonstrate that our method outperforms closed-source models like GPT-4o, surpassing existing routing methods on both in-distribution (+10.1%) and out-of-distribution (+13.1%) tasks. Furthermore, our framework shows significant gains in visual reasoning by orchestrating specialized multi-modal tools.

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

An Extensible and Lightweight Unified Architecture for Demosaicing Pixel-bin Image Sensors

Pixel-bin image sensors are becoming the default choice for smartphone cameras due to their resolution vs light-gathering trade-off. However, their larger inter-color separation compared to the Bayer color filter array (CFA) makes them challenging to demosaic. Furthermore, existing deep learning-based demosaicing methods are CFA-specific, requiring multiple individual models that take up precious onboard resources and demand larger development and maintenance efforts. In this work, we propose a modular unified architecture for demosaicing various pixel-bin sensors that provides higher image quality while being extensible and lightweight. Additionally, to enable plug-and-play operation, we introduce a learning-free CFA-identification module to detect the CFA type of raw data accurately.

17.
medRxiv (Medicine) 2026-06-24

Risk factors for suicide and repeat self-harm: a cohort study of adults with hospital-presenting self-harm

Background:Previous self-harm elevates the risk of repeat self-harm and suicide, but the prognostic value of events and clinician observations around the index event is unclear. We evaluated established and exploratory risk factors for suicide and repeat self-harm among patients presenting to emergency psychiatric units after a suicide attempt or nonsuicidal self-injury (NSSI). Methods: Multicentre cohort study in Sweden (n = 804). Outcomes were suicide and repeat self-harm at 1-year and 5-year follow-up, ascertained through linked national registers. Established risk factors included psychiatric diagnoses, prior suicidal behaviour, and sociodemographic characteristics; exploratory factors comprised past-week self-reported symptom changes and clinician observations. LASSO-regularised Cox regression models were fitted for established (n=21) and exploratory (n=11) risk factors. Results: During five-year follow-up, 285 (35%) individuals had a new episode of self-harm and 41 (5%) died by suicide. No risk factors reached statistical significance for suicide, although male sex was retained after regularisation (1-year hazard ratio [HR] = 3.57 [95% CI 0-8.33]; 5-year HR = 2.5 [0.03-4.55]). Three established risk factors were significantly associated with repeat self-harm: psychiatric inpatient care in the three months before the index event (1-year HR = 1.85 [1.3-2.6]; 5-year HR = 1.72 [1.23-2.65]), previous suicide attempt (1-year HR = 2.01 [0.79-2.4]; 5-year HR = 2.19 [1.27-2.6]), and borderline personality disorder (1-year HR = 1.82 [1.13-3]; 5-year HR = 1.67 [0.14-2.75]). Among exploratory risk factors, clinician-observed hopelessness (1-year HR = 1.72 [1.1-2.3]; 5-year HR = 1.51 [1.03-1.91]) and personality disorder features (1-year HR = 1.48 [0.96-2.05]; 5-year HR = 1.47 [1.04-1.95]) were associated with repeat self-harm. Conclusions: Risk factor profiles for repeat self-harm were consistent at 1 and 5 years. Beyond established risk factors, clinician-observed hopelessness and personality disorder features emerged as markers of risk, suggesting that qualitative clinician assessments may yield prognostic information not available from medical records alone.

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

Handbook of Error-Correcting Codes

arXiv:2606.11484v1 Announce Type: new Abstract: Barcode scans, clear phone calls, reliable data storage, satellite communication, and large-scale quantum computation are all made possible by error correction. We present a handbook version of The Error Correction Zoo, a curated reference of methods for protecting classical or quantum information from errors during storage and transmission. The handbook includes descriptions of these error-correcting codes and a classification according to the symbols they use. It also catalogues relations among codes and related objects such as sphere packings, lattices, designs, groups, and classical and quantum phases of matter. The collection is intended both as a rigorous reference and as a practical aid for tracing the web of code relationships and uncovering new connections.

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

DeepMine-Mamba: Mitigating Information Dilution in Mamba-Based State Space Models for Document Image Binarization

Document image binarization aims to separate foreground text from degraded backgrounds while preserving thin, broken, and low-contrast strokes. Although deep learning methods have improved binarization performance, most existing approaches rely on convolutional, transformer-based, or generative architectures, while Mamba-based state space models remain largely unexplored for this task. In this work, we investigate Mamba-based feature propagation and observe that direct state-space propagation may dilute weak foreground cues during long-range modeling, especially faint ink traces, fragmented characters, and boundary-sensitive stroke details. To address this problem, we propose DeepMine-Mamba, a Mamba-based binarization framework equipped with a novel Anti-Dilution Gate that estimates propagation-induced feature changes and selectively restores stroke-sensitive local responses while suppressing unnecessary background enhancement. Experiments on DIBCO/H-DIBCO benchmarks under a strict leave-one-year-out protocol show that DeepMine-Mamba achieves competitive overall performance, with strong average FM and Fps across benchmark years. Ablation results further show that the Anti-Dilution Gate is the key component for mitigating propagation-induced foreground dilution and improving stroke preservation.

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

Tyler: Typed Latent Reasoning for Language Models – When to Think, What to Compute, and How Much to Allocate

Chain-of-thought (CoT) prompting improves reasoning in large language models (LLMs) by externalizing intermediate computation as discrete text tokens, but this textual interface also introduces redundancy and inference overhead. Latent reasoning offers a promising alternative by carrying part of the computation in continuous representations. However, existing methods typically predefine when latent computation is invoked and how it is allocated during decoding, leaving a key problem unresolved: when to invoke latent computation, what type of computation to perform, and how much budget to allocate. We propose Typed Latent Reasoning (Tyler), a typed and budget-aware framework for latent reasoning during autoregressive decoding. Tyler learns a policy that, at each decoding step, chooses between emitting a text token and switching to a latent computation module specialized for a particular reasoning function. Once invoked, an operator maps the current reasoning state into latent tokens that support global planning, local state updates, or reusable procedural abstraction. Across extensive experiments on three backbone LLMs, Tyler improves accuracy by up to 14.49 points over CoT and by up to 4.30 points over the strongest competing baseline. It further generalizes across diverse reasoning domains and achieves the best final-stage performance with the lowest forgetting.

21.
arXiv (CS.LG) 2026-06-16

If These Walls Could Talk: Critical Play with Large Language Models in Museums

arXiv:2606.15565v1 Announce Type: cross Abstract: Large Language Models (LLMs) are increasingly being used in museums to as role playing chatbots which let visitors talk to simulated versions of people and artefacts from the past. While such installations can be playful and engaging, they are also problematic because LLMs cannot be trusted to speak truthfully. I identify a fundamental dilemma for the use of LLMs in museum chatbots: LLMs cannot be trusted to tell the truth, and efforts to make them more reliable may ruin that which is attractive about the bots in the first place - their ability to engage in life-like conversation. In response, I propose designing for critical play with LLM-based bots: Designing for playful interactions with bots that are unreliable but still able to represent the past in an adequate and engaging manner - as fictional characters representing historical narratives, styles of discourse, diverse perspectives, humor and satire.

22.
arXiv (CS.LG) 2026-06-25

A Single Stepsize Suffices for Unprojected Linear TD(0): Simultaneous Robust and Fast Rates via Polyak–Ruppert Averaging

arXiv:2606.24981v1 Announce Type: new Abstract: We study linear TD(0) under Markovian sampling, where data are generated along a single trajectory. We provide high-probability guarantees for a plain unprojected TD(0) algorithm with Polyak-Ruppert (PR) averaging, using a single stepsize schedule $\eta_t \propto \frac{1}{\tau_{\mathrm{mix}}\log(t)\sqrt{t}}$ that depends on the mixing time but requires no prior knowledge of the curvature parameter $\omega$. Our first result shows that such a choice of the stepsize guarantees that the TD(0) iterates are automatically and uniformly bounded with high probability, without projections and without any stability argument based on $\omega$. Building on this result, we establish a simultaneous high-probability convergence guarantee for the PR average: the same stepsize yields both a robust curvature-free $\widetilde{\mathcal{O}}\!\left(\frac{\tau_{\mathrm{mix}}}{\sqrt{T}}\right)$ rate and a fast curvature-dependent $\widetilde{\mathcal{O}}\!\left(\frac{\tau_{\mathrm{mix}}^2}{\omega T}\right)$rate, with the bound taking the minimum of the two. The core technical ingredient is a Poisson-equation toolkit for geometrically mixing Markov chains, which decomposes Markov noise into a martingale term plus a controlled remainder and enables a new self-bounding inductive argument for pathwise stability.

23.
arXiv (math.PR) 2026-06-19

Theory of uncertain probability: can we derive the probability density function of uncertain random experiments with continuously changing conditions?

作者:

arXiv:2606.20169v1 Announce Type: new Abstract: This paper aims to explore the formation mechanism of probability distribution in situations where the differences among random experiments are distinguishable, and these differences continue to evolve along with the dynamic changes in conditions and their mechanisms of action. To this end, we are motivated to devise a new theoretical system – theory of uncertain probability (TUP) with Kolmogorov's system and nonlinear theories as special cases. TUP develops a novel model that integrates probability and uncertainty as well as the known and unknown to more accurately depict numerous typical random phenomena under more realistic assumptions, and thus provides appropriate tools for greater variety of real needs. It also allows for pioneering interpretation of the causal mechanisms underlying many important distributional characteristics and incorporation of pathwise property to distribution model.

24.
arXiv (quant-ph) 2026-06-19

Operator Learning for efficient Quantum Computation

arXiv:2606.20184v1 Announce Type: new Abstract: An efficient implementation of quantum algorithms is often hindered by the lack of efficient primitives for operators and state preparation. This limits both the ability of near-term quantum hardware to simulate complex problems and the potential of fault-tolerant algorithms to achieve practical quantum advantage. To address this, we propose a full-stack variational framework that transforms arbitrary operators to compact quantum circuits. The resulting variational circuits can be tailored to the connectivity and long-range interaction of the target hardware. The learning process employs backpropagation together with a cost function that efficiently optimizes unitary operators and non-unitary – dense or sparse – operators using only a single ancilla qubit for block encoding. Additionally, we introduce a regularization term that reduces the approximation error. The approach is validated for both quantum mechanical and engineering applications. In the former case, we learn propagators that arise in native quantum problems – such as quantum simulation and quantum chemistry – and achieve improved resource scaling in comparison to standard Suzuki-Trotter expansions. In the latter case, we demonstrate the approach's ability to implement the second-order central finite difference approximation of the Laplace operator – relevant for solving partial differential equations – while improving upon current error metrics. The final example deals with learning a dense, non-unitary operator that arises in the analysis of inviscid potential flow around an airfoil. This universality of the framework opens the door for solving general problems beyond prototypical engineering and quantum applications.

25.
arXiv (CS.AI) 2026-06-11

Signed Compression Progress on a Sealed Audit is Goodhart-Resistant

arXiv:2606.11417v1 Announce Type: cross Abstract: Compression progress is a long-standing proposal for intrinsic motivation: reward an agent when its world model becomes better at predicting or compressing experience. The folk claim is that this reward is "credible" because it is paid only for learning. We make this precise and prove it. If intrinsic reward is the signed decrease of a fixed sealed-audit loss, r_t = E(theta_{t-1}) - E(theta_t), then cumulative reward telescopes exactly to endpoint audit improvement, so no policy can push reward up indefinitely while true audit performance stagnates or degrades. For finite audit panels the same result holds with a sharp false-positive budget: cumulative empirical reward is at most true audit improvement plus 2 Delta_n(F, delta), the uniform audit deviation of the model class. This is horizon-free: adaptivity over time costs nothing once the sealed panel uniformly controls the class. The theorem also identifies the failure modes: the guarantee disappears if progress is clipped, scored on the agent's own stream, exposed to a high-capacity model on a reusable panel, or applied to a neural class that makes Delta_n vacuous. We give a Lean 4 mechanization of the structural core (telescoping, the finite-audit bound, finite Gibbs, and the entropy floor) and an experiment suite on ARC-TGI grid-transformation generators with adaptive holdout attacks. Experiments confirm the theory: finite-audit deviation scales as n^{-0.527}; signed progress resists clip-farming, stream leakage, and noisy-TV curiosity; naive reusable audits are exploitable by black-box scalar feedback, while standard release defenses keep the attack below the 2 Delta_n threshold. Signed compression progress on a sealed audit is an accounting signal of genuine improvement.