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01.
arXiv (CS.CV) 2026-06-18

Confidence is Not Reliability: Rethinking MC Dropout in Brain Tumour Segmentation

Glioma segmentation in multiparametric MRI is a critical component of treatment planning. A segmentation model that fails silently on treatment-critical sub-regions represents a patient safety risk that overlap-based metrics such as Dice scores cannot expose. We ask whether voxel-level uncertainty estimation via Monte Carlo (MC) Dropout can reliably identify segmentation errors in clinically critical sub-regions, and whether calibration failure modes are detectable from standard reporting metrics alone. In an empirical two-model case study on 126 BraTS21 patients, we evaluate a high-performance pretrained SegResNet and a locally trained UNet with residual units (UNet-Res). MC dropout preserved segmentation accuracy ($|\Delta Dice|$ $

02.
arXiv (CS.LG) 2026-06-16

Stop the Sampler! Classifier-Based Adaptive Stopping for Sampling Kernels

arXiv:2606.16073v1 Announce Type: new Abstract: Sampling from complex, unnormalized probability densities is a fundamental challenge in Bayesian inference and probabilistic modeling. While Markov chain Monte Carlo (MCMC) methods provide asymptotic guarantees, they often suffer from slow mixing and high computational costs due to fixed or manually tuned trajectory lengths. In this work, we propose a novel framework that treats trajectory termination as a learnable component of the sampling dynamics. By framing MCMC within the theory of non-acyclic generative flow networks (GFlowNets), we train state-dependent neural classifiers to decide when a trajectory has reached a high-density region and should terminate. We theoretically establish the connection between optimal classifiers and the target density via detailed balance conditions and introduce a multilevel training scheme to facilitate exploration in complex geometries. Experimental results across various benchmark densities demonstrate that our approach significantly reduces average trajectory lengths while improving mode coverage and mixing compared to standard MCMC baselines.

03.
medRxiv (Medicine) 2026-06-15

International Consensus Guideline on Management of Genitourinary Adverse Events Associated with Prostate Cancer Radiotherapy

Purpose/Objective: Genitourinary (GU) adverse events (AEs) are common during and after pelvic radiation therapy (RT) for prostate cancer and can substantially impact quality of life. We convened an international committee to establish consensus in the prevention, mitigation, and management of radiation-related acute and late GU AEs, as there are no relevant evidence-based consensus guidelines to inform treating providers. Materials/Methods: A systematic evidence review focused on mitigation and management of radiation-related acute and late GU AEs was performed in PubMed, Embase and Cochrane. The following topics were addressed: management of acute GU AEs in the intact and post-operative settings; RT techniques; bladder outlet obstruction procedures; and indications for urology referral or hyperbaric oxygen therapy (HBO). Evidence-based consensus recommendations were developed using a Delphi process. We highlight the current state of evidence and evidence gaps worthy of future study. Results: Consensus was reached for 31 key questions. For management of lower urinary tract symptoms (LUTS), most evidence comes from trials in patients without cancer and not undergoing RT. A consensus algorithm for medical management of acute GU AEs was developed with the following highlights: (a) alpha blockers as 1st-line for obstructive symptoms in the intact setting, (b) anti-spasmodics as 1st -line for irritative symptoms in the intact setting, and (c) anti-spasmodics as 1st -line in the post-operative setting. The consensus algorithm provides an ordered list of medications to offer if 1st -line options afford inadequate relief. For RT fractionation, randomized clinical trial (RCT) data are available. 40% of panelists rarely or never use standard fractionation over moderate hypofractionation for patients with baseline LUTS, but most consider moderate hypofractionation over SBRT for AUA IPSS > 15. For patients with severe obstructive LUTS (most commonly AUA IPSS >20), the panel recommends a prophylactic bladder outlet obstruction procedure and, if obstructive symptoms improve, consideration of moderate hypofractionation or SBRT, based on retrospective data. There is one RCT supporting use of HBO for late radiation cystitis. Conclusions: The consensus guideline synthesizes available evidence and expert opinion across key clinical decision points to provide practical guidance in the prevention, mitigation, and management of radiation-related acute and late GU AEs in prostate cancer RT. Envisioned as a living document with periodic updates, this guideline serves as a resource for practicing radiation oncologists by outlining expert-derived consensus recommendations of evidence-based care in areas where high-quality data is limited.

04.
arXiv (quant-ph) 2026-06-19

Ultrafast nonadiabatic dynamics of tetraphenylsubstituted nitrogen-based heterocycles

arXiv:2604.16897v2 Announce Type: replace-cross Abstract: Tetraphenylpyrazine (TPP) and 2,3,4,5-tetraphenyl-1H-pyrrole (TePP) are closely related heterocycles bearing four phenyl substituents, whose structural similarity makes them a useful pair for comparing how intramolecular flexibility influences excited-state relaxation and emission in the gas phase and in the solid state. TPP is a prototypical solid-state luminescence enhancement (SLE) emitter, exhibiting a markedly increased quantum yield upon molecular aggregation. In contrast, TePP displays similar quantum yields in solution and solid state, characteristic of dual-state emission (DSE). This behaviour indicates that intramolecular rotations are already significantly hindered in the isolated-molecule regime, consistent with our previous observations for TPP and other solid-state emitters (Hernández-Rodríguez et al., ChemPhysChem, 2024, 25, e202400563). To unravel the excited-state dynamics underlying this contrasting behaviour, we performed mixed quantum-classical trajectory simulations on a single molecule of TPP and TePP employing the surface-hopping method. Twelve singlet states were included at the TD-B3LYP-D3/def2-SVP level, which were previously benchmarked against coupled cluster methods. Simulated observables such as gas phase ultrafast electron diffraction (GUED) and time-resolved fluorescence (TR-FL) signals allow us to dissect the distinct deactivation pathways operating in both systems in the gas phase, while also providing mechanistic insight into how these pathways are expected to evolve in solution and solid-state environments.

05.
arXiv (CS.LG) 2026-06-19

DisjunctiveNet: Neural Symbolic Learning via Differentiable Convexified Optimization Layers

arXiv:2605.30456v2 Announce Type: replace Abstract: Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches. At the same time, these problems are often accompanied by rich domain knowledge derived from physical laws, operational requirements, and expert heuristics. Such knowledge is frequently expressed as rules involving logical propositions and linear inequalities. Existing neuro-symbolic methods typically enforce these rules approximately through soft penalties, assume input-independent rules when designing specialized architectures, or rely on non-differentiable post-processing at inference time to achieve hard constraint satisfaction. While recent advances in differentiable optimization layers enable end-to-end feasibility enforcement within neural networks, extending these approaches to logical or mixed-integer rules remains challenging due to inherent nonconvexity. In this work, we propose a unified end-to-end framework for enforcing hard, input-dependent mixed integer linear constraints within neural networks. Our approach represents rules as disjunctive constraints and applies hierarchical convex relaxations to obtain convex hull formulations. These relaxations yield tractable linear constraints that can be embedded as differentiable optimization layers while enabling exact rule satisfaction. We demonstrate the effectiveness of the proposed framework on real-world datasets, achieving perfect rule satisfaction and strong predictive performance.

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

Experimental Observation of Dynamical Phase Transitions in a Dephased Photonic Quantum Walk

arXiv:2606.15935v1 Announce Type: new Abstract: Dynamical phase transitions in open quantum systems govern how non-equilibrium states relax toward a stationary state. We study these transitions experimentally using a discrete-time photonic quantum walk on a three-node graph. A tunable synthetic gauge flux and calibrated dephasing allow us to control time-reversal symmetry and the detailed balance properties of the effective Markovian dynamics. With detailed balance, we observe a first-order dynamical phase transition marked by a crossing of real Liouvillian eigenvalues. When detailed balance is broken, we observe a second-order dynamical phase transition at an exceptional point where eigenvalues and eigenvectors coalesce. By progressively reducing the dephasing strength, we track the crossover toward the quantum-coherent regime and determine that the transitions persist down to a finite threshold. Our results link Liouvillian spectral topology to relaxation criticality and demonstrate a controllable platform for engineered dissipative dynamics.

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

EndoCoT: Scaling Endogenous Chain-of-Thought Reasoning in Diffusion Models

Recently, Multimodal Large Language Models (MLLMs) have been widely integrated into diffusion frameworks primarily as text encoders to tackle complex tasks such as spatial reasoning. However, this paradigm suffers from two critical limitations: (i) MLLMs text encoder exhibits insufficient reasoning depth. Single-step encoding fails to activate the Chain-of-Thought process, which is essential for MLLMs to provide accurate guidance for complex tasks. (ii) The guidance remains invariant during the decoding process. Invariant guidance during decoding prevents DiT from progressively decomposing complex instructions into actionable denoising steps, even with correct MLLM encodings. To this end, we propose Endogenous Chain-of-Thought (EndoCoT), a novel framework that first activates MLLMs' reasoning potential by iteratively refining latent thought states through an iterative thought guidance module, and then bridges these states to the DiT's denoising process. Second, a terminal thought grounding module is applied to ensure the reasoning trajectory remains grounded in textual supervision by aligning the final state with ground-truth answers. With these two components, the MLLM text encoder delivers meticulously reasoned guidance, enabling the DiT to execute it progressively and ultimately solve complex tasks in a step-by-step manner. Extensive evaluations across diverse benchmarks (e.g., Maze, TSP, VSP, and Sudoku) achieve an average accuracy of 92.1%, outperforming the strongest baseline by 8.3 percentage points. The code and dataset are publicly available at https://internlm.github.io/EndoCoT/.

08.
arXiv (CS.LG) 2026-06-15

Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection

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arXiv:2405.03063v3 Announce Type: replace-cross Abstract: We propose a generalized debiased Lasso estimator based on a stability principle. When a single column of the design matrix is perturbed, the estimator admits a simple update formula that can be computed from the original solution. Under sub-Gaussian designs with well-conditioned covariance, this approximation is asymptotically accurate for all but a vanishing fraction of coordinates in the proportional growth regime. The proof relies on concentration and anti-concentration arguments to control error terms and sign changes. In contrast, establishing comparable distributional limits (e.g., Gaussianity) under similar assumptions remains open. As an application, we show that the approximation significantly reduces the computational cost of resampling-based variable selection procedures, including the conditional randomization test and a local knockoff filter.

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

Where Does Social Reasoning Come From? Capability Provenance in Language Models

We use training-data attribution as an interpretable tool for capability discovery, mapping which regions of the pretraining corpus support social-reasoning versus STEM-reasoning in OLMo3-7B. Training-data attribution measures how strongly each training document influences a model's predictions on a benchmark, but document-level scores are too noisy to identify which corpus regions support which capabilities, and prior work has emphasized factual knowledge rather than reasoning. We compute gradient-based attribution (TrackStar via Bergson) over a working set drawn from the de-duplicated Dolma3 mix, aggregate influence across WebOrganizer's 24-format x 24-topic taxonomy (576 bins), and contrast benchmark pairs in a 2x2 design that varies domain (social vs. STEM) and capability type (reasoning vs. knowledge): SocialIQA and MMLU Social Sciences against ARC-Challenge and MMLU STEM. Social and STEM reasoning draw on qualitatively distinct corpus regions, and the contrast is sharper at the reasoning level than at the knowledge level. Targeted machine unlearning provides partial causal validation: forgetting high-attribution topic bins (e.g., Literature for SocialIQA) degrades the aligned benchmark more than within-bin random baselines, and we open-source all code, sampling manifests, the bin-level influence matrix, and unlearning checkpoints.

10.
arXiv (CS.CL) 2026-06-12

AI SciBrief as a Gateway to Research: A Framework for Onboarding Students into New Research Areas

Students at all levels of higher education face a significant barrier in the form of information overload, which often paralyzes the initial stages of the research process and suppresses motivation. In response, this article introduces a pedagogical framework that leverages AI SciBrief, a platform powered by a Large Language Model (LLM) designed to automatically generate digests of scientific trends. We describe how this multidisciplinary tool - with initial coverage in finance, medicine, and education - can be integrated into the curriculum to overcome this "entry barrier." The framework provides concrete methodologies for utilizing these digests to facilitate topic selection for term papers, accelerate literature reviews for dissertations, and enable postgraduate students to continuously monitor emerging trends. We conclude that AI SciBrief functions as a "gateway to research" effectively reducing students' cognitive load and empowering them to transition more rapidly from information searching to knowledge creation.

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

Human-AI Agent Interaction in a Business Context

arXiv:2606.18716v1 Announce Type: cross Abstract: As AI agents are increasingly integrated into core business processes, understanding and designing effective interaction patterns between humans and AI agents becomes crucial for value creation. This study identifies and evaluates principles and criteria for a positive User Experience (UX) with AI agents, along with methods for its measurement. We identify user expectations and needs to facilitate adoption, build trust, and support user-centered decision-making by development teams. Using a mixed-methods approach that combines qualitative and quantitative techniques, we explore interaction patterns between humans and AI agents. The findings from this exploratory research serve as the basis to develop a survey experiment which evaluates the effectiveness of specific design elements on a larger scale. This foundational research contributes to the development of more intuitive and effective human-AI agent interactions in business settings.

12.
bioRxiv (Bioinfo) 2026-06-19

HTS-Oracle v2: Prospective AI-Guided Discovery and Experimental Validation of Small Molecule Modulators Across Multiple Targets

High-throughput screening (HTS) remains the cornerstone of early-phase small molecule discovery yet consistently underperforms against immunotherapy targets, yielding validated hit rates below 0.1%. Here we introduce HTS-Oracle v2, which features rigorous cross-validation that ensures honest performance estimates. HTS-Oracle v2 was trained and validated across four clinically significant immune checkpoint targets (CD28, ICOS, LAG-3, and TIGIT) achieving ROC-AUC values of 0.968, 0.969, 0.875, 0.928 respectively under rigorous cross-validation. For prospective experimental validation, HTS-Oracle v2 was applied to an 8,960-compound Enamine Protein Mimetic Library, selecting only 25 compounds per target for experimental testing using temperature-related intensity change (TRIC) technology, a 99.7% reduction in screening burden. HTS-Oracle v2 identified 4, 5, 4, and 6 validated binders from 25 prospectively selected compounds per target, corresponding to validated hit rates of 16%, 20%, 16%, and 24%, respectively. Notably, 67-80% of all experimentally confirmed hits across the full 8,960-compound library were captured within just 25 model-selected compounds per target. For CD28, this represents a 28-fold improvement over HTS-Oracle v1 (239x versus 8.4x), establishing HTS-Oracle v2 as an efficient platform for AI-guided prospective hit discovery across immunotherapy targets.

13.
arXiv (CS.AI) 2026-06-11

Erased but Not Forgotten: How Backdoors Compromise Concept Erasure

arXiv:2504.21072v3 Announce Type: replace-cross Abstract: The expansion of text-to-image diffusion models has raised concerns about harmful outputs, from fabricated depictions of public figures to sexually explicit imagery. To mitigate such risks, prior work has proposed concept erasure methods that aim to sever unwanted concepts from the model via fine-tuning, yet it remains unclear whether these approaches truly remove all links to the harmful concept or merely conceal superficial connections. In this work, we reveal a critical vulnerability, the Erasure Evasion Backdoor (EEB): an adversary binds a backdoor trigger to a concept slated for removal, and this malicious link survives subsequent erasure. We show that both black-box and white-box adversaries can instantiate this threat. Across six state-of-the-art erasure methods, including robust ones that explicitly search for alternative representations of the target concept, EEB consistently exposes harmful content: up to 82% success against celebrity-identity unlearning, up to 94% for object erasure, and up to 16 times amplification of explicit-content exposure. While EEB uncovers a blind spot in current erasure methods, it also provides a diagnostic tool for stress-testing future concept erasure techniques.

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

Learning to Refine Hidden States for Reliable LLM Reasoning

arXiv:2606.17524v1 Announce Type: new Abstract: Large language models show strong reasoning ability, but their internal reasoning process can remain unstable in complex multi-step settings, where early hidden-state errors may propagate to incorrect predictions. We propose ReLAR, a reinforcement-guided latent refinement framework that iteratively updates hidden representations before decoding. ReLAR maintains a compact latent reasoning state and uses learned depth and action controllers to adaptively determine both the number and direction of refinement steps. The controllers are trained with a policy gradient objective based on step-wise likelihood improvement, enabling efficient input-dependent reasoning without explicit chain-of-thought generation. Experiments on medical, mathematical, multi-hop reasoning, and open-ended generation benchmarks show that ReLAR improves accuracy, generation quality, and reasoning stability with substantially lower inference overhead than explicit reasoning baselines.

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

Rethinking Structural Anomaly Detection: From Decision Boundaries to Projection Operators

arXiv:2606.15280v1 Announce Type: new Abstract: Most existing anomaly detection methods rely on estimating a probability density or learning an enclosing decision boundary, implicitly assuming that normal data occupies a region of non-zero volume in the ambient space. In contrast, structural anomaly detection considers data that lies near a low-dimensional manifold, creating a mismatch between the inductive bias of existing methods and the structure of the data, often resulting in degraded performance. To address this mismatch, we introduce a geometric perspective. Specifically, we learn a projection operator onto the manifold of normal samples and define a sample as anomalous if it is altered by this projection. This formulation naturally integrates the inductive bias of manifold-supported data and reframes anomaly detection in terms of a projection residual, thereby resolving issues arising from modeling degenerate distributions. Notably, it provides a unifying interpretation of reconstruction-based methods by explaining their success and failure in terms of projection quality. In particular, it explains the strong generalization ability of projection-aligned models as a consequence of contraction behavior toward the manifold. Moreover, by decoupling anomaly detection from probabilistic modeling, it reduces the tendency to misclassify rare but normal samples, a widely recognized limitation of existing approaches. Empirically, we demonstrate that projection-aligned methods achieve strong performance, outperforming boundary-based methods while improving upon existing reconstruction-based approaches.

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

AFFORDANCE20Q: Evaluating Affordance Reasoning from Physical Properties

arXiv:2606.14240v1 Announce Type: new Abstract: Affordance reasoning, the inference of an object's action possibilities from its physical properties (e.g., shape and material), is fundamental to human physical understanding and increasingly critical for Large Language Models (LLMs). However, existing affordance benchmarks largely expose explicit object identities in the evaluation setup, allowing models to rely on memorized object-affordance mappings rather than reasoning over physical properties. To address this gap, we introduce Affordance20Q, a novel affordance reasoning benchmark formulated as a 20-Questions game without exposing the object's identity. In each game, the model identifies a hidden object's affordance from a candidate set by asking yes/no questions about its physical properties. Affordance20Q comprises 1,009 games over 454 objects and 59 affordances, all manually filtered, refined, and annotated. We conduct comprehensive experiments with 15 state-of-the-art LLMs and find a substantial gap (~20 points) compared to human performance. A KL-based information-gain (IG) analysis further shows that models fail to ask discriminating questions as the game progresses. To close the gap, we develop KB-Anchored Rule Induction (KARI), a pipeline based on LLMs that generates affordance rules grounded in evidence from knowledge bases (KBs). KARI improves open-source LLMs by up to 15.2 points, while the limited coverage of KBs hinders further gains. We release all our code and data at https://github.com/1171-jpg/Affordance20Q.git

17.
medRxiv (Medicine) 2026-06-18

Cardiac rhythm development: A wearable device index of risk for physical and mental illness in adolescence

Objective. The autonomic nervous system, which regulates cardiac rhythm, undergoes pronounced maturation across adolescence. How cardiac rhythm develops over this period, however, and whether individual differences in its development forecast mental and physical illness, remain open questions. We used three waves of Fitbit data from the Adolescent Brain Cognitive Development (ABCD) Study to characterize the developmental trajectory of the cardiac rhythm and to test whether variation in that trajectory predicts onset of psychopathology and cardiometabolic disease. Methods. 8,301 adolescents contributed 242,811 valid Fitbit wear days across Waves 2 (Mage=12), 4 (Mage=14), and 6 (Mage=16). Cosinor mixed-effects models yielded three rhythm parameters per session: mesor (24-hour mean), amplitude (diurnal swing), and acrophase (peak timing). We first characterized age- and sex-specific trajectories, cross-wave stability, and factors shaping the rhythm. We then used parallel-process latent growth models to test whether within-person changes in rhythm tracked symptom trajectories, and hierarchical logistic models to test whether rhythm parameters predicted the first clinical onset of psychopathology and of obesity and hypertension. Results. The cardiac rhythm changed substantially across adolescence: mesor decreased, amplitude flattened, and acrophase shifted later. Within-person change in the rhythm tracked change in blood pressure, BMI, and trajectories of depression and ADHD symptoms. Higher mesor predicted incident onset of all five outcomes controlling for demographics, baseline symptoms, and behavior (ORs 1.36-1.54); amplitude, acrophase, and rhythm instability conferred additional risk. Conclusions. The 24-hour cardiac rhythm is a passively measurable substrate of adolescent autonomic development that indexes transdiagnostic risk for psychiatric and cardiometabolic illness.

18.
arXiv (quant-ph) 2026-06-12

Quantum Network Routing based on Surface Code Error Correction

arXiv:2606.12781v1 Announce Type: new Abstract: Quantum networks encounter unavoidable channel noises and erasure errors, presenting a huge obstacle in designing protocols that attain both high reliability and efficiency. Typically, quantum networks fall into two categories: those utilize quantum entanglements for quantum teleportation, and those directly transfer the actual quantum messages. In this paper, we present SurfNet, a quantum network that inherits the main advantages from both categories. It employs surface codes as logical qubits for encoding messages, and utilizes two parallel communication channels to fault-tolerantly transfer each surface code in a modular manner. Our approach of using surface codes can timely correct both operational and photon loss errors within the network, and the integration of the two channels within the network can greatly improve network throughput. For the implementation of SurfNet, we propose a novel network architecture, designed to better integrate surface codes into quantum networks. We also propose a novel error correction decoder, designed to fully utilize the modular characteristic of surface codes within our network. Simulation results demonstrate that SurfNet with its decoder significantly enhances the communication fidelity within quantum networks.

19.
arXiv (CS.AI) 2026-06-15

Communication Policy Evolution for Proactive LLM Agents

arXiv:2606.14314v1 Announce Type: new Abstract: LLM agents have rapidly evolved into autonomous systems, yet a persistent information gap remains between users and agents: communication is costly, while users' identical preferences further limit information exchange. To investigate how agents should communicate across modalities, this paper formalizes Communication Policy, establishes textual and UI-based policies, and then evaluates communication policies across diverse environments, personas, and model combinations. Building information asymmetry for proactive agents, we set up two complementary settings, User-Agent and Planner-Executor. Experimental results reveal complementary strengths between interaction channels: text-based interaction often facilitates task performance, while structured UI improves agents' response quality and persona compliance. Motivated by that, a hybrid method combines these advantages. We further propose Communication Policy Evolution (CPE), a self-evolution framework for refining communication policies through rollout and prompt-level evolving. Without model modification, CPE achieves the best task success across multiple settings using prompt refinement alone. Our findings identify communication behavior as a critical yet underexplored design dimension for LLM agents.

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

LoLA: Low-Rank Linear Attention With Sparse Caching

The per-token cost of transformer inference scales with context length, preventing its application to lifelong in-context learning. Linear attention is an efficient alternative that maintains a constant memory footprint, even on infinite context lengths. While this is a potential candidate for lifelong learning, it falls short in memory capacity. In this paper, we propose LoLA, a training-free augmentation to linear attention that boosts associative recall. LoLA distributes past key-value pairs from context into three memory systems: (i) recent pairs in a local sliding window cache; (ii) difficult-to-memorize pairs in a sparse, global cache; and (iii) generic pairs in the recurrent hidden state of linear attention. We show through ablations that our self-recall error metric is crucial to efficiently manage long-term associative memories. On pass-key retrieval tasks, LoLA improves the base model's performance from 0.6% to 97.4% accuracy. This is achieved with a 4.6x smaller cache than Llama-3.1 8B on 4K context length. LoLA also outperforms other 1B and 8B parameter subquadratic models on zero-shot commonsense reasoning tasks.

22.
arXiv (CS.AI) 2026-06-16

SorryDB: Can AI Provers Complete Real-World Lean Theorems?

arXiv:2603.02668v2 Announce Type: replace Abstract: We present SorryDB, a dynamically-updating benchmark of open Lean tasks drawn from 78 real world formalization projects on GitHub. Unlike existing static benchmarks, often composed of competition problems, hillclimbing the SorryDB benchmark will yield tools that are aligned to the community needs, more usable by mathematicians, and more capable of understanding complex dependencies. Moreover, by providing a continuously updated stream of tasks, SorryDB mitigates test-set contamination and offers a robust metric for an agent's ability to contribute to novel formal mathematics projects. We evaluate a collection of approaches, including generalist large language models, agentic approaches, and specialized symbolic provers, over a selected snapshot of 1000 tasks from SorryDB. We show that current approaches are complementary: even though an agentic approach based on Gemini Flash is the most performant, it is not strictly better than other off-the-shelf large-language models, specialized provers, or even a curated list of Lean tactics.

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

Ellipse Meets Bit-Planes: A Novel Approach to RNFL based Glaucoma Detection Using Advanced Image Processing and Deep Learning

This work proposes an integrated pipeline for automatic glaucoma detection method from easily available colour fundas images based on an adaptive algorithm for ellipse-based polar transformation, to enhance the analysis of the Retinal Nerve Fiber Layer (RNFL) as the primary biomarker for observing glaucomatous changes, regardless of optic disc and macula position. Utilizing this transformation, we introduce two distinct frameworks tailored to different operational needs. The first framework, a deep learning-inspired feature fusion approach, achieves a 99.3% detection rate, ideal for settings where high precision is essential, despite higher computational demands. The second framework employs a novel image-processing algorithm based on bit-plane slicing, offering 92.31% accuracy and optimized for environments requiring rapid inference with minimal resource consumption. Both frameworks provide scalable and cost-effective solutions for early glaucoma detection. This study highlights the potential of RNFL-based diagnostic tools in addressing the global challenge of glaucoma, particularly in underserved regions.

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

Bayesian Tensor Decomposition with Diffusion Model Prior

arXiv:2606.03212v2 Announce Type: replace Abstract: Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise. Low-rankness is itself a useful but limited structural prior, and additional handcrafted priors (e.g., sparsity or smoothness) still fall short of capturing the rich statistics of real-world data. To compensate for this weak inductive bias under heavy corruption, one would like to inject a learned, data-driven prior; however, the state-of-the-art diffusion models are not readily compatible with current TD and tractable posterior inference. To address these challenges, we introduce DiffBCP, a hybrid-prior Bayesian CP decomposition framework that couples a cumulative shrinkage process prior over the CP factors for automatic rank selection with an off-the-shelf pre-trained diffusion model as an implicit data prior on the reconstructed tensor. To make posterior inference tractable despite the coupling among the likelihood, low-rank constraint, and diffusion prior, we develop a split Gibbs sampler: CP factors admit conjugate updates, while the diffusion block is sampled via low-rank-guided denoising. A noise-adaptive coupling schedule further reduces sensitivity to hand-tuned annealing. Experiments on image inpainting and denoising, including high-resolution out-of-distribution images, show consistent gains over Bayesian, nonlinear, and plug-and-play TD baselines.