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01.
Nature (Science) 2026-06-08

Distributed control circuits across a brain-and-cord connectome

Just as genomes revolutionized molecular genetics, connectomes (maps of neurons and synapses) are transforming neuroscience. To date, the only organisms with complete connectomes are worms1–3, sea squirts4, and comb jellies5 (103–104 synapses). By contrast, the fruit fly is more complex (108 synaptic connections), with a brain that supports learning and spatial memory6,7 and an intricate ventral nerve cord analogous to the vertebrate spinal cord8–12. Here we report the first densely-reconstructed adult fly connectome that unites the brain and ventral nerve cord, and we leverage this resource to investigate principles of neural control. We show that effector neurons (motor neurons, endocrine cells, and efferent neurons targeting the viscera) are primarily influenced by sensory neurons in the same body part, forming local feedback loops. These local loops are linked by long-range circuits involving ascending and descending neurons organized into behavior-centric modules. Single ascending and descending neurons are often positioned to influence the voluntary movements of multiple body parts, together with the endocrine cells or visceral organs that support those movements. Brain regions involved in learning and navigation supervise these circuits. These results reveal an architecture that is distributed, parallelized, and embodied, reminiscent of distributed control architectures in engineered systems13,14.

02.
arXiv (CS.CV) 2026-06-24

FlowerDance: MeanFlow for Efficient and Refined 3D Dance Generation

Music-to-dance generation aims to translate auditory signals into expressive human motion, with broad applications in virtual reality, choreography, and digital entertainment. Despite promising progress, the limited generation efficiency of existing methods leaves insufficient computational headroom for high-fidelity 3D rendering, thereby constraining the expressiveness of 3D characters during real-world applications. Thus, we propose FlowerDance, which not only generates refined motion with physical plausibility and artistic expressiveness, but also achieves significant generation efficiency on inference speed and memory utilization. Specifically, FlowerDance combines MeanFlow with Physical Consistency Constraints, which enables high-quality motion generation with only a few sampling steps. Moreover, FlowerDance leverages a simple but efficient model architecture with BiMamba-based backbone and Channel-Level Cross-Modal Fusion, which generates dance with efficient non-autoregressive manner. Meanwhile, FlowerDance supports motion editing, enabling users to interactively refine dance sequences. Extensive experiments on AIST++ and FineDance show that FlowerDance achieves state-of-the-art results in both motion quality and generation efficiency. Code will be released upon acceptance.

03.
arXiv (CS.AI) 2026-06-17

Adaptive Domain Models: Bayesian Evolution, Warm Rotation, and Principled Training for Geometric and Neuromorphic AI

arXiv:2603.18104v5 Announce Type: replace Abstract: Prevailing AI training assumes reverse-mode automatic differentiation over IEEE-754 arithmetic. The memory overhead of training relative to inference, optimizer complexity, and structural degradation of geometric properties through training are consequences of this arithmetic substrate. This paper develops an alternative training architecture grounded in three prior results: the Dimensional Type System and Deterministic Memory Management framework (Haynes 2026), which establishes stack-eligible gradient allocation and exact quire accumulation as design-time verifiable properties; the Program Hypergraph (Haynes 2026), which establishes grade preservation through geometric algebra computations as a type-level invariant; and the b-posit bounded-regime design (Jonnalagadda et al. 2025), which makes posit arithmetic tractable across hardware targets conventionally considered inference-only. Their composition enables depth-independent training memory bounded to approximately twice the inference footprint, grade-preserving weight updates, and exact gradient accumulation, applicable uniformly to loss-function-optimized and spike-timing-dependent neuromorphic models. We introduce *Bayesian distillation*, a mechanism by which the latent prior structure of a general-purpose model is extracted through the ADM training regime, resolving the data-scarcity bootstrapping problem for domain-specific training. For deployment, we introduce *warm rotation*, an operational pattern in which an updated model transitions into an active inference pathway without service interruption, with correctness formalized through PHG certificates and signed version records. The result is a class of domain-specific AI systems that are smaller and more precise than general-purpose models, continuously adaptive, verifiably correct with respect to the physical structure of their domains, and initializable from existing models.

04.
arXiv (CS.CL) 2026-06-24

Pigeonholing: Bad prompts hurt models to collapse and make mistakes

While in-context learning is generally shown to be effective in Large Language Models (LLMs), bad contexts can cause performance degradation and mode collapse, a phenomenon we call "pigeonholing." **Unintentionally bad** contexts can happen without malicious jailbreaking intents: For example, a user asks the model to justify an incorrect math theorem or fails to correct the model's buggy code. Specifically, we investigate ``pigeonholing" in two scenarios: (1) when the user suggests a solution, and (2) when the conversation context includes the assistant's previous (incorrect) responses. Our experiments across 10 verifiable and open-ended tasks with 10 different models show that pigeonholing manifests in several ways: (1) repeating the incorrect answers from context (leading to 38-40% performance drop), (2) converging on a narrow set of answers in coding and text generation without exploring alternatives, and (3) flipping stance on controversial topics to align with the user or the assistant's previous claims. We find that pigeonholing worsens almost monotonically with the number of conversation turns (performance drops by additional 14+% as repeated mistakes increase from 1 to 5), and pigeonholing-induced mode collapse can happen even when the provided example is correct. As a step toward mitigation, we propose RLVR with synthetic errors which improves models by 43-60% under bad contexts compared to vanilla RLVR baselines.

05.
arXiv (CS.CV) 2026-06-15

RepFusion: Leveraging Multimodal Priors for Denoising in Representation Space

Large language models (LLMs) are widely used in text-to-image (T2I) systems, but they are typically limited to text encoding, while denoising is handled by newly trained generative backbones. The emergence of representation autoencoders (RAEs) shifts the generation target toward semantically structured visual representations, creating a latent space that is more compatible with pretrained LLM priors. Inspired by multimodal LLMs (MLLMs), where an MLP projector is sufficient to align clean visual representations with a pretrained LLM, we repurpose the MLLM itself as a noisy representation encoder, extending this mechanism from clean to noisy inputs. We present RepFusion, which uses the resulting MLLM outputs as the conditioning signal for a diffusion transformer. In controlled comparisons at similar inference budgets, RepFusion outperforms baselines that devote comparable capacity to newly initialized denoisers. These results demonstrate that MLLMs provide strong priors for denoising visual representations and that, by conditioning on evolving noisy representations, test-time compute can be productively spent on repeated MLLM conditioning in modern T2I systems.

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

Ground-State Energy Solutions of the Lithium Atom: Zeroth-, First-, and Second-Order Perturbation Theory and the Variational Method

arXiv:2606.24238v1 Announce Type: new Abstract: In this work, the ground-state energy of the lithium atom is systematically investigated using both time-independent perturbation theory and the variational method to provide a comprehensive pedagogical analysis of many-body atomic systems. The unperturbed Hamiltonian is initially constructed by neglecting electron-electron interactions, treating the system as three independent hydrogen-like electrons to yield a zeroth-order energy baseline of -275.51 eV. The antisymmetric fermionic nature of the exact wave function is rigorously enforced through the Slater determinant formalism. First-order perturbation theory is applied to evaluate static inter-electronic repulsion using exact Coulomb and exchange integrals, refining the energy state to -192.01 eV. To account for dynamical electronic correlation, second-order perturbation theory is computed numerically for virtual single-electron s-orbital transitions, leading to a total perturbative energy of -196.36 eV. A brief discussion of two-electron excitations is also included to encapsulate further physical realism within the framework. Furthermore, a non-orthogonal two-parameter variational approach is employed to model the shell-specific shielding effect. By optimizing the effective nuclear charges, the variational method establishes a superior upper bound energy of -201.187 eV. The results of both methods are comprehensively contrasted against each other and the reference baseline to provide critical insights into the nature of electron correlation and screening in multi-electron atoms.

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

Visual Place Recognition in Forests with Depth-Aware Distillation

Visual place recognition in natural forest environments remains challenging due to repetitive vegetation, weak structural cues, and significant appearance variation across traversals. To address this limitation, this paper proposes a lightweight depth-aware distillation framework that injects geometric cues into a DINOv2-based place recognition model, while maintaining its pre-trained descriptor space. Evaluated on the recent WildCross benchmark, the proposed approach yields gains over an appearance-only counterpart, providing robustness to appearance variations. These results demonstrate the importance of depth as a strong complementary modality for place recognition in natural environments and identify depth-aware distillation as a promising direction for more robust forest perception.

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

Reinforcement Learning for Accelerated Aerodynamic Shape Optimisation

arXiv:2507.17786v2 Announce Type: replace Abstract: We introduce a reinforcement learning (RL) based adaptive optimization algorithm for aerodynamic shape optimization focused on dimensionality reduction. The form in which RL is applied here is that of a surrogate-based, actor-critic policy evaluation MCMC approach allowing for temporal 'freezing' of some of the parameters to be optimized. The goals are to minimize computational effort, and to use the observed optimization results for interpretation of the discovered extrema in terms of their role in achieving the desired flow-field. By a sequence of local optimized parameter changes around intermediate CFD simulations acting as ground truth, it is possible to speed up the global optimization if (a) the local neighbourhoods of the parameters in which the changed parameters must reside are sufficiently large to compete with the grid-sized steps and its large number of simulations, and (b) the estimates of the rewards and costs on these neighbourhoods necessary for a good step-wise parameter adaption are sufficiently accurate. We give an example of a simple fluid-dynamical problem on which the method allows interpretation in the sense of a feature importance scoring.

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

Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability

arXiv:2603.10384v3 Announce Type: replace Abstract: Evaluating LLM reliability via scalar probabilities often fails to capture the structural dynamics of reasoning. We introduce TRACED, a framework that assesses reasoning quality through theoretically grounded geometric kinematics. By decomposing reasoning traces into Progress (displacement) and Stability (curvature), we reveal a distinct topological divergence: correct reasoning manifests as high-progress, stable trajectories, whereas hallucinations are characterized by low-progress, unstable patterns (stalled displacement with high curvature fluctuations). Leveraging these signatures, our probabilistic framework achieves competitive performance and superior robustness across diverse benchmarks. Crucially, TRACED bridges geometry and cognition by mapping high curvature to ''Hesitation Loops'' and displacement to ''Certainty Accumulation'', offering a physical lens to decode the internal dynamics of machine thought.

10.
arXiv (CS.CV) 2026-06-24

Revealing Training Data Exposure in Vision Language Large Models via Parameter Gradients

Vision-Language Large Models (VLLMs) trained on massive crawled corpora raise pressing copyright and data-provenance concerns. These concerns are particularly acute in healthcare, where patient medical images paired with clinical reports demand rigorous privacy safeguards. However, existing training data detection methods either fail in cross-modal scenarios or rely on superficial output signals with insufficient discriminative power. We introduce GradAudit, a gradient-based auditing framework that examines internal optimization dynamics rather than treating VLLMs as black boxes. Our approach builds on a key observation: model parameters converge to regions where gradients on training samples become stable and well-aligned, whereas gradients on non-training samples remain noisy and inconsistent. By analyzing these gradient signatures, GradAudit achieves strong separability and detects genuine image-text associations learned during training, not merely individual modality membership. Empirically, across both medical and general-domain datasets, GradAudit substantially outperforms state-of-the-art baselines in both pretraining and fine-tuning VLLMs. In a case study employing copyrighted content, we show that existing training data detection methods not only underestimate the extent of unauthorized data usage, but that this underestimation becomes more pronounced as models become more recent and more advanced.

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

Power Term Polynomial Algebra for Boolean Logic

arXiv:2603.13854v2 Announce Type: replace-cross Abstract: We introduce power term polynomial algebra, a representation language for Boolean formulae designed to bridge conjunctive normal form (CNF) and algebraic normal form (ANF). The language is motivated by the tiling mismatch between these representations: direct CNFANF conversion may cause exponential blowup unless formulas are decomposed into smaller fragments, typically through auxiliary variables and side constraints. In contrast, our framework addresses this mismatch within the representation itself, compactly encoding structured families of monomials while representing CNF clauses directly, thereby avoiding auxiliary variables and constraints at the abstraction level. We formalize the language through power terms and power term polynomials, define their semantics, and show that they admit algebraic operations corresponding to Boolean polynomial addition and multiplication. We prove several key properties of the language: disjunctive clauses admit compact canonical representations; power terms support local shortening and expansion rewrite rules; and products of atomic terms can be systematically rewritten within the language. Together, these results yield a symbolic calculus that enables direct manipulation of formulas without expanding them into ordinary ANF. The resulting framework provides a new intermediate representation and rewriting calculus that bridges clause-based and algebraic reasoning and suggests new directions for structure-aware CNFANF conversion and hybrid reasoning methods.

12.
arXiv (CS.CL) 2026-06-17

ChLogic: Evaluating Robustness of Logical Reasoning in Chinese Expressions

Large language models perform increasingly well on standardized logical reasoning benchmarks, but whether this ability remains robust beyond English is unclear. We introduce ChLogic, an English–Chinese aligned benchmark that tests whether models preserve logical reasoning performance when the same latent logical structure is expressed in English and diverse Chinese surface realizations. Built from formal logical templates, the benchmark contains three data sets: (i) the General aligned set, derived from 60 General Propositions across nine template families; (ii) the Difficult aligned set, derived from 40 Difficult Problems; and (iii) the Chinese-only set, covering 15 language-specific phenomenon types. Each aligned item pairs one English reference expression with five Chinese realizations. Experiments on Qwen3, Ministral, and GLM models reveal a persistent English–Chinese performance gap. Back-translation from standard Chinese into English often improves performance on the General aligned set, but produces mixed effects on the Difficult aligned set, where Qwen3-32B and GLM-5.1 perform worse after translation. These results indicate that Chinese surface realization, translation artifacts, and model-specific behavior jointly affect multilingual logical reasoning. Overall, ChLogic provides a useful stress test for the robustness of multilingual reasoning.

13.
arXiv (math.PR) 2026-06-18

On a class of unbalanced step-reinforced random walks

arXiv:2504.14767v4 Announce Type: replace Abstract: A step-reinforced random walk is a discrete-time stochastic process with long-range dependence. At each step, with a fixed probability $\alpha$, the so-called positively step-reinforced random walk repeats one of its previous steps, chosen randomly and uniformly from its entire history. Alternatively, with probability $1-\alpha$, it makes an independent move. For the so-called negatively step-reinforced random walk, the process is similar, but any repeated step is taken with its direction reversed. These random walks have been introduced respectively by Simon (1955) and Bertoin (2024) and are sometimes refered to the self-confident step-reinforced random walk and the counterbalanced step-reinforced random walk respectively. In this work, we introduce a new class of unbalanced step-reinforced random walks for which we prove the strong law of large numbers and the central limit theorem. In particular, our work provides a unified treatment of the elephant random walk introduced by Schutz and Trimper (2004) and the positively and negatively step-reinforced random walks.

14.
arXiv (CS.LG) 2026-06-15

The Program Is Still There: A Conservation Law for Program Discovery

arXiv:2606.13799v1 Announce Type: cross Abstract: Finding the shortest program that generates a sequence is uncomputable, and for six decades that fact has been mistaken for a wall around finding any generating program. It is not a wall but a price, and this paper measures it. For every algorithm that learns about a candidate program only through its score, a class spanning Levin search, evolutionary methods, simulated annealing, and the cross-entropy method, we define the coupling width of a search problem and prove an unconditional worst-case lower bound, exponential in that width with base one less than the domain size. From it follows a conservation law: structural knowledge injected into a search trades one for one against the search it removes, and their sum can never fall below the length of the program sought. Levin's 1973 upper bound and the lower bound proved here are the two ends of one conserved quantity, closing on each other as the instruction set grows. The only escape is to read a candidate's structure rather than its score, and its price, which we prove for generic targets, is incompleteness. A deterministic engine built on this theory recovers a generating program, certified by compressing its data and predicting an unseen continuation, for 2,383 of 3,914 sequences across four independent populations, including 244 of the 256 elementary cellular automata, with measured discovery cost rising along program length more than an order of magnitude inside the score-oracle worst case.

15.
bioRxiv (Bioinfo) 2026-06-23

Model-based inference of gene expression noise from single-cell RNA-sequencing data

The heterogeneity of expression levels among genetically identical cells, termed gene expression noise, is a property of the gene expression process whose importance in the biology of organisms and their evolution is increasingly recognized. Measuring gene expression noise requires single-cell expression data, as obtained from single-cell RNA sequencing (scRNASeq). Its estimation, however, is challenging owing to (i) the presence of technical noise in addition to biological noise, and (ii) the heterogeneity of cell types in the sampled population. We propose a maximum-likelihood framework to infer biological noise from scRNASeq data, while accounting for technical noise, dropout probabilities, and distinct cell sequencing depths. We demonstrate the parameter identifiability using simulations and that the resulting noise estimates are uncorrelated from the mean gene expression, and therefore do not need extra correction in downstream analyses, easing intra- and inter- genome comparisons. Using two technical replicates of scRNASeq data from the wild yeast *Saccharomyces paradoxus*, we show that expression noise can be inferred in a reproducible manner.

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

SpaTeoGL: Spatiotemporal Graph Learning for Interpretable Seizure Onset Zone Analysis from Intracranial EEG

arXiv:2602.11801v2 Announce Type: replace Abstract: Accurate localization of the seizure onset zone (SOZ) from intracranial EEG (iEEG) is essential for epilepsy surgery but is challenged by complex spatiotemporal seizure dynamics. We propose SpaTeoGL, a spatiotemporal graph learning framework for interpretable seizure network analysis. SpaTeoGL jointly learns window-level spatial graphs capturing interactions among iEEG electrodes and a temporal graph linking time windows based on similarity of their spatial structure. The method is formulated within a smooth graph signal processing framework and solved via an alternating block coordinate descent algorithm with convergence guarantees. Experiments on a multicenter iEEG dataset with successful surgical outcomes show that SpaTeoGL is competitive with a baseline based on horizontal visibility graphs and logistic regression, while improving non-SOZ identification and providing interpretable insights into seizure onset and propagation dynamics.

17.
arXiv (CS.CL) 2026-06-24

Reinforcement Learning Towards Broadly and Persistently Beneficial Models

As AI systems are deployed across increasingly diverse and high-stakes settings, model alignment must generalize beyond the tasks and domains seen during training. This is especially important for reinforcement learning (RL), which can introduce unexpected misalignment through reward hacking, deception, or other unintended strategies. We study whether RL on beneficial behavior, instantiated in realistic domains, can produce broad and persistent alignment generalization beyond the training distribution. We construct a dataset of realistic situations designed to measure and train beneficial traits, such as truthfulness, fairness, risk awareness, and corrigibility, spanning varied domains, including health, science, and education. We then train models with RL on this dataset and evaluate them on more than 50 independent benchmarks of alignment and beneficial behavior. Compared to a compute-matched baseline, beneficial trait RL improves performance on over 80% of these out-of-distribution benchmarks. We observe substantial out-of-distribution alignment transfer: a beneficial-behavior RL intervention entirely limited to one domain, health, produces broad improvements on non-health alignment evaluations, including reduced reward hacking, deception, and general misalignment. Finally, we study alignment persistence: whether behavior remains robustly aligned under attempts to steer models towards misalignment. Models trained with beneficial trait RL show improved persistence, including greater resistance to adversarial prompting and harmful finetuning; further work is required to isolate the sources of these effects. These results suggest that RL to reinforce beneficial behavior in realistic domains can produce models that are more robustly aligned with human flourishing.

18.
PLOS Medicine 2026-06-12

Placenta accreta spectrum in the 21st century: Challenging dogma and redefining disorder

Authors:

by Eric Jauniaux, Helena C. Bartels, Yalda Afshar Placenta accreta spectrum (PAS) is a serious pregnancy complication caused by abnormal placental attachment to the uterus. In this Perspective, Eric Jauniaux and colleagues discuss emerging evidence that challenges our long-held pathophysiological understanding of PAS, and argue that a critical reassessment of definition, diagnosis, and management is overdue. In this Perspective, Jonathan Evans and colleagues discuss why restricting access to joint replacement surgery based on BMI alone is not supported by evidence, and highlight how such rest rictions risk exacerbating stigma, inequity and avoidable harm to those who would benefit from surgery.

19.
Nature (Science) 2026-06-09

People are turning to AI chatbots to plug gaps in health information

A systematic assessment of health-related queries to a chatbot powered by artificial intelligence highlights shortfalls in health-care provision and the responsibilities of AI companies. A systematic assessment of health-related queries to a chatbot powered by artificial intelligence highlights shortfalls in health-care provision and the responsibilities of AI companies.

20.
medRxiv (Medicine) 2026-06-10

General-purpose large language models can achieve physician-level accuracy in complex medical data extraction

Background: Unstructured data represent about 80% of total electronic health records (EHR) data. Structuring this free text is essential for advancing clinical research, including cohort selection for trials, retrospective studies, and the development of disease registries. While manual chart review (MCR) remains the gold standard for extracting this clinical data, the process is inherently slow, resource-intensive, and susceptible to errors from human fatigue. We evaluated the extraction accuracy, safety, and efficiency of the HeLIX (Hepatology Logic-Integrated Extraction) framework, a Large Language Model (LLM) protocol using Google Gemini 3 Pro, compared to a gold-standard Manual Chart Review (MCR). Methods: A prospective validation study was conducted using 50 high-complexity, simulated hepatology discharge summaries designed to replicate the real-world heterogeneity of EHRs. The HeLIX framework employed a Zero-Shot, Structured Chain-of-Thought (CoT) prompting strategy enforced by a three-layer architecture: Clinical Reasoning Trace, Schema Enforcement, and Evidence Verification. The model extracted 45 distinct clinical variables. Performance was benchmarked against a consensus MCR. Results: Across 2,250 evaluated data points, the model achieved an overall Extraction Accuracy of 99.24% (95% CI: 98.8%-99.5%), with perfect concordance in 35/45 (77.8%) variables. For binary diagnostic variables, the model demonstrated an overall F1-score of 0.98, Recall of 0.99 and substantial inter-rater reliability (Cohens {kappa} = 0.97). Hallucinations were exceptionally rare (2/2250; 0.08%). Critical errors affecting clinical management occurred in only 2 instances (

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

Hölder++: Improving the Quality-Coherence Trade-off in Multimodal VAEs

arXiv:2606.13381v1 Announce Type: new Abstract: Existing approaches for multimodal variational autoencoders (VAEs) face a trade-off between generative quality and coherence-i.e., they struggle to generate realistic and diverse samples that, at the same time, are semantically consistent across modalities. A recent work shows that using a simple approximation to Hölder pooling as an aggregation method improves coherence over the SOTA MMVAE+, despite assuming a single shared representation across all modalities. Yet, it slightly compromises sample diversity. Inspired by this insight, we propose Hölder++, a novel multimodal VAE that improves the generative quality-coherence trade-off through: (i) the first implementation of Hölder pooling without any approximation for multimodal VAEs; (ii) an extended architecture that models distinct shared and private (i.e., modality-specific) representations (Hölder+); and (iii) hierarchical inference that further enhances the disentanglement between the shared and private representations (Hölder++). Our experiments corroborate that Hölder++ consistently improves the generative quality-coherence trade-off, yields more structured latent spaces, and learns shared representations that are informative for downstream tasks.

22.
medRxiv (Medicine) 2026-06-10

Human genetic evidence links serine biosynthesis to diabetic peripheral neuropathy

Diabetic peripheral neuropathy (DPN) is a common and disabling condition for which no disease-modifying therapies are available. Glycemic and metabolic drivers do not fully explain why only a subset of individuals with diabetes develop DPN, and genetic contributors remain poorly defined. We aimed to perform a multi-population genome-wide association study (GWAS) of DPN to highlight potential new etiological pathways and therapeutic targets. Methods We performed a multi-population GWAS of neuropathy in people with and without diabetes using the VA Million Veteran Program and UK Biobank, followed by replication in the All of Us Research Program (AoU), and gene-based and gene-set analyses to identify implicated pathways. Causal relationships between circulating serine levels and DPN were further tested using two sample Mendelian randomization. To further evaluate pathogenic potential, we analyzed rare, high impact variants in GWAS implicated genes among individuals with unresolved inherited neuropathies using the GENESIS platform. Findings Among individuals with type 2 diabetes, we identified seven genome wide significant loci (p

23.
arXiv (CS.LG) 2026-06-24

A Fast and Effective Method for Euclidean Anticlustering: The Assignment-Based-Anticlustering Algorithm

arXiv:2601.06351v2 Announce Type: replace Abstract: Anticlustering is an NP-hard combinatorial optimization problem that consists of partitioning a set of objects into equal-sized groups called anticlusters such that the objects in the same anticluster are as dissimilar as possible and thereby representative of the entire set of objects. Here we study the case where the dissimilarity metric is the squared Euclidean distance between the respective feature vectors. Applications of Euclidean anticlustering include social studies, cross-validation, creating mini-batches for stochastic gradient descent, and finding balanced K-cut partitions. In particular, machine-learning applications such as mini-batch generation involve million-scale datasets and very large values of K, making scalable anticlustering algorithms essential. We propose a new algorithm, the Assignment-Based Anticlustering (ABA) algorithm, that scales to instances with millions of objects and hundreds of thousands of anticlusters within seconds to minutes, which is far beyond what existing anticlustering methods can manage. We demonstrate here, via an extensive computational study, that our algorithm outperforms existing anticlustering methods in both solution quality and running time. This is so also for anticlustering with categories. For the related problem of balanced K-cut partitioning, our algorithm is superior to the well-known METIS method. The code of our algorithm is available on GitHub.

24.
arXiv (math.PR) 2026-06-18

Power Partitions and Hayman Functions

arXiv:2602.18575v3 Announce Type: replace Abstract: We prove, within the probabilistic framework of Khinchin families, that the generating function $P_k$ of partitions into $k$-th powers is strongly Gaussian in the sense of Báez-Duarte, and even further that it is a Hayman function. Thus the Hardy–Ramanujan asymptotic formula for the number $p_k(n)$ of partitions of $n$ into $k$-th powers which reads \[ p_k(n) \sim \frac{\alpha_k}{n^{(3k+1)/(2k+2)}} \exp\!\Big(\beta_k\, n^{1/(k+1)}\Big), \qquad n\to\infty, \] where $\alpha_k$ and~$\beta_k$ are explicit constants depending only on $k$, follows directly from Hayman's asymptotic formula for strongly Gaussian power series. The proof of strong Gaussianity of $P_k$ combines a Gaussianity criterion for Khinchin families with certain bounds of Tenenbaum, Wu and Li on the generating function; the asymptotic formula is recovered by computing asymptotic approximations of the mean and variance of the associated family. Analogous results are presented for the generating function $Q_k$ of partitions into distinct $k$-th powers.

25.
arXiv (CS.CV) 2026-06-15

ClinHallu: A Benchmark for Diagnosing Stage-Wise Hallucinations in Medical MLLM Reasoning

Building trustworthy medical multimodal large language models (MLLMs) is critical for reliable clinical decision support. Existing medical hallucination benchmarks mainly focus on data collection, but often ignore where hallucinations originate within the reasoning process. We find that hallucination sources vary across samples: errors may arise from visual misrecognition, incorrect medical knowledge recall, or flawed reasoning integration. To enable source-level hallucination diagnosis, we introduce ClinHallu, a benchmark for stage-wise hallucination diagnosis in medical MLLM reasoning. ClinHallu contains 7,031 validated instances, where each instance is augmented with a structured reasoning trace decomposed into Visual Recognition, Knowledge Recall, and Reasoning Integration. We also use stage-replacement interventions to measure how correcting specific stages affects the final answer. Beyond evaluation, we show that trace-supervised fine-tuning reduces stage-wise hallucinations. ClinHallu provides a fine-grained hallucination testbed for diagnosing and mitigating reasoning failures in medical MLLMs. The benchmark is publicly available at https://github.com/alibaba-damo-academy/ClinHallu.