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01.
arXiv (math.PR) 2026-06-19

The systole of random hyperbolic 3-manifolds

作者:
Anna Roig-Sanchis↗

arXiv:2406.11783v2 Announce Type: replace-cross Abstract: We study the systole of a model of random hyperbolic 3-manifolds introduced by Petri and Raimbault, answering a question posed in that same article. These are compact manifolds with boundary constructed by randomly gluing truncated tetrahedra along their faces. We prove that the limit, as the volume tends to infinity, of the expected value of their systole exists and we give a closed formula of it. Moreover, we compute a numerical approximation of this value.

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02.
arXiv (CS.AI) 2026-06-18

OrthoReg: Orthogonal Regularization for Hybrid Symbolic-Neural Dynamical Systems

作者:
Till Richter↗Niki Kilbertus↗

arXiv:2606.19145v1 Announce Type: cross Abstract: Dynamical systems are fundamental to modeling the natural world, yet modeling them involves a persistent trade-off: manually prescribed mechanistic models are interpretable by design but often overly simplistic and misspecified; in contrast, flexible data-driven neural methods lack physical insight. Hybrid modeling aims for the best of both worlds by combining a prescribed or symbolic, physics-based component with a flexible neural network. A critical challenge, however, is that the neural component may relearn mechanistic parts, yielding redundant and uninterpretable models, especially when the symbolic structure itself is discovered from data. Existing methods based on standard $L^2$ regularization rely on a projection argument that breaks when the symbolic component is learned through sparse discovery, allowing the neural augmentation to overlap with symbolic structure. We introduce OrthoReg (Orthogonal Regularization), which directly penalizes overlap between the symbolic and neural components, preventing symbolic structure from being absorbed by the neural residual. This yields a complementary decomposition: the symbolic part captures what the library can express, and the neural part captures what remains. On benchmark dynamical systems with partial library mismatch, OrthoReg improves symbolic recovery and out-of-distribution behavior.

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03.
arXiv (CS.LG) 2026-06-18

PACT: Preserving Anchored Cores in Task-vectors for Model Merging

作者:
Ningyuan Shi↗Zhipeng Zhou↗Hao Wang↗Chunyan Miao↗Peilin Zhao↗

arXiv:2606.18627v1 Announce Type: new Abstract: Model merging has emerged as a training-free alternative to multi-task learning, aiming to combine multiple task-specific fine-tuned models into a single multi-task model. Most existing model merging approaches follow the Task Arithmetic paradigm, which decomposes fine-tuned weights into pre-trained parameters and task vectors, and performs merging exclusively in the task-vector space. The effectiveness of this paradigm implicitly relies on the assumption that task-specific knowledge is encoded solely within task vectors. We argue that this assumption generally does not hold due to the intrinsic task preferences of pre-trained models. Specifically, we identify Load-Bearing Wall (LBW) dimensions, namely some task-critical knowledge that remains embedded in the pre-trained weights rather than being fully transferred into task vectors. We characterize LBW dimensions from both scalar-weight and subspace perspectives, thereby covering the major paradigms of existing model merging methods. Our analysis reveals that, by ignoring LBW dimensions, task-vector-based approaches fail to fully resolve task conflicts and may inadvertently damage task-specific knowledge encoded in the pre-trained model, leading to degradation. To address this issue, we propose PACT, which preserves the anchored task-specific cores (i.e., LBW dimensions) within task vectors by aligning their orthogonal complements with the subspace of the pre-trained weights. These aligned subspace components are then removed from the task vectors before applying existing model merging algorithms. Furthermore, we develop an efficient variant based on randomized SVD to improve scalability. PACT can be seamlessly integrated with existing methods. Extensive experiments across multiple benchmarks demonstrate that PACT consistently enhances mainstream model merging approaches and establishes new state-of-the-art performance.

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04.
arXiv (CS.AI) 2026-06-25

Geo-Strat-RL: Learning Geological Event Reasoning from Verifiable Tasks

作者:
Lukas Mosser↗

arXiv:2606.25000v1 Announce Type: cross Abstract: To evaluate whether vision-language models can reason about geological histories, it is necessary to construct observations for which the underlying process history is known. Furthermore, reasoning over geological histories is not just a question of recognizing visual patterns, but also of understanding temporal and structural relationships that may be only indirectly visible or highly ambiguous. When ground-truth event histories are not uniquely identifiable or are unavailable, it remains an open challenge to teach models capable of visual reasoning to produce valid geological reconstructions that are consistent with both observed evidence and geological principles. We therefore investigate whether defining a verifiable geological reasoning task can improve geological event reconstruction across observation domains through reinforcement learning with verifiable rewards (RLVR). To this end, we present Geo-Strat-RL, a synthetic environment that generates stratigraphic observations and compact visible-evidence event histories. The environment combines a geological generator with an executable verifier that scores chronology, event identity, deposition, and structural relationships. We show that RLVR improves geological reconstruction in vision-language models (VLMs), increasing geological content scores on held out stratigraphic diagrams. We further evaluate the same held-out geological histories in a synthetic seismic observation domain by converting the generated scenes into acoustic-impedance-derived amplitude sections. In this controlled paired-renderer setting, we present evidence that geological reasoning learned from stratigraphic diagram-domain RLVR training transfers to synthetic seismic representations without seismic-specific training examples, supporting the hypothesis that RLVR can teach reusable geological reasoning concepts across related observation formats.

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06.
bioRxiv (Bioinfo) 2026-06-12

PeptiDIA: A Machine Learning Framework for Enhanced Peptide Identification in Fast-Gradient Data-Independent Acquisition Proteomics

作者:
Ortona↗Leclercq↗Roux-Dalvai↗Routy↗Bonnet↗Droit↗

Data-independent acquisition (DIA) mass spectrometry has become increasingly prevalent in proteomics as advances in instrumentation, chromatography, and computational analysis have enabled robust proteome identification across complex biological samples. However, analytical depth achieved with fast chromatographic gradients remains lower than that obtained using long-gradients, reflecting a throughput-depth trade-off. Here, we present PeptiDIA, a machine learning framework that enhances peptide identification in fast-gradient DIA data by leveraging paired fast and long-gradient acquisitions from identical samples. PeptiDIA processes DIA-NN outputs generated at relaxed false discovery rate thresholds to obtain expanded candidate peptide pools and trains gradient-boosted decision tree models using long-gradient identifications as reference labels. The model integrates DIA-NN features with engineered peptide descriptors and applies isotonic regression to calibrate probabilities, enabling controlled peptide recovery relative to the long-gradient reference. Applied to human and murine datasets spanning six tissues acquired on an Orbitrap Exploris 480, PeptiDIA increased peptide identifications by 25-34% at 1% target reference-discordance rate (RDR) and increased the number of protein groups containing at least one rescued peptide by 15-17%. Overall, PeptiDIA improves the identification depth of fast-gradient DIA-NN workflows without altering acquisition strategies. The framework is available as a web application and command-line tool at https://github.com/Jordano700/PeptiDIA.

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07.
arXiv (CS.LG) 2026-06-18

Fair Online Resource Allocation

作者:
Christopher En↗Yuri Faenza↗Andrea Lodi↗Gonzalo Mu\~noz↗

arXiv:2606.18679v1 Announce Type: cross Abstract: We study the problem of fair online resource allocation, motivated by applications such as refugee resettlement and airline scheduling, where agents arrive sequentially and must be assigned to facilities with limited capacities. We introduce a model that maximizes the overall welfare subject to resource constraints and a Lipschitz fairness requirement, which ensures that similar agents arriving in the same batch receive similar expected outcomes. We first analyze the offline problem, proving that the value of the optimal fair allocation is at least an $\Omega(1/\gamma)$ fraction of the optimal unfair allocation, where $\gamma$ is the fairness coefficient, thereby bounding the price of fairness. For the online setting, we propose an algorithm based on dual mirror descent that enforces fairness constraints within batches while estimating optimal dual variables. We prove that this algorithm achieves sublinear regret relative to the optimal offline fluid benchmark. Finally, we validate our theoretical results using real-world data from the Refugee Economies Programme, demonstrating the algorithm's performance and examining the trade-offs between welfare maximization and fairness enforcement.

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

Structural MRI Synthesis for Alzheimer's Disease via Conditional Diffusion on Anatomical Masks

作者:
Muge Zhang↗Muhammad Ali Khaliq↗Jamal Alsakran↗Byeong Kil Lee↗Jeeho Ryoo↗

arXiv:2606.18354v1 Announce Type: cross Abstract: Recent advances in generative machine learning models have significantly improved medical imaging, offering promising solutions for data augmentation, privacy preservation, and improved model generalization. However, synthesizing high-quality structural MRI data for Alzheimer's Disease (AD) remains challenging due to the subtle, region-specific, and progressive anatomical changes associated with neurodegeneration. In this paper, we extend the Med-DDPM conditional diffusion model – originally designed for brain tumor synthesis – to generate 3D structural MRIs specifically tailored to AD. We adopted Med-DDPM due to its established stability and structural fidelity compared to other generative models, which makes it particularly suitable for capturing the subtle anatomical changes characteristic of AD. Our approach conditions the diffusion process on anatomical segmentation masks derived from the ADNI dataset, incorporating key AD-relevant brain structures into the generation process. We systematically evaluate the quality and utility of the synthetic images by training segmentation models on real, synthetic, and hybrid (mixed) datasets. Experimental results demonstrate that segmentation models trained exclusively on synthetic data achieve comparable Dice scores (0.6532) to those trained on real data (0.6513), while exhibiting significantly enhanced recall. Notably, models trained on hybrid datasets (mixing real and synthetic images) outperform both real and synthetic-only baselines, achieving a Dice score of 0.7244. These findings underscore the successful use of conditional diffusion models for generating anatomically accurate, AD-specific synthetic MRIs, and highlight their potential for enhancing training data availability, improving diagnostic accuracy, and promoting research reproducibility in neuroimaging studies.

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09.
arXiv (CS.CL) 2026-06-24

To Compare, or Not to Compare: On Methodological Practices in Evaluating Social Bias

作者:
Federico Marcuzzi↗Xuefei Ning↗Roy Schwartz↗Iryna Gurevych↗

As Large Language Models are increasingly deployed in critical applications, robustly evaluating their social biases is paramount. However, the current literature suffers from widespread methodological fragmentation, which yields contradictory conclusions. This stems largely from ignoring the structural framing of benchmark-level evaluations. To resolve this, we introduce a unified and controllable framework that standardizes heterogeneous benchmarks to systematically contrast isolated demographic assessments with forced-choice comparative settings. Crucially, this allows us to disentangle the confounding effects of Chain-of-Thought reasoning, neutral fallback options, and other structural artifacts in social bias evaluations. Our evaluation across multiple model families reveals a massive, systematic paradigm gap: while isolated assessments limit prejudice activation, comparative settings act as aggressive catalysts for latent discrimination, a shift primarily driven by underspecified contexts. Alarmingly, CoT reasoning exacerbates social biases under comparative settings, and this systemic bias persists as a deterministic prejudice even when models are provided neutral fallback options or claim to answer randomly. Finally, we demonstrate that this comparative prejudice is a generalized phenomenon that scales positively with model size. Ultimately, we offer a crucial methodological guideline: while researchers must leverage comparative settings to robustly audit hidden biases, practitioners cannot safely rely on comparative deployments in ambiguous real-world tasks.

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

Scaling limit of additive functionals for reversible non-gradient exclusion process: critical cases

作者:
Chenlin Gu↗Linzhi Yang↗Linjie Zhao↗

arXiv:2606.13442v1 Announce Type: new Abstract: For the reversible speed-change exclusion process $(\eta_t)_{t \geq 0}$ in $\mathbb{Z}^d$, we study the scaling limit of additive functionals ${\Gamma_t(f) = \int_0^t f(\eta_s)\, \mathrm{d} s}$. Concerning the local centered function $f$, the previous work [Commun. Math. Phys. 104, 1-19, 1986] by Kipnis and Varadhan and [Comm. Pure Appl. Math., 66: 649-677, 2013] by Gon{ç}alves and Jara respectively covered the cases $d \geq 3$ and $d=1$. The present paper completes the missing part $d=2$, and also develops the theory for functions with higher degree. The novelty is a quantitative homogenization of the resolvent, which allows to overcome the obstacle of correlation function in non-gradient models.

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11.
arXiv (quant-ph) 2026-06-16

Optimal learning of quantum channels in diamond distance

作者:
Antonio Anna Mele↗Lennart Bittel↗

arXiv:2512.10214v3 Announce Type: replace Abstract: Quantum process tomography, the task of estimating an unknown quantum channel, is a central problem in quantum information theory. A long-standing open question is how many uses of an unknown channel are required to learn it in diamond distance, the standard metric for distinguishing quantum processes. While quantum state tomography is well understood, for general channels the problem remained open beyond the unitary case. Here we establish the query complexity of channel tomography with optimal dependence on the dimension parameters, at any fixed constant accuracy. We design an algorithm showing that any channel with input/output dimensions $d_{\mathrm{in}},d_{\mathrm{out}}$ and Kraus rank at most $k$ can be learned to accuracy $\varepsilon$ using $O(d_{\mathrm{in}}d_{\mathrm{out}}k/\varepsilon^{2})$ channel uses. Conversely, we prove that $\Omega(d_{\mathrm{in}}d_{\mathrm{out}}k)$ uses are necessary at constant accuracy and that, for non-minimal Kraus rank, a separate $\Omega(1/\varepsilon^{2})$ contribution is unavoidable. Since channels subsume states, unitaries, isometries, and measurements as special cases, our protocol provides a unified framework for these tomography tasks, yielding new guarantees for isometry and measurement tomography while recovering known optimal scalings for state and unitary tomography. Our algorithm follows the natural strategy of performing optimal tomography on the Choi state. The main technical contribution is to show that this suffices to control the induced diamond-distance error, avoiding the dimension loss incurred by a naive conversion from Choi-state trace distance to channel diamond distance. The protocol uses the channel non-adaptively to prepare Choi-state copies, purifies them in parallel, and performs optimal pure-state tomography on the resulting purifications. Hence, we reduce channel tomography to pure-state tomography.

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12.
arXiv (quant-ph) 2026-06-19

Subsystem Quantum Error Correction for Noisy Quantum Metrology

作者:
Qiushi Liu↗Sisi Zhou↗

arXiv:2606.19628v1 Announce Type: new Abstract: Quantum error correction has been successfully applied to enhance the precision of parameter estimation in the presence of noise. Nonetheless, existing methods require a number of noiseless, controllable ancillae and lack efficient encoding and decoding procedures. In this Letter, we demonstrate that subsystem error correction provides a new direction that can substantially simplify the metrological protocol. We derive general conditions under which subsystem stabilizer codes achieve the Heisenberg limit and show that, for broad classes of noise, this can be realized by syndrome-free protocols using at most a single ancilla qubit. Furthermore, we extend this framework to dynamical error correction and show that Floquet codes can protect time-dependent metrological signals in reaching the Heisenberg limit.

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

ASyMOB: Algebraic Symbolic Mathematical Operations Benchmark

作者:
Michael Shalyt↗Rotem Elimelech↗Ido Kaminer↗

Large language models (LLMs) are increasingly applied to symbolic mathematics, yet existing evaluations often conflate pattern memorization with genuine reasoning. To address this gap, we present ASyMOB, a high-resolution dataset of 35,368 validated symbolic math problems spanning integration, limits, differential equations, series, and hypergeometrics. Unlike prior benchmarks, ASyMOB systematically perturbs each seed problem using symbolic, numeric, and equivalence-preserving transformations, enabling a fine-grained assessment of generalization. Our evaluation reveals three key findings: (1) most models' performance collapses under minor perturbations, while top systems exhibit an apparent regime shift in robustness; (2) integrated code tools stabilize performance, particularly for weaker models; and (3) we identify examples where Computer Algebra Systems (CAS) fail while LLMs succeed, as well as problems solved only via a hybrid LLM-CAS approach, highlighting a promising integration frontier. ASyMOB serves as a principled diagnostic tool for measuring and accelerating progress toward building verifiable, trustworthy AI for scientific discovery.

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14.
arXiv (CS.LG) 2026-06-18

Reinforcement Learning for Accelerated Aerodynamic Shape Optimisation

作者:
Florian Sobieczky↗Alfredo Lopez↗Erika Dudkin↗Christopher Lackner↗Matthias Hochsteger↗Bernhard Scheichl↗Helmut Sobieczky↗

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.

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

Stringalign: Moving beyond summary statistics with a transparent Unicode-aware tool for evaluating automatic transcription models

作者:
Yngve Mardal Moe↗Marie Roald↗

Comparing text strings is crucial when evaluating and understanding the performance of various text processing tasks such as document recognition and audio transcription. With an increasingly complex landscape of AI-based handwritten text recognition (HTR), optical character recognition (OCR) and automatic speech recognition (ASR) models, there is a need for tools that facilitate evaluation in a flexible and reproducible way. This paper presents Stringalign, a Python library designed to simplify the evaluation process for automatic transcription projects and facilitate transparent evaluation. Stringalign's tools to examine and visualise both the rate of errors and the types of errors a model makes, give insights into possible improvements and help inform model selection for a particular task. Widely used string comparison metrics, such as the character and word error rates (CER and WER), although useful, can be ambiguous due to varying definitions of what constitutes a character and a word. Stringalign addresses this challenge by ensuring all preprocessing (i.e. normalisation and tokenisation) is transparent and easily replicable, and by providing tools to move beyond summary statistics and analyse common model errors. Moreover, Stringalign adheres to FAIR (Findable, Accessible, Interoperable, and Reusable) principles for research software while staying lightweight and easy to adapt into researchers existing workflows. In this paper, we discuss challenges with character and word level string comparisons and show through examples that where existing tools can yield opaque and sometimes confusing results, Stringalign provides an easy-to-use and unambiguous alternative.

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

FairGen: Preference-Aligned Diffusion for Demographically Equitable Medical Image Synthesis

作者:
Zhimin Li↗Ruichen Zhang↗Zhen Tan↗Howard J Aizenstein↗Jingtong Hu↗Tianlong Chen↗

Medical imaging is central to modern diagnostics, and artificial intelligence (AI) systems are increasingly used to support image-based analysis by improving efficiency, accuracy, and access to care. However, inequities in healthcare access and differential disease prevalence create severe demographic imbalances in clinical image data. Such imbalances are compounded by the fact that diseases can manifest with distinct features across demographic groups, rendering certain phenotypic presentations naturally rare. AI models trained on such imbalanced data risk perpetuating diagnostic bias and widening healthcare disparities. Here we introduce FairGen, a fairness-aware diffusion framework that synthesizes demographically balanced medical images while preserving pathology-relevant visual features. By embedding physician-aligned preferences into the generation process, FairGen improves subgroup coverage during synthesis and downstream classification. Applied to dermatology, radiology, and neuroimaging benchmark tasks, FairGen achieves fairness improvements of 95.9% for skin images, 80.0% for chest radiography, and 35.2% for brain MRI, while maintaining competitive diagnostic accuracy relative to models trained on original clinical data. Clinician-facing expert review and external validation on independent cohorts further support that these gains extend beyond standard fidelity metrics and are not confined to the original in-distribution datasets.

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17.
arXiv (CS.LG) 2026-06-25

Breaking Data Symmetry is Needed For Generalization in Feature Learning Kernels

作者:
Marcel Tom\`as Bernal↗Neil Rohit Mallinar↗Mikhail Belkin↗

arXiv:2604.00316v2 Announce Type: replace-cross Abstract: Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, such as learning modular arithmetic (Power et al., 2022). We study grokking on algebraic tasks in a class of feature learning kernels via the Recursive Feature Machine (RFM) algorithm (Radhakrishnan et al., 2024), which iteratively updates feature matrices through the Average Gradient Outer Product (AGOP) of an estimator in order to learn task-relevant features. Our main experimental finding is that generalization occurs only when a certain symmetry in the training set is broken. Furthermore, we empirically show that RFM generalizes by recovering the underlying invariance group action inherent in the data. We find that the learned feature matrices encode specific elements of the invariance group, explaining the dependence of generalization on symmetry.

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18.
arXiv (CS.CL) 2026-06-19

Pruning via Causal Attribution Preserves Reasoning Performance in Large Language Models

作者:
Amogh Sheth↗Biruk Assefa↗Yi Wen Huang↗Andrew Lin↗Yuhao Ge↗

Large language models (LLMs) excel at multi-step reasoning but incur substantial inference cost. We introduce Causal Attribution Pruning (CAP), a training-free method that identifies critical attention heads by measuring their causal impact on reasoning tasks and uses these head-level scores to guide fine-grained weight pruning. For each attention head, CAP estimates the expected performance degradation when the head is masked during forward passes on a small calibration set of reasoning problems. These causal scores are then converted into weight-level importance values for the corresponding projection matrices. Unlike magnitude-only or activation-based criteria, CAP's interventional measurement directly captures each head's functional contribution, yielding relative accuracy gains of up to 61% over Wanda on ARC-Challenge at 20% sparsity. We evaluate CAP on GSM8K, StrategyQA, and ARC-Challenge using Llama-3-8B-Instruct and Mistral-7B-Instruct at 10%, 20%, and 50% sparsity. At moderate sparsity (10-20%), CAP improves over Wanda in most model-benchmark configurations. with especially large gains on ARC-Challenge for Llama-3. Our results suggest that attention-head-level causal attribution can better preserve reasoning performance on downstream benchmarks than correlational pruning criteria at equivalent sparsity, while remaining limited by coarse MLP attribution at 50% sparsity.

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19.
arXiv (CS.AI) 2026-06-18

Why SWAVE May Not Be All You Need:A Concept-Evolution Retrospective on Complex-Valued Recurrent Language Models

作者:
Ramprasath Ganesaraja↗Swathika N↗Sahil Dilip Panse↗

arXiv:2606.18324v1 Announce Type: cross Abstract: SWave is a complex-valued recurrent language model (169.26M parameters, D=384, L=16, T=2048) trained on FineWeb-Edu using 2xH100 NVL. It was designed around three founding premises: that representing language as complex waves rather than real-valued numbers enables richer information encoding; that a Cayley-parameterised unitary transition provides a mathematical guarantee against state decay or explosion; and that a hidden state which rotates rather than shrinks preserves signal integrity over arbitrarily long contexts. The core of SWave evolved substantially across three development phases. The Resonance Head was found to structurally admit imaginary-channel collapse as a global loss minimum (a failure mode we term cos-domination collapse) and was superseded by an untied head with independent real and imaginary embedding tables from the Phase-Associative Memory (PAM) architecture. This resolved the degenerate minimum and enabled stable 200,000-step training (best-step PPL 22.0 at step 89,861). ComplexNorm and the Wave Propagation Scan proved load-bearing throughout all three phases and were retained to the final architecture. ProtectGatedScan was reframed as a structural prior rather than a learned behaviour. The four multi-scale retention concepts showed no measurable improvement under controlled evaluation and were found non-load-bearing. The ComplexGatedUnit was superseded by a real-valued squared-ReLU channel mixer with fewer parameters. The auxiliary training objectives showed no benefit once structural constraints were resolved. The investigation yields a formal characterisation of cos-domination collapse, a parallel scan with a log-space backward pass for numerical stability, six transferable engineering principles for complex-valued recurrent training, and a plan-to-code traceability methodology for catching structural divergences that conventional test suites miss.

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20.
arXiv (math.PR) 2026-06-11

Multiple Poisson-Dirichlet diffusions on generalized Kingman simplices

作者:
Cristina Costantini↗Matteo Ruggiero↗

arXiv:2602.20266v2 Announce Type: replace Abstract: We construct a new class of infinite-dimensional diffusions with values in a generalized Kingman simplex with finitely many marks. The model describes the temporal evolution of the relative frequencies of infinitely many types that are labeled by a finite number $H$ of marks, but unlabeled within each mark. We first establish a blockwise skew-product representation for a finite-type Wright-Fisher diffusion, extending the aggregation-renormalization self-similarity property of Dirichlet laws. The decomposition separates an $H$-dimensional Wright-Fisher diffusion governing the evolving random mark masses, from $H$ Wright-Fisher diffusions, each run on its own random clock, which describe the evolution of the relative frequencies within each mark. After ranking the within-mark frequencies in decreasing order, we identify the distributional limit as the number of types per mark tends to infinity and we derive an explicit form of its infinitesimal generator on a suitable domain. The limiting diffusion admits the multiple Poisson-Dirichlet distribution as a stationary distribution; it recovers the infinitely-many-neutral-alleles diffusion when all types share the same mark and yields a diffusion on the Thoma simplex when there are two marks.

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21.
arXiv (CS.CV) 2026-06-24

Cyclic Denoising Reveals Ultrastable Memories in Diffusion Models

作者:
Rishabh Sharma↗Stefano Martiniani↗

We introduce cyclic denoising – repeated forward and reverse diffusion at controlled noise amplitudes – as an extraction attack for image diffusion models. Inspired by random organization in disordered solids, cyclic denoising exposes regions of the learned distribution that are largely inaccessible to standard sampling. The dynamics drive samples toward attractors with a broad stability spectrum. The deepest attractors are ultrastable: they regenerate after near-total corruption and persist through thousands of noising-denoising cycles. Many of these attractors correspond to memorized training images, including stock photographs, brand watermarks, and web-crawl artifacts. The attack requires only sampler-level control, with no gradients, weight inspection, prompts, captions, or prior knowledge of the training data. Unlike generate-and-filter attacks, which rely on large-scale prompted generation and post-hoc similarity or membership-inference filtering, our main protocol is fully unconditioned. We demonstrate the phenomenon in Stable Diffusion v1.4 and in a pixel-space DDPM, showing consistent behavior across latent- and pixel-space diffusion models. Across noise amplitudes, we observe a yielding-like transition: low-amplitude cycling produces trivial absorbing fixed points or limit cycles, while larger amplitudes induce rearrangements, basin hopping, and long-lived trapping in structured memorized attractor basins. We also observe hierarchical partial absorption, prompt-stabilized basins, and cross-initial-condition universality of the recovered attractor set. Our results therefore show that cyclic denoising is both a physics-inspired probe of generative landscapes and a practical tool for memorization auditing, with implications for privacy, copyright compliance, and model fingerprinting.

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

Supervised Reinforcement Learning for the Coordination of Distributed Energy Resources

作者:
Haoyuan Deng↗Yihong Zhou↗Thomas Morstyn↗Yi Wang↗

arXiv:2606.24947v1 Announce Type: new Abstract: The increasing integration of distributed energy resources (DERs) is crucial for power system decarbonization, yet unlocking DERs' flexibility is challenged by their inherent uncertainties and modelling complexity. As traditional optimization methods struggle with such uncertainty and complexity of DERs, reinforcement learning (RL) has emerged as a promising alternative for DER management. However, standard RL methods suffer from sample inefficiency and sub-optimality when trained from scratch. Inspired by the training paradigms in large language models, this paper proposes a Supervised Reinforcement Learning (SRL) framework for learning DER coordination policies. This framework first pre-trains a policy on demonstration data in a supervised-learning fashion, which is then further fine-tuned using RL. Furthermore, we propose a two-step fine-tuning process: offline fine-tuning for enhancing policy performance and online fine-tuning for adapting it to the real-world dynamics. Experiments demonstrate that RL implementations based on the proposed framework significantly outperform all benchmarks, achieving high cost efficiency even under low-quality demonstration data.

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

Weight-Space Geometry of Offline Reasoning Training

作者:
Aleksandr Nikolich↗Igor Kiselev↗Vladimir Platonov↗Karina Romanova↗

arXiv:2606.23740v1 Announce Type: cross Abstract: Offline reinforcement-learning losses (RFT, RIFT, DFT, Offline GRPO, DPO) are widely used to distill reasoning from large teachers into smaller students, and are typically compared on downstream accuracy alone. We ask whether they are mechanistically distinct or converge to a similar weight update. Training six methods (SFT, RFT, DFT, RIFT, Offline GRPO, DPO) on identical math rollouts from a single base model (Qwen3-4B) with attention-only LoRA, we analyze the resulting deltas via cosine similarity, principal-angle subspace analysis, linear mode connectivity, and CKA. We observe: (i) SFT, RFT, and RIFT have nearly colinear weight deltas (cosine >= 0.97, top-1 principal angle ~7 deg median over 144 modules) and comparable GSM8K accuracy (87-88%, n=1319; pairwise McNemar p >= 0.15); (ii) DFT diverges further in direction than any reward-weighted method despite using the same data; (iii) Offline GRPO adds a substantial component orthogonal to the SFT direction (~67% globally, up to ~86% in late layers) while staying in the SFT loss basin; (iv) DPO sits in a near-orthogonal subspace, shows a mode-connectivity barrier, and collapses late-layer CKA to ~0.46. DPO also reaches the highest accuracy in our protocol on both GSM8K (93.5%, McNemar p < 10^-9 vs. each other method) and AIME26 (30.0% vs. 3.3-10.0%); its training uses a 10x smaller learning rate than the others (the standard convention), so the update-norm and accuracy gaps reflect loss-function and optimizer choices jointly, and a learning-rate-matched DPO comparison is left for future work.

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24.
arXiv (quant-ph) 2026-06-12

Exploring Exotic Spin-Dependent Interactions Beyond the Standard Model: Theoretical Foundations and Experimental Investigations

作者:
L. Y. Wu↗H. Yan↗

arXiv:2606.13318v1 Announce Type: cross Abstract: New interactions mediated by novel particles propose solutions to several important questions in modern physics. Axions serve as examples of such particles; they are lightweight and interact weakly with ordinary matter. This category of particles, including those similar to axions-termed Axion-Like Particles (ALPs)-arises from diverse theoretical frameworks, such as the Peccei-Quinn mechanism addressing the strong CP problem, string theory, and spontaneous supersymmetry breaking. Given their light mass and weak coupling, ALPs are also possible candidates for cold dark matter. Introducing these new interactions mediated by novel particles not only tackles several challenges in modern physics but also raises a crucial question: Are there undiscovered interactions beyond the Standard Model? Many of the interactions predicted by these theories are spin-dependent, which is the primary focus of this review. In this review, we first outline the theoretical foundations for investigating exotic spin-dependent interactions, highlighting their importance in various models beyond the Standard Model. We examine the potential roles of new lightweight particles in mediating these interactions, which may enhance our understanding of dark matter. Relevant formulas derived from theoretical models are included to support experimental investigations. Following this theoretical framework, we conduct a detailed review of recent experimental efforts to detect these exotic interactions. A systematic review of current constraints on these interactions is presented, along with an assessment of various detection approaches.

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

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

作者:
Xuanlang Dai↗Yujie Zhou↗Long Xing↗Jiazi Bu↗Xilin Wei↗Yuhong Liu↗Beichen Zhang↗Kai Chen↗Yuhang Zang↗

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/.

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