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01.
arXiv (CS.LG) 2026-06-11

What Uncertainties Do We Need for Dynamical Systems?

arXiv:2606.11988v1 Announce Type: new Abstract: The distinction between aleatoric and epistemic uncertainty has received considerable attention in machine learning research, mainly in the context of supervised learning but also in other settings such as generative modeling. In this paper, we offer a machine learning perspective on uncertainty modeling for dynamical systems, which has been studied much less so far. In particular, we ask: what uncertainties do we need for dynamical systems? We discuss sources of uncertainty, clarify their nature (aleatoric or epistemic), and consider how the objectives of representing and quantifying uncertainty vary across different tasks.

02.
arXiv (CS.LG) 2026-06-12

Efficient Stochastic Optimisation via Sequential Monte Carlo

arXiv:2601.22003v2 Announce Type: replace-cross Abstract: The problem of optimising functions with intractable gradients frequently arises in machine learning and statistics, ranging from maximum marginal likelihood estimation procedures to fine-tuning of generative models. Stochastic approximation methods for this class of problems typically require inner sampling loops to obtain (biased) stochastic gradient estimates, which rapidly becomes computationally expensive. In this work, we develop sequential Monte Carlo (SMC) samplers for optimisation of functions with intractable gradients. Our approach replaces expensive inner sampling methods with efficient SMC approximations, which can result in significant computational gains. We establish convergence results for the basic recursions defined by our methodology which SMC samplers approximate. We demonstrate the effectiveness of our approach on the reward-tuning of energy-based models within various settings.

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

ForecastBench-Sim: A Simulated-World Forecasting Benchmark

Forecasting benchmarks for general-purpose AI systems usually inherit the constraints of the real world: outcomes resolve slowly, tail events are rare, and counterfactual questions are difficult to score. We introduce ForecastBench-Sim, a simulated-world forecasting benchmark built on game rollouts from Freeciv, a turn-based strategy game modelled on the Civilization series. Forecasters receive a fixed world report (a structured snapshot of the current game state) and answer questions about hidden future states; the benchmark then continues the simulation and scores forecasts. Because the world is simulated, the same setup can generate continuous or binary forecasting questions at arbitrary time horizons, paired intervention worlds for conditional or causal questions, and resolved examples of rare or disruptive outcomes. We describe the benchmark pipeline, question families, scoring protocol, and release artifacts, and report validation slices from model evaluations and an anonymized human pilot. ForecastBench-Sim is intended to complement real-world forecasting benchmarks by providing controlled, immediately resolvable tasks for studying probabilistic reasoning under dynamic world states.

04.
arXiv (CS.LG) 2026-06-18

Self-Driving Datasets: From 20 Million Papers to Nuanced Biomedical Knowledge at Scale

arXiv:2605.07022v3 Announce Type: replace Abstract: Manually curated biomedical repositories – spanning bioactivity, genomics, and chemistry – are expensive to maintain, lag behind primary literature, and discard experimental context, obscuring nuances needed to assess data correctness and coverage. We show that PubMed itself can be autonomously and cost-effectively turned into structured datasets that are larger, more nuanced, and more accurate than the curated databases they replace. We present three coupled contributions: (1) an LLM-based entity-tagging pipeline, grounded in nine biomedical ontologies, that tags 4.5B entities across 19 categories in a 22.5M-paper, 2.5T-token PubMed corpus; (2) hybrid sparse-dense retrieval supporting entity-filtered semantic queries over the tagged corpus; and (3) Starling, a multi-agent deep research system that, given only a natural-language task description, designs precision- and recall-targeted retrieval filters, induces an extraction schema, and emits structured records with nuance-rich fields and supporting passages. Across six tasks – blood-brain barrier permeability, oral bioavailability, acute toxicity (LD50), gene-disease associations, protein subcellular localization, and chemical reactions – Starling produces ~6.3M records (91K-3M per task); several are, to our knowledge, the largest public datasets for their property. Frontier-model rejection of our extractions is 0.6-7.7% across tasks, far below error rates we measure on widely used curated counterparts (e.g., 16.5% on BBB_Martins, 7.3% on Bioavailability_Ma). Beyond scale and accuracy, the supporting passages carry nuance tabular databases discard – e.g., oral bioavailability may depend on fed vs. fasted state. Together, the corpus, retrieval, and agent establish a foundation for AI-driven therapeutic design. Code and datasets: https://github.com/starling-labs/starling.

05.
arXiv (CS.LG) 2026-06-11

Reverse Flow Matching: A Unified Framework for Online Reinforcement Learning with Diffusion and Flow Policies

arXiv:2601.08136v2 Announce Type: replace Abstract: Diffusion and flow policies are gaining prominence in online reinforcement learning (RL) due to their expressive power, yet training them efficiently remains a critical challenge. A fundamental difficulty that distinguishes online RL from standard generative modeling is the lack of direct samples from the target Boltzmann distribution defined by the Q-function. To address this, two seemingly distinct families of methods have been proposed for diffusion policies: a noise-expectation family, which uses a weighted average of noise as the training target, and a gradient-expectation family, which employs a weighted average of Q-function gradients. However, it remains unclear how these objectives are formally related, or whether they can be synthesized into a more general formulation. In this paper, we propose a unified framework, reverse flow matching (RFM), which rigorously addresses the problem of training diffusion and flow models without direct target samples. By adopting a reverse inferential perspective, we formulate the training target as a posterior mean estimation problem given an intermediate noisy sample. Crucially, we introduce Langevin Stein operators to construct zero-mean control variates, deriving a general class of estimators that share the same expectation. We show that existing noise-expectation and gradient-expectation methods are simply two specific instances within this broader class. This unified view yields two key advancements: it extends the capability of targeting Boltzmann distributions from diffusion to flow policies, and it enables the principled combination of Q-value and Q-gradient information to form an effective estimator, thereby improving training efficiency and stability. We instantiate RFM to train a flow policy in online RL and demonstrate improved performance on continuous-control benchmarks compared to diffusion policy baselines.

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

Compiler-First State Space Duality and Portable $O(1)$ Autoregressive Caching for Inference

arXiv:2603.09555v2 Announce Type: replace-cross Abstract: High-throughput Mamba-2 inference is usually tied to fused CUDA and Triton kernels, limiting portability across accelerator backends. We show that the state space duality (SSD) recurrence has a compiler-friendly structure: diagonal per-head dynamics, fixed-size chunking, einsum-dominated compute, and static control flow. Expressing this structure in standard JAX primitives gives a single-source inference path with no custom kernels, a registered JAX PyTree cache, and a compiled on-device autoregressive loop. On a single Google Cloud TPU v6e, batch-1 prefill reaches approximately 140 TFLOPS, or 15% model FLOP utilisation (MFU), the roofline ceiling for this regime, and cached decode reaches up to 64% hardware bandwidth utilisation (HBU). At a 4096-token context, cached decode is 27x–36x faster than full-prefix recomputation across five Mamba-2 checkpoints from 130M to 2.7B parameters. The same source runs unmodified on NVIDIA L40S, where cached decode remains sequence-length independent across all model scales. WikiText-103 validation perplexity matches the Triton reference mamba_ssm v2.2.2 within +/-0.0005 points, and hidden states agree to float32 rounding tolerance. Code is available at https://github.com/CosmoNaught/mamba2-jax.

07.
arXiv (CS.AI) 2026-06-17

MathVis-Fine: Aligning Visual Supervision with Necessity via Progressive Dependency-Guided Training for Multimodal Mathematical Reasoning

arXiv:2606.17888v1 Announce Type: new Abstract: Chain-of-Thought (CoT) reasoning has extended from purely linguistic domains to multimodal scenarios; however, existing approaches often treat visual inputs as homogeneous or auxiliary signals, failing to capture the intricate and sample-specific dependencies between text and images in mathematical problem-solving. This gives rise to two core issues: first, the supervisory signals for visual content are generalized and coarse-grained, lacking adaptation to the actual necessity of visual information in each sample; second, training feedback becomes inaccurate when visual rewards are uniformly applied without distinguishing the complementary relationships among inputs. These limitations hinder models from achieving precise multimodal reasoning. In this work, we propose a framework for modeling fine-grained visual dependencies in mathematical reasoning. We first construct the MathVis-Fine dataset, augmenting fine-grained visual annotations with visual dependency ratings. Building upon this dataset, we introduce a two-stage progressive visual enhancement training paradigm that balances answer correctness rewards and visual grounding rewards according to the intrinsic visual dependency level of each sample, thereby mitigating reward bias and improving supervision accuracy. Extensive experiments demonstrate that the MathVis-Fine framework effectively enhances visual perception progressively based on visual dependency, offering a more precise training framework for multimodal mathematical reasoning. We will release the dataset upon acceptance.

08.
PLOS Computational Biology 2026-06-22

Adhesion and polarity-driven morphogenesis: Mechanisms and constraints in tissue formation

by Yoshiyuki T. Nakamura, Chikara Furusawa, Kunihiko Kaneko Embryonic development in multicellular organisms exhibits diverse morphogenetic patterns, which can generally be categorized into fundamental types such as monolayer and multilayer spheres, as well as cell masses. Furthermore, we identify two distinct processes for the formation of spherical structures. These basic patterns are thought to be governed by the microscopic properties of intercellular adhesion. However, the specific mechanisms linking the microscopic factors to the emergence of distinct macroscopic morphogenetic patterns remain poorly understood. In this study, we explore how different morphogenetic patterns arise by employing a computational model that incorporates intercellular adhesion and polarity. Our results demonstrate that all fundamental morphogenetic patterns can be generated through the interplay of two key parameters: the polarity strength of the cell and the regulation of polarity via mechanical signals. Furthermore, analytical considerations reveal key mechanisms underlying the formation of these patterns. These findings highlight the critical role of physical constraints in morphogenesis and suggest potential applications to the design of artificial tissues and organoids.

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

VSANet: View-aware Sparse Attention Network for Light Field Image Denoising

Light field (LF) image denoising is challenging due to the high-dimensional structure of LF data. While noise is independent across sub-aperture images, scene content exhibits strong cross-view correlations. We introduce VSANet, a view-aware sparse attention network for LF denoising. Specifically, we propose a view-aware sparse attention (VSA) block that represents the 4D LF feature map as a unified spatial-angular token space and performs cross-view aggregation via locality-sensitive hashing-based sparse attention. This enables global feature interactions with linear complexity, effectively exploiting LF correlations across views and spatial locations. In addition, we design a feature refinement (FR) block to emphasize informative features in spatial, angular, and epipolar subspaces. The VSA and FR blocks are integrated within a sequential attention refinement module, forming the core of VSANet. Experiments demonstrate VSANet outperforms stateof-the-art LF denoising methods.

10.
arXiv (CS.AI) 2026-06-18

Veriphi: Attack-Guided Neural Network Verification with Dataset-Dependent Training Methods

arXiv:2606.18454v1 Announce Type: cross Abstract: We present Veriphi, a GPU-accelerated neural network verification system that combines fast adversarial attacks with formal bound certification using alpha,beta-CROWN methods. Through systematic experiments on MNIST and CIFAR-10 using three training methodologies (standard, adversarial, certified), we demonstrate that training method effectiveness is fundamentally dataset-dependent. Interval Bound Propagation (IBP) achieves 78% certified accuracy on simple MNIST (784 dimensions) but provides negligible certification performance on the more complex CIFAR-10 dataset, where PGD adversarial training dominates with 94% certification at small perturbations. We achieve 5x verification speedup through attack-guided falsification and scale our approach to production-size models (105.8M parameters) for real-world aerospace logistics optimization. Our results challenge the assumption that certified training universally outperforms adversarial training, showing context matters critically for verification strategy selection.

11.
arXiv (CS.LG) 2026-06-24

Task Vector Bases: A Unified and Scalable Framework for Compressed Task Arithmetic

arXiv:2502.01015v5 Announce Type: replace Abstract: Task arithmetic, representing downstream tasks through linear operations on task vectors, has emerged as a simple yet powerful paradigm for transferring knowledge across diverse settings. However, maintaining a large collection of task vectors introduces scalability challenges in both storage and computation. We propose Task Vector Bases, a framework compressing $T$ task vectors into $M < T$ basis vectors while preserving the functionality of task arithmetic. By representing each task vector as a structured linear combination of basis atoms, our approach supports standard operations such as addition, negation, as well as more advanced arithmetic ones. The framework is orthogonal to other efficiency-oriented improvements in task arithmetic and can be used in combination with them. We provide theoretical analysis showing that basis compression retains addition generalization guarantees and enables principled unlearning, with error bounds depending on reconstruction quality. Empirically, our proposed basis construction methods consistently outperform heuristic basis construction baselines and, in some cases, even surpass the performance of full task vector collections across diverse downstream applications while reducing storage and computational requirements. The code is available at https://github.com/uiuctml/TaskVectorBasis.

12.
arXiv (CS.AI) 2026-06-24

CRAFT: A Tendon-Driven Hand with Hybrid Hard-Soft Compliance

arXiv:2603.12120v2 Announce Type: replace-cross Abstract: We introduce CRAFT hand, a tendon-driven anthropomorphic hand with hybrid hard-soft compliance for contact-rich manipulation. The design is based on a simple idea: contact is not uniform across the hand. Impacts concentrate at joints, while links carry most of the load. CRAFT places soft material at joints and keeps links rigid, and uses rollingcontact joint surfaces to keep flexion on repeatable motion paths. Fifteen motors mounted on the fingers drive the hand through tendons, keeping the form factor compact and the fingers light. In structural tests, CRAFT improves strength and endurance while maintaining comparable repeatability. In teleoperation, CRAFT improves handling of fragile and low-friction items, and the hand covers 33/33 grasps in the Feix taxonomy. The full design costs under $600 and will be released open-source with visionbased teleoperation and simulation integration. Project page: http://craft-hand.github.io/

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

From Sparse Features to Trustworthy Proxies: Certifying SAE-Based Interpretability

Sparse autoencoders (SAEs) are increasingly used to extract interpretable features from language models (LMs), yet a central question remains: when can an SAE-based explanation be treated as a faithful view of an underlying frozen LM We study this through a post-hoc generalization framework that certifies the LM via a sparse proxy, obtained by replacing a native hidden activation with its pretrained SAE reconstruction. Our framework derives an upper bound on the base model's expected risk using four measurable quantities: proxy risk, SAE reconstruction gap, concept-pool mismatch, and sparse complexity. We interpret this certificate as an operational criterion for explanatory faithfulness. In particular, a non-vacuous bound indicates that the extracted sparse features retain meaningful predictive information, while small reconstruction and mismatch errors indicate that the proxy remains behaviorally close to the original model. Empirically, we show that the bound becomes non-vacuous on GPT-2 Small, Gemma-2B, and Llama-3-8B at practical sample sizes. A detailed layerwise analysis of Llama-3-8B reveals a strong depth dependence, with later layers becoming much easier to certify, associated with both stronger local fidelity and weaker downstream error amplification. Finally, through feature-shuffling ablations, we show that the decomposition distinguishes genuine semantic alignment from mere statistical sparsity, providing a useful diagnostic for when SAE-based explanations become less reliable.

14.
arXiv (CS.CL) 2026-06-16

Compositional Reasoning Depth Predicts Clinical AI Failure: Empirical Evidence Consistent with Transformer Compositionality Limits in Electronic Health Record Question Answering

Authors:

Aggregate accuracy benchmarks conceal a systematic structure in how large language models fail at electronic health record (EHR) question answering: questions requiring more inferential steps produce disproportionately more errors. Motivated by theoretical results on transformer compositionality limits, we introduce a pre-specified hop-count taxonomy – the number of distinct reasoning steps required to answer a clinical question from an EHR – as a principled predictor of model failure. We annotate 313 clinician-generated MedAlign EHR question-answer pairs across four hop levels and evaluate 301 questions in a within-model ablation (claude-sonnet-4-6, zero-shot vs. extended thinking) and cross-architecture replications (gpt-4o and gpt-5.4-2026-03-05, zero-shot). All three models, spanning two providers and two OpenAI generations (GPT-4 and GPT-5), show monotone accuracy decline with hop count: Claude Sonnet zero-shot falls from 30.6% (hop=1) to 17.6% (hop=4) (Cochran-Armitage z=-2.30, p=0.011; OR per hop 0.72, 95% CI [0.56,0.92], p=0.008); GPT-4o replicates this (37.8% to 14.7%; OR 0.58 [0.45,0.75], p

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

ADAPT: An Autonomous Forklift for Construction Site Operation

Efficient material logistics play a critical role in controlling costs and schedules in the construction industry. However, manual material handling remains prone to inefficiencies, delays, and safety risks. Autonomous forklifts offer a promising solution to streamline on-site logistics, reducing reliance on human operators and mitigating labor shortages. This paper presents the development and evaluation of ADAPT (Autonomous Dynamic All-terrain Pallet Transporter), a fully autonomous off-road forklift designed for construction environments. Unlike structured warehouse settings, construction sites pose significant challenges, including dynamic obstacles, unstructured terrain, and varying weather conditions. To address these challenges, our system integrates AI-driven perception techniques with traditional approaches for decision making, planning, and control, enabling reliable operation in complex environments. We validate the system through extensive real-world testing, comparing its continuous performance against an experienced human operator across various weather conditions. Our findings demonstrate that autonomous outdoor forklifts can operate near human-level performance, offering a viable path toward safer and more efficient construction logistics.

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

FLaRA: Predicting Future Latent Representations for Accident Anticipation

Anticipating traffic accidents from dashcam videos is a critical challenge in intelligent transportation systems. Existing methods typically map visual context directly to a collision probability without explicitly modeling the future evolution of the driving scene. In this paper we propose FLaRA (Predicting Future Latent Representations for Accident Anticipation), a novel predictive architecture that shifts this paradigm by forecasting future latent representations for accident anticipation. Building upon the Video Joint-Embedding Predictive Architecture (V-JEPA2), our model conditions a predictor network on observed context frames to predict the forthcoming latent features of the scene. A classifier then operates on these predicted future representations rather than only on past observations. To ensure these forecasts remain grounded in realistic future dynamics, we introduce a joint training objective that simultaneously optimizes an auxiliary feature-level reconstruction loss and a cross-entropy classification loss. Extensive evaluations on the Nexar dataset, alongside cross-domain validations on the DAD, DADA-2000, and DoTA benchmarks, demonstrate that our approach achieves state-of-the-art performance while maintaining realistic early warning capabilities.

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

Dual-Anchoring: Addressing State Drift in Vision-Language Navigation

arXiv:2604.17473v4 Announce Type: replace-cross Abstract: Vision-Language Navigation(VLN) requires an agent to navigate through 3D environments by following natural language instructions. While recent Video Large Language Models(Video-LLMs) have largely advanced VLN, they remain highly susceptible to State Drift in long scenarios. In these cases, the agent's internal state drifts away from the true task execution state, leading to aimless wandering and failure to execute essential maneuvers in the instruction. We attribute this failure to two distinct cognitive deficits: Progress Drift, where the agent fails to distinguish completed sub-goals from remaining ones, and Memory Drift, where the agent's history representations degrade, making it lose track of visited landmarks. In this paper, we propose a Dual-Anchoring Framework that explicitly anchors the instruction progress and history representations. First, to address progress drift, we introduce Instruction Progress Anchoring, which supervises the agent to generate structured text tokens that delineate completed versus remaining sub-goals. Second, to mitigate memory drift, we propose Memory Landmark Anchoring, which utilizes a Landmark-Centric World Model to retrospectively predict object-centric embeddings extracted by the Segment Anything Model, compelling the agent to explicitly verify past observations and preserve distinct representations of visited landmarks. Facilitating this framework, we curate two extensive datasets: 3.6 million samples with explicit progress descriptions, and 937k grounded landmark data for retrospective verification. Extensive experiments in both simulation and real-world environments demonstrate the superiority of our method, achieving a 15.2% improvement in Success Rate and a remarkable 24.7% gain on long-horizon trajectories. To facilitate further research, we will release our code, data generation pipelines, and the collected datasets.

18.
arXiv (CS.CL) 2026-06-24

SHERLOC: Structured Diagnostic Localization for Code Repair Agents

LLM agents solve repository-level coding tasks through multi-turn tool use, but utilize half their budget on locating faults before editing. Dedicated localization frameworks have emerged, yet are still evaluated as file retrieval rather than actionable diagnosis, producing locations without the diagnostic context a repair agent needs. We introduce SHERLOC (Structured Hypothesis-driven Exploration and Reasoning for Localization), a training-free framework pairing a reasoning LLM with compact repository tools and self-recovery, without fine-tuning or multi-agent orchestration. SHERLOC reaches state-of-the-art localization across model scales: 84.33% accuracy@1 on SWE-Bench Lite and 81.27% recall@1 on SWE-Bench Verified; at ~30B parameters, it matches or outperforms other agentic methods. Injecting our locations and diagnostic findings into repair agents yields, on average, +5.95 pp resolve rate on SWE-Bench Verified while cutting localization and total tokens by 36.7% and 23.1%.

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

MAWARITH: A Dataset and Benchmark for Legal Inheritance Reasoning with LLMs

Islamic inheritance law is challenging for large language models because solving inheritance cases requires complex, structured, multi-step reasoning and the correct application of juristic rules to compute heirs' shares. We introduce MAWARITH, a large-scale annotated dataset of 12,500 Arabic inheritance cases for training and evaluating models on the full reasoning chain: (i) identifying eligible heirs, (ii) applying blocking (\d{hajb}) and allocation rules, and (iii) computing exact inheritance shares. To the best of our knowledge, MAWARITH is the first Arabic corpus and benchmark designed for end-to-end Islamic inheritance reasoning. Unlike prior datasets that restrict inheritance case solving to multiple-choice questions, MAWARITH supports the full reasoning chain and provides step-by-step solutions with justifications grounded in classical juristic sources and established inheritance rules, as well as exact share calculations. This enables models to learn how to generate detailed, step-by-step responses to user queries that reflect real-world Islamic inheritance cases. To evaluate models beyond final-answer accuracy, we propose MIR-E (Mawarith Inheritance Reasoning Evaluation), a weighted multi-stage metric that scores key reasoning stages and captures error propagation across the pipeline. We evaluate six large language models in a zero-shot setting. A commercial model achieves about 90\%, whereas all evaluated open-source models remain below 50\%. Our error analysis identifies recurring failure patterns, including scenario misinterpretation, errors in heir identification, errors in share allocation, and missing or incorrect application of key inheritance rules such as \textquotesingle awl and radd. The MAWARITH dataset is publicly available at https://gitlab.com/nlpresearcher/mawarith.

20.
bioRxiv (Bioinfo) 2026-06-19

SteerAF: Distogram-based Steering of AlphaFold2 toward Alternative Conformations

End-to-end structure predictors, such as AlphaFold2, typically output only the dominant conformational state of a given protein, which is biased by the training data set. Existing strategies for recovering alternative conformations are often computationally expensive and offer limited biological interpretability. Here, we present SteerAF, an inference-time optimization framework based on AlphaFold2 that leverages information encoded in the distogram derived from deep multiple sequence alignments (MSAs) to predict alternative protein conformations. Across four benchmark datasets, SteerAF matches or surpasses existing methods in predicting alternative conformations for the majority of systems. Sparse MSA-feature modifications generated via block gradient ascent exhibit a strong correlation with experimentally characterized functional residues, recovering them with approximately 50% precision in the tested proteins. Furthermore, SteerAF enables effective decoy selection in the absence of experimental structures, and its predictions can serve as seed structures for molecular dynamics simulations to map conformational landscapes. Thus, SteerAF provides an efficient and interpretable approach for predicting alternative conformations, offering a framework that can be extended to other similar predictors and problems.

21.
arXiv (math.PR) 2026-06-19

A Cycle Walk for Sampling Measures on Spanning Forests for Redistricting

arXiv:2509.08629v2 Announce Type: replace-cross Abstract: We introduce the Cycle Walk, a new Markov chain Monte Carlo method for sampling distributions on balanced graph partitions, motivated by applications in political redistricting. The method operates on spanning forests and combines two types of updates: local "cycle" moves within districts and global moves that exchange population between adjacent districts while preserving balance constraints. This construction enables efficient Metropolis–Hastings correction while allowing proposals at multiple spatial scales. We show that the Cycle Walk naturally interpolates between existing approaches based on local updates and a class of global update methods derived from recombination (RECOM). Through a range of numerical experiments on synthetic graphs and real-world precinct data, we demonstrate that the Cycle Walk exhibits improved empirical convergence diagnostics for distributions that place weaker weight on spanning-tree counts, a regime that is challenging for existing methods. In particular, the algorithm remains effective when incorporating alternative compactness measures that more closely reflect policy-relevant criteria. These results suggest that the Cycle Walk provides a flexible and computationally efficient framework for sampling from a broader class of redistricting distributions than previously accessible with MCMC techniques.

22.
arXiv (CS.CL) 2026-06-12

Operads for compositional reasoning in LLMs

Question decomposition, i.e. breaking a complex query into simpler sub-queries whose answers are composed to produce a final answer, is a widely used strategy for improving LLM reasoning, yet it currently lacks a rigorous mathematical foundation. In this paper, we propose operads, mathematical structures that model many-in, one-out operations and compositions thereof, as a natural framework for describing question decomposition. We define the questions operad $Q$, in which operations correspond to question templates and composition corresponds to substitution of sub-answers, and show how QA models can be interpreted as algebras over $Q$. Beyond reframing existing practice, this operadic perspective points toward new methods, in particular a notion of operadic consistency, which measures whether a QA model's answers agree across the partial collapses of a question decomposition tree. Empirical evaluation of operadic consistency is reported in our companion paper (Bottman, Liu, and Richardson, 2026), which finds it strongly correlated with accuracy across twelve LLMs and four multi-hop QA datasets and outperforming standard temperature-based self-consistency baselines. We argue that operads are the natural mathematical home for question decomposition, and that invariants such as operadic consistency open new directions for analyzing and improving the reliability of multi-step reasoning.

23.
medRxiv (Medicine) 2026-06-22

Anterior-superior hypothalamic enlargement as specific marker in episodic migraine: converging evidence from an independent discovery-replication design

Background: Growing evidence implicates the hypothalamus as a key structure in migraine pathophysiology; however, our understanding of its precise role and of the specific nuclei involved remains limited. We combined MRI data from our laboratory with publicly available MRI datasets from OpenNeuro to examine hypothalamic subunit volumes in episodic migraine and assess the specificity of these alterations relative to chronic pain conditions. Methods: Structural MRI combined with an automated atlas-based segmentation algorithm and a discovery-replication design was employed to investigate cross-sectional volumetric differences across 5 bilateral hypothalamic subunits in two independent migraine cohorts: DS1-MIG (DS1-MIG-base, n = 111 patients, n = 35 controls) and DS2-MIG (n = 27 patients, n = 31 controls). The adjusted volumes were compared between groups using MANOVA as an omnibus test, followed by Welch t-tests to test univariate follow-up. Longitudinal volumetric changes were additionally assessed in DS1-MIG participants with available follow-up scans using linear mixed models. To assess the specificity of findings to migraine, the same pipeline was applied to two chronic pain datasets, one including patients with fibromyalgia (DS-FM, n = 33 patients, n = 33 controls) and the other including patients with trigeminal neuralgia (n = 119 patients, n = 55 controls). Results: MANOVA revealed significant multivariate group differences in the discovery and replication migraine cohorts (DS1-MIG-base: = .006; DS2-MIG: = .008). Follow-up univariate analyses identified a consistent enlargement of the left anterior-superior subunit across both cohorts (FDR = .023 in DS1-MIG-base and FDR = .046 in DS2-MIG), representing the only cross-cohort replication finding. Beyond this shared signature, DS2-MIG exhibited additional significant enlargements of the right anterior-inferior and right tubular-inferior subunits. Longitudinal analyses in DS1-MIG showed that hypothalamic subunit volumes remained broadly stable over time within both migraine patients and control participants. No significant volumetric alterations were detected in the fibromyalgia or trigeminal neuralgia cohorts, either in multivariate or univariate analyses, underscoring migraine-specific findings. Conclusions: These findings provide evidence for subunit-specific hypothalamic structural alterations in migraine localized in the left anterior hypothalamic subunit. The stability of these differences over time and their absence in other chronic pain conditions suggest a migraine-specific structural organisation of hypothalamic circuitry.

24.
arXiv (CS.CV) 2026-06-16

Analyzing Visual Aircraft Representations with Sparse Autoencoders

Vision models can achieve strong performance on classification tasks, but the internal representations supporting their predictions are often difficult to interpret. This work investigates whether sparse autoencoders can decompose intermediate representations of a vision model into interpretable features. We train a ConvNeXt classifier on the FGVC-Aircraft dataset, extract spatial activations from its final feature stage, and train a sparse autoencoder on these activations. The learned sparse features are analyzed using top-activating image patches, activation strength, and class selectivity. Qualitative visual inspection reveals that several features correspond to recognizable aircraft structures and visual patterns. We evaluate a subset of selected features using input-space and feature-space ablations, measuring how blurring image patches and suppressing sparse features affect class logits, classification margins, and prediction confidence. The results suggest that sparse autoencoders can reveal partially interpretable, class-relevant visual features associated with aircraft recognition, while also exposing limitations such as polysemanticity and coarse spatial localization.

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

SuperThoughts: Reasoning Tokens in Superposition

Long Chain-of-Thought (CoT) reasoning improves LLM problem-solving but is computationally expensive due to sequential token generation. While recent works explore reasoning in continuous latent spaces to bypass discrete token generation, they often struggle with training stability and fail to scale to complex, long-horizon tasks due to lack of supervision signal. We propose SuperThoughts, which compresses pairs of consecutive CoT tokens into single latent representations and decodes two tokens per step via a lightweight Multi-Token Prediction (MTP) module. This preserves discrete token supervision at training time while doubling throughput at inference time. We finetune Qwen2.5-Math-1.5B-Instruct, Qwen2.5-Math-7B-Instruct, Qwen2.5-Math-14B-Instruct, and evaluate on MATH500, AMC, OlympiadBench, and GPQA-Diamond. With a confidence-based adaptive mechanism that falls back to standard decoding when uncertain, SuperThoughts achieves $\sim$20–30\% CoT length reduction while maintaining accuracy with minimal degradation (1-2 points accuracy drop on most tasks).