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Computer Science Machine Learning

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Wednesday 3 June

Machine Learning · Cross-listed from cs.CV

What neurosurgeons need to see: synthetic intra-operative MRI from ultrasound for brain-shift compensation in brain tumour surgery

Maximal safe resection is the primary objective in glioma surgery. Neuronavigation guidance is progressively degraded by brain shift after dural opening. Intraoperative MRI can compensate but needs dedicated infrastructure and is rarely available, whereas intraoperative ultrasound (ioUS) is inexpensive, repeatable, and compatible with routine workflows. Navigation systems combining ioUS with preoperative MRI usually rely on rigid registration; even deformable multimodal registration is limited by ultrasound speckle contrast, a narrow field of view, and the inability to represent structures absent from the preoperative scan, most critically the resection cavity and residual tumor. We propose an end-to-end pipeline that generates a new whole-brain MRI volume in the preoperative imaging space by merging the preoperative MRI, a synthetic MRI generated from the ioUS, and a deformable registration anchored on that synthetic image. It integrates a 2.5D residual-transformer synthesis backbone (ResViT-2.5D) and a two-stage registration coupling NiftyReg with a synthesis-anchored SynthMorph stage, operating directly on raw scanner inputs. On a post-resection ReMIND cohort, ResViT-2.5D produced synthetic images closely matching the intraoperative T2 across structural, intensity, and perceptual metrics. In 14 subjects with 215 expert landmarks, the synthesis-anchored registration reduced the mean target registration error from 6.27 to 5.86 mm, matching a strong classical NiftyReg baseline (5.85 mm) while yielding a diffeomorphic deformation field in every subject. The contribution is not a gain in registration accuracy but the integrated volume itself, which inside the ultrasound field of view it reflects the intraoperative post-resection state. This provides the surgeon with an MRI-like update of the operative field with potential for integration into surgical-navigation workflows.
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All authors Santiago Cepeda, Olga Esteban-Sinovas, Ignacio Arrese, Rosario Sarabia

Machine Learning · Cross-listed from cs.NE

QDS-SNN: Energy-efficient Quantum Deeply-Supervised Spiking Neural Network Algorithm for Traffic Sign Recognition

Traffic sign recognition is crucial for intelligent transportation and autonomous driving, as it can improve driving efficiency and ensure road safety. However, traditional recognition methods are based on large datasets and intensive computation, which limits their real-time applicability. Spiking Neural Networks (SNNs) offer a biologically inspired, energy-efficient alternative due to their spatiotemporal processing capabilities, but suffer from information loss and vanishing gradients during training. To overcome these limitations, this study proposes a Quantum Deep-supervised Spiking Neural Network (QDS-SNN) that integrates Quantum Neural Networks (QNNs) for efficient, low-power deep supervision. Using quantum superposition and entanglement, QNNs enable expressive representations and parallel computation, thereby enhancing performance without compromising energy efficiency. The proposed QDS-SNN incorporates a temporally and spatially adaptive LIF (TSA-LIF) neuron and a quantum-assisted classifier module (QACM) to mitigate gradient issues and improve training effectiveness. This study conducts experiments on the PennyLane quantum simulation platform, and the results show that QDS-SNN achieves 99.72% accuracy on the GTSRB dataset in only 6 time steps – outperforming the MS-ResNet baseline by 1.32% while reducing energy consumption by 55.77%. In the TSRD dataset, it achieves 97.90% accuracy while reducing energy use to 52.68% of the baseline. These results demonstrate that QDS-SNN offers a high-performance, energy-efficient solution for traffic sign recognition in intelligent transportation systems.
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All authors Zhiguo Qu, Keqi Li, Le Sun, Wenjie Liu, Yimin Yu, Saif Al-Kuwari, Ahmed Farouk

Machine Learning · Cross-listed from physics.chem-ph

SC3: The Multi-Solvent Solubility Challenge and Benchmark

Solubility prediction is a standard benchmark in computational chemistry, yet multi-solvent models which reportedly approach the experimental-noise ceiling (i.e. the aleatoric limit) are not yet reliable enough to be deployed. We argue that this gap is partly artefactual: published benchmarks differ in curation policies, evaluate on count-weighted RMSE that hides failure on tail-heavy solvent distributions, and treat the widely cited 0.6-0.8 log S inter-laboratory figure as the aleatoric ceiling even though it reflects worst-case, not expected, disagreement. We introduce SC3, a multi-solvent solubility benchmark built on BigSolDB v2.1 with three contributions: (i) a reproducible curation pipeline yielding 101,535 measurements over 1,327 solutes and 206 solvents, with a recalibrated aleatoric floor of 0.106 log S-roughly 6 times tighter than the conventional figure; (ii) nested Gold/Silver/Bronze consensus tiers with per-point standard deviation, three leakage-checked splits, and a multi-solvent metric suite (PS-RMSE, Z-RMSE); and (iii) a 31-model benchmark across six families, whose best Bronze PS-RMSE sits at 5 times the aleatoric limit, and we observe this is a gap unclosed by any deep alternative tested. We perform three follow-on analyses: data scaling, transfer from quantum-chemistry solvation energies, and feature-level attribution, which demonstrates that calibrated per-point uncertainty is a reusable infrastructure for diagnosis beyond point prediction.
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All authors Vansh Ramani, Har Ashish Arora, Dhairya Kuchhal, Sergei Tatarin, Lev Krasnov, Sayan Ranu, Tarak Karmakar

Machine Learning · Cross-listed from cs.CV

Attention-Guided Autoencoder Fusion for Insulator Defect Detection Using UAV Transmission-Line Imaging

Automated defect detection in high-voltage transmission-line insulators remains challenging due to severe class imbalance, large scale variation, and the small spatial extent of defect instances in Unmanned Aerial Vehicle (UAV) imagery. To address these challenges, this paper proposes AE-YOLO, an Attention-Guided AutoEncoder-Enhanced YOLO framework for robust insulator defect detection. The architecture integrates lightweight bottleneck autoencoders within a Feature Pyramid Network-Path Aggregation Network (FPN-PAN) neck. This preserves anomaly-sensitive information during multi-scale feature fusion. Convolutional Block Attention Modules (CBAM) are used throughout the backbone, enhancing feature discrimination and suppressing background interference. The framework also introduces a variance-maximizing autoencoder regularization strategy, which encourages diverse, defect-discriminative latent representations. The network trains using a unified objective that combines focal loss, Complete IoU (CIoU) loss, and autoencoder regularization to address foreground-background imbalance and improve localization accuracy. During inference, Weighted Boxes Fusion (WBF) combines predictions from YOLOv8, YOLOv10, and YOLO11. An autoencoder-guided confidence boosting mechanism improves sensitivity to rare defect categories. Experiments on the Insulator-Defect Detection dataset show that AE-YOLO with an EfficientNetV2 backbone achieves 95.10 percent mAP at 0.5, 96.40 percent precision, and 93.80 percent recall. This performance surpasses the strongest YOLO-family baseline by 5.0 points in mAP at 0.5 and 6.7 points in recall. These results confirm the effectiveness and adaptability of the framework. The model is a practical and scalable solution for UAV-based transmission-line inspection and defect monitoring.
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Machine Learning · Cross-listed from cs.SE

Architecturally Significant MLOps Guidelines for ML Model Integration and Deployment: a Gray Literature Review

Context. Despite the growing adoption of Machine Learning Operations (MLOps), teams often approach MLOps projects in an ad hoc manner due to the lack of consolidated architectural guidance. The community would benefit from a reference that synthesizes knowledge to inform the architectural design of MLOps systems, especially regarding the integration and deployment of ML models. Objective. In response, our goal is to provide a comprehensive overview of architecturally significant guidelines for the integration and deployment of ML models in MLOps systems. Method. We conduct a gray literature review of 103 web sources to analyze state-of-practice knowledge on MLOps model integration and deployment. We then apply thematic analysis to synthesize these practices into recommended guidelines. Results. We contribute a collection of 25 architecturally significant MLOps guidelines for model integration and deployment, organized into five categories, and describe their impact on the overall system architecture. Conclusion. Our results serve as an overview of state-of-practice MLOps guidelines to support researchers and practitioners with the integration and deployment of ML models in their MLOps systems.
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All authors Faezeh Amou Najafabad, Markus Haug, Keerthiga Rajenthiram, Justus Bogner, Ilias Gerostathopoulos

Machine Learning · Cross-listed from cs.AI

Attack Selection in Agentic AI Control Evaluations Meaningfully Decreases Safety

An attacker that strategically chooses when to attack is much harder to catch than one that attacks indiscriminately. AI control is a safety framework for deploying capable but untrusted AI agents under the oversight of a weaker, trusted monitor and a limited human audit budget. Control evaluations stress-test these protocols by pitting a red-team attack policy against the blue-team monitor, but current evaluations typically assume attackers that do not strategically select when to attack. We study this capability, attack selection, in agentic settings by decomposing attack decisions into a start policy, which decides when an attacker should attack, and a stop policy, which decides when an attacker should abort an ongoing attack. Across two agentic settings, BashArena and LinuxArena, both policies substantially lower measured empirical safety without changing the underlying attack capability. At a 1% audit budget, our start policy reduces safety by 20pp on both BashArena and LinuxArena, and our stop policy reduces safety by 20pp on BashArena and 28pp on LinuxArena. These reductions should be interpreted as upper bounds on the effect of attack selection. Existing control evaluations may therefore yield overly optimistic safety estimates against selective attackers. We recommend that future evaluations, system cards, and safety cases elicit attack selection to produce more realistic safety estimates.
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All authors Catherine Ge-Wang, Tyler Crosse, Benjamin Hadad IV, Joachim Schaeffer, Ram Potham, Tyler Tracy

Machine Learning · Cross-listed from cs.AR

Characterizing the Impact of NVFP4 Quantization for Low-Power Edge AI Deployment

Energy-efficient neural-network inference at the edge requires reducing arithmetic cost, memory traffic, computation energy, and storage overhead while maintaining acceptable accuracy. This paper presents an ablation-focused study of NVFP4 quantization for edge-efficient neural networks, with emphasis on the relationship between activation precision, weight precision, block-size scaling, retraining, and model accuracy. NVFP4 activations are represented using 4-bit FP4 data, an FP8 block scale, and an FP32 tensor scale, enabling ultra-low precision inference while preserving activation dynamic range. A block-size ablation over six edge-efficient models shows that block size B = 16 provides a practical accuracy/storage trade-off, requiring only 4.5078 bits per input for N = 4096. A weight precision ablation further shows that FP8 and FP16 weights provide only modest gains over FP4 weights under the same NVFP4 activation path, suggesting that activation quantization and scaling dominate much of the accuracy behavior. To isolate the benefit of the NVFP4 data type, this work compares conventional unscaled FP4 activation inference and NVFP4 activation inference with and without retraining. The results show that conventional FP4 inference collapses accuracy for most compact models, while NVFP4 without retraining already recovers substantial accuracy by restoring activation dynamic range through FP8 block scaling and FP32 tensor scaling. When combined with retraining, NVFP4 achieves the best accuracy across the evaluated models, demonstrating the effectiveness of scaling-aware FP4 (NVFP4) inference. These findings provide general design guidance for hardware-software co-design of low power edge inference across a broad range of accelerator platforms, including GPUs, Tensor Cores, FPGAs, domain-specific AI accelerators, near-memory computing systems, and emerging edge-computing architectures.
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All authors Ovishake Sen, Venkata Nithin Kamineni, Daniel Lobo, Swarup Bhunia, Rickard Ewetz, Baibhab Chatterjee

Machine Learning

Dominant-Layer ZO: A Single Layer Dominates Zeroth-Order Fine-Tuning of LLMs

Zeroth-order (ZO) optimization enables memory-efficient fine-tuning of large language models (LLMs) using only forward passes, but it remains unclear how useful adaptation is distributed across layers. In this work, we reveal a surprising phenomenon: ZO fine-tuning is sharply dominated by a single decoding layer. Across multiple LLM families and downstream tasks, fine-tuning this dominant layer alone consistently matches or even exceeds full-model ZO fine-tuning. We further show that the dominant layer is task-agnostic but model-specific, and can be identified before training through a simple inference-only analysis of activation outliers. Specifically, the dominant layer consistently aligns with the first activation-outlier layer in the pre-trained model. To explain this phenomenon, we analyze how perturbation effects propagate under ZO optimization. We find that the dominant layer combines two key properties: high perturbation sensitivity and early placement in the residual stream, allowing perturbation-induced effects to propagate and accumulate through remaining subsequent decoding layers. As a result, this layer produces disproportionately strong and stable optimization signals under forward-only updates. Extensive experiments on LLaMA2-7B and Qwen3-8B across nine benchmarks show that dominant-layer ZO fine-tuning improves average performance over full-model MeZO and LoRA-based ZO fine-tuning while achieving up to 4.52$\times$ training speedup.
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All authors Wanhao Yu, Ziyan Wang, Zheng Wang, Abeer Matar Almalky, Yihang Zuo, Shuteng Niu, Sen Lin, Adnan Siraj Rakin, Deliang Fan, Li Yang

Machine Learning

LEVANTE-bench: Multi-Scale Comparison of VLMs to Children Using Cognitive Tasks (or, "Is Your VLM Smarter Than a 5th Grader?")

Given the inherently multimodal nature of human experience, vision-language models (VLMs) hold substantial promise for modeling human cognition as it grows and develops with experience. Realizing their potential requires tools for comparing VLMs with human cognitive development across tasks, ages, and populations. We present LEVANTE-bench, a benchmark based on tasks and data from the Learning Variability Network (LEVANTE), which distributes open-source tasks and data measuring children's cognition across languages and cultures. In LEVANTE-bench, we systematically assess VLMs on six tasks, comparing their alignment with children aged 5-12 ($N$ = 1547) across three countries. We compare models at multiple scales, assessing their overall accuracy, their task- and item-level alignment with children, and how well they match children's trial-level error distributions. Alignment was heterogeneous across scales: at the level of tasks and items, more capable models aligned better with humans. However, match to human error distributions varied widely across tasks, and for several tasks, smaller models matched younger children's errors better. In addition, even the best-performing VLMs struggled on matrix reasoning and mental rotation tasks. Thus, current VLM architectures align only partially with the cognitive abilities of children.
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All authors Alvin Wei Ming Tan, David Cardinal, Tania Lorido-Botran, Laura Bravo-Sanchez, Sunny Yu, Michael C. Frank

Machine Learning · Cross-listed from stat.ML

Sparse Functional Singular Value Decomposition for Biclustering and Triclustering Longitudinal Data

Identifying subtypes of complex conditions, such as Inflammatory Bowel Disease (IBD), often requires capturing latent patterns in longitudinal omics data. However, these data are typically high-dimensional, sparsely sampled, and irregularly observed over time, posing substantial challenges for conventional (bi)clustering and functional data analysis methods. We propose Tri-SfSVD, a unified sparse functional Singular Value Decomposition framework for discovering biclusters and triclusters in longitudinal data. Unlike existing functional biclustering methods that rely on ad hoc imputation or enforce restrictive shape-homogeneity assumptions, Tri-SfSVD integrates continuous trajectory estimation with simultaneous subject, feature, and temporal selection within a single optimization framework. By imposing sparse penalties across subjects, variables, and temporal subregions, the proposed method works directly on observed data to uncover localized structures at the subject, subject-feature, and subject-feature-time levels. Extensive simulations demonstrate that Tri-SfSVD outperforms existing approaches in high-dimensional settings. Applied to IBD multi-omics data, the method identified three biclusters linking sample clusters with distinct IBD-related clinical characteristics to microbial pathway groups associated with specific bacterial taxa, providing interpretable subject-pathway associations for characterizing disease heterogeneity. Applied to multi-channel EEG data, the method identified three triclusters linking sample clusters with distinct alcohol-related phenotypes to localized brain activity patterns, including subgroup differences separated by temporal subregions within the same spatial region.
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Machine Learning · Cross-listed from cs.CL

Localizing Prompt Ambiguity in Large Language Models with Probe-Targeted Attribution

Prompt ambiguity is a common source of failure in large language models, but is difficult to localize because it is a latent property of the prompt, while existing attribution methods are designed to explain observable outputs such as logits or generated tokens. We introduce PRIG, a gradient attribution method that uses a probe logit to attribute latent ambiguity to token positions. Specifically, PRIG trains a linear probe to distinguish clear prompts from ambiguous prompts and attributes the probe score to earlier token representations in the residual stream. To enable token-level evaluation, we construct synthetic ambiguity datasets across coding, math, and writing by rewriting one task-critical sentence per prompt, and complement them with a human-written gold benchmark. In this setting, PRIG localizes ambiguous spans substantially better than gradient attribution baselines, achieving 0.840 AUROC on the combined synthetic benchmark and 0.891 AUROC on the gold set. It also outperforms GPT-5.4 on sentence-level ambiguity identification and retains useful signal out-of-domain. These results establish PRIG as a practical tool for identifying which parts of a prompt are ambiguous. More broadly, they suggest that latent prompt properties can be localized through intermediate representations, rather than through output-level attribution.
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Machine Learning

Learned Subspace Compression for Communication-Efficient Pipeline Parallelism

Pipeline parallelism enables training of large language models that exceed single-device memory, yet inter-stage activation communication becomes the dominant bottleneck when trained on low-bandwidth networks. Recent work in this area has proposed using fixed orthogonal projections to compress activations. However, this still results in a significant performance degradation and requires a number of non-standard adaptations to constrain the optimization. A natural alternative is to learn a low rank projection for each pipeline stage, however maintaining the necessary orthogonality of these projectors during training remains a challenge. We present Manifold Aware Projection Learning (MAPL), a method that treats inter-stage compression as a learnable orthogonal projection under explicit Stiefel manifold (orthogonal matrices) constraints. Rather than prescribing a fixed global subspace, MAPL lets each pipeline stage discover and continuously adapt its own task-optimal compression subspace via manifold-constrained steepest descent. To recover token-specific signals at stage boundaries, we introduce per-stage factorized anchor embeddings that allow for full-rank activation reconstruction with negligible communication overhead. We further show that we can incorporate residual vector quantization after projection with a streaming codebook synchronization protocol that amortizes dictionary communication. Across LLaMA models from 150M to 1B parameters we show that MAPL can be easily applied to the existing pipeline and can achieve high compression with neglibile performance degradation with a drastically improved tradeoffs in performance vs. compression compared to Subspace Networks.
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Machine Learning

Towards Unified and Data-Efficient Prognostics and Health Management with Tabular Foundation Models

Data-driven Prognostics and Health Management (PHM) uses time-varying condition-monitoring data to diagnose system states and estimate remaining useful life in engineered assets. These tasks are central to maintenance planning, but industrial PHM data are often fragmented, partially observed, and poorly labeled, which hinders supervised learning. Foundation models offer a route toward reusable predictive systems, yet most time-series foundation models are designed for forecasting and assume long, coherent, regularly sampled sequences. To address this gap, we propose a framework for applying Tabular Foundation Models to industrial time series using in-context learning, and we evaluate them on a variety of PHM tasks. By converting raw unit-level signals into tabular rows, we show that these models perform well across multiple tasks - including prognostics, and diagnostics - and are highly data efficient. We compare them directly with sequence models, transformer baselines, and gradient-boosted trees under a common evaluation protocol. The results indicate that tabular foundation models achieve the best average ranks across prognostic and diagnostic tasks. Our findings further show that PFN-based models are competitive in low-data regimes, that temporal context can be preserved in the tabular representation, and that performance depends on representative context construction under subsampling. These results demonstrate that tabular foundation models provide a practical and general interface for heterogeneous PHM problems.
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All authors Raffael Theiler, Lev Telyatnikov, Leandro Von Krannichfeldt, Olga Fink

Machine Learning · Cross-listed from cs.CV

Can We Predict The Human Preference For Text-to-Image Content Prior To Generation And Is It Even Useful To Do So?

Diffusion Models (DM) have revolutionized text-driven generation by enabling the synthesis of high-quality, photorealistic visual content from user prompts. Whereas prior advances in visual generation such as VAEs and GANs were primarily evaluated on perceptual or visual similarity metrics such as FID PSNR, DM advances have fostered the development of more advanced Human Preference Metrics (HPM) that model and quantify human judgment as scalar values. However, DMs synthesize content using an inherently stochastic process where random noise seeds generation. The initial random noise directly affects the quality of generated outputs, both qualitatively and quantitatively. This influence is pronounced in smaller models for local deployment scenarios. Given this phenomenon, we first investigate to what extent we can predict scalar HPM scores prior to committing compute resources for generation. Further, we then investigate to what extent we can leverage such prediction to improve the quality of generated images, and also study which HPMs are best suited for this task. Our investigation reveals that not only is this possible, but that it is feasible to achieve negligible hardware overhead.
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Machine Learning · Cross-listed from q-bio.BM

AlloGen: Conformation-Selective Binder Generation with Differential State Scoring

Protein binder design has largely optimized for affinity alone, leaving conformational selectivity unaddressed: for allosteric targets such as kinases, nuclear receptors, and GPCRs, a binder that engages both active and inactive states provides no functional specificity regardless of how tightly it binds. We introduce AlloGen, a modular framework that decouples backbone generation from a learned state-selectivity scorer $Q_\theta$, an SE(3)-invariant interface graph transformer trained via a two-phase curriculum that first learns interface geometry before imposing conformational discrimination. Because $Q_\theta$ is fully differentiable and generator-agnostic, it integrates with any backbone generator as a passive reranker or an active gradient-based guide without retraining. Across a diverse benchmark of proteins spanning multiple families and conformational mechanisms, AlloGen consistently identifies binders that preferentially recognize desired structural states while rejecting alternative conformations. Experimental validation on calmodulin further demonstrates that these computational selectivity signals translate to physical molecules, yielding de novo peptides that bind the desired holo conformation while exhibiting no detectable binding to the apo state. Together, these results establish conformational selectivity as a learnable property and provide a general framework for state-selective protein binder design.
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All authors Hanqun Cao, Zachary Quinn, Aastha Pal, Sumi Kimura, Jingjie Zhang, Pheng Ann Heng, Pranam Chatterjee

Machine Learning · Cross-listed from cs.CL

Multilingual Coreference Resolution via Cycle-Consistent Machine Translation

Coreference resolution is a core NLP task, having a broad range of downstream applications, e.g.~machine translation, question answering, document summarization, etc. While the task is well-studied in English, comparatively less attention is dedicated to coreference resolution in other languages, especially low-resource ones. To mitigate this gap, we propose a novel coreference resolution pipeline that harnesses machine translation (MT) from English to a target low-resource language, to generate or expand training data. To automatically validate the quality of the translated samples, we back-translate the samples and assess the similarity with the original English samples via cosine similarity in the latent space of a BERT model. The resulting similarity scores are integrated into the loss function to weight training samples according to their MT cycle consistency. Extensive experiments on four low-resource languages show that our pipeline brings significant performance gains in coreference resolution. Moreover, our pipeline enables accurate coreference resolution in languages where no previous corpora were available.
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All authors Adriana-Valentina Costache, Eduard Poesina, Silviu-Florin Gheorghe, Paul Irofti, Radu Tudor Ionescu

Machine Learning

GOTabPFN: From Feature Ordering to Compact Tokenization for Tabular Foundation Models on High-Dimensional Data

We investigate how to make small tabular foundation models effective for High-Dimensional, Low-Sample Size (HDLSS) tabular prediction without retraining large backbones. We introduce Graph-guided Ordering with Local Refinement (GO-LR), show its equivalence to weighted Minimum Linear Arrangement, and interpret the practical solver as a TSP-path-style surrogate. We propose GOTabPFN,which builds on GO-LR, and a Neuro-Inspired Subunit Compression (NSC) unit to pool locally adjacent ordered features into meta-features, yielding a compact representation that makes TabPFN-style prediction practical in HDLSS regimes. Across tabular benchmarks, GOTabPFN improves stability and accuracy under tight token budgets.
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All authors Al Zadid Sultan Bin Habib, Md Younus Ahamed, Prashnna Kumar Gyawali, Gianfranco Doretto, Donald A. Adjeroh

2606.05441 · 3 Jun · Accepted to the 43rd International Conference on Machine Learning (ICML 2026). Code and resources GitHub https://github.com/zadid6pretam/GOTabPFN PyPI https://pypi.org/project/gotabpfn Project webpage https://www.zadidhabib.com/gotabpfn.html Hugging Face ZeroGPU https://huggingface.co/spaces/zadid6pretam/GOTabPFN CPU backup https://huggingface.co/spaces/zadid6pretam/GOTabPFN_CPU

Machine Learning

Sharp First-Order Lower Bounds for Higher-Order Smooth Nonconvex Optimization

We study the deterministic first-order oracle complexity of finding \(\epsilon\)-stationary points in smooth nonconvex optimization when the objective satisfies higher-order smoothness assumptions. While the classical \(\epsilon^{-2}\) rate is optimal under only Lipschitz gradients, higher-order smoothness leads to accelerated first-order upper bounds, most notably the \(\epsilon^{-7/4}\) rate under Lipschitz Hessians and the \(\epsilon^{-5/3}\) rate under Lipschitz third derivatives. The matching lower bounds, however, have remained open. We resolve this gap by proving a new dimension-free first-order lower bound for higher-order smooth nonconvex functions, valid for every finite smoothness order. In particular, our construction gives a matching \(\Omega(\epsilon^{-7/4})\) lower bound in the Hessian-Lipschitz case and a matching \(\Omega(\epsilon^{-5/3})\) lower bound in the third-order-smooth regime. The hard instance is based on a block-chain mechanism that enforces blockwise oracle revelation while preserving the smoothness structure needed for the scalar hard instance. The lower-bound construction was discovered with the assistance of ChatGPT 5.5 Pro and subsequently verified by the authors.
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Machine Learning

DP-MacAdam: Differentially Private Mechanism with Adaptive Clipping and Adaptive Momentum

Differentially private stochastic gradient descent (DP-SGD) has become the standard framework for privacy-preserving machine learning, yet its reliance on a fixed gradient clipping threshold to limit sensitivity remains a significant practical limitation. Adaptive clipping algorithms such as AdaClip shift and scale the gradient prior to clipping and adding noise so that the clipped gradient yields a more informative descent direction. The shift and scaling parameters are selected adaptively based on the empirical mean and variance. However, in existing adaptive clipping algorithms, these empirical estimates have not been also used for momentum to accelerate training itself. On the other hand, DP-Adam is an algorithm that exploits Adam-like momentum updates based on the gradient mean and variance to accelerate training, but does not exploit these estimates for adaptive clipping. In this work, we propose Differentially Private Mechanism with Adaptive Clipping and Adaptive Momentum (DP-MacAdam), a novel algorithm that combines these two approaches so as to use the same mean and variance estimates for both clipping and momentum. We perform an analysis showing that DP-MacAdam estimates the gradient variances in a bias-free manner. In addition, we empirically evaluate the privacy and accuracy of DP-MacAdam, demonstrating that it achieves improved model utility compared to DP-SGD, AdaClip, and DP-Adam baselines, without requiring manual tuning of the clipping threshold.
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Machine Learning

Selective-Advantage Entropy-Adaptive Horizon GRPO: Asymmetric Token-Level Discounting for Efficient Reinforcement Learning of Language Models

Group Relative Policy Optimisation (GRPO) has emerged as an effective reinforcement-learning algorithm for aligning language models on reasoning tasks, but it treats every token position and every sampled rollout symmetrically. We introduce two complementary extensions: (i) Adaptive-Horizon GRPO (AH-GRPO), which weights each token's policy gradient using a cumulative entropy-based discount that reduces the effective horizon when the model is uncertain, and (ii) Selective-Advantage AH-GRPO (SA-AH-GRPO), which applies this discounting only to negative-advantage rollouts, leaving positive-advantage, successful trajectories unattenuated. We evaluate standard GRPO with alpha = 0, AH-GRPO with alpha = 0.5, and SA-AH-GRPO with alpha = 0.5 on the GSM8K mathematical reasoning benchmark using both Qwen 2.5-1.5B-Instruct and Qwen 2.5-3B-Instruct fine-tuned with LoRA. On the 3B model, SA-AH-GRPO achieves Pass@1 = 0.858 at its peak at step 30 and maintains 0.846 at 180 steps, with training variance reduced to 0.0246, a 3.6 times reduction relative to GRPO while matching its peak accuracy. On the 1.5B model, SA-AH-GRPO achieves a peak Pass@1 of 0.686, improving over the zero-shot baseline of 0.637. Our analysis shows that asymmetric discounting preserves the full gradient signal on correct solutions, prevents entropy collapse, and substantially stabilises training, suggesting a principled inductive bias for reinforcement learning with verifiable rewards on structured generation tasks.
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Machine Learning · Cross-listed from cs.CL

Executable Schema Contracts: From Automatic Ingestion to Multi-Source Retrieval

Real-world data spans tables, documents, and semi-structured files with implicit semantics. Querying this data requires integrating evidence across inconsistent schemas and formats, yet existing approaches either demand costly manual engineering or bypass structure entirely. We present a system that automatically discovers an executable schema from raw multi-source data and uses it as a shared contract for knowledge graph construction and query-time retrieval. A closed-world field catalog constrains LLM-based schema discovery to attested fields; deterministic structural analysis infers identity keys, foreign keys, and source hierarchy; and the resulting schema drives extraction, deduplication, and cross-source linking into a provenance-aware knowledge graph. At query time the schema – optionally extended via a monotonic protocol – conditions a multi-tool agent routing retrieval across structured lookup, graph traversal, and vector search, returning grounded answers with traceable citations. In controlled zero-shot comparisons using the same LLM, data, and evaluation harness, the system improves over retrieval-only and decomposition-based baselines across four QA benchmarks, with ablations showing that schema-conditioned routing, structural intelligence, and schema-guided construction each contribute to the gains.
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All authors Padmaja Jonnalagedda, Yuguang Yao, Xiang Gao, Hilaf Hasson, Kamalika Das

Machine Learning · Cross-listed from cs.CL

When Evidence is Sparse: Weakly Supervised Early Failure Alerting in Dialogs and LLM-Agent Trajectories

Early failure alerting requires deciding, while a dialog or agent trajectory unfolds, whether it is likely to fail. Existing approaches broadly follow two directions. LLM-based uncertainty monitoring either elicits confidence from the acting model, tying reliability to its own self-assessment, or queries an external frontier judge at each prefix, incurring costly repeated inference. Trained monitors instead either rely on per-turn annotations, which are rarely available, or train every prefix to predict the terminal outcome without explicitly modeling where failure-indicating evidence appears. We address these limitations with a lightweight external monitor trained only from trajectory-level outcomes, motivated by a pattern across five benchmarks: turns rated highly relevant to failure are sparse and often late. Its attention-based multiple instance learning (MIL) component learns turn-level contributions from trajectory outcomes and distills them into online evidence features that complement prefix predictions. We pair the resulting failure estimates with $\alpha$-STOP, a single preference-conditioned policy that selects accuracy-earliness operating points at inference time. The predictor improves Pareto-frontier quality (hypervolume) by 1-10% over naive prefix supervision, while the full system improves it by 3-42% over state-of-the-art trigger policies without per-preference retraining. By avoiding repeated frontier-model calls, our lightweight monitor reduces measured per-decision serving cost by 1,103-3,749$\times$ and latency by 31-106$\times$ relative to the LLM-based uncertainty monitor (GPT-5.2).
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All authors Avinash Baidya, Xinran Liang, Ruocheng Guo, Xiang Gao, Kamalika Das

Machine Learning

CausalPOI: Spatio-Temporal Graph-Based Causal Modeling for Cold-Start POI Check-in Forecasting

As urban environments continue to evolve rapidly, accurately modeling the dynamic behaviour of Points of Interest is essential for supporting data-driven urban planning and commercial decision-making. While recent advancements in spatio-temporal graph learning have improved POI forecasting, most methods rely on proximity-based graphs and correlation-driven modeling, which overlook the functional dependencies between POIs and fail to capture the causal effects of urban interventions. In this paper, we introduce a novel research problem – cold-start POI check-in forecasting, which aims to predict the future check-in pattern of a newly introduced POI, by modeling its temporal evolution and functional interactions with nearby POIs in a structured urban spatial context. To address these challenges, we propose CausalPOI, a spatio-temporal graph-based causal representation learning framework. CausalPOI leverages Spatio-Temporal Functional Interaction Graph to model semantic and spatial relationships between POIs, and constructs structurally aligned treatment and control graphs to simulate factual and counterfactual scenarios. Extensive experiments on real-world SafeGraph datasets demonstrate that CausalPOI significantly outperforms state-of-the-art baselines across the board, validating its effectiveness in spatio-temporal forecasting, semantic interaction modeling, and causal effect estimation, providing a more interpretable and actionable foundation for urban intervention analysis. Source code is available at Github.
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All authors Zhaoqi Zhang, Miao Xie, Yi Li, Linyou Cai, Siqiang Luo, Gao Cong

Machine Learning · Cross-listed from cs.AI

Agents' Last Exam

Recent AI systems have achieved strong results on a wide range of benchmarks, yet these gains have not translated into economically meaningful deployment across many professional domains. We argue that this gap is largely an evaluation problem: widely used benchmarks lack sustained performance measurement on real and economically valuable workflows. This paper introduces Agents' Last Exam (ALE), a benchmark designed to evaluate AI agents on long horizon, economically valuable, real world tasks with verifiable outcomes. Developed in collaboration with 250+ industry experts, ALE covers non-physical industries defined with reference to O*NET / SOC 2018 (the U.S. federal occupational taxonomy). It is organized around a task taxonomy with 55 sub fields grouped into 13 industry clusters covering 1K+ tasks. Current results show that the hardest tier remains far from saturated: across mainstream harness and backbone configurations, the average full pass rate is below 1%. ALE is designed as a living benchmark: its task pool grows continuously as new workflows and industries are onboarded. More broadly, ALE is intended not merely as another leaderboard, but as an instrument for closing the gap between benchmark success and GDP relevant impact.
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All authors Yiyou Sun, Xinyang Han, Weichen Zhang, Yuanbo Pang, Tianyu Wang, Yuhan Cao, Yixiao Huang, Xiang Liu, Zonglin Di, Chris Duroiu, Haoyun Zhang, Jeffrey Lin, Weishu Zhang, Tyler Zeng, Ying Yan, Bo Liu, Hanson Wen, Mingyang Xu, Xiaoyuan Liu, Zimeng Chen, Zhaowei Zhang, Weiyan Shi, Amanda Dsouza, Vincent Sunn Chen, Jingxu Xie, Dewen Lei, Hanxuan Zhang, Yinhe Wang, Xinran Zhang, Chao Zhou, Sheldon Huang, Patrick Bryant, Carl Boettiger, Yamini Rangan, Bradley Rothenberg, Kyle Steinfeld, Arvind Rao, Tapio Schneider, Georgios Yannakakis, Laure Zanna, Kaan Ozbay, Ida Sim, Tarek Zohdi, George Em Karniadakis, Jack Gallant, Teresa Head-Gordon, Chris Yuhao Liu, Rongwang Hu, Yafei Cheng, Aras Bacho, Zengyi Qin, Alan Yuille, Yixiong Chen, Hao Liu, Lin Zeng, Bo Chen, Zhendong Li, Litian Gong, Shashank Muralidhar Bharadwaj, Thorben Jansen, Haixiang Tang, Jianhong Tu, Jixian Liu, Maojia Song, Ruheng Wang, Shengcao Cao, Yanxin Zhang, Yingxuan Yang, Zongzheng Zhang, Honglin Bao, Hyunjun Kim, Peiran Xu, Shuo Lu, Zheng Zhang, Zhonghua Wang, Aditya Prakash, Bohan Lyu, Chang Ma, Haoxuan Chen, Hengduan Fan, Molei Tao, Roman Sitelew, Russell Alan Poldrack, Yang Liu, Yang Liu, Yichen Wu, Yuanze Lin, Zhenglu Li, Zibu Wei, Zijiao Chen, Abderrahim Bendahi, Alexander Schubert, Chase Broderick, Chengzhi Liu, Haoran Sun, Haoyang Li, Haoyue Hua, Jiayuan Ding, Jing Huang, Shangding Gu, Tuan Vinh, Xiatao Sun, Yanqiong Jiang, Yiran Hu, Zechen Xu, Ziao Yang, Chenguang Wang, Costas Spanos, Dongrong Yang, Haocheng Wang, Jiayi Cheng, Jicheng Wang, Junbo Peng, Kangqi Zhang, Keying Kuang, Lichao Sun, Ming Yin, Orson Xu, Vincent Siu, Wanzhe Liao, Wenqi Shi, Wenxi Deng, Xiaopan Zhang, Yangjunfeng Zhu, Yifan Shen, Yi Jiang, Yinsheng Li, Youbang Pan, Yuan Li, Yuchen Zhu, Yunshi Zhang, Zhenning Yang, Ziyan Rao, Alireza Rafiei, Andrew Glover, Bixuan Ren, Boqin Yuan, Chonghao Cai, Deren Lei, Hanwen Xing, Haoran Jin, Hector Gomez, Ishaan Singh Chandok, Jiaming Hu, Jianxin Sun, Justin Purnomo, Kunyang Sun, Lei Ding, Longtai Liao, Lukas Kim, Ming Liu, Qingpo Wuwu, Ran Jin, Ruiqi Zhang, Ting Sun, Wenbo Huang, Xuandong Zhao, Peter Chen, Chuanyang Jin, Qiming Bao, Xuhuan Shen, Yifan Zhang, Yi Li, Yingze Wang, Yixin Wang, Yushi Yang, Zhen Dong, Zhiling Yan, Zhongxing Xu, Zibo Zhao, Zixin Jiang, Ali Emami, Andy Zeyi Liu, Angela Wu, Aylin Caliskan, Baihe Huang, Baixiang Huang, Benjamin Yang, Benran Zhang, Brian Zhao, Carlo Bosio, Charlie Guo, Che Liu, Chenchen Du, Chen Dai, Chenlong Zhang, Chenyu Li, Chenyu Zhu, Chi Zhang, Core Francisco Park, Daofeng Li, Dehao Wu, Dowling Wong, Erin Kasson, Fangyu Wu, Fan Xu, Fiona Shen, Haimin Hu, Haitao Li, Hang Zhou, Hannah Szlyk, Hanning Zhang, Hanwen Zhang, Hao Fan, Haoran Ye, HaoYang Shang, Haoyue Bai, Hengyu Fu, Hongwei Li, Huiqi Wang, Jiachen Li, Jialu Wang, Jiaming Liu, Jiawei Shen, Jierui Zuo, Jingxuan Fan, Jingyan Li, Jirong Yang, Jonah So, Jorin Overwiening, Joseph Cavanagh, Joseph Lee, Junge Zhang, Kaiyuan Liu, Kaustubh Dhole, Kevin Qinghong Lin, Kunpeng Zhang, Kyle Montgomery, Layna Paraboschi, Liana, Lihui Liu, Liwei Zhou, Lu Lu, Mengyuan "Millie" Wu, Mikko Tolonen, Mingxuan Yan, Minqi Shi, Murphy Niu, Pan Lu, Patricia Cavazos-Rehg, Qijian Zhao, Qiuyang Mang, Rimika Jaiswal, Ruiling Xu, Run-Ze Fan, Ruoxi Ning, Santanu Bosu Antu, Scott Rankin, Sen Yang, Shi Gu, Shi Qiu, Sichen Zhu, Sihan Xu, Siqi Zhu, Song Zhang, Sophia Sun, Stefano De Castro, Swati Rajwal, Tianneng Shi, Tianxing Chen, Tianyue Zhou, Ting Wang, Ventus Shaw, Vladislav Susoy, Weihang Xiao, Wei Wang, Wenbo Lv, Wenjin Zhang, Wenshuo Zhang, Wenyu Liang, Xiaohu Yu, Xiao Li, Xiaoli Yang, Xin Lan, Xinyu Wang, Xuan Liu, Xuewen Chen, Xu Pan, Yan Zhu, Yicheng Lyu, Yifan Gu, Yimin Zhao, Ying Zhang, Yin Ren, Yipu Chen, Yiren Rong, Yi Shao, Yishu Zhu, Yizhi Zhang, Yongyi Xiong, Yuangang Li, Yuchen Wu, Yuhaohua Zheng, Yuhao Wu, Yunfu Deng, Yushan Li, Yu Wu, Yuzheng Xu, Yuzhou Nie, Zehao Wang, Zhehang Du, Zhengming Yu, Zhihan Jiang, Zhi Li, Zhixu Li, Zhuoran Yi, Tao Sun, Zhun Wang, Justin Xu, Shi Bo, Helena Casademunt, Wenjia Chen, Cheng Cheng, Nawen Deng, Rao Fu, Tianfu Fu, Yifan Han, Zhenyu He, Qiao Jin, Langlang Li, Yuetai Li, Sylvia Liu, Subhabrata Mukherjee, Yunqi Ouyang, He Ren, Dawei Shi, Haoran Wu, Zhiyue Wu, Hannah Yao, Jenny Yu, Rhea Zhan, Luqing Zhou, Blake Zhu, Junfan Zhu, Sanjiv Das, Yanjun Gao, Wenbo Guo, Erika J Schneider, Bing Liu, Zhiyong Lu, Yian Ma, Mark Mueller, Radha Poovendran, Somayeh Sojoudi, Huaxiu Yao, Yinglun Zhu, Károly Zsolnai-Fehér, Yegor Denisov-Blanch, Changran Hu, Vincent Koc, Hezheng Yin, Naomi Xia, Xinyi Bai, Arsh Shah Dilbagi, Jing Gu, Yutong Liu, Lin Shi, Qizheng Zhang, Yuexing Hao, Xiaoming Li, Xiangyi Li, Bingran You, Wenjun Ke, Daoan Zhang, Ari Nemet, Tianyi Zhang, Xingda Lyu, Pranit Chawla, Genta Indra Winata, Maosen Tang, Purva Chiniya, Qiuyi Chen, Steven Dillmann, Wanghan Xu, Wenqi Yang, Xiaojun Wu, Xin Luo, Yue Huang, Dawn Song

Machine Learning · Cross-listed from cs.AI

Harnessing Generalist Agents for Contextualized Time Series

Time series are often embedded in rich contexts that are essential for holistic modeling. Moreover, real-world practitioners often require end-to-end workflows for analyzing temporal dynamics, where widely studied tasks such as forecasting are only one step in a broader solution loop. While generalist AI agents offer a promising interface for such workflows under complex contexts, they still operate primarily in textual spaces that are not fully aligned with structured temporal signals. In this work, we introduce TimeClaw, an agentic harness framework for time series that equips generalist LLM agents with the time series-native runtime support needed for contextualized temporal reasoning. TimeClaw integrates executable temporal tools for grounded and auditable analysis, experience-driven capability evolution for creating reusable analytical routines, and episodic multimodal memory for retrieving relevant reasoning traces. Together, these components unlock harnessed open-ended temporal reasoning with contextual information. Extensive evaluation on multiple benchmarks covering diverse tasks across energy, finance, weather, traffic, and other real-world domains demonstrates improved performance of TimeClaw. Code is available at https://github.com/iDEA-iSAIL-Lab-UIUC/TimeClaw.
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All authors Zihao Li, Kaifeng Jin, Yuanchen Bei, Jiaru Zou, Avaneesh Kumar, Xuying Ning, Yanjun Zhao, Mengting Ai, Baoyu Jing, Hanghang Tong, Jingrui He

Machine Learning

Trust, but Don't Verify: Epistemic Blind Spots in LLM Source Evaluation

Language models increasingly act as epistemic proxies, synthesizing evidence from multiple sources to inform decisions. Whether they evaluate the quality of that evidence, or merely aggregate it based on surface presentation, remains poorly understood. We show that models possess the capability to detect fabricated statistics in isolation but do not recruit this capability during multi-source synthesis, producing similar numeric estimates whether the statistics are fabricated or valid. Specifically, source influence is governed by a methodology-register gate that responds to the distributional register of analytical text but not to numeric validity: for example, statistically impossible confidence intervals receive the same weight as valid ones. The behavioral dissociation replicates across six models from four families (Anthropic Claude, Qwen, OLMo, and OpenAI GPT-5.4) and three professional domains. Mechanistic analyses, including causal tracing, linear probes, and component-level attribution, converge on the same account: the model encodes and causally uses a methodology-register representation that transfers across domains, while numeric-validity signals, decodable in isolation, are suppressed to chance during multi-source synthesis. Prompting-based mitigations, even an oracle checklist naming the exact statistical checks, produce blanket skepticism rather than selective discernment, and the post-training pipelines we examine reinforce the shortcut without building numeric verification. Unlike sycophancy, which tracks user preference, this failure tracks whether a source presents as analytically credible, not whether its claims are consistent. We term this epistemic alignment: like preference and safety alignment, the question is not capability but deployment.
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Machine Learning · Cross-listed from cs.AI

LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization

Long-horizon autoformalization of research mathematics fails not only at hard lemmas, but at scale: statements drift, dependencies tangle, context decays, and local repairs corrupt distant work. We present LeanMarathon, a multi-agent harness for reliable research-level Lean autoformalization. Its core abstraction is an evolving blueprint: a Lean file that serves simultaneously as formal proof skeleton, natural-language proof graph, and shared system of record. Four contract-scoped agents construct, audit, prove, and repair this blueprint. These agents are coordinated by a two-stage orchestrator that first stabilizes target fidelity through adversarial review and then discharges the proof directed acyclic graph (DAG) from its dynamic leaves upward in parallel CI-gated rounds. LeanMarathon turns one brittle multi-hour run into many local, recoverable, parallel transactions. We evaluate LeanMarathon on two recent research papers spanning four Erdős problems (#1051, #1196, #164, #1217). Across three autonomous runs, it formalizes all seven target theorems with no sorry, proving 258 lemmas and theorems. These results show that reliable AI co-mathematics requires not only stronger provers, but durable harnesses that preserve target fidelity across long mathematical developments. The code can be found at https://github.com/YuanheZ/LeanMarathon.
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All authors Yuanhe Zhang, Yuekai Sun, Taiji Suzuki, Jason D. Lee, Fanghui Liu

Machine Learning

Generalized TV–$\ell_p$ Structured Priors for Bayesian $T_1$ Mapping

We propose an extended family of structured spatial priors that incorporates the total variation (TV) function with $\ell_p$ norms. The prior is proven to be proper and incorporated into a Bayesian regression framework to enable uncertainty quantification in $T_1$ mapping, with posterior inference performed using the No-U-Turn Sampler (NUTS). This TV–$\ell_p$ construction is proven to constitute a well-defined family of prior distributions, and it naturally enforces spatial consistency and smooth variations in the estimated parameter maps. The method was evaluated in comparison to maximum-likelihood estimation and several Bayesian alternative priors based on the uniform, Gamma, and bounded TV priors. The evaluation includes experiments on synthetic brain and cardiac $T_1$ mapping datasets, as well as a real in-vivo breast $T_1$ mapping dataset. The results show that the TV–$\ell_p$ prior yields more concentrated posterior densities, indicating reduced uncertainty. It also consistently achieves lower variance and smaller (negative) bias, leading to more reliable estimates. Overall, embedding a TV-based structured penalty along with $\ell_p$ norms in a prior in a Bayesian model improves spatial coherence in $T_1$ maps and enhances uncertainty quantification, offering a robust approach for $T_1$ mapping with uncertainties.
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Machine Learning · Cross-listed from cs.DS

Learning-Augmented Online Minimization with Dual Predictions

We present learning-augmented algorithms for two general classes of online minimization problems: metrical task systems and laminar set cover. Both algorithms achieve improved theoretical guarantees using machine-learned predictions of an optimal solution to the dual linear program. Unlike optimal primal solutions, which can change drastically under tiny instance perturbations, these dual solutions are much more stable, which ensures the existence of good (and learnable) predictions for families of similar instances. While previous work has used dual predictions in offline settings and for online maximization problems, our algorithms are, to the best of our knowledge, the first demonstration that such dual predictions can be effective for online minimization. Our theoretical results are complemented by experiments on the $k$-server problem and the parking permit problem.
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Machine Learning

Pattern Selectivity is Not Task-Causal Structure: A Cross-Architecture Mechanistic Study of Composed-Task Circuits in 1B-Class Language Models

We test whether a single screen-and-ablate recipe – identify attention-head circuits by task-pattern selectivity, then verify by causal ablation against a matched-random null – produces consistent mechanistic claims across model families. The recipe ports across pipelines; the specific circuit it identifies does not. Across four composed tasks (indirect-object identification, greater-than, successor sequences, variable binding) and three 1B-class language models from distinct training pipelines (Pythia 1B / Pile / dense; OLMo 1B / DCLM / dense; OLMoE 1B-7B / DCLM / mixture-of-experts), we run a unified protocol with the matched-random null sampled across ten seeds per cell. The resulting 12 (task, model) cells contain no two that share the same primary causal screen at comparable effect size: the same task, with the same behavioral capability, is implemented through different attention-pattern types across models. We introduce a five-category screen-outcome taxonomy – primary cause, secondary cause, correlate, interferer, null – with quantitative thresholds, and show that all five outcomes appear in the panel. We propose a falsifiable hypothesis: the MoE model in our panel builds composed-task circuits on top of a foundational previous-token positional substrate (the prev-token-circuit ablation is the strongest causal screen on 3 of 4 tasks for OLMoE 1B-7B), with the IOI exception consistent with IOI being a final-position name-copying task whose structure directly probes a different pattern. The hypothesis comes with explicit predictions for other MoE language models. We frame the methodology honestly: the spectral participation-ratio signal from the companion methodology paper is a general indicator of specialized computation; what makes a finding task-specific is the task-pattern screen plus a per-model causal verification.
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