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02.
arXiv (math.PR) 2026-06-15

Sharp Favard length of random Cantor sets

Authors:
Alan Chang↗Pablo Shmerkin↗Ville Suomala↗

arXiv:2512.17753v2 Announce Type: replace-cross Abstract: We show that for a large class of planar $1$-dimensional random fractals $S$, the Favard length $\operatorname{Fav}(S(r))$ of the neighborhood $S(r)$ is comparable to $\log^{-1}(1/r)$, matching a universal lower bound; up to now, this was only known in expectation for a few concrete models. In particular, we show that there exist $1$-Ahlfors regular sets with the fastest possible Favard length decay. For a wide class of planar one-dimensional "grid random fractals", including fractal percolation and its Ahlfors-regular variants, we further show that $\operatorname{Fav}(S(r))/\log(1/r)$ converges almost surely, and we identify the limit explicitly. Furthermore, we prove that for some $1$-dimensional Ahlfors-regular random fractals $S$, the Favard length of $S(r)$ decays instead like $\log\log(1/r)/\log(1/r)$, showing that the $1/\log(1/r)$ decay is not universal among random fractals, as might be expected from previous results.

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

PowerOPD: Stabilizing On-Policy Distillation with Bounded Power Transformation

Authors:
Anhao Zhao↗Junlong Tong↗Yingqi Fan↗Ping Nie↗Wenjie Li↗Xiaoyu Shen↗

arXiv:2606.17199v1 Announce Type: cross Abstract: Standard on-policy distillation (OPD) for large language models estimates the reverse-KL objective using student-sampled tokens, yielding an unbiased single-sample Monte Carlo estimator that avoids vocabulary-wide computation. However, we show that this estimator suffers from severe training pathologies in practice: sample inefficiency, unstable generation dynamics, and a substantial performance gap compared to exact full-vocabulary OPD. Reward-level diagnosis traces these pathologies to the log-ratio reward, which is unbounded by construction, producing extremely high-variance gradients concentrated at early positions and persisting throughout training; standard post-hoc scaling fail as they operate only after this distortion occurs. To solve this problem, we propose PowerOPD: a family of natively bounded, sign-consistent rewards from the Box-Cox power transformation, parameterized by alpha > 0, of which the log-ratio is the degenerate alpha -> 0 limit. Across six mathematical reasoning benchmarks and four Qwen3 teacher-student pairs, PowerOPD achieves benchmark-averaged Avg@8/Pass@8 gains of up to +6.37/+5.71 over vanilla OPD, +3.01/+3.54 over post-hoc stabilization, and +2.59/+8.90 over full-vocabulary OPD, while reducing wall-clock time by 59.2% and peak GPU memory by 23.1%. Larger alpha generally improves accuracy, consistently shortens responses, and keeps gradient norms more than 3,000x smaller than vanilla OPD.

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04.
arXiv (CS.AI) 2026-06-19

QueryGaussian: Scalable and Training-Free Open-Vocabulary 3D Instance Retrieval

Authors:
Xiuyuan Zhu↗Ke Lu↗Zijie Yang↗Chao Yue↗Jian Xue↗Dongming Zhang↗

arXiv:2606.19733v1 Announce Type: cross Abstract: Efficiently retrieving specific 3D instances from large-scale scenes via natural language prompts remains a formidable challenge in multimedia analysis. Existing approaches predominantly follow a "scene-level embedding" paradigm, which requires distilling high-dimensional semantic features into every 3D primitive. This strategy suffers from a fundamental architectural bottleneck: memory and computational costs scale linearly with scene complexity, inevitably triggering out-of-memory (OOM) failures in city-scale environments. To address this barrier, we propose QueryGaussian, a training-free framework for expeditious and scalable open-vocabulary 3D instance retrieval. Unlike holistic semantic distillation, QueryGaussian employs an instance-level query mechanism that decouples semantic understanding from geometric representation. Specifically, we leverage pre-trained 2D vision models to interpret user prompts and lift segmentation masks into 3D via a concurrent maximum-weight association strategy, ensuring semantic-visual consistency. To mitigate projection ambiguity, we introduce a temporal fusion module with multi-stage adaptive density clustering. Experimental results demonstrate that QueryGaussian not only matches the accuracy of state-of-the-art methods but also delivers a decisive efficiency leap, reducing GPU memory usage by over 70% and accelerating inference by 180x. Crucially, QueryGaussian enables expeditious instance retrieval on city-scale scenes containing tens of millions of Gaussians using consumer-grade hardware.

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05.
arXiv (CS.CL) 2026-06-12

Localizing Anchoring Pathways in Language Models

Authors:
Hillary N. Owusu↗Sarah Wiegreffe↗Naomi H. Feldman↗

Irrelevant numbers in a prompt can shift language model judgments, producing anchoring effects in numerical reasoning. We study where this anchor-sensitive signal is carried inside language models using a controlled multiple-choice setup with shared answer options. We define a logit-difference metric comparing the correct answer option with the answer option corresponding to the anchor, and validate that it tracks behavioral anchoring. Using attribution-based circuit localization on 7B–8B Qwen and Llama base and instruction-tuned models, we find that edge-level methods recover this signal more faithfully than node-level methods. Low- and high-anchor circuits transfer strongly within a model, suggesting shared pathway structure across anchor direction. However, sparse transfer across base and instruction-tuned variants is less reliable, indicating that post-training changes which pathways matter most. Overall, our results provide a mechanistic account of how anchoring-related decision signals are carried inside language models.

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

TetherCache: Stabilizing Autoregressive Long-Form Video Generation with Gated Recall and Trusted Alignment

Authors:
Yu Meng↗Xiangyang Luo↗Letian Li↗Wenyuan Jiang↗Chen Gao↗Xinlei Chen↗Yong Li↗Xiao-Ping Zhang↗

Autoregressive video diffusion models provide a natural formulation for streaming and variable-length video generation by conditioning newly generated frames on previously generated content. However, extending these models to minute-level generation remains challenging: the limited KV-cache budget prevents the model from retaining the full history, while repeatedly conditioning on self-generated frames induces a context distribution shift that accumulates over time, leading to visual artifacts, quality degradation, and temporal drift. In this paper, we propose TetherCache, a training-free and plug-and-play cache management strategy for drift-resistant long video generation. TetherCache organizes the cache into sink, memory, and recent regions, and introduces two complementary mechanisms. First, GRAB (Gated Recall with Attention-Diversity Balancing) selects long-range memory frames using a gated score that combines attention-based relevance with temporal diversity, preserving informative yet diverse historical context under a fixed cache budget. Second, TAME (Trusted Alignment via Memory Editing) lightly edits newly recalled memory tokens by aligning their statistics to a trusted context distribution, reducing the pollution caused by drifted historical features. Built on Self-Forcing, TetherCache consistently improves long-video generation quality on VBench-Long across 30s, 60s, and 240s settings. In particular, for 240s generation, it substantially improves overall and semantic scores while reducing quality drift from 7.84 to 1.33, demonstrating its effectiveness for stable long-horizon autoregressive video diffusion.

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07.
Nature (Science) 2026-06-08

GPR15-guided CD8<sup>+</sup> T regulatory cells control intestinal inflammation

Authors:
Jing Cui↗

Inflammatory bowel disease (IBD) causes chronic suffering from gastrointestinal inflammation and dysfunction that can progress to colon cancer1,2. The disease prevalence is increasing and there is an urgent need to better understand its pathogenic mechanisms to improve treatment. We show that GPR15, a G protein-coupled receptor (GPCR) expressed in immune cells and previously described as an entry co-factor for human and simian immunodeficiency viruses3, is a marker and homing receptor for a subset of intramucosal GPR15-guided regulatory CD8+ T lymphocytes (CD8+ TIGR). Deleterious GPR15 gene variants in humans cause defective homing of CD8+ TIGR and are associated with severe early-onset IBD. Moreover, CD8+ TIGR cells are reduced in the intestinal mucosa of sporadic IBD patients. In mice, GPR15 deficiency impairs colonic homing of CD8+ TIGR cells, leading to accumulation of inflammatory macrophages and increased susceptibility to colitis. CD8+ TIGR cells potently kill macrophages activated by intestinal damage or disease using Fas ligand (FasL) and TNF-related weak inducer of apoptosis (TWEAK). The identification of CD8+ TIGR cells yields new insights into organ-specific immune regulation and potential therapeutics for IBD.

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

User as Engram: Internalizing Per-User Memory as Local Parametric Edits

Authors:
Bojie Li↗

arXiv:2606.19172v1 Announce Type: new Abstract: Personal memory in a language model is two problems: content and reasoning skill. The brain keeps the two apart (a sparse, local engram in the hippocampus for each episode, a slow neocortex for the shared skills that interpret it), so a new fact need not overwrite everything else. Most personalization today keeps a user's facts outside the weights, in a natural-language memory file or a retrieval index. When facts are written into the model instead, the standard recipe is the per-user LoRA adapter, which does the opposite of the brain, folding content and skill into one global weight delta. Writing a user's facts as a LoRA contaminates text unrelated to them; writing the same facts as local Engram rows leaves it mathematically untouched, resulting in a roughly 33,000x smaller memory footprint. We therefore propose User as Engram: store a user's content as surgical edits to the hash-keyed memory table of an Engram model, and carry the reasoning skill in one shared adapter. This layered design matches per-user LoRA's direct recall while delivering 5.6x higher indirect-reasoning accuracy on average, and never makes a single user worse at reasoning than the untouched base. The edit is a glass box: writing a fact switches on its lookup at exactly the trigger, adds the value the answer needs, leaves every other position unchanged to the last bit, and fails if written into the wrong layer. Because different users' facts land in disjoint hash slots, their edits compose: many users live in one shared table at once, stacking additively and losslessly, where a per-user LoRA, a single global weight delta, admits only one. Upon retrieval, a per-user Engram table does not grow with the population the retriever must search, so past ~100 facts it overtakes a retrieval pipeline on a 2.5x larger model.

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09.
arXiv (CS.CL) 2026-06-12

Helping Figures Tell their Story! Paper-Grounded Video Generation Explaining Complex Scientific Figures

Authors:
Ishani Mondal↗Javad Baghirov↗Jordan Boyd-Graber↗

Scientific figures compress complex pipelines into a single canvas, yet understanding them requires paper-grounded, step-by-step narration aligned with visual highlights a capability missing from current video generation systems and benchmarks. To address this, we introduce paper-grounded figure-to-video generation: generating narrated, region-grounded walkthrough videos from a figure and its paper. We propose MINARD (Multimodal Interpretation of Narrated Architecture via Region Decomposition), a pipeline that generates paper-grounded narrations and sequentially grounds them to figure regions. We also release FigTalk, a benchmark with new sequential and component-level grounding metrics derived. On FigTalk, MINARD generates humanlike, paper-faithful narrations and outperforms narration-conditioned figure spatial grounding compared to existing approaches in both automatic and human evaluation

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10.
arXiv (CS.CV) 2026-06-16

Efficient Flow Matching using Latent Variables

Authors:
Anirban Samaddar↗Yixuan Sun↗Viktor Nilsson↗Sandeep Madireddy↗

Flow matching models have shown great potential in image generation tasks among probabilistic generative models. However, most flow matching models in the literature do not explicitly utilize the underlying clustering structure in the target data when learning the flow from a simple source distribution like the standard Gaussian. This leads to inefficient learning, especially for many high-dimensional real-world datasets, which often reside in a low-dimensional manifold. To this end, we present $\texttt{Latent-CFM}$, which provides efficient training strategies by conditioning on the features extracted from data using pretrained deep latent variable models. Through experiments on synthetic data from multi-modal distributions and widely used image benchmark datasets, we show that $\texttt{Latent-CFM}$ exhibits improved generation quality with significantly less training and computation than state-of-the-art flow matching models by adopting pretrained lightweight latent variable models. Beyond natural images, we consider generative modeling of spatial fields stemming from physical processes. Using a 2d Darcy flow dataset, we demonstrate that our approach generates more physically accurate samples than competing approaches. In addition, through latent space analysis, we demonstrate that our approach can be used for conditional image generation conditioned on latent features, which adds interpretability to the generation process.

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

Predicting Poets' Origins from Verse: A Computational Analysis of Regional Linguistic Fingerprints in the Complete Tang Poems

Authors:
Chi-Sheng Chen↗Hung-Yun Liu↗

We ask whether the geographic origin of Tang-dynasty poets leaves a detectable linguistic trace in their work. Aggregating every poem attributed to each author in the Complete Tang Poems (Quan Tang Shi) and linking poets to their administrative circuit of origin via the China Biographical Database (CBDB), we build a poet-level corpus of 357 poets across the ten Tang circuits and frame origin prediction as multi-class classification. Using character $n$-gram TF-IDF together with interpretable domain features (imagery, season, and allusion), classical and neural models predict a poet's broad region (South vs.\ North) at $0.69$ accuracy, well above the $0.53$ majority baseline, and finer circuit-level origin above chance. Beyond classification, three findings emerge. (i) Linguistic distance between circuits grows with geographic distance (Mantel $r=0.40$, $p\approx0.09$ over nine circuits), evidence of a distance-decay effect in poetic language. (ii) The signal interacts with time: South/North separability is at chance in the High Tang and strongest in the Late Tang, consistent with court-driven homogenization at the empire's height followed by regional divergence. (iii) The model's confident errors are historically meaningful – in the Early Tang, every misclassification is a southern poet read as northern, reflecting the prestige of the northern court idiom. We further show that, when given the whole corpus through a hierarchical frozen-encoder representation, a classical-Chinese transformer (GuwenBERT) only matches – not beats – simple TF-IDF, and that combining them adds nothing, indicating that character $n$-grams already capture the regional signal. Our results position interpretable machine learning as a hypothesis generator for literary history.

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12.
arXiv (CS.AI) 2026-06-19

Assessment of Personality Dimensions Across Situations in Dyadic Role-Play Scenarios

Authors:
Alice Zhang↗Skanda Muralidhar↗Daniel Gatica-Perez↗Mathew Magimai-Doss↗

arXiv:2507.19137v3 Announce Type: replace-cross Abstract: Prior research indicates that users prefer assistive technologies whose personalities align with their own. This has sparked interest in automatic personality perception (APP), which aims to predict an individual's perceived personality traits. Previous studies in APP have treated personalities as static traits, independent of context. However, perceived personalities can vary by context and situation as shown in psychological research. In this study, we investigate the relationship between conversational speech and perceived personality for participants engaged in two work situations (a neutral interview and a stressful client interaction). Our key findings are: 1) perceived personalities differ significantly across interactions, 2) loudness, sound level, and spectral flux features are indicative of perceived extraversion, agreeableness, conscientiousness, and openness in neutral interactions, while neuroticism correlates with these features in stressful contexts, 3) handcrafted acoustic features and non-verbal features outperform speaker embeddings in inference of perceived personality, and 4) stressful interactions are more predictive of neuroticism, aligning with existing psychological research.

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13.
medRxiv (Medicine) 2026-06-22

Sequential Deep Learning to Predict Non-Central to Central Geographic Atrophy Progression from OCT Imaging

Authors:
Siraz↗Kamanda↗Nabil↗A. S↗Gholami↗Rao↗N. T↗Ong↗S. S↗Alam↗

Purpose: To develop and validate a temporal deep learning framework for predicting geographic atrophy (GA) progression across multi-year horizons using longitudinal optical coherence tomography (OCT) sequences. Design: Retrospective longitudinal cohort study. Subjects, Participants, and/or Controls: A total of 91 patients with dry age-related macular degeneration (AMD) were identified from Wake Forest University School of Medicine (2013-2023), yielding 455 OCT volumes. Two prediction cohorts were defined: 32 patients with no GA (NGA) at baseline who subsequently developed GA, and 35 patients whose earliest GA manifestation was non-central GA (NCGA). Non-progressing patients served as negative controls. Methods: OCT B-scan volumes were encoded into visit-level feature representations using three pretrained architectures (ResNet-18, ResNet-50, ViT-B/16). Chronologically ordered visit embeddings, optionally augmented with inter-visit time intervals ({Delta}t), were processed through recurrent neural networks (RNN), long short-term memory networks (LSTM), and Transformer encoders to model longitudinal disease trajectories. Models were trained and evaluated independently for prediction horizons of 2, 3, 4, 5, and 6 years using patient-level stratified splits (80/20). Performance was assessed across five random seeds. Main Outcome Measures: Area under the receiver operating characteristic curve (ROC-AUC), F1-score, and accuracy for predicting two clinically critical transitions: NGA to GA onset and NCGA to central GA (CGA) involvement. Results: For NGA to GA prediction, models achieved ROC-AUC of 0.84-0.94 at 2-4 years and 1.00 at 5-6 years. For NCGA to CGA prediction, Transformer-based models achieved peak AUC of 0.95 at 4 years and 0.96 at 5 years. Longer input sequences (8 visits vs. 4 visits) consistently improved NCGA to CGA performance at extended horizons. Temporal interval encoding improved stability in several LSTM configurations.

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

Hybrid NARX-LLM for Greenland Iceberg Discharge: Prompt-Driven Residual Correction

Authors:
Yiquan Gao↗Duohui Xu↗

arXiv:2606.15288v1 Announce Type: cross Abstract: Greenland iceberg discharge exhibits complex nonlinear dynamics with limited observability, challenging traditional predictive models. We present a Hybrid NARX-LLM framework that combines a nonlinear autoregressive model with exogenous inputs (NARX) and a large language model (LLM) for residual correction. We further propose a Physics-Informed Prompt (PIP) method that transforms unstructured physical knowledge into structured prompts for zero-shot in-context reasoning. The primary objective is to explore the corrective potential of this framework for modeling Greenland iceberg discharge, rather than merely optimizing predictive accuracy. The NARX component captures intrinsic temporal dependencies, while the LLM, guided by PIP, encodes glacier dynamics and environmental drivers and perceives key trend patterns to correct systematic prediction errors. This integration allows the model to reason about unmodeled factors and produce interpretable residuals, enhancing overall predictive accuracy. Applied to Greenland iceberg discharge time series, our approach addresses extreme events that are difficult to predict due to rare variations and nonstationary trends, a limitation often overlooked by traditional methods. By fusing structured time-series modeling with knowledge-driven foundation AI, the framework offers a scalable and interpretable pathway to bridge data-limited climate forecasting with physics-informed LLM reasoning. The code is available.

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

Uncertainty Estimation and Generalization Bounds for Modern Deep Learning

Authors:
Luis A. Ortega↗

arXiv:2606.13818v1 Announce Type: new Abstract: This thesis investigates how Bayesian principles can deepen our understanding of modern deep learning systems. While neural networks achieve remarkable predictive performance, their ability to generalize and to quantify uncertainty remains only partly understood. This thesis approaches this challenge from both methodological and theoretical angles: unifying Bayesian inference, function-space modeling, and large-deviation theory under a common probabilistic perspective. On the methodological side, the thesis introduces the Deep Variational Implicit Process (DVIP), a scalable Bayesian framework that extends implicit processes to deep architectures. Complementing this, two post-hoc methods – the Variational Linearized Laplace Approximation (VaLLA) and the Fixed-Mean Gaussian Process (FMGP) – are proposed to equip pretrained deterministic networks with calibrated uncertainty estimates. The theoretical contributions focus on one of the central open questions in modern machine learning: why do large, over-parameterized neural networks generalize so well? To address this, the thesis develops a unified probabilistic framework that connects three key mechanisms – diversity, smoothness, and stochasticity – within the language of PAC-Bayesian and large-deviation theory.

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

Performance and Interpretability of Convolutional, Transformer, and Hybrid Deep Learning Models in Colorectal Histology Classification

Authors:
Reza Bozorgpour↗

Deep learning has become an important tool in computational pathology, enabling automated analysis of histopathological images. While convolutional neural networks (CNNs) have traditionally dominated this field, transformer-based and hybrid architectures have recently demonstrated promising performance. However, comprehensive comparisons of these approaches for colorectal histopathology remain limited. This study evaluated twelve ImageNet-pretrained CNN, transformer, and hybrid architectures using the Kather colorectal histopathology dataset containing 5,000 image tiles from eight tissue classes. All models were trained using a standardized transfer-learning and fine-tuning protocol and assessed using multiple performance metrics, including accuracy, precision, sensitivity, specificity, F1-score, ROC-AUC, Cohen's kappa, and Matthews correlation coefficient. All evaluated models achieved high classification performance, with accuracies ranging from 93.2% to 97.1%. EVA-02 achieved the highest overall performance (97.1% accuracy, 97.0% F1-score), closely followed by ViT-B/16. Among CNNs, ResNet34 and ConvNeXt-Tiny demonstrated highly competitive performance, achieving accuracies of 96.4% and 96.3%, respectively. Transformer architectures generally produced the strongest results across evaluation metrics, although the performance gap between the best transformer and CNN models was relatively small. Per-class analysis showed consistently strong classification performance across all tissue categories, with Complex Stroma representing the most challenging class. Overall, transformer-based architectures achieved the highest predictive performance, whereas modern CNNs provided a favorable balance between accuracy and model complexity. These findings provide a comprehensive benchmark of major deep learning paradigms for colorectal histopathology classification.

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17.
arXiv (CS.CV) 2026-06-16

FlexPooling with Simple Auxiliary Classifiers in Deep Networks

Authors:
Muhammad Ali↗Omar Alsuwaidi↗Salman Khan↗

In computer vision, the basic pipeline of most convolutional neural networks consists of multiple feature extraction layers, where the input signal is downsampled to a lower resolution in each subsequent layer. This downsampling process is commonly referred to as pooling, which is an essential operation in CNNs. Pooling improves robustness against transformations, reduces the number of trainable parameters, increases the receptive field, and lowers computation time. Since pooling is a lossy process but remains important for extracting high-level information from low-level representations, it is important to preserve the most prominent information from previous activations to improve network discriminability. Standard pooling is usually performed using dense pooling methods, such as max pooling or average pooling, or through strided convolutional kernels. In this paper, we propose a simple yet effective adaptive pooling method, called FlexPooling, which generalizes average pooling by learning a weighted average over activations jointly with the rest of the network. We further show that attaching Simple Auxiliary Classifiers (SAC) to the CNN improves performance and demonstrates the effectiveness of the proposed method compared with standard pooling methods. Experiments on multiple popular image classification datasets show that FlexPooling consistently outperforms baseline networks, achieving approximately 1 to 3 percent improvement in accuracy.

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18.
arXiv (CS.AI) 2026-06-16

Input-Dependent Fisher Information for Local Sensitivity Analysis of Medical Image Classifiers

Authors:
Sourya Sengupta. Mark A. Anastasio↗

arXiv:2606.16362v1 Announce Type: cross Abstract: Deep neural networks have achieved strong performance in medical image classification, but often work like black-box. Commonly used post-hoc interpretation methods often provide heuristic visualizations whose relationship to the classifier's predictive distribution is indirect. This work introduces a local sensitivity analysis framework based on the input-dependent Fisher Information Matrix (iFIM) of a trained classifier. The iFIM characterizes how the classifier's predictive distribution changes under infinitesimal perturbations of the input image. By using a Gram-matrix formulation, the nonzero eigenspectrum of the iFIM can be recovered without explicitly forming the full image-dimensional Fisher matrix. The leading iFIM eigenspace is then used to project an input image into a high local-sensitivity component and its orthogonal component. These components provide a model-intrinsic description of local predictive sensitivity, rather than a conventional pixel-wise attribution heatmap or a causal segmentation of task-relevant anatomy. The framework is evaluated on controlled and clinical medical image classification tasks using multiple classifier architectures. Perturbation-based experiments show that high-sensitivity iFIM components are more strongly coupled to changes in predictive confidence and classification performance than lower-sensitivity complementary components. The results support the iFIM framework as a principled tool for analyzing local decision sensitivity and for complementing existing attribution-based interpretability methods in medical imaging.

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

Optimal Transport for Machine Learners

Authors:
Gabriel Peyr\'e↗

arXiv:2505.06589v2 Announce Type: replace-cross Abstract: Modern machine learning repeatedly manipulates probability measures: empirical datasets, generated samples, latent distributions, class-conditional laws, particle systems, weights of wide networks and attention patterns. Optimal transport is useful in this setting because it compares such objects by asking how mass should move. It therefore combines a statistically meaningful notion of discrepancy with a geometry of interpolation, dual certificates and variational dynamics. This makes OT a common language for losses, generative modeling, domain adaptation, robust learning, barycenters, gradient flows and mean-field descriptions of learning algorithms. This book presents the main OT techniques with these machine-learning uses in mind. It starts from finite assignment and the Monge map viewpoint, passes to Kantorovich couplings and dual potentials, and then explains the algorithmic ideas that make transport usable: linear programming, semi-discrete cells, Sinkhorn scaling and low-dimensional projections. The same objects are then reused as a geometry of measures, giving Wasserstein distances, barycenters, gradient flows, dynamic formulations and Gaussian/Bures formulas. The final chapters emphasize the variants most relevant to modern ML: divergences and adversarial losses, entropic and unbalanced relaxations, robust or spectral ground geometries, Gromov and quantum extensions, and transport-based views of generative models, mean-field networks and attention dynamics. The goal is to keep the mathematics explicit while exposing the computational and geometric intuitions needed to turn OT into a working toolbox for machine learners.

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20.
arXiv (CS.LG) 2026-06-24

FuseSampleAgg: One-Pass Neighborhood Estimation for Budgeted Knowledge-Graph Refresh and Validation

Authors:
Aleksandar Stankovi\'c↗Haoran Du↗Xinming Wang↗

arXiv:2511.13645v2 Announce Type: replace Abstract: Operational knowledge-graph (KG) pipelines in networking and cybersecurity increasingly need to refresh embeddings under strict time, memory, and audit budgets, especially as curated feeds and LLM-assisted extraction accelerate KG updates. A recurring per-step cost in mini-batch KG learning is neighborhood-context estimation: uniform neighbor sampling without replacement followed by mean aggregation. Common frameworks implement this estimator through sampled-subgraph materialization and intermediate feature gathers, adding kernel launches, allocator pressure, and transient memory spikes. We present One-Pass Neighborhood Estimation, a fused PyTorch CUDA operator that samples neighbors and directly emits the sampled-neighborhood mean, avoiding explicit block construction while preserving GraphSAGE-mean semantics for the same sampled neighbor IDs. It supports seed-controlled sampling and optional saved-index replay for reproducible validation and regression testing. Across large-graph mini-batch workloads, it improves FP32 end-to-end step latency by 2.24x-3.48x over tuned DGL baselines and reduces transient GPU memory by up to 160x in our measurements. On OGB KG completion benchmarks such as WikiKG2 and BioKG, it reduces step time and peak VRAM while matching ranking quality within seed variability, improving time-to-quality for budgeted KG refresh.

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21.
arXiv (CS.LG) 2026-06-15

Provably Safe, Yet Scalable Reinforcement Learning

Authors:
Kai S. Yun↗Zeyang Li↗Navid Azizan↗

arXiv:2606.14536v1 Announce Type: new Abstract: Safe reinforcement learning (RL) aims to learn policies that optimize rewards while satisfying constraints. Predominant approaches rely on soft-constrained policy optimization, which has achieved empirical success but does not provide formal safety guarantees for the learned policy. In contrast, methods with strict guarantees typically rely on explicit certificate functions, whose construction requires the direct synthesis and verification of control-invariant sets, a process that scales poorly with state dimension and often yields overly conservative behavior. In this paper, we present the Provably Safe, yet Scalable RL (PS2-RL) framework, a novel two-phase architecture for learning provably safe policies in a scalable manner, designed to overcome the key bottlenecks of prior methods. Rather than explicitly computing invariant sets, PS2-RL leverages a learned backup policy to forward-integrate the system dynamics, generating an implicit control-invariant set online. In the first phase, the backup policy is trained with our proposed safe-arrival value function, which characterizes the optimal backup policy for invariant-set construction. In the second phase, an RL policy is trained end-to-end through a differentiable projection layer that strictly enforces the safety guarantees induced by the learned backup policy. By maximizing the volume of the implicit control-invariant set in the first phase, the resulting PS2 policy from the second phase is performant and scalable, while maintaining provable safety. Crucially, PS2-RL imposes no restrictions on the underlying RL algorithm and can be plugged into any existing training pipeline. We establish theoretical guarantees for the proposed framework and evaluate it on robotic control tasks with state dimensions up to 10, a regime in which prior provably safe RL methods struggle or become impractical.

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22.
arXiv (CS.AI) 2026-06-24

Heterogeneous 2D/1D Signal Representation Fusion for Underwater Acoustic Modulation Recognition Under Distribution Shift

Authors:
Ronglai Qian↗Liang An↗Xiaoyan Wang↗Qing Fan↗Ziwei Huang↗Yang Ye↗

arXiv:2606.23702v1 Announce Type: cross Abstract: Modulation recognition systems rely on heterogeneous signal representations. 2D signal-image modalities such as time-frequency and cyclostationary maps capture structural patterns, while 1D statistical descriptors such as higher-order power spectra encode complementary cues. Under distribution shift, these modalities degrade unevenly, making robust fusion a central challenge for practical deployment. Progress is further limited by the lack of a unified evaluation protocol that systematically separates different shift types. This paper addresses both challenges through a joint benchmark-and-model study in underwater acoustic modulation recognition. UAMR-ShiftBench is the first benchmark to jointly cover in-distribution, low-SNR, unseen-environment, unseen-communication-parameter, and measured sea-trial evaluation under a single matched protocol, with two independent real-world subsets collected during two sea-trial campaigns conducted in March and November in the South China Sea. SCP-TriCA fuses STFT, cyclostationary, and P2/P4 (second- and fourth-order power spectra) modalities hierarchically: the two 2D modalities are first aligned through bidirectional cross-attention, and the 1D statistical modality is then incorporated through a sample-adaptive selective gate. On UAMR-ShiftBench, SCP-TriCA achieves 95.33% in-distribution accuracy and 74.59% simulated OOD average, outperforming the strongest baseline by 5.12 percentage points, and reaches 91.14% and 94.86% on the two sea-trial subsets, exceeding the best baseline by 15.71 and 23.00 percentage points respectively. Ablation results confirm that the gains stem from modality complementarity and the hierarchical fusion design. Code and models are available at https://github.com/ronglaiqian/UAMR-ShiftBench.

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

Exact Posterior Score Estimation for Solving Linear Inverse Problems

Authors:
Abbas Mammadov↗Ozgur Kara↗Kaan Oktay↗Iskander Azangulov↗Adil Kaan Akan↗Hyungjin Chung↗James Matthew Rehg↗Yee Whye Teh↗

Diffusion and flow-based models learn powerful data priors by training a denoiser to reverse Gaussian corruption. To use this prior to solve a linear inverse problem, one needs to sample from the posterior, but the score that the prior provides is the unconditional score, not the posterior score. Existing methods either steer a fixed pretrained denoiser with approximate measurement-matching corrections, or train a conditional restoration model that abandons the denoising structure of the prior. We derive the exact posterior score in closed form for linear Gaussian inverse problems under general Gaussian interpolants, and show that posterior sampling reduces to a denoising problem at an operator-dependent shifted pivot under an anisotropic noise covariance. We turn this identity into Exact Posterior Score (EPS), a denoising training objective that preserves the input/output structure of standard pretraining and can therefore be trained from scratch or fine-tuned from a pretrained denoiser. At inference, EPS uses the same sampler as the underlying backbone, with no likelihood gradients or projections. We evaluate EPS on five linear inverse problems across FFHQ and ImageNet, where it outperforms training-free and training-based baselines on fidelity, perceptual, and distributional metrics, while using roughly an order of magnitude fewer denoiser evaluations than gradient-based posterior samplers.

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24.
medRxiv (Medicine) 2026-06-11

Electrical signatures of divergent connectivity in the human subgenual cingulate cortex

Authors:
Qianq↗Kerezoudis↗Gregg↗Hermes↗Klassen↗B. T↗Chari↗Tisdall↗M. M↗Baker↗M. R↗Miller↗…

Background: Major depressive disorder remains a leading cause of disability. While subgenual cingulate cortex (sgCC) deep brain stimulation (DBS) shows promise for medically refractory depression, clinical outcomes have been heterogeneous, suggesting that individual differences in neural circuitry engagement may critically influence therapeutic efficacy. We aimed to define the electrophysiological signatures of sgCC efferent connectivity using single-pulse electrical stimulation (SPES) with intracranial stereo-EEG (sEEG) to inform rational targeting and physiological biomarkers for sgCC-DBS. Methods: In four patients undergoing clinically indicated sEEG for seizure mapping, SPES was delivered through sgCC pairs, while distributed brain stimulation-evoked potentials (BSEPs) were recorded across cortical and subcortical sites. Responses were characterized using Canonical Response Parameterization to extract reproducible waveforms and per-trial reliability. Results: sgCC stimulation elicited reproducible, spatially organized BSEPs across frontal, limbic, and paralimbic networks, aligning with known anatomical pathways. Frontal recruitment featured robust, lateralized orbitofrontal activation favoring the ipsilateral central, medial OFC and bilateral ventromedial prefrontal responses. Limbic effects demonstrated bilateral cingulate activation with stronger ipsilateral recruitment and lateralized amygdala and hippocampal responses. Paralimbic engagement included insular responses with subject-specific anterior predominance and bi-hemispheric temporal-polar slow-wave deflections. Conclusion: These findings provide direct electrophysiological evidence of distributed, lateralized sgCC divergent network connectivity in the human brain, offering physiologic confirmation of its role in affective circuitry. The observed topography and laterality have direct applications for sgCC-DBS targeting and implicate BSEP signatures as candidate biomarkers to guide patient-specific therapy.

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

On the Geometry and Optimization of Polynomial Convolutional Networks

Authors:
Vahid Shahverdi↗Giovanni Luca Marchetti↗Kathl\'en Kohn↗

arXiv:2410.00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions. Specifically, we prove that their parameterization map is regular and is an isomorphism almost everywhere, up to rescaling the filters. By leveraging on tools from algebraic geometry, we explore the geometric properties of the image in function space of this map - typically referred to as neuromanifold. In particular, we compute the dimension and the degree of the neuromanifold, which measure the expressivity of the model, and describe its singularities. Moreover, for a generic large dataset, we derive an explicit formula that quantifies the number of critical points arising in the optimization of a regression loss.

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