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

Teach-and-Repeat: Accurately Extracting Operational Knowledge from Mobile Screen Demonstrations to Empower GUI Agents

作者:
Yudong Zhang↗Lei Hu↗Daoyang Liu↗Jiawei Liu↗Yangfan Luo↗Xingyu Liu↗Zuojian Wang↗Zhilin Gao↗

arXiv:2606.12817v1 Announce Type: new Abstract: Understanding the digital world on mobile devices is shifting from static UI perception to dynamic action comprehension. This capability enables models to convert visual state transitions into operational knowledge, defined as short natural-language sentences that describe action types, target UI elements, textual arguments, and execution orders. However, due to the highly diverse and heterogeneous UI designs across applications, existing vision-language models (VLMs) struggle to accurately infer these underlying operations. To bridge this gap, we introduce Teach VLM, a core model designed to translate mobile screen trajectories into step-wise operational knowledge by extracting and analyzing operation-related keyframes from demonstration videos. To address the scarcity of aligned training data, we develop a systematic data flywheel for scalable data acquisition. We further introduce a novel Chinese Mobile Screen Teach Benchmark for fine-grained evaluation. Building upon Teach VLM, we propose the Teach-and-Repeat paradigm, where the generated operational knowledge serves as an interpretable procedural reference to guide downstream screen-based execution agents. Extensive evaluations demonstrate that Teach VLM significantly outperforms strong VLM baselines, achieving state-of-the-art performance in operation semantics prediction. Furthermore, experiments in Android World show that our paradigm yields consistent Task Success Rate improvements for downstream agents. Together, Teach VLM and the Teach-and-Repeat paradigm offer a practical pathway from raw demonstrations to reusable task automation.

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04.
arXiv (CS.LG) 2026-06-11

CaReTS: A Multi-Task Framework Unifying Classification and Regression for Time Series Forecasting

作者:
Fulong Yao↗Wanqing Zhao↗Chao Zheng↗Xiaofei Han↗

arXiv:2511.09789v2 Announce Type: replace Abstract: Recent advances in deep forecasting models have achieved remarkable performance, yet most approaches still struggle to provide both accurate predictions and interpretable insights into temporal dynamics. This paper proposes CaReTS, a novel multi-task learning framework that combines classification and regression tasks for multi-step time series forecasting problems. The framework adopts a dual-stream architecture, where a classification branch learns the stepwise trend into the future, while a regression branch estimates the corresponding deviations from the latest observation of the target variable. The dual-stream design provides more interpretable predictions by disentangling macro-level trends from micro-level deviations in the target variable. To enable effective learning in output prediction, deviation estimation, and trend classification, we design a multi-task loss with uncertainty-aware weighting to adaptively balance the contribution of each task. Furthermore, four variants (CaReTS1–4) are instantiated under this framework to incorporate mainstream temporal modelling encoders, including convolutional neural networks (CNNs), long short-term memory networks (LSTMs), and Transformers. Experiments on real-world datasets demonstrate that CaReTS outperforms state-of-the-art (SOTA) algorithms in forecasting accuracy, while achieving higher trend classification performance.

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05.
arXiv (CS.AI) 2026-06-24

CompressKV: Semantic-Retrieval-Guided KV-Cache Compression for Resource-Efficient Long-Context LLM Inference

作者:
Xiaolin Lin↗Jingcun Wang↗Olga Kondrateva↗Yiyu Shi↗Bing Li↗Grace Li Zhang↗

arXiv:2606.24467v1 Announce Type: new Abstract: Long-context large language model (LLM) inference is increasingly constrained by the memory footprint and decoding cost of key-value (KV) caches, limiting sustainable deployment on resource-constrained hardware. Existing KV cache eviction methods typically apply heuristic token scoring over all heads in GQA-based LLMs. These methods ignore the different functionalities of attention heads, leading to the eviction of critical tokens and thus degrading the performance of LLMs. To address this issue, we propose CompressKV, a resource-efficient KV-cache compression framework for GQA-based LLMs. Instead of aggregating attention scores from all heads, CompressKV identifies Semantic Retrieval Heads (SRHs) that capture both the initial and final tokens of a prompt and semantically important mid-context evidence, and uses them to select tokens whose KV pairs should be retained. Furthermore, CompressKV allocates cache budgets across layers according to offline estimates of layer-wise eviction error. Experiments on LongBench and Needle-in-a-Haystack show that CompressKV consistently outperforms existing KV-cache eviction methods across memory budgets. Notably, it preserves over 97\% of full-cache performance using only 3\% of the KV cache on LongBench question-answering tasks and achieves 90\% accuracy with just 0.7\% KV storage on Needle-in-a-Haystack. These results demonstrate an improved resource–performance trade-off for long-context LLM inference. Our code is publicly available at: https://github.com/TUDa-HWAI/CompressKV

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

CoVR-R:Reason-Aware Composed Video Retrieval

作者:
Omkar Thawakar↗Dmitry Demidov↗Vaishnav Potlapalli↗Sai Prasanna Teja Reddy Bogireddy↗Viswanatha Reddy Gajjala↗Alaa Mostafa Lasheen↗Rao Muhammad Anwer↗Fahad Khan↗

Composed Video Retrieval (CoVR) aims to find a target video given a reference video and a textual modification. Prior work assumes the modification text fully specifies the visual changes, overlooking after-effects and implicit consequences (e.g., motion, state transitions, viewpoint or duration cues) that emerge from the edit. We argue that successful CoVR requires reasoning about these after-effects. We introduce a reasoning-first, zero-shot approach that leverages large multimodal models to (i) infer causal and temporal consequences implied by the edit, and (ii) align the resulting reasoned queries to candidate videos without task-specific finetuning. To evaluate reasoning in CoVR, we also propose CoVR-Reason, a benchmark that pairs each (reference, edit, target) triplet with structured internal reasoning traces and challenging distractors that require predicting after-effects rather than keyword matching. Experiments show that our zero-shot method outperforms strong retrieval baselines on recall at K and particularly excels on implicit-effect subsets. Our automatic and human analysis confirm higher step consistency and effect factuality in our retrieved results. Our findings show that incorporating reasoning into general-purpose multimodal models enables effective CoVR by explicitly accounting for causal and temporal after-effects. This reduces dependence on task-specific supervision, improves generalization to challenging implicit-effect cases, and enhances interpretability of retrieval outcomes. These results point toward a scalable and principled framework for explainable video search. The model, code, and benchmark are available at https://github.com/mbzuai-oryx/CoVR-R.

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08.
Nature (Science) 2026-06-24

AI tool spots antibiotics that fight drug-resistant gonorrhoea

作者: 未知作者

The bacterium Neisseria gonorrhoeae has evolved resistance to most antibiotics used to treat it, but a machine-learning screen reveals potential therapies. The bacterium Neisseria gonorrhoeae has evolved resistance to most antibiotics used to treat it, but a machine-learning screen reveals potential therapies.

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10.
arXiv (quant-ph) 2026-06-24

The Quantum Split-Step Fourier Algorithm for Nonlinear Optical Waveguides

作者:
Fabio Biancalana↗

arXiv:2606.24643v1 Announce Type: cross Abstract: We introduce the Quantum Split-Step Fourier (QSSF) algorithm for nonlinear optical waveguides, a numerical framework that combines split-step propagation of the nonlinear Schrödinger equation with a commutator-preserving Bogoliubov evolution of Gaussian quantum fluctuations. The method propagates the classical mean field together with the Bogoliubov matrices $U$ and $V$, from which reduced second moments, covariance matrices, symplectic eigenvalues, and entropic measures are constructed for arbitrary spectral windows. Applied to soliton-driven resonant radiation, QSSF shows that the selected radiation band acquires a steadily increasing von Neumann entropy and a corresponding loss of purity, quantifying its entanglement with the rest of the spectrum in the lossless Gaussian setting. The analysis also reveals a surprisingly pronounced low-dimensional structure: although the radiation occupies many Fourier bins, its reduced Gaussian state is dominated by only a few Williamson modes. QSSF therefore provides a practical information-theoretic diagnostic for quantum correlations in nonlinear frequency conversion, supercontinuum generation, and multimode squeezed-light formation in ultrafast waveguide platforms.

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11.
arXiv (CS.CL) 2026-06-12

ArogyaSutra: A Multi-Agent Framework for Multimodal Medical Reasoning in Indic Languages

作者:
Tanmoy Kanti Halder↗Akash Ghosh↗Subhadip Baidya↗Arijit Roy↗Sriparna Saha↗

Multimodal Large Language Models (MLLMs) have shown promising reasoning capabilities in general domains, yet their performance remains limited in specialized settings such as healthcare, especially in multilingual and low-resource scenarios. This gap is critical in regions like rural India, where patients often express complex medical queries in native Indic languages and rely on multimodal inputs such as medical images. Existing English-centric MLLMs struggle to support such use cases, limiting equitable access to AI-driven healthcare assistance. To address this challenge, we introduce ArogyaBodha, a large-scale multilingual multimodal medical question-answer dataset constructed from eight heterogeneous sources, covering 31 body systems, six imaging modalities, and 21 clinical domains across English and seven major Indian languages. We further propose ArogyaSutra, an actor-critic-based multi-agent framework that integrates tool grounding with dual-memory mechanisms for step-wise, reasoning-aware decision making, and uses stored actor-critic simulation trajectories for distillation. Experiments show that our dataset and framework improve multilingual medical reasoning accuracy across all Indic languages, with ablations validating the contribution of each component. The source code and dataset are available at: https://iitp-cse.github.io/ ArogyaSutra/

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

Abstractions of Queries in Ontology-Based Data Access

作者:
Michel Lecl\`ere↗Marie-Laure Mugnier↗Guillaume P\'erution-Kihli↗

arXiv:2606.24618v1 Announce Type: new Abstract: In ontology-based data access (OBDA), multiple data sources are integrated via mappings to an ontology. We consider an OBDA setting based on existential rules and the certain answer semantics. We address the recent issue of query abstraction, which consists of abstracting data queries by translating them to the ontology layer. Since a perfect abstraction may not exist, the notions of minimally complete and maximally sound abstractions have been introduced. We study abstractions within an extension of UCQs with a limited form of inequality and a special predicate marking database constants. While this extension does not lead to an increased complexity of the problems of interest, it is able to express minimally complete abstractions, hence perfect abstractions when they exist. We also characterize maximally sound abstractions by making a new connection with the notion of maximum recovery stemming from data exchange.

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13.
bioRxiv (Bioinfo) 2026-06-11

Robust semi-supervised scRNA-seq integration from virtual adversarial learning

作者:
He↗Filippidis↗Xing↗Kleinstein↗Guan↗

Single-cell RNA sequencing integration methods that rely solely on transcriptomic data often struggle to preserve fine-grained distinctions between closely related cell subtypes. As a result, cell populations that are separable in the raw data may become over-mixed after integration, reducing biological resolution and interpretability. Incorporating marker gene information can potentially address these issues; however, the variability and complexity of available marker sets limit their effective application. To address this, we introduce scCRAFT+, a semi-supervised integration model that innovatively incorporates marker gene information through Virtual Adversarial Training (VAT). By jointly optimizing marker-derived supervision and transcriptome-wide representations, VAT enforces local prediction smoothness among transcriptionally similar cells, improving robustness to noisy marker annotations while enhancing both integration quality and cell type auto-annotation. This targeted approach significantly enhances annotation accuracy and robustness, particularly when faced with incomplete or incorrect marker gene sets. Benchmarking shows that scCRAFT+ achieves consistently stronger performance than current unsupervised and supervised integration approaches, resulting in improved integration quality and biologically meaningful sub-cell type auto-annotations.

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14.
arXiv (CS.LG) 2026-06-12

LLM-ODDR: A Large Language Model Framework for Joint Order Dispatching and Driver Repositioning

作者:
Tengfei Lyu↗Siyuan Feng↗Hao Liu↗Hai Yang↗

arXiv:2505.22695v2 Announce Type: replace Abstract: Ride-hailing platforms face significant challenges in optimizing order dispatching and driver repositioning operations in dynamic urban environments. Traditional approaches based on combinatorial optimization, rule-based heuristics, and reinforcement learning often overlook driver income fairness, interpretability, and adaptability to real-world dynamics. To address these gaps, we propose LLM-ODDR, a novel framework leveraging Large Language Models (LLMs) for joint Order Dispatching and Driver Repositioning (ODDR) in ride-hailing services. LLM-ODDR framework comprises three key components: (1) Multi-objective-guided Order Value Refinement, which evaluates orders by considering multiple objectives to determine their overall value; (2) Fairness-aware Order Dispatching, which balances platform revenue with driver income fairness; and (3) Spatiotemporal Demand-Aware Driver Repositioning, which optimizes idle vehicle placement based on historical patterns and projected supply. We also develop JointDR-GPT, a fine-tuned model optimized for ODDR tasks with domain knowledge. Extensive experiments on real-world datasets from Manhattan taxi operations demonstrate that our framework significantly outperforms traditional methods in terms of effectiveness, adaptability to anomalous conditions, and decision interpretability. To our knowledge, this is the first exploration of LLMs as decision-making agents in ride-hailing ODDR tasks, establishing foundational insights for integrating advanced language models within intelligent transportation systems. While the current framework incurs higher computational costs than traditional methods, we show that parallel decomposition and model distillation can reduce latency to production-viable levels for deployment.

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15.
arXiv (math.PR) 2026-06-18

Evolution of Conditional Entropy for Diffusion Dynamics on Graphs

作者:
Samuel Koovely↗Alexandre Bovet↗

arXiv:2510.19441v2 Announce Type: replace-cross Abstract: The modeling of diffusion processes on graphs is the basis for many network science and machine learning approaches. Entropic measures of network-based diffusion have recently been employed to investigate the reversibility of these processes and the diversity of the modeled systems. While results about their steady state are well-known, very few exact results about their finite-time evolution exist. Here, we introduce the conditional entropy of heat diffusion in graphs, and outline a mathematical framework that contextualizes diffusion and conditional entropy within the theories of continuous-time Markov chains and information theory. In particular, we highlight that this entropic measure satisfies an information-theoretical version of the second law of thermodynamics, thereby providing a parallelism between diffusion dynamics on networks and their physical counterparts. Furthermore, we obtain explicit results for its evolution on complete, path, and circulant graphs, as well as a mean-field approximation for Erdös-Rényi graphs. We also obtain asymptotic results for general networks and provide bounds for the evolution of conditional entropy. Finally, we experimentally demonstrate several properties of conditional entropy for diffusion over random graphs, such as the Watts-Strogatz model.

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16.
PLOS Computational Biology 2026-06-22

A lactylation- and autophagy-associated prognostic signature reveals LSEC-derived CLEC3B as a novel mediator of hepatocellular carcinoma suppression

作者:
Youai Song↗

by Youai Song, Yinkuan Ning, Meihui Li, Jianwei Lan, Liangchen Lei, Yufei Han, Zhuo Meng, Binjie Li, Pengpeng Liu, Quanyan Liu The crosstalk between lactylation and autophagy within the hepatocellular carcinoma (HCC) microenvironment is a burgeoning field with profound implications. By integrating multi-omics data from public cohorts, we delineated two molecular subtypes of HCC with divergent clinical outcomes and established a lactylation-autophagy-related prognostic signature. This signature highlighted CLEC3B as a pivotal gene. Subsequent single-cell RNA sequencing and experimental validation unequivocally pinpointed liver sinusoidal endothelial cells (LSECs) as the principal cellular source of CLEC3B, which was significantly downregulated in HCC tissues. Functionally, conditioned media derived from CLEC3B-overexpressing LSECs potently inhibited HCC cell proliferation. Mechanistic investigations revealed that this tumor-suppressive effect was orchestrated through the concurrent suppression of autophagy and diminution of lactylation levels. Our findings position LSEC-secreted CLEC3B as a novel metabolic mediator in HCC, bridging two key pathways in tumor suppression, and endorse its clinical value both as a prognostic indicator and a promising therapeutic target.

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17.
arXiv (CS.LG) 2026-06-18

Smoothness-Based Derandomization of PAC-Bayes Bounds

作者:
Alexandre Lemire Paquin↗Brahim Chaib-Draa↗Philippe Gigu\`ere↗

arXiv:2606.19105v1 Announce Type: new Abstract: We study PAC-Bayes derandomization for smooth loss functions. Our goal is to obtain generalization bounds that hold with high probability for deterministic predictors by exploiting smoothness properties of both the loss and the predictor class. We show that passing from the Gibbs predictor to the deterministic predictor at the posterior mean has a precise cost, given by the generalization gap of the Jensen gap class. We control this class through its Rademacher complexity, leading to bounds for deterministic predictors that involve flatness quantities expressed in terms of parameter Jacobians and Hessians of the score map. The framework applies to both bounded and unbounded smooth loss functions, and we specialize the results to linear predictors and smooth neural networks. Finally, the Jacobian and Hessian quantities appearing in the theory motivate a practical regularizer. For BatchNorm networks, we compute this regularizer with respect to effective BatchNorm weights obtained by folding the BatchNorm transformation into the adjacent affine weights. Experiments on CIFAR-10 illustrate the behavior of this regularizer under different batch sizes.

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

Multi-LCB: Extending LiveCodeBench to Multiple Programming Languages

作者:
Maria Ivanova↗Pavel Zadorozhny↗Rodion Levichev↗Ivan Petrov↗Adamenko Pavel↗Ivan Lopatin↗Alexey Kutalev↗Dmitrii Babaev↗

arXiv:2606.20517v1 Announce Type: new Abstract: LiveCodeBench (LCB) has recently become a widely adopted benchmark for evaluating large language models (LLMs) on code-generation tasks. By curating competitive programming problems, constantly adding fresh problems to the set, and filtering them by release dates, LCB provides contamination-aware evaluation and offers a holistic view of coding capability. However, LCB remains restricted to Python, leaving open the question of whether LLMs can generalize across the diverse programming languages required in real-world software engineering. We introduce Multi-LCB, a benchmark for evaluating LLMs across twelve programming languages, including Python. Multi-LCB transforms Python tasks from the LCB dataset into equivalent tasks in other languages while preserving LCB's contamination controls and evaluation protocol. Because it is fully compatible with the original LCB format, Multi-LCB will automatically track future LCB updates, enabling systematic assessment of cross-language code generation competence and requiring models to sustain performance well beyond Python. We evaluated 24 LLMs for instruction and reasoning on Multi-LCB, uncovering evidence of Python overfitting, language-specific contamination, and substantial disparities in multilingual performance. Our results establish Multi-LCB as a rigorous new benchmark for multi-programming-language code evaluation, directly addressing LCB's primary limitation and exposing critical gaps in current LLM capabilities.

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19.
arXiv (CS.LG) 2026-06-19

Weighted Bayesian Conformal Prediction

作者:
Xiayin Lou↗Peng Luo↗

arXiv:2604.06464v2 Announce Type: replace Abstract: Conformal prediction provides distribution-free prediction intervals with finite-sample coverage guarantees, and recent work by Snell \& Griffiths reframes it as Bayesian Quadrature (BQ-CP), yielding powerful data-conditional guarantees via Dirichlet posteriors over thresholds. However, BQ-CP fundamentally requires the i.i.d. assumption. Meanwhile, weighted conformal prediction handles distribution shift via importance weights but remains frequentist, producing only point-estimate thresholds. We propose Weighted Bayesian Conformal Prediction (WBCP), which generalizes BQ-CP to arbitrary importance-weighted settings by replacing the uniform Dirichlet $\Dir(1,\ldots,1)$ with a weighted Dirichlet $\Dir(\neff \cdot \tilde{w}_1, \ldots, \neff \cdot \tilde{w}_n)$, where $\neff$ is Kish's effective sample size. We prove four theoretical results: (1)~$\neff$ is the unique concentration parameter matching frequentist and Bayesian variances; (2)~posterior standard deviation decays as $O(1/\sqrt{\neff})$; (3)~BQ-CP's stochastic dominance guarantee extends to per-weight-profile data-conditional guarantees; (4)~the HPD threshold provides $O(1/\sqrt{\neff})$ improvement in conditional coverage. We instantiate WBCP for spatial prediction as Geographical BQ-CP, where kernel-based spatial weights yield per-location posteriors with interpretable diagnostics. Experiments on synthetic and real-world spatial datasets demonstrate that WBCP maintains coverage guarantees while providing substantially richer uncertainty information.

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20.
arXiv (CS.CL) 2026-06-18

G-IdiomAlign: A Gloss-Pivoted Benchmark for Cross-Lingual Idiom Alignment

作者:
Fengying Ye↗Yanming Sun↗Runzhe Zhan↗Zheqi Zhang↗Lidia S. Chao↗Derek F. Wong↗

Idioms are difficult to transfer across languages due to their non-compositionality and weak surface-form grounding, making literal mappings unreliable. We present G-IdiomAlign, a gloss-pivoted benchmark where each idiom is anchored by an English gloss from Wiktionary. We further construct a high-confidence reference alignment set for reproducible evaluation. G-IdiomAlign supports two protocols: (1) a controlled Multiple-Choice Idiom Equivalence with typed distractors for error attribution; and (2) a Gloss-Contrastive Generation contrasting No-gloss and With-gloss inputs to isolate the effect of an explicit semantic pivot. Across diverse LLMs, a bias to literal translation is a dominant failure mode, especially when the target is a low-resource language. Glosses consistently improve Gloss-Contrastive Generation under an embedding-based semantic proxy, but performance remains modest, indicating substantial headroom in the open output space. Subsequent analysis on Qwen3-8B further suggests that cross-condition differences are concentrated more in attention heads than in layers, while better With-gloss generations coincide with stronger gloss anchoring.

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21.
arXiv (CS.CL) 2026-06-19

Actionable Activation Directions for Detecting and Mitigating Emergent Misalignment Across Language Model Families

作者:
Abdul Rafay Syed↗

Fine-tuning language models on insecure code induces emergent misalignment with poorly understood internal structure. We investigate whether this misalignment corresponds to a causally actionable activation-space direction shared across architectures. Across four instruction-tuned model families (Qwen2.5-1.5B, Gemma-2-2B, Llama-3.2-1B, Ministral-3-3B) finetuned identically, a difference-in-means direction achieves 99.6% separation of aligned and misaligned activations at each model's final layer. Causal steering by subtracting this direction reduces code spillover by 21-51 points, while a secure-code control confirms content specificity. Cross-architecture transfer via ridge regression maps yields large behavioral suppression (up to 46 points) but fails specificity controls as random and orthogonal directions perform comparably. We identify a two-tier specificity structure: within-model directions are causally specific and actionable; cross-model directions are causally real but non-specific. An asymmetric transfer topology emerges, with Gemma and Qwen acting as geometric donors and Llama as a receiver. These findings define the limits of linear cross-architecture correction and recommend within-model probing for auditing.

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

When to Align, When to Predict: A Phase Diagram for Multimodal Learning

作者:
Ilay Kamai↗Hugues Van Assel↗Aviv Regev↗Hagai B. Perets↗Randall Balestriero↗

arXiv:2606.11190v2 Announce Type: replace Abstract: Cross-modal alignment (CA) and cross-modal prediction (CP) are the dominant paradigms for multimodal representation learning, yet there is no systematic understanding of when each succeeds, when each fails, and when cross-modal training helps at all – a gap that leaves practitioners, especially in scientific domains like biomedicine or astrophysics, with heterogeneous instruments and multiple levels of organization and measurement, unable to diagnose why standard methods underperform the best single modality. We develop a unified linear framework that addresses both questions. Under a spiked signal-plus-noise model with structured cross-modal nuisance correlation, we derive separation ratios for both objectives that expose complementary failure modes: alignment whitens each modality and fails when nuisance is strongly correlated across views; prediction encodes whatever is cross-predictable through a one-sided whitening, with recovery governed by source-modality quality. The resulting phase diagram partitions multimodal problems into four regimes: Both, CA only, CP only, and Neither. We present a data-driven procedure to locate real-world datasets in this diagram using a small labeled subsample, identifying the preferred objective and prediction direction before any cross-modal training. Experiments on synthetic data, stereo-vision benchmarks, image-caption pairs, and real astrophysical data validate the predictions in the nonlinear regime, including the Neither regime where cross-modal training is actively harmful. Our framework lets practitioners diagnose their multimodal problem and choose the right objective before committing to training. Code to reproduce the results is available at https://github.com/IlayMalinyak/mm_align_vs_pred.

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23.
arXiv (CS.LG) 2026-06-11

A Riemannian Approach to Low-Rank Optimal Transport

作者:
Pratik Jawanpuria↗Bamdev Mishra↗

arXiv:2606.12120v1 Announce Type: new Abstract: Low-rank optimal transport (OT) mitigates the quadratic scaling of classical solvers, yet existing approaches rely heavily on first-order mirror-descent updates that require careful hyperparameter tuning and ignore the optimization landscape's curvature. To address these limitations, we propose a unified Riemannian geometric framework for low-rank OT, modeling balanced and unbalanced rank-$r$ positive factored couplings as novel smooth embedded submanifolds of the positive orthant. By equipping these manifolds with the Fisher-Rao product metric, we derive tractable formulations for Riemannian projectors, retractions, and Hessian-vector products. Our cost-agnostic framework seamlessly extends to linear OT, Gromov-Wasserstein (GW), fused GW, and their unbalanced counterparts. For balanced OT, our geometric ingredients are computed via efficient conjugate-gradient and iterative Bregman updates. For the unbalanced OT, our operations elegantly reduce to closed-form scalings, completely eliminating inner iterative loops. In both regimes, per-iteration complexity scales linearly with dataset size, and we provide a rank-sufficiency certificate for global optimality verification. Extensive experiments across a range of problem sizes demonstrate that our regularization-free first- and second-order solvers achieve faster convergence and superior performance over existing state-of-the-art low-rank OT solvers.

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

Deep numerical schemes for systems of Ergodic BSDEs with applications to regime-switching forward utilities

作者:
Guillaume Broux-Quemerais↗Sarah Kaakai↗Anis Matoussi↗Wissal Sabbagh↗

arXiv:2606.24271v1 Announce Type: cross Abstract: In this paper, we introduce two neural-network-based numerical schemes for solving systems of coupled ergodic Backward Stochastic Differential Equations (eBSDEs), motivated by the approximation of optimal strategies within the framework of forward utilities in a regime-switching stochastic factor model. Our approach builds on the representation of such models through systems of eBSDEs introduced in [HLT20]. We first establish a link between the solution of the system of ergodic BSDEs and that of an associated multidimensional BSDE with random terminal time, given by the hitting time of the positive recurrent stochastic factor. Building on this representation, we introduce a locally additive deep learning scheme obtained by minimizing aggregated local error terms. We then present a new Deep Galerkin Method (DGM) inspired algorithm that minimizes the residual of the associated ergodic PDE system, relying on a representation of the ergodic cost. Finally, we apply this framework to regime-switching forward utilities in a stochastic factor model. We first derive a general consistency SPDE that characterizes regime-switching forward utilities and retrieve their representation with systems of ergodic BSDEs in the homothetic case. Numerical experiments demonstrate the performance of the proposed methods, with a particular focus on the impact on forward preferences of taking into account regime switches.

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25.
arXiv (CS.LG) 2026-06-11

Understanding Sample Efficiency in Predictive Coding

作者:
Gaspard Oliviers↗Elene Lominadze↗Rafal Bogacz↗

arXiv:2605.11911v2 Announce Type: replace Abstract: Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning that is more sample efficient and effective in many contexts, though a thorough theoretical understanding of the phenomena remains elusive. To address this, we quantify the efficiency of learning in BP and PC through a metric called ``target alignment'', which measures how closely the change in the output of the network is aligned to the output prediction error. We then derive and empirically validate analytical expressions for target alignment in Deep Linear Networks. We show that learning in PC is more efficient than BP, which is especially pronounced in deep, narrow and pre-trained networks. We also derive exact conditions for guaranteed optimal target alignment in PC and validate our findings through experiments. We study full training trajectories of linear and non-linear models, and find the predicted benefits of PC persist in practice even when some assumptions are violated. Overall, this work provides a mechanistic understanding of the higher learning efficiency observed for PC over BP in previous works, and can guide how PC should be parametrised to learn most effectively.

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