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01.
arXiv (CS.CV) 2026-06-16

InfoGeo: Information-Theoretic Object-Centric Learning for Cross-View Generalizable UAV Geo-Localization

Cross-view geo-localization (CVGL) is fundamental for precise localization and navigation in GPS-denied environments, aiming to match ground or UAV imagery with satellite views. Existing approaches often rely on global feature alignment, but they suffer from substantial domain shifts induced by varying regional textures and weather conditions. This issue becomes even more pronounced in UAV-based scenarios, where the broader perspective inevitably introduces dense, fine-grained objects, creating significant visual clutter. To address this, we draw inspiration from Object-Centric Learning (OCL) and propose InfoGeo, an information-theoretic framework designed to enhance robustness and generalization. InfoGeo reformulates the optimization as an information bottleneck process with two core objectives: (i) maximizing view-invariant information by aligning the object-centric structural relations across views, and (ii) minimizing view-specific noisy signals through cross-view knowledge constraints. Extensive evaluations across diverse benchmarks and challenging scenarios demonstrate that InfoGeo significantly outperforms state-of-the-art methods.

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

Learning to Reason by Analogy via Retrieval-Augmented Reinforcement Fine-Tuning

Retrieval-augmented generation (RAG) has become a standard mechanism for grounding language models in external knowledge, yet conventional retrieval based on lexical or semantic similarity is poorly suited for complex reasoning tasks: a semantically similar problem may demand an entirely different solution strategy, while a superficially different problem may share the same underlying reasoning pattern. We propose Retrieval-Augmented Reinforcement Fine-Tuning (RA-RFT), a post-training framework that teaches language models to reason by analogy. RA-RFT uses gold-relevance distillation to train a retriever that ranks contexts by expected reasoning benefit rather than semantic overlap, and then fine-tunes the policy model via reinforcement fine-tuning methods with retrieved analogous demonstrations, so the model learns to leverage reasoning traces under verifiable outcome rewards. We further analyze the diversity of retrieved contexts and find that reasoning-aware retrieval surfaces complementary solution strategies that provide distinct reasoning scaffolds for individual problems. Across challenging mathematical reasoning benchmarks, RA-RFT consistently outperforms standard reinforcement fine-tuning methods. For example, it improves AIME 2025 average@32 accuracy by 7.1 and 2.8 points over GRPO for Qwen3-1.7B and Qwen3-4B respectively – suggesting that reasoning-aware retrieval is a complementary axis of improvement and orthogonal to advances in reward design or training curricula.

03.
arXiv (CS.CV) 2026-06-15

Boundary-Centric Clip-Budgeted Active Learning for Temporal Action Segmentation

Temporal action segmentation (TAS) in untrimmed videos requires dense temporal supervision. However, most of the annotation cost is spent identifying action transitions where segmentation errors concentrate and small temporal shifts can disproportionately degrade segment-level metrics. We introduce B-ACT, a clip-budgeted active learning framework that explicitly allocates supervision to these error-prone boundary regions. B-ACT operates in a hierarchical two-stage loop: (i) it ranks and queries unlabeled videos using predictive uncertainty, and (ii) within each selected video, it detects candidate transitions from the current model predictions and selects the top-$K$ boundaries via a novel boundary score. The boundary score fuses neighborhood uncertainty, class ambiguity, and temporal prediction dynamics to reveal the underlying importance of each frame. Importantly, our annotation protocol requests labels only at the boundary frames while still training on boundary-centered clips to exploit temporal context through the model's receptive field. Extensive experiments on GTEA, 50Salads, and Breakfast demonstrate that boundary-centric supervision delivers strong label efficiency and consistently surpasses representative TAS active learning baselines and prior state of the art under sparse budgets. Gains are largest on datasets where performance is highly sensitive to boundary placement, as measured by edit and overlap-based F1 metrics.

04.
arXiv (CS.CV) 2026-06-16

Contrastive Learning for Seismic Horizon Tracking with Domain-Specific Priors

Unsupervised 3D seismic horizon tracking faces a key limitation: signal-based propagators provide accurate trace-level alignment but often fail near faults, whereas texture-driven deep models are more robust to discontinuities, typically at the cost of labeled data requirements and reduced trace-level precision. We propose a self-supervised fusion of both paradigms in which signal-derived local horizon correspondences act as domain-specific priors to train a texture-based deep learning model. Specifically, we estimate reliable trace-to-trace flows from reflector slopes and use them to form positive pairs in a contrastive objective, while restricting training to high-confidence neighborhoods, optionally augmented with a fault mask. The objective is not to infer ambiguous correspondences close to discontinuities, but to preserve horizon identity across them. As a result, the network learns voxel-wise embeddings that preserve local signal continuity while enabling horizon propagation beyond discontinuities through similarity search. Experiments on the public F3 dataset and a faulted synthetic dataset achieve lower mean absolute error (MAE) than unsupervised baselines and competitive performance against a semi-supervised method using a single labeled slice.

05.
arXiv (math.PR) 2026-06-17

Full $\Gamma-$expansion for the level-two large deviation rate functionals of non-reversible one-dimensional diffusions with periodic boundary conditions

arXiv:2606.17859v1 Announce Type: new Abstract: Consider the diffusion process \begin{equation*} dX_{\epsilon}(t) = \mss b(X_{\epsilon}(t)) \, dt + \sqrt{2\, \epsilon\, \mss a(X_\epsilon(t))} \, dW_{t}, \end{equation*} on the one-dimensional torus $\bb T = [0,1)$. Here $\epsilon$ is the temperature, $W_{t}$ a Brownian motion on $\bb T$ and $\mss a$, $\mss b$ functions of class $C^{2}(\bb T)$ satisfying further conditions. Denote by $\mss P(\bb T)$ the set of probability measures on $\bb T$ equipped with the weak topology, and by $\ms I_{\epsilon}\colon \mss P(\bb T)\to [0,+\infty)$ the level two large deviation rate functional of the diffusion $X_{\epsilon}(\cdot)$. We derive a full $\Gamma-$expansion of $\ms I_{\epsilon}$, as $\epsilon \to 0$, expressing it as \begin{equation*} \ms I_{\epsilon} = \frac{1}{\epsilon} \;\ms J^{(-1)} \; +\; \ms J^{(0)} \;+\; \sum_{p=1}^{\widehat{\mf q}}\frac{1}{\theta^{(p)}_{\epsilon}}\;\ms J^{(p)}\,, \end{equation*} where $\ms J^{(-1)}$, $\ms J^{(0)}$, $\ms J^{(p)} \colon \mss P(\bb T)\to [0,+\infty]$ represent rate functionals, independent of $\epsilon$, and $\theta^{(p)}_{\epsilon}$ are the time-scales at which the Markov process $X_{\epsilon}(\cdot)$ exhibits a metastable behaviour.

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

3D Masked Autoencoders are Robust Learners of Volumetric and Multimodal Cellular Representations for Microscopy

Self-supervised learning in fluorescence microscopy often relies on 2D projections, despite the inherently three-dimensional nature of cells. We present a systematic comparison of 2D and 3D masked autoencoders (MAE-2D vs. MAE-3D) on volumetric microscopy data. Under matched architectures and training protocols, MAE-3D consistently outperforms 2D max-projection and slice-based variants on downstream single-cell tasks. We further align visual representations with a pretrained protein language model (ESM2) and show that cross-modal supervision yields larger gains for volumetric models. Channel cross-attention and frequency-domain regularization are critical for leveraging 3D spatial context. On a protein–protein interaction task, MAE-3D achieves a ROC–AUC of 0.865, outperforming prior methods by up to +0.025. For protein localization, our best 3D model attains state-of-the-art AUC$_{micro}$ (0.952) and F1$_{micro}$ (0.742), improving over previous approaches by +0.003 and +0.010 absolute, respectively. Overall, these results demonstrate the advantages of native 3D modeling and multimodal alignment for representation learning in single-cell microscopy.

07.
arXiv (CS.CV) 2026-06-16

BRITE: A Benchmark for Reliable and Interpretable T2V Evaluation on Implausible Scenarios

The rapid advancement of photorealistic Text-to-Video (T2V) generation brings in an urgent need for up-to-date evaluation methods. Existing benchmarks largely overlooked implausible scenarios and do not measure audio-visual alignment. We introduce BRITE, the first framework that unifies (1) implausible prompting, (2) fine-grained assessment of audio-visual consistency, and (3) QA-based interpretable evaluation into a comprehensive T2V benchmark. Unlike fully automated Multimodal LLM-based pipelines, which are prone to hallucination and prompt ambiguity, BRITE guarantees reliability through a rigorous human-in-the-loop protocol for benchmark creation. Evaluating five state-of-the-art models (Sora 2, Veo 3.1, Runway Gen4.5, Pixverse V5.5, and Qwen3Max), we reveal a critical performance gap: while models excel at static object composition, they exhibit significant degradation in object-action binding and audio-visual synchronization. Our framework offers the community a reliable, interpretable benchmark and evaluation framework that can detect and locate limitations in the next generation of T2V models, especially for off-manifold prompts

08.
arXiv (CS.AI) 2026-06-17

WEQA: Wearable hEalth Question Answering with Query-Adaptive Agentic Reasoning

arXiv:2606.18147v1 Announce Type: new Abstract: Language models are remarkably capable at medical question answering, in some cases surpassing the accuracy of general physicians. However, answering questions about wearable health data remains challenging and understudied, as these ubiquitous sensors produce continuous, high-dimensional, and longitudinal data, which is non-trivial to align with text-centric distributions in LLM pretraining. The diversity of sensor modalities and user intents cannot be effectively handled by a fixed reasoning workflow or a single pretrained foundation model. To address these challenges, we propose WEQA, a query-adaptive agent framework that unifies LLM reasoning with specialized wearable analytical and modeling tools. An LLM controller is employed to synthesize execution plans and dynamically route each query to the appropriate combination of sensor analysis and pretrained models, and perform grounded response auditing with external knowledge. We also curate a benchmark spanning four open wearable datasets comprising analytic and predictive tasks in three different health domains. Experiments show that our framework is 24% more accurate than LLM and agentic baselines, and a blinded study with 12 medical experts and 8 users shows substantial gains in usefulness and clinical soundness.

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

Random Rule Forest (RRF): Interpretable and Manageable Ensembles of LLM-Generated Questions for Predicting Success from Unstructured Data

arXiv:2505.24622v3 Announce Type: replace Abstract: Many high-stakes screening tasks require predicting rare outcomes from unstructured text, where errors are costly and decisions must be auditable. We introduce Random Rule Forest (RRF), an interpretable ensemble that uses a large language model (LLM) not as an end-to-end predictor but as a generator of simple YES/NO questions. Each question acts as a weak learner, and their responses are combined by a plain unit-weight vote into an auditable ``green-flags'' scorecard: enough independent positive signals indicate a higher chance of success. We argue this deliberate simplicity is a robust default when positives are scarce and learned weights are hard to estimate. We evaluate RRF in two low-base-rate domains. On early-stage startup screening from founder profiles, RRF produces a transparent scorecard whose precision is several times the base rate (with light expert input raising it further) and, unlike direct prompting, its operating point can be controlled directly. On an established Phase~I clinical-trial benchmark, RRF outperforms published baselines on the threshold-independent metrics PR-AUC and ROC-AUC. Together these show that LLMs can serve as auditable feature generators for high-stakes text-based decisions, combining transparency with competitive predictive performance.

10.
arXiv (CS.CV) 2026-06-19

MMD-SLAM: Structure-Enhanced Multi-Meta Gaussian Distribution-Guided Visual SLAM

3D Gaussian Splatting (3DGS) has significantly boosted novel view synthesis and high-fidelity scene reconstruction, expanding the potential of 3DGS-based Visual Simultaneous Localization and Mapping (SLAM) methods. However, most existing systems fail to fully exploit the underlying structural information, which limits rendering quality and often leads to inconsistent maps. To address these limitations, we propose MMD-SLAM, a structure-enhanced Visual SLAM framework that leverages the Atlanta World (AW) assumption to guide a Multi-Meta Gaussian representation for photorealistic mapping. First, we introduce a point-line fusion strategy for pose optimization, where 3D line segments are incorporated to improve tracking robustness and provide additional constraints for mapping. Second, we design a Multi-Meta Gaussian representation with dominant directions, explicitly encoding structural priors from the AW hypothesis. Finally, we propose a Gaussian evolution strategy that adapts to scene geometry and incorporates structural cues into global optimization. Extensive experiments demonstrate that these innovations enable MMD-SLAM to achieve state-of-the-art performance in both tracking accuracy and mapping quality. e.g., our method achieves a 48.56% reduction in ATE RMSE on ScanNet and a 5.71% improvement in PSNR on Replica, compared with MonoGS.

11.
arXiv (CS.CL) 2026-06-16

Beyond Monolingual Deep Research: Evaluating Agents and Retrievers with Cross-Lingual BrowseComp-Plus

Deep research agents are increasingly evaluated on their ability to search for evidence, reason over retrieved sources, and produce grounded answers. Existing browsing benchmarks, however, largely assume that the user's query and the supporting evidence are written in the same language, leaving open whether agentic search systems can operate when relevant evidence appears in another language. We introduce XBCP (Cross-lingual BrowseComp-Plus), a controlled benchmark that preserves the English question-and-answer space of BrowseComp-Plus but varies the languages of the supporting documents. XBCP instantiates two complementary settings: in the cross-lingual setting, each query is paired with evidence in a single assigned language. In the multilingual setting, the full evidence corpus is distributed equally and randomly across 12 languages spanning high-resource and low-resource regimes. We evaluate four deep research agents using sparse and dense multilingual retrievers, measuring answer accuracy, evidence recall, search behavior, calibration, citation fidelity, and oracle retrieval. Results reveal substantial degradation when evidence is translated. Even strong, dense retrievers lose evidence recall, and agents become less calibrated and cite evidence less reliably. Notably, accuracy remains lower even when all gold evidence is supplied directly. These findings suggest that cross-lingual deep research exposes both retrieval failures and an independent, agent-side difficulty in integrating language-mismatched evidence.

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

Token-Operations-Oriented Inference Optimization Techniques for Large Models

Large model inference optimization serves as a key foundation for supporting the scalable, low-cost, and highly stable operation of large model services. Centered on token-oriented inference optimization technology, this paper proposes for the first time a four-layer technical architecture consisting of Multi-model Fusion, Model Optimization, Compute-Model Fusion, and Compute-Network-Model Fusion. It systematically reviews the key technologies and current industry status across these four levels and analyzes the application value of related technologies in real-world business scenarios. This paper provides a practical technical path for reducing token production costs, improving token service efficiency, ensuring the stability of token supply, and driving the transition of large model services from being merely callable to being operable.

13.
bioRxiv (Bioinfo) 2026-06-21

DeepCDS: Ab initio coding sequence prediction in prokaryotic short reads

Accurate coding sequence prediction in short prokaryotic metagenomic reads remains challenging due to sequence fragmentation, unknown sequence origins, and sequencing errors. Here we introduce DeepCDS, a deep learning-based ab initio coding sequence predictor trained on short prokaryotic sequences with and without simulated Illumina-like sequencing errors. DeepCDS integrates ESM-2 protein language model embeddings with nucleotide-level information to predict complete and fragmented coding sequence regions. Benchmarking on 215 phylogenetically diverse prokaryotic organisms demonstrates that DeepCDS consistently outperforms current state-of-the-art methods in coding sequence detection, start and stop codon localization, and robustness to different sequencing error profiles, while remaining operational at shorter sequence lengths than existing tools support. These findings demonstrate that protein language models capture distinct signals relevant for nucleotide-level coding sequence detection, especially at very short lengths. Ultimately, DeepCDS may help uncover the functional potential of the vast microbial diversity that remains genomically uncharacterized.

14.
PLOS Computational Biology 2026-06-17

Combining machine learning and iterative experiments to keep pace with emerging viral variants of concern

by Thomas Sheffield, Ryan C. Bruneau, Stephen Won, Kenneth L. Sale, Brooke Harmon, Le Thanh Mai Pham Modeling and predicting viral mutations before they emerge plays a crucial role in pandemic preparedness, enabling the early identification of emerging variants of concern (VOCs) and guiding timely updates to vaccines, diagnostic tests, and therapeutic strategies. However, existing machine learning models and large-scale experiments lose their predictive power as viral variants evolve further from the original strains in sequence space. Here, we present a scalable framework that integrates random forest and neural network machine learning models with targeted high-throughput experimentation to anticipate and evaluate emerging SARS-CoV-2 receptor-binding domain (RBD) variants. Using public datasets, we trained predictive models for binding to human Angiotensin-converting enzyme 2 (ACE2), RBD expression, and antibody escape, and refined these models through iterative integration of experimental data focused on over 200 variants derived from wild-type (WT) and Omicron strains. Through an indirect transfer learning approach, our machine learning models achieved high accuracy having correlation coefficients of up to 0.79 for antibody binding. The models were also generalizable across diverse antibody types including heavy-chain-only antibodies (HCAbs) by encoding complementarity-determining regions (CDRs) as input features. This dynamic approach enables rapid assessment of emerging variants, facilities prioritization of the therapeutic strategies, and supports a proactive, data-driven response to evolving viral threats.

15.
arXiv (quant-ph) 2026-06-16

Inflationary branch decoherence and the cosmological arrow of time

Authors:

arXiv:2602.21263v3 Announce Type: cross Abstract: We analyze branch decoherence in inflationary quantum cosmology by computing reduced density matrices and branch-overlap factors for long-wavelength perturbations. The Hartle-Hawking no-boundary state is real in the semiclassical regime and contains both expanding and contracting WKB components, whereas the tunneling state is selected as an outgoing complex WKB branch; expanding-contracting decoherence is therefore central for the former and mainly diagnostic for the latter. Using the influence-functional formalism, we derive the noise kernel for a light spectator environment and evaluate decoherence under horizon-based and EFT-motivated coarse grainings. We then compute the single-mode branch overlap directly from the Bunch-Davies mode functions, obtaining $|\mathcal{D}_k(z)|=[z^2/(z^2+1)]^{1/4}$ in the massless limit and $|\mathcal{D}_k(z)|\sim z^\nu$ on superhorizon scales for massive fields, where $z=-k\eta$ is the dimensionless wavenumber with $\eta$ the conformal time. In the massless case, the accumulated geometric branch functional is evaluated in closed form, with a leading cutoff-sensitive phase-space term and a universal subleading contribution. The calculation provides an explicit quantitative bridge between quantum-cosmological boundary conditions, inflationary squeezing, and the emergence of effectively classical cosmological histories.

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

Entanglement preservation and Clauser-Horne nonlocality in electromagnetically induced transparency quantum memories

arXiv:2507.15453v4 Announce Type: replace Abstract: Entanglement preservation in noisy quantum memories represents a central challenge in quantum information science. While experiments have shown that electromagnetically induced transparency (EIT) memories can store entangled photons, a quantitative theoretical analysis of whether nonlocal quantum correlations can survive storage loss induced by ground-state decoherence remains limited. Here we combine the dark-state polariton formalism with a reduced density-operator treatment to derive an EIT-specific effective pure-loss description for the retrieved photonic state in the ground-state-decoherence-limited regime. The analysis reveals that decoherence transforms an initially pure Bell state into a mixed state with a vacuum component and predicts a protocol-dependent storage-efficiency benchmark of 89.7% for violating the chosen unconditional Clauser-Horne (CH) inequality. Above this benchmark, the retrieved photonic state violates the CH inequality without post-selection, whereas below it, this unconditional CH violation is no longer obtained. This framework provides a quantitative theoretical description of entanglement retention, retrieved photonic density operators, and protocol-dependent Bell-test benchmarks in EIT quantum memories.

17.
arXiv (math.PR) 2026-06-16

Uniform integrability of the distance to the nearest leaf in random trees

arXiv:2606.15339v1 Announce Type: new Abstract: We study the distance from the root to the nearest leaf, the analogous quantity for a uniformly chosen vertex, and its protection number, in size-conditioned simply generated trees. We prove a uniform exponential tail bound for each of these quantities, valid for arbitrary offspring distributions. As a consequence, these random variables are uniformly integrable of every order. This yields convergence of all moments to those of the corresponding local limit. The argument is probabilistic and unified across the three quantities.

18.
arXiv (CS.CL) 2026-06-11

Beyond Compaction: Structured Context Eviction for Long-Horizon Agents

We present Context Window Lifecycle (CWL), a context-management scheme that gives long-horizon LLM agents an effectively unbounded working horizon. As a session accumulates history, CWL keeps the context within budget through graduated, semantically-aware eviction: the agent annotates its trajectory as typed, dependency-linked episodes as work proceeds, and a deterministic, LLM-free policy evicts content in priority order within that structure when a token budget is exceeded. CWL preserves user turns and the exploratory context the agent is actively reasoning over, while aggressively shedding action episodes whose effects are already persisted in the environment, keeping active context near a stable ceiling that also avoids the performance degradation associated with very large prompts. Compared to summarization-based compaction, CWL avoids four well-known limitations: unpredictable lossiness, destruction of causal structure, blocking model cost, and compression-induced hallucination. Compared to recency truncation, CWL is semantically aware: it drops the oldest-and-most-recoverable content according to the dependency graph rather than oldest-in-time regardless of relevance. We describe the annotation protocol, the episode graph, the eviction policy, and the token-accounting loop, and evaluate CWL on long-horizon agentic benchmarks: a single agent session completing 89 sequential tasks across 80 million tokens with no measurable degradation in task accuracy relative to per-task isolated sessions

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

ARB4WM: An Adversarial Robustness Benchmark for World Models in Continuous Control

arXiv:2606.16605v1 Announce Type: new Abstract: World models are widely used in robotic and agentic engineering control systems due to their ability to learn latent dynamics for planning and decision-making. As these systems are increasingly deployed in safety-critical settings, understanding their robustness under adversarial conditions has become essential. However, existing evaluations lack a unified benchmark for testing adversarial threats across the policy, value, and latent-dynamics levels of world-model agents. To fill this gap, we present ARB4WM, a unified evaluation framework for pre-deployment robustness and risk assessment of world-model agents under visual perturbations. ARB4WM defines five white-box loss objectives across these three levels and studies their effects when combined with single-step or multi-step perturbation strategies and temporal attack modes, including full-frame, half-sequence, and sparse-frame exposure. Specifically, we evaluate four Dreamer-style agents across 20 tasks from MetaWorld and the DeepMind Control Suite under different loss objectives, perturbation strategies, and temporal attack modes. Results show that attacks targeting value estimation, latent representations, and RSSM dynamics can be as damaging as direct policy disruption, and that early or frequent perturbations are especially harmful, while input-level defenses provide limited recovery under adaptive attacks. These findings suggest that safety, risk, and reliability assessment for world models should cover multiple component-oriented attack objectives and temporal exposure protocols rather than relying solely on action-space robustness. Source code is available at https://github.com/zaoanguai/ARB4WM.

20.
arXiv (CS.AI) 2026-06-16

Discovering Symmetry Groups with Flow Matching

arXiv:2512.20043v3 Announce Type: replace Abstract: Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries automatically is challenging. We propose LieFlow, a novel framework that reframes symmetry discovery as a distribution learning problem on Lie groups. Instead of searching for the symmetry generators, our approach operates directly in group space, modeling a symmetry distribution over a large hypothesis group $G$. The support of the learned distribution reveals the underlying symmetry group $H \subseteq G$. Unlike previous works, LieFlow can discover both continuous and discrete symmetries within a unified framework, without assuming a fixed Lie algebra basis or a specific distribution over the group elements. Experiments on synthetic 2D and 3D point clouds, ModelNet10 and a real-world MI-Motion dataset show that LieFlow accurately discovers continuous and discrete subgroups, significantly outperforming a state-of-the-art baseline, LieGAN, in identifying discrete symmetries.

21.
arXiv (math.PR) 2026-06-11

Approximation Properties of Evolutionary Dynamics in Continuous-Time Finite State Space Games

Authors:

arXiv:2606.11193v1 Announce Type: cross Abstract: This thesis studies the convergence of finite-population stochastic evolutionary dynamics to their deterministic mean-field limit in continuous-time finite state space games. We first develop refined ergodic theorems for Markov chains with a single positive-recurrent class, guaranteeing the existence of a unique invariant distribution and almost-sure convergence of time averages. Next, we prove that the mean-field model, described by a system of Lipschitz-continuous ordinary differential equations, admits a unique solution that depends continuously on its initial condition and that constitutes the almost-sure limit for the empirical distributions with fixed policy. Furthermore, we show that every Mixed Stationary Nash Equilibrium of the mean-field game is approximated by a Nash equilibrium of the corresponding $N$-player game within an error $\epsilon$ for sufficiently large $N$. We finally demonstrate, by Kurtz's theorem, that the empirical state-policy distribution converges in probability to the mean-field trajectory. Numerical simulations conducted in MATLAB confirm the theoretical $\mathcal{O}(N^{-1/2})$ convergence rate in both models across a range of population sizes.

22.
arXiv (CS.LG) 2026-06-17

A Dynamical Systems Perspective on the Analysis of Neural Networks

arXiv:2507.05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic) gradient descent, and related topics into dynamical statements. We also tackle three concrete challenges. First, we consider the process of information propagation through a neural network, i.e., we study the input-output map for different architectures. We explain the universal embedding property for augmented neural ODEs representing arbitrary functions of given regularity, the classification of multilayer perceptrons and neural ODEs in terms of suitable function classes, and the memory-dependence in neural delay equations. Second, we consider the training aspect of neural networks dynamically. We describe a dynamical systems perspective on gradient descent and study stability for overdetermined problems. We then extend this analysis to the overparameterized setting and describe the edge of stability phenomenon, also in the context of possible explanations for implicit bias. For stochastic gradient descent, we present stability results for the overparameterized setting via Lyapunov exponents of interpolation solutions. Third, we explain several results regarding mean-field limits of neural networks. We describe a result that extends existing techniques to heterogeneous neural networks involving graph limits via digraph measures. This shows how large classes of neural networks naturally fall within the framework of Kuramoto-type models on graphs and their large-graph limits. Finally, we point out that similar strategies to use dynamics to study explainable and reliable AI can also be applied to settings such as generative models or fundamental issues in gradient training methods, such as backpropagation or vanishing/exploding gradients.

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

PIGEON: VLM-Driven Object Navigation via Points of Interest Selection

Object navigation in unseen indoor environments requires agents to perform semantic search under partial observability. Vision-language models (VLMs) provide strong semantic-spatial priors for this task, but how to interface them with robot navigation remains challenging: dense VLM inference is expensive, while abstracting environments into symbolic memories often separates high-level reasoning from the raw visual evidence that supports it. We propose we propose PIGEON (Point of Interest Guided Exploration for Object Navigation), a VLM-driven framework that formulates object navigation as raw-observation-grounded sparse decision problem. PIGEON introduces Points of Interest (PoIs) as sparse visual decision units that couple geometrically executable waypoints with raw egocentric observations. Rather than using VLMs as dense controllers or restricting them to frontier ranking, PIGEON enables VLMs to select among task-critical PoIs, including exploration frontiers, suspected target objects, traversable stairs, and floor-level summaries, while low-level planners execute continuous motion between them. This PoI interface further makes high-level navigation decisions verifiable, allowing us to develop an RLVR pipeline that improves local VLMs without manual Chain-of-Thought annotations. Extensive experiments on Habitat ObjectNav benchmarks show that PIGEON achieves state-of-the-art zero-shot performance, scales consistently with foundation model capacity, and transfers to Active Embodied Question Answering with only prompt modifications. Real-world deployments on physical robots further demonstrate its robustness and efficiency.

24.
arXiv (CS.CL) 2026-06-19

Characterizing Narrative Content in Web-scale LLM Pretraining Data

The narrative composition of web-scale LLM pretraining corpora remains largely unexplored even though narrative is a fundamental mode of human communication. We present the first fine-grained study of narrative features in Dolma, a 3-trillion-token open pretraining corpus. Drawing on narrative theory, we design a framework spanning three core narrative elements (agency, setting, and events) operationalized as 11 interpretable dimensions. After sampling and annotating a diverse set of 400 passages, we finetune and validate NarraBERT, a RoBERTa-based model for fine-grained narrative prediction. We apply NarraBERT to 3M passages, resulting in a new dataset, NarraDolma. We find (i) narrative structure is measurable at scale across extremely heterogeneous data, (ii) we uncover a continuous, multidimensional narrative structure underlying web text, and (iii) narrative qualities are unequally distributed across pretraining sources and topics in ways that current curation practices neither measure nor account for. Our framework, dataset, and analyses provide a foundation for understanding how narrative qualities are distributed in LLM pretraining data and for studying how data composition affects narrative reasoning tasks. We publicly release NarraDolma and NarraBERT.

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

Hybrid Iterative Neural Low-Regularity Integrator for Nonlinear Dispersive Equations

arXiv:2605.04853v2 Announce Type: replace Abstract: We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error. A base low-regularity integrator provides a consistent first-order approximation to nonlinear dispersive PDEs, while a lightweight neural network, operating on a low-dimensional latent manifold, learns the residual defect that analytical methods cannot close. An explicit time-step scaling on the neural correction ensures that its Lipschitz contribution remains $\mathcal{O}(\tau)$, yielding a Gronwall stability factor bounded uniformly in the step size and independent of the spatial resolution. The network is trained end-to-end through a solver-in-the-loop objective that unrolls the full iteration and penalises trajectory error in a Bourgain-type norm, aligning learning with multi-step solver dynamics rather than isolated one-step targets. Under stated assumptions, the global error satisfies $C(\varepsilon_{net}+\delta)\,\tau^\gamma\ln(1/\tau)$, where $\varepsilon_{net}$ measures the network approximation quality and $\delta$ the training shortfall. Experiments on three dispersive benchmarks with rough data show that HIN-LRI improves accuracy over analytical integrators, splitting methods, and neural PDE surrogates, with stable spatial refinement, effective out-of-distribution transfer, and modest online overhead.