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

How Auxiliary Reasoning Unleashes GUI Grounding in VLMs

Graphical user interface (GUI) grounding is a fundamental task for building GUI agents. However, general vision-language models (VLMs) struggle with this task due to a lack of specific optimization. We identify a key gap in this paper: while VLMs exhibit significant latent grounding potential, as demonstrated by their performance measured by Pointing Game, they underperform when tasked with outputting explicit coordinates. To address this discrepancy and bypass the high data and annotation costs of current fine-tuning approaches, we propose three zero-shot auxiliary reasoning methods. By providing explicit spatial cues such as axes, grids and labeled intersections as part of the input image, these methods enable VLMs to better articulate their implicit spatial understanding capabilities. We evaluate these methods on four GUI grounding benchmarks across seven open-source and proprietary VLMs. Experimental results show substantial gains from auxiliary reasoning. Mark-Grid Scaffold boosts Gemini-3.1-Pro from 11.72\% under direct inference to 95.20\% on ScreenSpot-v2, achieves state-of-the-art performance on ScreenSpot, and approaches the strongest fine-tuned methods on ScreenSpot-v2 and UI-I2E-Bench. Our code is available at https://github.com/liweim/AuxiliaryReasoning.

02.
arXiv (CS.CV) 2026-06-18

Low-Cost Neuromorphic Fall Detection Using Synthetic Event Data and Hybrid SNNs

This work presents the development of hybrid models that integrate spiking neural networks (SNNs) with components of convolutional neural networks (CNNs) to learn from simulated event-based camera data (Dynamic Vision Sensor, DVS) generated from conventional smartphone videos. Aimed primarily at human fall detection, the approach leverages the energy efficiency and spatio-temporal processing capabilities of SNNs by converting video frames into event-based data. The proposed models are evaluated through simulations on multiple datasets, comparing their performance to that of traditional machine learning models. Results demonstrate significant gains in efficiency without sacrificing accuracy, underscoring the potential of combining SNNs and DVS technology for complex tasks in real-world environments.

03.
medRxiv (Medicine) 2026-06-12

Genetic basis of dynamic brain states reveals cellular and disease associations

Dynamic resting-state fMRI captures the time-varying patterns of brain activity that are obscured by static approaches. Hidden Markov Models (HMMs) characterise these dynamics as recurring whole-brain states and quantify their fractional occupancy (FO), the proportion of time spent in each state, yet the biological basis of inter-individual variation in FO remains unclear. Using data from 52,335 White UK Biobank participants, with replication in East and South Asian subsamples, this study examined the heritability, cellular and neurotransmitter basis of brain states, and their links with complex phenotypes. FO was significantly heritable and enriched for neuronal populations, particularly glutamatergic and GABAergic signalling. Analyses identified shared and state-specific loci and revealed genetic correlations, colocalisation, and potential causal relationships between FO and several phenotypes, including educational attainment, sleep duration, and disease risk. These findings establish dynamic brain states as biologically grounded intermediate phenotypes, linking genetic variation to neural dynamics, diseases and traits.

04.
arXiv (CS.CV) 2026-06-12

VDE Bench: Evaluating The Capability of Image Editing Models to Modify Visual Documents

In recent years, image editing models have made significant progress, enabling users to manipulate visual content in a flexible and interactive manner through natural language instructions. However, an important yet underexplored research direction remains dense visual document image editing, which involves modifying textual content within images while faithfully preserving the original text style and background context. Existing methods primarily focus on English scenarios and images with relatively sparse text, and thus cannot adequately address dense, structurally complex documents or non-Latin scripts such as Chinese. To bridge this gap, we propose VDE Bench (Visual Doc Edit Bench), a rigorously human annotated and evaluated benchmark specifically designed to assess the performance of image editing models on bilingual Chinese-English and complex visual document editing tasks. The benchmark comprises a high quality dataset of 942 instruction based image editing samples, whose seed images encompass dense Chinese and English text documents including academic papers, posters, presentation slides, examination materials, and newspapers. Furthermore, we introduce a novel evaluation framework that systematically quantifies editing performance at the OCR parsing level, thereby enabling fine grained assessment of text modification accuracy. Based on this benchmark, we conduct a comprehensive evaluation of representative image editing models. Human verification demonstrates a high degree of consistency between human judgments and automated evaluation metrics. VDE Bench constitutes the first systematic benchmark for evaluating the performance of image editing models on bilingual dense text visual documents.

05.
arXiv (CS.CV) 2026-06-15

A Pragmatic VLA Foundation Model

Offering great potential in robotic manipulation, a capable Vision-Language-Action (VLA) foundation model is expected to faithfully generalize across tasks and platforms while ensuring cost efficiency (e.g., data and GPU hours required for adaptation). To this end, we develop LingBot-VLA with around 20,000 hours of real-world data from 9 popular dual-arm robot configurations. Through a systematic assessment on 3 robotic platforms, each completing 100 tasks with 130 post-training episodes per task, our model achieves clear superiority over competitors, showcasing its strong performance and broad generalizability. We have also built an efficient codebase, which delivers a throughput of 261 samples per second with an 8-GPU training setup, representing a 1.5~2.8$\times$ (depending on the relied VLM base model) speedup over existing VLA-oriented codebases. The above features ensure that our model is well-suited for real-world deployment. To advance the field of robot learning, we provide open access to the code, base model, and benchmark data, with a focus on enabling more challenging tasks and promoting sound evaluation standards.

07.
arXiv (CS.LG) 2026-06-18

KANEL\'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluation

arXiv:2512.12850v3 Announce Type: replace-cross Abstract: Low-latency, resource-efficient neural network inference on FPGAs is essential for applications demanding real-time capability and low power. Lookup table (LUT)-based neural networks are a common solution, combining strong representational power with efficient FPGA implementation. In this work, we introduce KANEL\'E, a framework that exploits the unique properties of Kolmogorov-Arnold Networks (KANs) for FPGA deployment. Unlike traditional multilayer perceptrons (MLPs), KANs employ learnable one-dimensional splines with fixed domains as edge activations, a structure naturally suited to discretization and efficient LUT mapping. We present the first systematic design flow for implementing KANs on FPGAs, co-optimizing training with quantization and pruning to enable compact, high-throughput, and low-latency KAN architectures. Our results demonstrate up to a 2700x speedup and orders of magnitude resource savings compared to prior KAN-on-FPGA approaches. Moreover, KANEL\'E matches or surpasses other LUT-based architectures on widely used benchmarks, particularly for tasks involving symbolic or physical formulas, while balancing resource usage across FPGA hardware. Finally, we showcase the versatility of the framework by extending it to real-time, power-efficient control systems.

08.
arXiv (CS.AI) 2026-06-11

Sample-Efficient Hypergradient Estimation for Decentralized Bi-Level Reinforcement Learning

arXiv:2603.14867v4 Announce Type: replace-cross Abstract: Many strategic decision-making problems, such as environment design for warehouse robots, can be naturally formulated as bi-level reinforcement learning (RL), where a leader agent optimizes its objective while a follower solves a Markov decision process (MDP) conditioned on the leader's decisions. In many situations, a fundamental challenge arises when the leader cannot intervene in the follower's optimization process; it can only observe the optimization outcome. We address this decentralized setting by deriving the hypergradient of the leader's objective, i.e., the gradient of the leader's strategy that accounts for changes in the follower's optimal policy. Unlike prior hypergradient-based methods that require extensive data for repeated state visits or rely on gradient estimators whose complexity can increase substantially with the high-dimensional leader's decision space, we leverage the Boltzmann covariance trick to derive an alternative hypergradient formulation. This enables efficient hypergradient estimation solely from interaction samples, even when the leader's decision space is high-dimensional. Additionally, to our knowledge, this is the first method that enables hypergradient-based optimization for 2-player Markov games in decentralized settings. Experiments highlight the impact of hypergradient updates and demonstrate our method's effectiveness in both discrete and continuous state tasks.

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

Geometry of Lightning Self-Attention: Identifiability and Dimension

arXiv:2408.17221v3 Announce Type: replace Abstract: We consider function spaces defined by self-attention networks without normalization, and theoretically analyze their geometry. Since these networks are polynomial, we rely on tools from algebraic geometry. In particular, we study the identifiability of deep attention by providing a description of the generic fibers of the parametrization for an arbitrary number of layers and, as a consequence, compute the dimension of the function space. Additionally, for a single-layer model, we characterize the singular and boundary points. Finally, we formulate a conjectural extension of our results to normalized self-attention networks, prove it for a single layer, and numerically verify it in the deep case.

10.
arXiv (CS.LG) 2026-06-11

Reinforcement Learning with Action-Triggered Observations

arXiv:2510.02149v2 Announce Type: replace Abstract: We introduce Action-Triggered Sporadically Traceable Markov Decision Processes (ATST-MDPs), a reinforcement learning framework for partial observability in which full state observations occur stochastically at each step, with probability determined by the chosen action. We derive Bellman equations tailored to this setting and establish the existence of an optimal policy. Exploiting the fact that sporadic observations reveal the full state, we provide an equivalent formulation in which agents commit to action-sequences between consecutive observations. Under the linear MDP assumption, we show that the value function over such action-sequences admits a linear representation in a finite-dimensional feature map, enabling standard regression-based methods. As an application, we derive ATST-LSVI-UCB, an optimistic algorithm achieving regret $\widetilde{O}(\sqrt{Kd^3(1-\gamma)^{-3}})$ for episodic learning with geometrically distributed horizons, where $K$ is the number of episodes, $d$ the feature dimension, and $\gamma$ the discount factor (episode continuation probability), matching the known rate for linear MDPs with full observability.

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

Robust Dual-Signal Fusion: Hybrid Neuro-Symbolic Gating with Compressed Chain-of-Thought Refinement for Irony Detection in Social Media Texts

Large Language Models (LLMs) natively default to literal semantic interpretations, making zero-shot irony detection a persistent challenge. We introduce the Robust Dual-Signal (RDS) Fusion framework, a hybrid neuro-symbolic architecture that compresses Chain-of-Thought (CoT) reasoning trajectories without Supervised Fine-Tuning (SFT). Evaluated on a strictly held-out TweetEval test set (N=734), RDS achieves 78.1% accuracy and a Macro F1 of 0.777, matching the absolute performance ceiling of the fine-tuned BERTweet. On the heavily imbalanced iSarcasm dataset, the frozen CoT pipeline filters 22.5% of out-of-distribution hallucinations, yielding a zero-shot Macro F1 of 0.6726 and Ironic F1 of 0.4821, outperforming multiple heavily supervised SemEval transformer ensembles. A statistical ablation confirms this structural synergy: adding the symbolic prior to the neural baseline yields no significant gain (p = 0.242), and the marginal benefit of adding the CoT pipeline to that prior is heavily compressed (p = 0.149). Only the complete, concurrent fusion of all three signals achieves a statistically validated improvement over the baseline (p = 0.005).

12.
Nature (Science) 2026-06-17

A distant brown dwarf coplanar to a warm Jupiter and a hot super-Earth

In transiting planetary systems, in which planetary sizes are accurately determined from transit observations, the presence of transit-timing variations1 (TTVs), especially when combined with radial velocity (RV) data, provides powerful constraints on masses and orbital eccentricities. Together, these measurements offer crucial insights into system architecture, formation mechanisms and dynamical evolution. We present long-term RV and transit/TTV monitoring of the relatively young star (age approximately 1 Gyr) TOI-201, revealing an exceptional multi-planet system composed of a hot super-Earth (SE) size planet transiting every 5.8 days, a warm Jupiter (WJ) on a 53-day orbit and an eccentric (e = 0.62) low-mass brown dwarf (BD) on an approximately 8-year orbit, with an estimated mass MBD of about 16 Jupiter masses. The BD is the longest-period transiting substellar object ever characterized by means of RVs and the only one known to be coplanar with inner planets. The architecture of this system suggests that the SE was formed isolated and in the innermost region of the gaseous disk. On the other hand, the orbital configuration of the outer companions suggests a nearly in situ formation of both objects, with the WJ forming in a dense inner disk. Alternatively, the BD might have formed farther out and migrated inward, while increasing its eccentricity owing to interactions with the disk. Analysis of long-term radial velocity data and transit time variations, induced by a super-Earth, a warm Jupiter and a brown dwarf in a coplanar orbit around the relatively young star TOI201.

13.
arXiv (CS.CL) 2026-06-19

NAMESAKES: Probing Identity Memorization in Text-to-Image Models

Text-to-image (T2I) models generate realistic likenesses of some individuals when prompted with their names, raising privacy concerns. However, distinguishing whether a generated face is memorized or fabricated currently requires ground-truth photos, access to training data, or white-box access to model internals, limiting applicability. We introduce a fully black-box behavioral probe that distinguishes between these regimes while requiring no reference photos or prior knowledge of training data. To benchmark this task, we present the NAMESAKES dataset of over one thousand names and faces of public figures spanning a wide range of fame levels, along with perturbed, less famous names. Experiments on state-of-the-art T2I models show that our probe substantially predicts identity memorization and separates memorized from unrecognized names, with further insights into differences across model families.

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

MixTeX: Data-Efficient LaTeX OCR via Synthetic Pretraining and Limited Fine-Tuning

LaTeX OCR converts scientific document images into editable LaTeX code. Existing systems rely on large paired datasets, which are costly to collect and limited for low-resource languages. This paper presents MIXTEX, a data-efficient system using synthetic pretraining without real LaTeX sources. Unlike Nougat that depends on arXiv datasets, we generate training data by randomly pairing grammatical Wikipedia text with LaTeX formulas, requiring only syntactic correctness. This eliminates dependency on real document collections, enables scalable data generation (120M tokens), and supports low-resource languages. Following synthetic pretraining, adaptation requires only 400 real samples. Evaluation on a 977-sample benchmark with printed and handwritten English and Chinese shows that this two-stage strategy outperforms methods trained on large real datasets while requiring less human effort and computation. Data, code, and models are publicly available.

15.
arXiv (CS.AI) 2026-06-11

The Art of Interrogation: Consistency Amplifies Factuality in Spatial Reasoning

arXiv:2606.11918v1 Announce Type: new Abstract: Current Large Reasoning Models (LRMs) exhibit remarkable general capabilities but significantly underperform in spatial reasoning tasks. Existing approaches treat this gap as a knowledge deficit, relying on supervised fine-tuning (SFT) to ingest labeled spatial data from external vision sources or synthetic engines. In contrast, we argue that for many tasks, spatial reasoning capabilities are already present in pre-trained LRMs but require alignment through logical coherence under geometric 2D and 3D constraints. In this work, we propose a self-supervised reinforcement learning (RL) framework that targets the internal reasoning process without requiring ground-truth annotations. By formalizing the notion of consistency verifiers – reward functions that check for geometric and semantic consistency under transformations – we demonstrate that models can improve their spatial reasoning abilities. We use both image transformations, like flipping, and textual transformations, like swapping the order of objects in the question, and propose a new optimal transport-based RL strategy, OT-GRPO, which is a minimal-matching variant of group relative policy optimization tailored to pairwise verifiers. We show that this label-free consistency training approaches the accuracy of models trained with ground-truth supervision and achieves similar generalization across diverse tasks and data domains.

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

CropTrack: A Tracking with Re-Identification Framework for Precision Agriculture

Multiple-object tracking (MOT) in agricultural environments presents major challenges due to repetitive patterns, similar object appearances, sudden illumination changes, and frequent occlusions. Contemporary trackers in this domain rely on the motion of objects rather than appearance for association. Nevertheless, they struggle to maintain object identities when targets undergo frequent and strong occlusions. The high similarity of object appearances makes integrating appearance-based association nontrivial for agricultural scenarios. To solve this problem we propose CropTrack, a novel MOT framework based on the combination of appearance and motion information. CropTrack integrates a reranking-enhanced appearance association, a one-to-many association with appearance-based conflict resolution strategy, and an exponential moving average prototype feature bank to improve appearance-based association. Evaluated on publicly available agricultural MOT datasets, CropTrack demonstrates consistent identity preservation, outperforming traditional motion-based tracking methods. Compared to the state of the art, CropTrack achieves significant gains in association accuracy and identification precision scores with a lower number of identity switches.

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

Functional Equivalence in Attention: A Comprehensive Study with Applications to Linear Mode Connectivity

arXiv:2606.17830v1 Announce Type: cross Abstract: Neural network parameter spaces are inherently non-injective, as distinct parameter configurations can realize identical functions through functional equivalence. While this symmetry is well understood in classical fully connected and convolutional models, it becomes substantially more intricate in modern attention-based architectures. Existing analyses of multihead attention have largely focused on the vanilla formulation, overlooking positional encodings that fundamentally reshape architectural symmetries. In this work, we provide a formal study of functional equivalence in Transformers with positional encodings. Focusing on the two most widely used variants–sinusoidal and rotary positional encodings (RoPE)–we show that sinusoidal encodings preserve the equivalence structure of vanilla attention, whereas rotary encodings significantly reduce the symmetry group, thereby enhancing expressivity. This offers a principled explanation for the growing prominence of RoPE in practice. We further examine how positional encodings affect linear mode connectivity, and through an alignment algorithm, empirically demonstrate that the presence and variability of connectivity across Transformer settings crucially depend on the positional encoding.

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

LibriConvo: Simulating Conversations from Read Literature for ASR and Diarization

We introduce LibriConvo, a synthetic conversational speech corpus for speaker diarization and automatic speech recognition (ASR), built by instantiating the previously proposed Speaker-Aware Simulated Conversation (SASC) framework in a dataset and benchmarking setting. The main contribution of this paper is a corpus construction pipeline and benchmark derived from that framework. To make the data more suitable for downstream ASR and diarization, conversational timing statistics are estimated from English CallHome using external voice activity detection, long pauses are compressed, LibriTTS utterances are grouped by book to improve local semantic continuity, and room impulse responses are selected with a spatial-plausibility heuristic. The resulting corpus contains 240.1 hours of audio across 1,496 dialogues involving 830 speakers, partitioned into speaker-disjoint train, validation, and test splits. We report baseline results for both diarization and ASR. On the test split, Sortformer outperforms the pyannote pipeline in diarization (11.1\% vs.~24.4\% DER). For ASR, a Fast Conformer-CTC XLarge model fine-tuned with Serialized Output Training achieves 7.29\% WER and 6.97\% cpWER, outperforming zero-shot Whisper-large-v3. These results position LibriConvo as a practical benchmark for studying synthetic conversational speech and for evaluating multi-speaker speech processing systems.

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

Structuring The Future: Diffusion LLM Speculative Decoding via Calibrated Draft Graphs

Diffusion LLMs (dLLMs) have recently emerged as a powerful alternative to autoregressive LLMs (AR-LLMs) with the potential to operate at significantly higher token-generation rates. To unlock this potential, we present Spiffy, a speculative decoding algorithm to accelerate dLLM inference while provably preserving the model's output distribution. This work addresses the unique challenges involved in applying ideas from speculative decoding of AR-LLMs to dLLMs. Spiffy performs auto-speculation to eliminate the overheads of an independent draft model, structuring draft states in the form of a novel directed draft graph to take advantage of the bidirectional, blockwise nature of dLLM generation. These draft graphs are calibrated offline to maximize acceptance rates and are dynamically pruned during inference for improved computational efficiency. We present a detailed formulation of Spiffy and demonstrate its ability to accelerate LLaDA, Dream, and SDAR models in combination with KV caching and threshold-based dynamic unmasking leading to up to $8.6\times$ reduction in model inferences and $6.3\times$ acceleration in token rate.

20.
arXiv (CS.CV) 2026-06-17

Disentangling Perception and Reasoning in Multimodal LLMs via Reward Design

Reinforcement learning with verifiable rewards has driven major gains in LLM reasoning, and it is intuitive to assume this recipe will transfer well to multimodal models. However, multimodal models do two things: first, perceive what is in an image, then reason about what it implies. Because these stages are graded jointly, it is hard to tell how much room reasoning alone has to grow. We study this on algorithmic visual puzzles, where both components are necessary and show that perception, not reasoning, is the binding constraint. Replacing images with simple textual descriptions raises performance by over 20 points on average for Claude models. We then evaluate six reward designs aimed at inducing visual grounding during reasoning without chain-of-thought supervision. Training Qwen-2.5-VL-7B with GRPO, reward design induces long, structured reasoning with self-reflection and visual references, yielding a 5.56-point gain over the base model. These gains are, however, uneven; no single reward improves all categories, and rewards with verifiable accuracy signals trade out-of-domain transfer for in-domain accuracy. These results point to perception-aware reward design as a path forward, so that signals correct perception at its source rather than the reasoning that inherits its errors.

21.
arXiv (CS.LG) 2026-06-18

Learning Augmented Exact Exponential Algorithms

arXiv:2606.18807v1 Announce Type: cross Abstract: The field of learning-augmented algorithms has demonstrated that machine-learned predictions can bypass worst-case lower bounds across a wide range of problems. So far, however, the focus has been almost exclusively on polynomial-time algorithms, where predictions improve competitive ratios, approximation guarantees, or running times. In this paper, we raise the question of whether predictions can push the frontier of exact exponential-time algorithms for NP-hard problems. We answer this question affirmatively by proposing a general approach that augments an entire family of state-of-the-art exact algorithms for a variety of subset selection problems. We show that a noisy predictor that is only marginally better than random guessing suffices to provably reduce the search space, and that the resulting runtime speedup scales smoothly with the prediction quality. Importantly, our algorithms require only pairwise independence of predictions or, alternatively, do not require the knowledge of the predictor's accuracy - both strictly weaker and more realistic settings than typically assumed.

22.
medRxiv (Medicine) 2026-06-12

Disentangling Confounders from Pathology in Long-COVID Trajectory Prediction for Women: An Interpretable Large-Language-Model Approach

Objective. Post-acute sequelae of SARS-CoV-2 infection (PASC, "Long COVID") dispropor- tionately affects women, in whom hallmark symptoms–insomnia, fatigue, palpitations, cogni- tive difficulty–overlap with comorbidities and hormonal transitions such as menopause. This diagnostic overlap is a confounding problem: models that forecast future symptom severity risk attributing baseline physiological noise to viral pathology. We ask whether an interpretable, causally disentangled language model can separate true pathological signal from such con- founders while remaining competitive with strong predictors of future PASC severity

23.
arXiv (CS.AI) 2026-06-18

A DeepLearning Framework for Dynamic Estimation of Origin-Destination Sequence

arXiv:2307.05623v2 Announce Type: replace-cross Abstract: OD matrix estimation is a critical problem in the transportation domain. The principle method uses the traffic sensor measured information such as traffic counts to estimate the traffic demand represented by the OD matrix. The problem is divided into two categories: static OD matrix estimation and dynamic OD matrices sequence(OD sequence for short) estimation. The above two face the underdetermination problem caused by abundant estimated parameters and insufficient constraint information. In addition, OD sequence estimation also faces the lag challenge: due to different traffic conditions such as congestion, identical vehicle will appear on different road sections during the same observation period, resulting in identical OD demands correspond to different trips. To this end, this paper proposes an integrated method, which uses deep learning methods to infer the structure of OD sequence and uses structural constraints to guide traditional numerical optimization. Our experiments show that the neural network(NN) can effectively infer the structure of the OD sequence and provide practical constraints for numerical optimization to obtain better results. Moreover, the experiments show that provided structural information contains not only constraints on the spatial structure of OD matrices but also provides constraints on the temporal structure of OD sequence, which solve the effect of the lagging problem well.

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

Variational autoencoders with latent high-dimensional steady geometric flows for dynamics

arXiv:2410.10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework such that manifold geometries, subject to our geometric flow, embedded in Euclidean space are learned in the intermediary latent space developed by encoders and decoders. By tailoring the geometric flow in which the latent space evolves, we induce latent geometric properties of our choosing, which are reflected in empirical performance. We reformulate the traditional evidence lower bound (ELBO) loss with a considerate choice of prior. We develop a linear geometric flow with a steady-state regularizing term. This flow requires only automatic differentiation of one time derivative, and can be solved in moderately high dimensions in a physics-informed approach, allowing more expressive latent representations. We discuss how this flow can be formulated as a gradient flow, and maintains entropy away from metric singularity. This, along with an eigenvalue penalization condition, helps ensure the manifold is sufficiently large in measure, nondegenerate, and a canonical geometry, which contribute to a robust representation. Our methods focus on the modified multi-layer perceptron architecture with tanh activations for the manifold encoder-decoder. We demonstrate, on our datasets of interest, our methods perform at least as well as the traditional VAE, and oftentimes better. Our methods can outperform this and a VAE endowed with our proposed architecture, frequently reducing out-of-distribution (OOD) error between 15% to 35% on select datasets. We highlight our method on ambient PDEs whose solutions maintain minimal variation in late times. We provide empirical justification towards how we can improve robust learning for external dynamics with VAEs.

25.
arXiv (CS.LG) 2026-06-16

Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems

arXiv:2606.16510v1 Announce Type: cross Abstract: This study proposes a Petrov-Galerkin based Variational Physics-Informed Neural Network (VPINN) for efficiently solving two-dimensional singularly perturbed problems (SPPs) with one and two small perturbation parameters. The approach employs neural networks to construct the trial solution space, while tensor-product hat functions are adopted as test functions to enforce the variational form. To accurately resolve of sharp boundary layers, the variational form is implemented using a Petrov-Galerkin formulation. Dirichlet boundary conditions are imposed directly, while the source terms are computed using automatic differentiation. Computational experiments on standard two-dimensional problems demonstrate that the proposed method achieves high accuracy in both the maximum and L_2 norms. These results confirm the efficiency and robustness of the Petrov-Galerkin VPINN approach in accurately capturing the multiscale features of two-dimensional SPPs.