论文检索

Applications · Everything Else

Guoqing Hu, An Zhang, Shuchang Liu, Wenyu Mao, Jiancan Wu, Xun Yang, Xiang Li, Lantao Hu, Han Li, Kun Gai 等

Recommenders aim to rank items from a discrete item corpus in line with user interests, yet suffer from extremely sparse user preference data. Recent advances in diffusion models have inspired diffusion-based recommenders, which alleviate sparsity by injecting noise during a forward process to prevent collapse of perturbed preference distributions. However, current diffusion‑based recommenders predominantly rely on continuous Gaussian noise, which is intrinsically mismatched with the discrete nature of user preference data in recommendation. In this paper, building upon recent advances in discrete diffusion, we propose \textbf{PreferGrow}, a discrete diffusion-based recommender modeling preference ratios by fading and growing user preferences over the discrete item corpus. PreferGrow differs from existing diffusion-based recommenders in three core aspects: (1) Discrete modeling of preference ratios: PreferGrow models relative preference ratios between two items, where a positive value indicates a more preferred one over another less preferred. This formulation aligns naturally with the discrete and ranking-oriented nature of recommendation tasks. (2) Perturbing via preference fading: Instead of injecting continuous noise, PreferGrow fades user preferences by replacing the preferred item with alternatives---physically akin to negative sampling---thereby eliminating the need for any prior noise assumption. (3) Preference reconstruction via growing: PreferGrow reconstructs user preferences by iteratively growing the preference signal from the estimated ratios. We further provide theoretical analysis showing that PreferGrow preserves key properties of discrete diffusion processes. PreferGrow provides a well-defined matrix‑based formulation for discrete diffusion-based recommendation and empirically outperforms existing diffusion‑based recommenders across five benchmark datasets, underscoring its superior effectiveness. Our codes are available at \url{https://anonymous.4open.science/r/PreferGrow_Commit-2259/}.

Applications · Robotics

Wenke Xia, Yichu Yang, Hongtao Wu, Xiao Ma, Tao Kong, Di Hu

Establishing a reliable and iteratively refined robotic system is essential for deploying real-world applications. While Vision-Language-Action (VLA) models are widely recognized as the foundation model for such robotic deployment, their reliance on offline expert demonstrations critically limits their capacity for post-deployment refinement. To mitigate this limitation, we introduce Action Preference Optimization (APO), a method designed to refine VLA models by human-assisted preference alignment gathered through interaction with environments. This method begins with a human-robot collaboration framework for reliable failure correction and interaction trajectory collection through human intervention. However, directly leveraging these interaction trajectories for preference optimization is non-trivial due to the challenges of irreversible robotic actions and token distribution mismatch. To solve this, APO proposes an adaptive reweighting algorithm with binary desirability signals derived from interaction, empowering VLA models effectively suppress failure-prone actions while enhancing corrective action adaptation. Ultimately, APO equips VLA models with the crucial capability to learn from failure, paving the way for their iterative refinement and reliable deployment in dynamic environments. The experiments conducted in simulation and real-world scenarios prove superior generalization and robustness of our human-assisted framework across a variety of manipulation tasks. We believe this work could bring insights for efficient and stable optimization of VLA models through human-robot collaboration. The code and dataset are released at https://github.com/GeWu-Lab/Action-Preference-Optimization.

Deep Learning · Graph Neural Networks

Yi Li, Zhichun Guo, Guanpeng Li, Bingzhe Li

Training Graph Neural Networks (GNNs) often relies on repeated, irregular, and expensive message-passing operations over all nodes (e.g., $N$), leading to high computational overhead. To alleviate this inefficiency, we revisit the GNNs training from a spectral perspective. In many real-world graphs, node features and embeddings exhibit sparse representation in the Graph Fourier domain. This inherent spectral sparsity aligns well with the principles of Compressed Sensing, which posits that signals sparse in one transform domain can be accurately reconstructed from a significantly reduced number of measurements. This observation motivates the design of a more efficient GNNs that operates predominantly in compressed spectral subspace. Thus, we propose You Only Spectralize Once (YOSO), a GNN training scheme that performs single Graph Fourier Transformation to project features onto a learnable orthonormal Fourier basis, retaining only $M$ spectral coefficients ($M \ll N$). The entire GNN computation is then carried out in reduced spectral domain. Final full-graph embeddings are recovered only at output layer by solving a bounded $\ell_{2,1}$-regularized optimization problem. Theoretically, drawing upon Compressed Sensing theory, we prove stable recovery throughout training by showing that the projection onto our learnable Fourier basis can satisfy the Restricted Isometry Property when $M=\mathcal{O}(k \log N)$ for $k$-row-sparse spectra, acting as the measurement process. Empirically, YOSO achieves an average 74\% reduction in training time across five benchmark datasets compared to state-of-the-art methods, while maintaining competitive accuracy.

Optimization · Neural Network Optimization

Léo Dana, Loucas Pillaud-Vivien, Francis Bach

We analyse the convergence of one-hidden-layer ReLU networks trained by gradient flow on $n$ data points. Our main contribution leverages the high dimensionality of the ambient space, which implies low correlation of the input samples, to demonstrate that a network with width of order $\log(n)$ neurons suffices for global convergence with high probability. Our analysis uses a Polyak–Łojasiewicz viewpoint along the gradient-flow trajectory, which provides an exponential rate of convergence of $\frac{1}{n}$. When the data are exactly orthogonal, we give further refined characterizations of the convergence speed, proving its asymptotic behavior lies between the orders $\frac{1}{n}$ and $\frac{1}{\sqrt{n}}$, and exhibiting a phase-transition phenomenon in the convergence rate, during which it evolves from the lower bound to the upper, and in a relative time of order $\frac{1}{\log(n)}$.

Mohammad Pedramfar, Christopher Quinn, Vaneet Aggarwal

This paper presents novel contributions to the field of online optimization, particularly focusing on the adaptation of algorithms from concave optimization to more challenging classes of functions. Key contributions include the introduction of uniform wrappers, a class of meta-algorithms that could be used for algorithmic conversions such as converting algorithms for convex optimization into those for quadratizable optimization. Moreover, we propose a guideline that, given a base algorithm $\mathcal{A}$ for concave optimization and a uniform wrapper $\mathcal{W}$, describes how to convert a proof of the regret bound of $\mathcal{A}$ in the concave setting into a proof of the regret bound of $\mathcal{W}(\mathcal{A})$ for quadratizable setting. Through this framework, the paper demonstrates improved regret guarantees for various classes of DR-submodular functions under zeroth-order feedback. Furthermore, the paper extends zeroth-order online algorithms to bandit feedback and offline counterparts, achieving notable improvements in regret/sample complexity compared to existing approaches.

Reinforcement Learning · Multi-agent

Hao Liang, shuqing shi, Yudi Zhang, Biwei Huang, Yali Du

Large‑scale networked systems, such as traffic, power, and wireless grids, challenge reinforcement‑learning agents with both scale and environment shifts. To address these challenges, we propose \texttt{GSAC} (\textbf{G}eneralizable and \textbf{S}calable \textbf{A}ctor‑\textbf{C}ritic), a framework that couples causal representation learning with meta actor‑critic learning to achieve both scalability and domain generalization. Each agent first learns a sparse local causal mask that provably identifies the minimal neighborhood variables influencing its dynamics, yielding exponentially tight approximately compact representations (ACRs) of state and domain factors. These ACRs bound the error of truncating value functions to $\kappa$-hop neighborhoods, enabling efficient learning on graphs. A meta actor‑critic then trains a shared policy across multiple source domains while conditioning on the compact domain factors; at test time, a few trajectories suffice to estimate the new domain factor and deploy the adapted policy. We establish finite‑sample guarantees on causal recovery, actor-critic convergence, and adaptation gap, and show that \texttt{GSAC} adapts rapidly and significantly outperforms learning-from-scratch and conventional adaptation baselines.

Deep Learning · Theory

Rishi Sonthalia, Michael Murray, Guido Montufar

This paper investigates low-rank structure in the gradients of the training loss for two-layer neural networks while relaxing the usual isotropy assumptions on the training data and parameters. We consider a spiked data model in which the bulk can be anisotropic and ill-conditioned, we do not require independent data and weight matrices and we also analyze both the mean-field and neural-tangent-kernel scalings. We show that the gradient with respect to the input weights is approximately low rank and is dominated by two rank-one terms: one aligned with the bulk data–residue, and another aligned with the rank one spike in the input data. We characterize how properties of the training data, the scaling regime and the activation function govern the balance between these two components. Additionally, we also demonstrate that standard regularizers, such as weight decay, input noise and Jacobian penalties, also selectively modulate these components. Experiments on synthetic and real data corroborate our theoretical predictions.

Social Aspects · Trustworthy Machine Learning

Gaojian Xiong, Yu Sun, Jianhua Liu, Jian Cui, Jianwei Liu

While Large Language Models (LLMs) have gained remarkable success, they are consistently at risk of being stolen when deployed on untrusted edge devices. As a solution, TEE-based secure inference has been proposed to protect valuable model property. However, we identify a statistical vulnerability in existing protection methods, and furtherly compromise their security guarantees by proposed Model Stealing Attack with Prior. To eliminate this vulnerability, LoRO is presented in this paper, which leverages dense mask to completely obfuscate parameters. LoRO includes two innovations: (1) Low Rank Mask, which uses low-rank factors to generate dense masks efficiently. The computing complexity in TEE is hence reduced by an exponential amount to achieve inference speed up, while providing robust model confidentiality. (2) Factors Multiplexing, which reuses several cornerstone factors to generate masks for all layers. Compared to one-mask-per-layer, the secure memory requirement is reduced from GB-level to tens of MB, hence avoiding the hundred-fold latency introduced by secure memory paging. Experimental results indicate that LoRO achieve a $0.94\times$ Model Stealing (MS) accuracy, while SOTA methods presents $3.37\times$ at least. The averaged inference latency of LoRO is only $1.49\times$, compared to the $112\times$ of TEE-shielded inference. Moreover, LoRO results no accuracy loss, and requires no re-training and structure modification. LoRO can solve the concerns regarding model thefts on edge devices in an efficient and secure manner, facilitating the wide edge application of LLMs.

Optimization · Stochastic & Convex Optimization

Tianqi Qiao, Marie Maros

We propose and study Sparse Polyak, a variant of Polyak’s adaptive step size, designed to solve high-dimensional statistical estimation problems where the problem dimension is allowed to grow much faster than the sample size. In such settings, the standard Polyak step size performs poorly, requiring an increasing number of iterations to achieve optimal statistical precision-even when, the problem remains well conditioned and/or the achievable precision itself does not degrade with problem size. We trace this limitation to a mismatch in how smoothness is measured: in high dimensions, it is no longer effective to estimate the Lipschitz smoothness constant. Instead, it is more appropriate to estimate the smoothness restricted to specific directions relevant to the problem (restricted Lipschitz smoothnes constant). Sparse Polyak overcomes this issue by modifying the step size to estimate the restricted Lipschitz smoothness constant. We support our approach with both theoretical analysis and numerical experiments, demonstrating its improved performance.

Social Aspects · Fairness, Equity, Justice and Safety

Xiaorui Wu, Fei Li, Xiaofeng Mao, Xin Zhang, Li Zheng, Yuxiang Peng, Chong Teng, Donghong Ji, Zhuang Li

Large language models (LLMs) frequently refuse to respond to pseudo-malicious instructions: semantically harmless input queries triggering unnecessary LLM refusals due to conservative safety alignment, significantly impairing user experience. Collecting such instructions is crucial for evaluating and mitigating over-refusals, but existing instruction curation methods, like manual creation or instruction rewriting, either lack scalability or fail to produce sufficiently diverse and effective refusal-inducing prompts. To address these limitations, we introduce EVOREFUSE, a prompt optimization approach that generates diverse pseudo-malicious instructions consistently eliciting confident refusals across LLMs. EVOREFUSE employs an evolutionary algorithm exploring the instruction space in more diverse directions than existing methods via mutation strategies and recombination, and iteratively evolves seed instructions to maximize evidence lower bound on LLM refusal probability. Using EVOREFUSE, we create two novel datasets: EVOREFUSE-TEST, a benchmark of 582 pseudo-malicious instructions that outperforms the next-best benchmark with 85.34% higher average refusal triggering rate across 9 LLMs, 34.86% greater lexical diversity, and 40.03% improved LLM response confidence scores; and EVOREFUSE-ALIGN, which provides 3,000 pseudo-malicious instructions with responses for supervised and preference-based alignment training. LLAMA3.1-8B-INSTRUCT supervisedly fine-tuned on EVOREFUSE-ALIGN achieves up to 29.85% fewer over-refusals than models trained on the second-best alignment dataset, without compromising safety. Our analysis with EVOREFUSE-TEST reveals models trigger over-refusals by overly focusing on sensitive keywords while ignoring broader context. Our code and datasets are available at https://github.com/FishT0ucher/EVOREFUSE.

Applications · Robotics

Xinyue Zhu, Binghao Huang, Yunzhu Li

Handheld grippers are increasingly used to collect human demonstrations due to their ease of deployment and versatility. However, most existing designs lack tactile sensing, despite the critical role of tactile feedback in precise manipulation. We present a portable, lightweight gripper with integrated tactile sensors that enables synchronized collection of visual and tactile data in diverse, real-world, and in-the-wild settings. Building on this hardware, we propose a cross-modal representation learning framework that integrates visual and tactile signals while preserving their distinct characteristics. The learning procedure allows the emergence of interpretable representations that consistently focus on contacting regions relevant for physical interactions. When used for downstream manipulation tasks, these representations enable more efficient and effective policy learning, supporting precise robotic manipulation based on multimodal feedback. We validate our approach on fine-grained tasks such as test tube insertion and pipette-based fluid transfer, demonstrating improved accuracy and robustness under external disturbances. Our project page is available at \url{https://binghao-huang.github.io/touch_in_the_wild/}.

Deep Learning · Everything Else

Peiwen Yuan, Yiwei Li, Shaoxiong Feng, Xinglin Wang, Yueqi Zhang, Jiayi Shi, Chuyi Tan, Boyuan Pan, Yao Hu, Prof. Kan

LLM-as-Benchmark-Generator methods have been widely studied as a supplement to human annotators for scalable evaluation, while the potential biases within this paradigm remain underexplored. In this work, we systematically define and validate the phenomenon of inflated performance in models evaluated on their self-generated benchmarks, referred to as self-bias, and attribute it to sub-biases arising from question domain, language style, and wrong labels. On this basis, we propose Silencer, a general framework that leverages the heterogeneity between multiple generators at both the sample and benchmark levels to neutralize bias and generate high-quality, self-bias-silenced benchmark. Experimental results across various settings demonstrate that Silencer can suppress self-bias to near zero, significantly improve evaluation effectiveness of the generated benchmark (with an average improvement from 0.655 to 0.833 in Pearson correlation with high-quality human-annotated benchmark), while also exhibiting strong generalizability.

Data-centric AI · Data augmentation

Leitian Tao, Xuefeng Du, Sharon Li

Reward modeling, crucial for aligning large language models (LLMs) with human preferences, is often bottlenecked by the high cost of preference data. Existing textual data synthesis methods are computationally expensive. We propose a novel framework LENS for synthesizing preference data directly in the LLM's latent embedding space. Our method employs a Variational Autoencoder (VAE) to learn a structured latent representation of response embeddings. By performing controlled perturbations in this latent space and decoding back to the embedding space, we efficiently generate diverse, semantically consistent synthetic preference pairs, bypassing costly text generation and annotation. We provide theoretical guarantees that our synthesized pairs approximately preserve original preference ordering and improve reward model generalization. Empirically, our latent-space synthesis significantly outperforms text-based augmentation on standard benchmarks, achieving superior results while being 18× faster in generation and using a 16,000× smaller model. Our work offers a scalable and effective alternative for enhancing reward modeling through efficient data augmentation. Code is publicly available at https://github.com/deeplearning-wisc/lens.

Data-centric AI · Data-centric AI methods and tools

Muquan Li, Hang Gou, Dongyang Zhang, Shuang Liang, Xiurui Xie, Deqiang Ouyang, Ke Qin

The growing demand for efficient deep learning has positioned dataset distillation as a pivotal technique for compressing training dataset while preserving model performance. However, existing inner-loop optimization methods for dataset distillation typically rely on random truncation strategies, which lack flexibility and often yield suboptimal results. In this work, we observe that neural networks exhibit distinct learning dynamics across different training stages—early, middle, and late—making random truncation ineffective. To address this limitation, we propose Automatic Truncated Backpropagation Through Time (AT-BPTT), a novel framework that dynamically adapts both truncation positions and window sizes according to intrinsic gradient behavior. AT-BPTT introduces three key components: (1) a probabilistic mechanism for stage-aware timestep selection, (2) an adaptive window sizing strategy based on gradient variation, and (3) a low-rank Hessian approximation to reduce computational overhead. Extensive experiments on CIFAR-10, CIFAR-100, Tiny-ImageNet, and ImageNet-1K show that AT-BPTT achieves state-of-the-art performance, improving accuracy by an average of 6.16\% over baseline methods. Moreover, our approach accelerates inner-loop optimization by 3.9 × while saving 63\% memory cost.

Social Aspects · Privacy-preserving Statistics and Machine Learning

Kaiqi Guan, Wenke Huang, Xianda Guo, Yueyang Yuan, Bin Yang, Mang Ye

Federated Learning is a promising technique that enables collaborative machine learning while preserving participant privacy. With respect to multi-party collaboration, achieving performance fairness acts as a critical challenge in federated systems. Existing explorations mainly focus on considering all parameter-wise fairness and consistently protecting weak clients to achieve performance fairness in federation. However, these approaches neglect two critical issues. 1) Parameter Redundancy: Redundant parameters that are unnecessary for fairness training may conflict with critical parameters update, thereby leading to performance degradation. 2) Persistent Protection: Current fairness mechanisms persistently enhance weak clients throughout the entire training cycle, hindering global optimization and causing lower performance alongside unfairness. To address these, we propose a strategy with two key components: First, parameter adjustment with mask and rescale which discarding redundant parameter and highlight critical ones, preserving key parameter updates and decrease conflict. Second, we observe that the federated training process exhibits distinct characteristics across different phases. We propose a dynamic aggregation strategy that adaptively weights clients based on local update directions and performance variations. Empirical results on single-domain and cross-domain scenarios demonstrate the effectiveness of the proposed solution and the efficiency of crucial modules. The code is available at https://github.com/guankaiqi/FedPW.

Applications · Language, Speech and Dialog

Benjamin Matthias Ruppik, Julius von Rohrscheidt, Carel van Niekerk, Michael Heck, Renato Vukovic, Shutong Feng, Hsien-chin Lin, Nurul Lubis, Bastian Rieck, Marcus Zibrowius 等

Understanding the internal mechanisms of large language models (LLMs) remains a challenging and complex endeavor. Even fundamental questions, such as how fine-tuning affects model behavior, often require extensive empirical evaluation. In this paper, we introduce a novel perspective based on the geometric properties of contextual latent embeddings to study the effects of training and fine-tuning. To that end, we measure the local dimensions of a contextual language model's latent space and analyze their shifts during training and fine-tuning. We show that the local dimensions provide insights into the model's training dynamics and generalization ability. Specifically, the mean of the local dimensions predicts when the model’s training capabilities are exhausted, as exemplified in a dialogue state tracking task, overfitting, as demonstrated in an emotion recognition task, and grokking, as illustrated with an arithmetic task. Furthermore, our experiments suggest a practical heuristic: reductions in the mean local dimension tend to accompany and predict subsequent performance gains. Through this exploration, we aim to provide practitioners with a deeper understanding of the implications of fine-tuning on embedding spaces, facilitating informed decisions when configuring models for specific applications. The results of this work contribute to the ongoing discourse on the interpretability, adaptability, and generalizability of LLMs by bridging the gap between intrinsic model mechanisms and geometric properties in the respective embeddings.

Social Aspects

Ran Li, Hao Wang, Chengzhi Mao

Efficient red-teaming method to uncover vulnerabilities in Large Language Models (LLMs) is crucial. While recent attacks often use LLMs as optimizers, the discrete language space make gradient-based methods struggle. We introduce LARGO (Latent Adversarial Reflection through Gradient Optimization), a novel latent self-reflection attack that reasserts the power of gradient-based optimization for generating fluent jailbreaking prompts. By operating within the LLM's continuous latent space, LARGO first optimizes an adversarial latent vector and then recursively call the same LLM to decode the latent into natural language. This methodology yields a fast, effective, and transferable attack that produces fluent and stealthy prompts. On standard benchmarks like AdvBench and JailbreakBench, LARGO surpasses leading jailbreaking techniques, including AutoDAN, by 44 points in attack success rate. Our findings demonstrate a potent alternative to agentic LLM prompting, highlighting the efficacy of interpreting and attacking LLM internals through gradient optimization.

Deep Learning · Generative Models and Autoencoders

Jon Saad-Falcon, Estefany Kelly Buchanan, Mayee Chen, Tzu-Heng (Brian) Huang, Brendan McLaughlin, Tanvir Bhathal, Shang Zhu, Ben Athiwaratkun, Frederic Sala, Scott Linderman 等

Verifiers can improve language model (LM) capabilities by providing feedback or selecting the best response from a pool of generated candidates. Currently, high-quality verifiers are either unscalable (e.g., humans) or limited in utility (e.g., tools like Lean for formal proofs). While LM judges and reward models have become broadly useful as general-purpose verifiers, a significant performance gap remains between them and oracle verifiers. To help close this gap, we introduce Weaver, a framework for designing a strong verifier by combining multiple weak, imperfect verifiers. First we find that weighted ensembles of verifiers, which typically require learning from labeled data, significantly outperform unweighted combinations due to differences in the verifiers. To reduce the dependency on labeled data, Weaver leverages weak supervision to estimate each verifier’s accuracy and combines their outputs into a unified score that better reflects true response quality. However, directly applying weak supervision algorithms poses several challenges, including inconsistent verifier output formats and handling low-quality verifiers. Weaver addresses these challenges by using dataset statistics to normalize outputs and filter specific verifiers. We study the effectiveness of Weaver in repeated sampling settings, where a model generates multiple candidate responses at test time and a verifier is used to select the correct one. Our evaluations demonstrate that Weaver significantly improves the pass@1 performance across several reasoning and math tasks, achieving o3-mini level accuracy with Llama 3.3 70B Instruct (a much cheaper non-reasoning model) as the generator, and an ensemble of smaller judge and reward models as the verifiers (86.2% average). This gain mirrors the jump achieved between GPT-4o and o3-mini (69.0% vs. 86.7%), which required extensive finetuning and post-training interventions. To make Weaver more efficient, we train a compact 400M cross-encoder using Weaver's combined output scores. This distilled model retains 98.7% of Weaver's full accuracy while reducing verification compute by up to 99.97%.

Social Aspects · Accountability, Transparency and Interpretability

Clément Bénard

Tree ensembles have demonstrated state-of-the-art predictive performance across a wide range of problems involving tabular data. Nevertheless, the black-box nature of tree ensembles is a strong limitation, especially for applications with critical decisions at stake. The Hoeffding or ANOVA functional decomposition is a powerful explainability method, as it breaks down black-box models into a unique sum of lower-dimensional functions, provided that input variables are independent. In standard learning settings, input variables are often dependent, and the Hoeffding decomposition is generalized through hierarchical orthogonality constraints. Such generalization leads to unique and sparse decompositions with well-defined main effects and interactions. However, the practical estimation of this decomposition from a data sample is still an open problem. Therefore, we introduce the TreeHFD algorithm to estimate the Hoeffding decomposition of a tree ensemble from a data sample. We show the convergence of TreeHFD, along with the main properties of orthogonality, sparsity, and causal variable selection. The high performance of TreeHFD is demonstrated through experiments on both simulated and real data, using our treehfd Python package (https://github.com/ThalesGroup/treehfd). Besides, we empirically show that the widely used TreeSHAP method, based on Shapley values, is strongly connected to the Hoeffding decomposition.

General Machine Learning · Representation Learning

Alejandro García-Castellanos, David Wessels, Nicky J. van den Berg, Remco Duits, Daniel M. Pelt, Erik Bekkers

We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. Our approach employs a single neural field where a unified shared backbone is conditioned on signal-specific latent variables – represented as point clouds in a Lie group – to model diverse Eikonal solutions. The ENF integration ensures equivariant mapping from these latent representations to the solution field, delivering three key benefits: enhanced representation efficiency through weight-sharing, robust geometric grounding, and solution steerability. This steerability allows transformations applied to the latent point cloud to induce predictable, geometrically meaningful modifications in the resulting Eikonal solution. By coupling these steerable representations with Physics-Informed Neural Networks (PINNs), our framework accurately models Eikonal travel-time solutions while generalizing to arbitrary Riemannian manifolds with regular group actions. This includes homogeneous spaces such as Euclidean, position–orientation, spherical, and hyperbolic manifolds. We validate our approach through applications in seismic travel-time modeling of 2D, 3D, and spherical benchmark datasets. Experimental results demonstrate superior performance, scalability, adaptability, and user controllability compared to existing Neural Operator-based Eikonal solver methods.