论文检索

Theory · Reinforcement Learning and Planning

ERIC EATON, Marcel Hussing, Michael Kearns, Aaron Roth, Sikata Sengupta, Jessica Sorrell

Replication of experimental results has been a challenge faced by many scientific disciplines, including the field of machine learning. Recent work on the theory of machine learning has formalized replicability as the demand that an algorithm produce identical outcomes when executed twice on different samples from the same distribution. Provably replicable algorithms are especially interesting for reinforcement learning (RL), where algorithms are known to be unstable in practice. While replicable algorithms exist for tabular RL settings, extending these guarantees to more practical function approximation settings has remained an open problem. In this work, we make progress by developing replicable methods for linear function approximation in RL. We first introduce two efficient algorithms for replicable random design regression and uncentered covariance estimation, each of independent interest. We then leverage these tools to provide the first provably efficient replicable RL algorithms for linear Markov decision processes in both the generative model and episodic settings. Finally, we evaluate our algorithms experimentally and show how they can inspire more consistent neural policies.

Deep Learning · Theory

Yuanhe Zhang, Ilja Kuzborskij, Jason Lee, Chenlei Leng, Fanghui Liu

Large Language Models (LLMs) demonstrate strong performance on mathematical problems when prompted with Chain-of-Thought (CoT), yet it remains unclear whether this success stems from search, rote procedures, or rule-consistent reasoning. To address this, we propose modeling CoT as a certain rule-based stochastic process over directed acyclic graphs (DAGs), where nodes represent intermediate derivation states and edges encode rule applications. Within this framework, we introduce \textbf{logical closeness}, a metric that quantifies how well a model’s CoT trajectory (i.e., the LLM's final output) adheres to the DAG structure, providing evaluation beyond classical PASS@$k$ metrics. Building on this, we introduce the \emph{DAG-MATH} CoT format and construct a benchmark that guides LLMs to generate CoT trajectories in this format, thereby enabling the evaluation of their reasoning ability under our framework. Across standard math reasoning datasets, our analysis uncovers statistically significant differences in reasoning fidelity among representative LLM families-even when PASS@$k$ is comparable-highlighting gaps between final-answer accuracy and rule-consistent derivation. Our framework provides a balance between free-form CoT and formal proofs systems, offering actionable diagnostics for LLMs reasoning evaluation. Our benchmark and code are available at https://github.com/YuanheZ/DAG-MATH.

Deep Learning · Generative Models and Autoencoders

Yung Hwei Lai, Kaiming Liu, Ziyue Wang, Weizhi Ma, Yang Liu

The professionalism of a human doctor in outpatient service depends on two core abilities: the ability to make accurate medical decisions and the medical consultation skill to conduct strategic, empathetic patient inquiry. Existing Large Language Models (LLMs) have achieved remarkable accuracy on medical decision-making benchmarks. However, they often lack the ability to conduct the strategic and empathetic consultation, which is essential for real-world clinical scenarios. To address this gap, we propose Doctor-R1, an AI doctor agent trained to master both of the capabilities by ask high-yield questions and conduct strategic multi-turn inquiry to guide decision-making. Our framework introduces three key components: a multi-agent interactive environment, a two-tiered reward architecture that separately optimizes clinical decision-making and communicative inquiry skills, and an experience repository to ground policy learning in high-quality prior trajectories. We evaluate Doctor-R1 on OpenAI's HealthBench and MAQuE, assessed across multi-facet metrics, such as communication quality, user experience, and task accuracy. Remarkably, Doctor-R1 surpasses state-of-the-art open-source specialized LLMs by a substantial margin with higher parameter efficiency and outperforms powerful proprietary models. Furthermore, the human expert evaluations show that Doctor-R1 achieves superior clinical capability and patient-centric performance, demonstrating the effectiveness of the framework.

General Machine Learning · Everything Else

Thomas Adler, Marco Grassia, Ziheng Liao, Giuseppe Mangioni, Carlo Vittorio Cannistraci

Complex networks model the structure and function of critical technological, biological, and communication systems. Network dismantling, the targeted removal of nodes to fragment a network, is essential for analyzing and improving system robustness. Existing dismantling methods suffer from key limitations: they depend on global structural knowledge, exhibit slow running times on large networks, and overlook the network’s latent geometry, a key feature known to govern the dynamics of complex systems. Motivated by these findings, we introduce Latent Geometry-Driven Network Automata (LGD-NA), a novel framework that leverages local network automata rules to approximate effective link distances between interacting nodes. LGD-NA is able to identify critical nodes and capture latent manifold information of a network for effective and efficient dismantling. We show that this latent geometry-driven approach outperforms all existing dismantling algorithms, including spectral Laplacian-based methods and machine learning ones such as graph neural networks and . We also find that a simple common-neighbor-based network automata rule achieves near state-of-the-art performance, highlighting the effectiveness of minimal local information for dismantling. LGD-NA is extensively validated on the largest and most diverse collection of real-world networks to date (1,475 real-world networks across 32 complex systems domains) and scales efficiently to large networks via GPU acceleration. Finally, we leverage the explainability of our common-neighbor approach to engineer network robustness, substantially increasing the resilience of real-world networks. We validate LGD-NA's practical utility on domain-specific functional metrics, spanning neuronal firing rates in the Drosophila Connectome, transport efficiency in flight maps, outbreak sizes in contact networks, and communication pathways in terrorist cells. Our results confirm latent geometry as a fundamental principle for understanding the robustness of real-world systems, adding dismantling to the growing set of processes that network geometry can explain.

Applications · Language, Speech and Dialog

Seungbin Yang, Jihwan Kim, Jaemin Choi, Dongjin Kim, Soyoung Yang, ChaeHun Park, Jaegul Choo

Web information extraction (WIE) is the task of automatically extracting data from web pages, offering high utility for various applications. The evaluation of WIE systems has traditionally relied on benchmarks built from HTML snapshots captured at a single point in time. However, this offline evaluation paradigm fails to account for the temporally evolving nature of the web; consequently, performance on these static benchmarks often fails to generalize to dynamic real-world scenarios. To bridge this gap, we introduce LiveWeb-IE, a new benchmark designed for evaluating WIE systems directly against live websites. Based on trusted and permission-granted websites, we curate natural language queries that require information extraction of various data categories, such as text, images, and hyperlinks. We further design these queries to represent four levels of complexity, based on the number and cardinality of attributes to be extracted, enabling a granular assessment of WIE systems. In addition, we propose Visual Grounding Scraper (VGS), a novel multi-stage agentic framework that mimics human cognitive processes by visually narrowing down web page content to extract desired information. Extensive experiments across diverse backbone models demonstrate the effectiveness and robustness of VGS. We believe that this study lays the foundation for developing practical and robust WIE systems.

Computer Vision · Vision Models & Multimodal

Jinhyung Park, Chensheng Peng, yihan hu, Wenzhao Zheng, Kris Kitani, Wei Zhan

Despite the efficiency and performance of sparse query-based representations for detection, state-of-the-art 3D occupancy estimation methods still rely on voxel-based or dense Gaussian-based 3D representations. However, dense representations are slow, and they lack flexibility in capturing the temporal dynamics of driving scenes. Distinct from prior work, we instead summarize the scene into a compact set of 3D queries which are propagated through time in an online, streaming fashion. These queries are then decoded into semantic Gaussians at each timestep. We couple our framework with a denoising rendering objective to guide the queries and their constituent Gaussians in effectively capturing scene geometry. Due to its efficient, query-based representation, S2GO achieves state-of-the-art performance on the nuScenes and KITTI occupancy benchmarks, outperforming prior art (e.g., GaussianWorld) by 2.7 IoU with 4.5x faster inference.

Deep Learning · Generative Models and Autoencoders

Yi-Chung Chen, David Inouye, Jing Gao

Generative classifiers, which leverage conditional generative models for classification, have recently demonstrated desirable properties such as robustness to distribution shifts. However, recent progress in this area has been largely driven by diffusion-based models, whose substantial computational cost limits their scalability in practice. To address the efficiency concern, we investigate generative classifier built upon recent advances in visual autoregressive (VAR) modeling. Owing to their tractable likelihood, VAR-based generative classifier enable significantly more efficient inference compared to diffusion-based counterparts. Building on this foundation, we introduce the Adaptive VAR Classifier$^+$ (A-VARC$^+$), which further improves accuracy while reducing computational cost, substantially enhancing practical usability. Beyond efficiency, we also study several properties of VAR-based generative classifiers that distinguish them from conventional discriminative models. In particular, the tractable likelihood facilitates visual explainability via token-wise mutual information, and the model naturally adapts to class-incremental learning without requiring additional replay data.

Optimization · Everything Else

Natalie Abreu, Nikhil Vyas, Sham Kakade, Depen Morwani

Recent efforts to accelerate LLM pretraining have focused on computationally-efficient approximations that exploit second-order structure. This raises a key question for large-scale training: how much performance is forfeited by these approximations? To probe this question, we establish a practical upper bound on iteration complexity by applying full Gauss-Newton (GN) preconditioning to transformer models of up to 150M parameters. Our experiments show that full GN updates yield substantial gains over existing optimizers, achieving a 5.4x reduction in training iterations compared to strong baselines like SOAP and Muon. Furthermore, we find that a precise layerwise GN preconditioner, which ignores cross-layer information, nearly matches the performance of the full GN method. Collectively, our results suggest: (1) the GN approximation is highly effective for preconditioning, implying higher-order loss terms may not be critical for convergence speed; (2) the layerwise Hessian structure contains sufficient information to achieve most of these potential gains; and (3) a significant performance gap exists between current approximate methods and an idealized layerwise oracle.

Applications · Time Series

Roussel Nzoyem, Nawid Keshtmand, Enrique Crespo Fernandez, Idriss TSAYEM, Raul Santos-Rodriguez, David Barton, Tom Deakin

We introduce WARP (**W**eight-space **A**daptive **R**ecurrent **P**rediction), a simple yet powerful model that unifies weight-space learning with linear recurrence to redefine sequence modeling. Unlike conventional recurrent neural networks (RNNs) which collapse temporal dynamics into fixed-dimensional hidden states, WARP explicitly parametrizes its hidden state as the weights and biases of a distinct auxiliary neural network, and uses input differences to drive its recurrence. This brain-inspired formulation enables efficient gradient-free adaptation of the auxiliary network at test-time, in-context learning abilities, and seamless integration of domain-specific physical priors. Empirical validation shows that WARP matches or surpasses state-of-the-art baselines on diverse classification tasks, featuring in the top three in 4 out of 6 real-world challenging datasets. Furthermore, extensive experiments across sequential image completion, multivariate time series forecasting, and dynamical system reconstruction demonstrate its expressiveness and generalization capabilities. Remarkably, a physics-informed variant of our model outperforms the next best model by more than 10x. Ablation studies confirm the architectural necessity of key components, solidifying weight-space linear RNNs as a transformative paradigm for adaptive machine intelligence.

Deep Learning · Everything Else

Alexey Yermakov, Yue Zhao, Marine Denolle, Yiyu Ni, Philippe Wyder, Judah Goldfeder, Stefano Riva, Jan Williams, David Zoro, Amy Rude 等

Seismology faces fundamental challenges in state forecasting and reconstruction (e.g., earthquake early warning and ground motion prediction) and managing the parametric variability of source locations, mechanisms, and Earth models (e.g., subsurface structure and topography effects). Addressing these with simulations is hindered by their massive scale, both in synthetic data volumes and numerical complexity, while real-data efforts are constrained by models that inadequately reflect the Earth's complexity and by sparse sensor measurements from the field. Recent machine learning (ML) efforts offer promise, but progress is obscured by a lack of proper characterization, fair reporting, and rigorous comparisons. To address this, we introduce a Common Task Framework (CTF) for ML for seismic wavefields, demonstrated here on three distinct wavefield datasets. Our CTF features a curated set of datasets at various scales (global, crustal, and local) and task-specific metrics spanning forecasting, reconstruction, and generalization under realistic constraints such as noise and limited data. Inspired by CTFs in fields like natural language processing, this framework provides a structured and rigorous foundation for head-to-head algorithm evaluation. We evaluate various methods for reconstructing seismic wavefields from sparse sensor measurements, with results illustrating the CTF's utility in revealing strengths, limitations, and suitability for specific problem classes. Our vision is to replace ad hoc comparisons with standardized evaluations on hidden test sets, raising the bar for rigor and reproducibility in scientific ML.

Applications · Language, Speech and Dialog

Subrata Biswas, Mohammad Khan, Bashima Islam

Spatial reasoning is fundamental to auditory perception, yet current audio large language models (ALLMs) largely rely on unstructured binaural cues and single- step inference. This limits both perceptual accuracy in direction and distance estimation and the capacity for interpretable reasoning. Recent work such as BAT demonstrates spatial QA with binaural audio, but its reliance on coarse categorical labels (left, right, up, down) and the absence of explicit geometric supervision constrain resolution and robustness. We introduce the $\textbf{Spatial-Acoustic Geometry Encoder (SAGE}$), a geometry-aware audio encoder that aligns binaural acoustic features with 3D spatial structure using panoramic depth images and room-impulse responses at training time, while requiring only audio at inference. Building on this representation, we present $\textbf{OWL}$, an ALLM that integrates $\textbf{SAGE}$ with a spatially grounded chain-of-thought to rationalize over direction-of-arrivals (DoA) and distance estimates. Through curriculum learning from perceptual QA to multi-step reasoning, $\textbf{OWL}$ supports o’clock-level azimuth and DoA estimation. To enable large-scale training and evaluation, we construct and release $\textbf{BiDepth}$, a dataset of over one million QA pairs combining binaural audio with panoramic depth images and room impulse responses across both in-room and out-of-room scenarios. Across two benchmark datasets, our new $\textbf{BiDepth}$ and the public SpatialSoundQA, $\textbf{OWL}$ reduces mean DoA error by $\textbf{11$^{\circ}$}$ through $\textbf{SAGE}$ and improves spatial reasoning QA accuracy by up to $\textbf{25}$% over BAT. Our dataset and code are available at: https://github.com/BASHLab/OWL

Applications · Language, Speech and Dialog

Thinh Pham, Nguyen Nguyen, Pratibha Zunjare, Weiyuan Chen, Yu-Min Tseng, Tu Vu

We introduce SealQA, a challenge benchmark for evaluating SEarch-Augmented Language models on fact-seeking questions where web search yields conflicting, noisy, or unhelpful results. SealQA comes in three flavors: (1) SEAL-0 (main) and (2) SEAL-HARD, both of which assess factual accuracy and reasoning capabilities, where SEAL-0 targets the most challenging questions that frontier non-reasoning models (e.g., GPT-4.1) answer with near-zero accuracy; and (3) LongSeal, which extends SealQA to test long-context, multi-document reasoning in "needle-in-a-haystack" settings. Our evaluation reveals critical limitations in current models. Even frontier reasoning models face significant challenges across SealQA flavors. On SEAL-0, GPT-5 with tools achieves only 43.2% accuracy at its best reasoning effort. We also find that even advanced reasoning models (e.g., DeepSeek-R1) can be vulnerable to noisy search results. Notably, increasing test-time compute does not yield reliable gains across GPT-5 and the o-series of models, with performance often plateauing or even declining early. Finally, while current models are less affected by the "lost-in-the-middle" issue, they still fail to reliably identify relevant documents in LongSeal when faced with numerous distractors. To facilitate future work, we release SealQA at https://huggingface.co/datasets/vtllms/sealqa.

Computer Vision · Everything Else

Ke Han, Yueming Lyu, Nicu Sebe

Existing text-to-motion (T2M) generation models typically rely on pretrained large language models to encode textual inputs. However, these models, trained on generic text corpora, lack explicit alignment between motion-related words (e.g., "clockwise'', "quickly'') and human skeletal movements. This misalignment, fundamentally rooted in the word embedding layers, severely limits the ability of T2M models to understand and generalize fine-grained motion semantics. To tackle this issue, we propose Motion-Aligned Text Encoding (MATE), a novel framework that explicitly incorporates motion semantics into the word embedding layers of large language models to enhance text-motion alignment for motion generation. To address the challenge of inherent semantic entanglement in motion sequences, MATE introduces two key components: 1) a motion localization strategy that establishes localized correspondences between sub-texts and motion segments, enabling soft attention guidance for semantic localization; and 2) a motion disentanglement module that isolates word-specific motion semantics via contrastive kinematic prototypes, ensuring word-level alignment between linguistic and kinematic representations. Remarkably, language models enhanced with MATE can be seamlessly integrated into existing T2M methods, significantly surpassing state-of-the-art performance on two standard benchmarks with minimal modifications.

Deep Learning · Generative Models and Autoencoders

Pengxiang Li, Jiayin Cai, Hongwei Xue, Kunyu Shi, Shilin Yan

Diffusion Language Models (DLMs) promise highly parallel text generation, yet their practical inference speed is often bottlenecked by suboptimal decoding schedulers. Standard approaches rely on ``scattered acceptance''---committing high-confidence tokens at disjoint positions throughout the sequence. This approach inadvertently fractures the Key-Value (KV) cache, destroys memory locality, and forces the model into costly, repeated repairs across unstable token boundaries. To resolve this, we present the \textbf{Longest Stable Prefix (LSP)} scheduler, a training-free and model-agnostic inference paradigm based on \textit{monolithic prefix absorption}. In each denoising step, LSP evaluates token stability via a single forward pass, dynamically identifies a contiguous left-aligned block of stable predictions, and snaps its boundary to natural linguistic or structural delimiters before an atomic commitment. This prefix-first topology yields dual benefits: systemically, it converts fragmented KV cache updates into efficient, contiguous appends; algorithmically, it preserves bidirectional lookahead over a geometrically shrinking active suffix, drastically reducing token flip rates and denoiser calls. Extensive evaluations on LLaDA-8B and Dream-7B demonstrate that LSP accelerates inference by up to 3.4$\times$ across rigorous benchmarks---including mathematical reasoning, code generation, multilingual (CJK) tasks, and creative writing---while matching or slightly improving output quality. By fundamentally restructuring the commitment topology, LSP bridges the gap between the theoretical parallelism of DLMs and practical hardware efficiency.

Computer Vision · 3D Rendering & Reconstruction

Qianfan Shen, Ningxiao Tao, Qiyu Dai, Tianle Chen, Minghan Qin, Yongjie Zhang, Mengyu Chu, Wenzheng Chen, Baoquan Chen

We consider the problem of synthesizing photorealistic, physically plausible combustion effects in in-the-wild 3D scenes. Traditional CFD and graphics pipelines can produce realistic fire effects but rely on handcrafted geometry, expert-tuned parameters, and labor-intensive workflows, limiting their scalability to the real world. Recent scene modeling advances like 3D Gaussian Splatting (3DGS) enable high-fidelity real-world scene reconstruction, yet lack physical grounding for combustion. To bridge this gap, we propose FieryGS, a physically-based framework that integrates physically-accurate and user-controllable combustion simulation and rendering within the 3DGS pipeline, enabling realistic fire synthesis for real scenes. Our approach tightly couples three key modules: (1) multimodal large-language-model-based physical material reasoning, (2) efficient volumetric combustion simulation, and (3) a unified renderer for fire and 3DGS. By unifying reconstruction, physical reasoning, simulation, and rendering, FieryGS removes manual tuning and automatically generates realistic, controllable fire dynamics consistent with scene geometry and materials. Our framework supports complex combustion phenomena—including flame propagation, smoke dispersion, and surface carbonization—with precise user control over fire intensity, airflow, ignition location and other combustion parameters. Evaluated on diverse indoor and outdoor scenes, FieryGS outperforms all comparative baselines in visual realism, physical fidelity, and controllability.

Theory · Everything Else

Cyrus Cousins, Vijay Keswani, Vincent Conitzer, Hoda Heidari, Jana Borg, Walter Sinnott-Armstrong

Recent AI trends seek to align AI models to learned human-centric objectives, such as personal preferences, utility, or societal values. Using standard preference elicitation methods, researchers and practitioners build models of human decisions and judgments, to which AI models are aligned. However, standard elicitation methods often fail to capture the true cognitive processes behind human decision making, such as the use of heuristics or simplifying structured thought patterns. To address this limitation, we take an axiomatic approach to learning cognitively faithful decision processes from pairwise comparisons. Building on the vast literature characterizing cognitive processes that contribute to human decision-making and pairwise comparisons, we derive a class of models in which individual features are first processed with learned rules, then aggregated via a fixed rule, such as the Bradley-Terry rule, to produce a decision. This structured processing of information ensures that such models are realistic and feasible candidates to represent underlying human decision-making processes. We demonstrate the efficacy of this modeling approach by learning interpretable models of human decision making in a kidney allocation task, and show that our proposed models match or surpass the accuracy of prior models of human pairwise decision-making.

Computer Vision · Image and Video Generation

Zheng Tan, Weizhen Wang, Andrea Bertozzi, Ernest Ryu

Diffusion models (DMs) and flow-matching models have demonstrated remarkable performance in image and video generation. However, such models require a significant number of function evaluations (NFEs) during sampling, leading to costly inference. Consequently, quality-preserving fast sampling methods that require fewer NFEs have been an active area of research. However, prior training-free sampling methods fail to simultaneously address two key challenges: the stiffness of the ODE (i.e., the non-straightness of the velocity field) and dependence on the semi-linear structure of the DM ODE (which limits their direct applicability to flow-matching models). In this work, we introduce the Stabilized Taylor Orthogonal Runge–Kutta (STORK) method, addressing both design concerns. We demonstrate that STORK consistently improves the quality of diffusion and flow-matching sampling for image and video generation.

Computer Vision · Image and Video Generation

Kaiyuan Deng, Gen Li, Yang Xiao, Bo Hui, Xiaolong Ma

While multi-concept unlearning has shown progress, extending to large-scale scenarios remains difficult, as existing methods face three persistent challenges: **(i)** they often introduce conflicting weight updates, making some targets difficult to unlearn or causing degradation of generative capability; **(ii)** they lack precise mechanisms to keep unlearning strictly confined to target concepts, resulting in collateral damage on similar content; **(iii)** many approaches rely on additional data or auxiliary modules, causing scalability and efficiency bottlenecks as the number of concepts grows. To simultaneously address these challenges, we propose **Scalable-Precise Concept Unlearning (ScaPre)**, a unified and lightweight framework tailored for scalable and precise large-scale unlearning. ScaPre introduces a *conflict-aware stable design*, which integrates the spectral trace regularizer and geometry alignment to stabilize the optimization space, suppress conflicting updates, and preserve the pretrained global structure. Furthermore, the *Informax Decoupler* identifies concept-relevant parameters and adaptively reweights updates, ensuring that unlearning is confined to the target subspace without collateral damage. ScaPre yields an efficient closed-form solution, requiring no additional data or auxiliary sub-models, while maintaining both scalability and precision. Comprehensive experiments across large-scale objects, styles, and explicit content benchmarks demonstrate that ScaPre effectively removes target concepts while maintaining generation quality. It can forget up to **×5** more concepts than the best baseline within the limits of acceptable generative quality, and outperforms existing multi-concept approaches in precision and efficiency, achieving a new state of the art for large-scale unlearning.

Reinforcement Learning · Batch/Offline

Wenjie Qiu, Guofeng Cui, Shicheng Liu, Yuanlin Duan, He Zhu

Offline reinforcement learning (RL) holds the promise of training effective policies from static datasets without the need for costly online interactions. However, offline RL faces key limitations, most notably the challenge of generalizing to unseen or infrequently encountered state-action pairs. When a value function is learned from limited data in sparse-reward environments, it can become overly optimistic about parts of the space that are poorly represented, leading to unreliable value estimates and degraded policy quality. To address these challenges, we introduce a novel approach based on contrastive preference learning that bypasses direct value function estimation. Our method trains policies by contrasting successful demonstrations with failure behaviors present in the dataset, as well as synthetic behaviors generated outside the support of the dataset distribution. This contrastive formulation mitigates overestimation bias and improves robustness in offline learning. Empirical results on challenging sparse-reward offline RL benchmarks show that our method substantially outperforms existing state-of-the-art baselines in both learning efficiency and final performance.

Optimization · Zero-order and Black-box Optimization

Shaocong Ma, Heng Huang

In this paper, we study Riemannian zeroth-order optimization in settings where the underlying Riemannian metric $g$ is geodesically incomplete, and the goal is to approximate stationary points with respect to this incomplete metric. To address this challenge, we construct structure-preserving metrics that are geodesically complete while ensuring that every stationary point under the new metric remains stationary under the original one. Building on this foundation, we revisit the classical symmetric two-point zeroth-order estimator and analyze its mean-squared error from an intrinsic perspective, depending only on the manifold’s geometry rather than any ambient embedding. Leveraging this intrinsic analysis, we establish convergence guarantees for stochastic gradient descent (SGD) with this intrinsic estimator. Under additional suitable conditions, an $\epsilon$-stationary point under the constructed metric $g'$ also corresponds to an $\epsilon$-stationary point under the original metric $g$, thereby matching the best-known complexity in the geodesically complete setting. Empirical studies on synthetic problems confirm our theoretical findings, and experiments on a practical mesh optimization task demonstrate that our framework maintains stable convergence even in the absence of geodesic completeness.