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2,546篇论文匹配“Everything Else”
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Reinforcement Learning · Everything Else

Xiangyan Liu, Jinjie Ni, Zijian Wu, Chao Du, Longxu Dou, Haonan Wang, Tianyu Pang, Michael Qizhe Shieh

Recent advances in reinforcement learning (RL) have strengthened the reasoning capabilities of vision-language models (VLMs). However, enhancing policy exploration to better scale test-time compute remains largely underexplored. In addition, VLMs continue to struggle with imperfect visual perception, which in turn affects the subsequent reasoning process. To this end, we propose **NoisyRollout**, a simple yet effective data augmentation method that mixes trajectories from both clean and moderately distorted images during RL training. By injecting targeted diversity in visual perception and the resulting reasoning patterns, NoisyRollout promotes better policy exploration through vision-oriented inductive biases, ultimately leading to more robust reasoning behaviors. We further adopt a noise annealing schedule that gradually reduces distortion strength over training, leveraging noisy signals early on while ensuring training stability in later stages. Crucially, our method is easy-to-adopt—**requiring no additional training cost and no modifications to the RL objective**. Extensive experiments on $2$ distinct training datasets demonstrate that NoisyRollout achieves state-of-the-art performance among open-source RL-tuned models across $5$ out-of-domain reasoning and perception benchmarks. Furthermore, we validate the effectiveness of NoisyRollout across model sizes ($7$B and $32$B) and data scales (from $1$K to $6$K), highlighting its generalizability and scalability.

Applications · Everything Else

Xingbo Du, Ruizhe Zhong, Junchi Yan

Rectilinear Steiner Minimum Tree (RSMT) is widely used in Very Large Scale Integration (VLSI) and aims at connecting a set of pins using rectilinear edges while minimizing wirelength. Recently, learning-based methods have been explored to tackle this problem effectively. However, existing methods either suffer from excessive exploration of the search space or rely on heuristic combinations that compromise effectiveness and efficiency, and this limitation becomes notably exacerbated when extended to the obstacle-avoiding RSMT (OARSMT). To address this, we propose OAREST, a reinforcement learning-based framework for constructing an Obstacle-Avoiding Rectilinear Edge Sequence (RES) Tree. We theoretically establish the optimality of RES in obstacle-avoiding scenarios, which forms the foundation of our approach. Leveraging this theoretical insight, we introduce a dynamic masking strategy that supports parallel training across varying numbers of pins and extends to obstacles during inference. Empirical evaluations on both synthetic and real-world benchmarks show superior effectiveness and efficiency for RSMT and OARSMT problems, particularly in handling obstacles without training on them. Code available: https://github.com/Thinklab-SJTU/EDA-AI/.

Deep Learning · Everything Else

Zhongwei Yu, Wannian Xia, Xue Yan, Bo Xu, Haifeng Zhang, Yali Du, Jun Wang

Advanced large language models (LLMs) frequently reflect in reasoning chain-of-thoughts (CoTs), where they self-verify the correctness of current solutions and explore alternatives. However, given recent findings that LLMs detect limited errors in CoTs, how reflection contributes to empirical improvements remains unclear. To analyze this issue, in this paper, we present a minimalistic reasoning framework to support basic self-verifying reflection for small transformers without natural language, which ensures analytic clarity and reduces the cost of comprehensive experiments. Theoretically, we prove that self-verifying reflection guarantees improvements if verification errors are properly bounded. Experimentally, we show that tiny transformers, with only a few million parameters, benefit from self-verification in both training and reflective execution, reaching remarkable LLM-level performance in integer multiplication and Sudoku. Similar to LLM results, we find that reinforcement learning (RL) improves in-distribution performance and incentivizes frequent reflection for tiny transformers, yet RL mainly optimizes shallow statistical patterns without faithfully reducing verification errors. In conclusion, integrating generative transformers with discriminative verification inherently facilitates CoT reasoning, regardless of scaling and natural language.

Probabilistic Methods · Everything Else

Yinxu Tang, Stylianos Loukas Vasileiou, Vincent Derkinderen, William Yeoh

In human-AI interaction, effective communication relies on aligning the AI agent’s model with the human user’s mental model -- a process known as model reconciliation. However, existing model reconciliation approaches predominantly assume deterministic models, overlooking the fact that human knowledge is often uncertain or probabilistic. To bridge this gap, we present a probabilistic model reconciliation framework that resolves inconsistencies in MPE outcome probabilities between an agent’s and a user’s models. Our approach is built on probabilistic logic programming (PLP) using ProbLog, where explanations are generated as cost-optimal model updates that reconcile these probabilistic differences. We develop two search algorithms - a generic baseline and an optimized version. The latter is guided by theoretical insights and further extended with greedy and weighted variants to enhance scalability and efficiency. Our approach is validated through a user study on explanation types and computational experiments showing that the optimized version consistently outperforms the generic baseline.

Social Aspects · Everything Else

Jakob de Raaij, Ariel Procaccia, Alexandros Psomas

A panel satisfies *descriptive representation* when its composition reflects the population. We examine the role of descriptive representation in collective decision making through an optimization lens, asking whether representative panels make decisions that maximize social welfare for the underlying population. Our main results suggest that, in general, representation with respect to *intersections* of two or more features guarantees higher social welfare than that achieved by the status quo of proportionally representing individual features. Moreover, an analysis of real data suggests that representation with respect to pairs of features is feasible in practice. These results have significant implications for the design of *citizens' assemblies*, which are gaining prominence in AI governance.

Theory · Everything Else

Kevin Aydin, Honghao Lin, David Woodruff, Peilin Zhong

$k$-anonymity is a widely-used privacy-preserving concept that ensures each record in a dataset is indistinguishable from at least $k-1$ other records. In this paper, we revisit $k$-anonymity by suppression and give an $O(k)$-approximation algorithm with a nearly-linear runtime of $\tilde{O}(nd + n^{1+1/C^2}/k^{1/C^2})$ for an arbitrary constant $C$, where $n$ is the number of records and $d$ is the number of attributes. Previous algorithms with provable guarantees either (1) achieve the same $O(k)$ approximation ratio but require at least $O(n^2 k)$ runtime, or (2) provide a better $O(\log k)$ approximation ratio at the cost of an impractical $O(n^{2k})$ worst-case runtime for general $d$ and $k$. Our algorithm extends to the Massively Parallel Computation (MPC) model, where it can be adapted into an MPC algorithm requiring $\tilde{O}(\log^{1+\epsilon} n)$ rounds and total space $O(n^{1+1/C^2}(d+k))$. Empirically, we also demonstrate that our algorithmic ideas can be adapted to existing heuristic methods, leading to significant speed-ups while preserving comparable performance. Although~\citep{PS07} introduced improvements to achieve more practical runtimes for their $O(\log k)$-approximation algorithm, its worst-case runtime remains $O(n^{2k})$. A natural question arises: can we develop an algorithm with an $o(k)$ approximation ratio and a polynomial runtime? We investigate the single-point $k$-anonymity problem, where the goal is to select $k-1$ additional records to make a given record indistinguishable. Surprisingly, assuming the dense vs random conjecture in complexity theory, we show that for $n = k^c$, no algorithm can achieve a $k^{1 - O(1/c)}$ approximation in $\mathrm{poly}(k)$ time. This provides evidence of the inherent hardness of the $k$-anonymity problem.

Deep Learning · Everything Else

Annan Yu, N. Benjamin Erichson

Mamba extends earlier state space models (SSMs) by introducing input-dependent dynamics, and has demonstrated strong empirical performance across a range of domains, including language modeling, computer vision, and foundation models. However, a surprising weakness remains: despite being built on architectures designed for long-range dependencies, Mamba performs poorly on long-range sequential tasks. Understanding and addressing this gap is important for improving Mamba's universality and versatility. In this work, we analyze Mamba’s limitations through three perspectives: expressiveness, inductive bias, and training stability. Our theoretical results show how Mamba falls short in each of these aspects compared to earlier SSMs such as S4D. To address these issues, we propose $\text{B}\_{2}\text{S}\_{6}$, a simple extension of Mamba's S6 unit that combines block-wise selective dynamics with a channel-specific bias. We prove that these changes equip the model with a better-suited inductive bias and improve its expressiveness and stability. Empirically, $\text{B}\_{2}\text{S}\_{6}$ outperforms S4 and S4D on Long-Range Arena (LRA) tasks while maintaining Mamba's performance on language modeling benchmarks.

General Machine Learning · Everything Else

En Yu, Jie Lu, Xiaoyu Yang, Guangquan Zhang, Zhen Fang

Modern machine learning models struggle to maintain performance in dynamic environments where temporal distribution shifts, \textit{i.e., concept drift}, are prevalent. Temporal Domain Generalization (TDG) seeks to enable model generalization across evolving domains, yet existing approaches typically assume smooth incremental changes, struggling with complex real-world drifts involving both long-term structure (incremental evolution/periodicity) and local uncertainties. To overcome these limitations, we introduce FreKoo, which tackles these challenges through a novel frequency-domain analysis of parameter trajectories. It leverages the Fourier transform to disentangle parameter evolution into distinct spectral bands. Specifically, the low-frequency components with dominant dynamics are learned and extrapolated using the Koopman operator, robustly capturing diverse drift patterns including both incremental and periodic drifts. Simultaneously, potentially disruptive high-frequency variations are smoothed via targeted temporal regularization, preventing overfitting to transient noise and domain uncertainties. In addition, this dual-spectral strategy is rigorously grounded through theoretical analysis, providing stability guarantees for the Koopman prediction, a principled Bayesian justification for the high-frequency regularization, and culminating in a multiscale generalization bound connecting spectral dynamics to improved generalization. Extensive experiments demonstrate FreKoo's significant superiority over state-of-the-art TDG methods, particularly excelling in real-world streaming scenarios with complex drifts and uncertainties.

Deep Learning · Everything Else

Yinuo Jiang, Yan Xiaodong, Keyan Ding, Deng Zhao, Lei Liang, Qiang Zhang, Huajun Chen

Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, have enabled the efficient adaptation of large language models (LLMs) by updating only a small subset of parameters. However, their robustness under out-of-distribution (OOD) conditions remains insufficiently studied. In this paper, we identify the limitations of conventional LoRA in handling distributional shifts and propose $\textbf{HiMoLE}$($\textbf{Hi}$erarchical $\textbf{M}$ixture of $\textbf{L}$oRA $\textbf{E}$xperts), a new framework designed to improve OOD generalization. HiMoLE integrates hierarchical expert modules and hierarchical routing strategies into the LoRA architecture and introduces a two-phase training procedure enhanced by a diversity-driven loss. This design mitigates negative transfer and promotes effective knowledge adaptation across diverse data distributions. We evaluate HiMoLE on three representative tasks in natural language processing. Experimental results evidence that HiMoLE consistently outperforms existing LoRA-based approaches, significantly reducing performance degradation on OOD data while improving in-distribution performance. Our work bridges the gap between parameter efficiency and distributional robustness, advancing the practical deployment of LLMs in real-world applications.

Computer Vision · Everything Else

Changhan Liu, xunzhi xiang, Zixuan Duan, Wenbin Li, Qi Fan, Yang Gao

Cross-Domain Few-Shot Object Detection (CD-FSOD) aims to generalize to unseen domains by leveraging a few annotated samples of the target domain, requiring models to exhibit both strong generalization and localization capabilities. However, existing well-trained detectors typically have strong localization capabilities but lack generalization, whereas vision foundation models (VFMs) generally exhibit better generalization but lack accurate localization capabilities. In this paper, we propose a novel Mixture-of-Experts (MoE) structure that integrates the detector's localization capability and the VFM's generalization by using VFM features to improve detector features. Specifically, we propose Expert-wise Router (ER) that selects the most relevant VFM experts for each backbone layer, and Region-wise Router (RR) that emphasizes foreground and suppress background. To bridge representation gaps, we further propose Shared Expert Projection (SEP) module and Private Expert Projection (PEP) module, which align VFM features to the detector feature space while decoupling shared image feature from private image feature in the VFM feature map. Finally, we propose MoE module to transfer the VFM’s generalization to the detector without altering the detector original architecture. Furthermore, our method extend well-trained detectors for detecting novel classes in unseen domains without re-training on the base classes. Experimental results on multiple cross-domain datasets validate the effectiveness of our method.

Reinforcement Learning · Everything Else

Muzhi Dai, Chenxu Yang, Qingyi Si

As Test-Time Scaling emerges as an active research focus in the large language model community, advanced post-training methods increasingly emphasize extending chain-of-thought (CoT) generation length, thereby enhancing reasoning capabilities to approach Deepseek R1-like reasoning models. However, recent studies reveal that reasoning models (even Qwen3) consistently exhibit excessive thought redundancy in CoT generation. This overthinking issue arises from the inherent limitations of conventional outcome-reward reinforcement learning, which systematically overlooks the regulation of intermediate reasoning processes. This paper introduces Serial-Group Decaying-Reward Policy Optimization (S-GRPO), a novel reinforcement learning paradigm that enables models to implicitly evaluate the sufficiency of intermediate reasoning steps, thereby facilitating early exit in CoT generation. Unlike GRPO, which samples multiple possible reasoning paths in parallel (parallel group), S-GRPO only samples one reasoning path and serially selects multiple temporal positions from the path to exit thinking and directly generate answers (serial group). For correct answers within a serial group, rewards gradually decrease based on the exit positions along the reasoning path from front to back. This design encourages the model to produce more accurate and concise thoughts, while also incentivizing early thinking termination when appropriate. Empirical evaluations demonstrate that S-GRPO is compatible with state-of-the-art reasoning models, including Qwen3 and Deepseek-distill. Across diverse benchmarks such as GSM8K, AIME 2024, AMC 2023, MATH-500, and GPQA Diamond, S-GRPO achieves a substantial reduction in sequence length (40.4%~61.1%) while simultaneously improving accuracy (absolute 0.72%~3.92%).

Computer Vision · Everything Else

Karthikeyan Chandra Sekaran, Markus Geisler, Dominik Rößle, Adithya Mohan, Daniel Cremers, Wolfgang Utschick, Michael Botsch, Werner Huber, Torsten Schön

Recent cooperative perception datasets have played a crucial role in advancing smart mobility applications by enabling information exchange between intelligent agents, helping to overcome challenges such as occlusions and improving overall scene understanding. While some existing real-world datasets incorporate both vehicle-to-vehicle and vehicle-to-infrastructure interactions, they are typically limited to a single intersection or a single vehicle. A comprehensive perception dataset featuring multiple connected vehicles and infrastructure sensors across several intersections remains unavailable, limiting the benchmarking of algorithms in diverse traffic environments. Consequently, overfitting can occur, and models may demonstrate misleadingly high performance due to similar intersection layouts and traffic participant behavior. To address this gap, we introduce UrbanIng-V2X, the first large-scale, multi-modal dataset supporting cooperative perception involving vehicles and infrastructure sensors deployed across three urban intersections in Ingolstadt, Germany. UrbanIng-V2X consists of 34 temporally aligned and spatially calibrated sensor sequences, each lasting 20 seconds. All sequences contain recordings from one of three intersections, involving two vehicles and up to three infrastructure-mounted sensor poles operating in coordinated scenarios. In total, UrbanIng-V2X provides data from 12 vehicle-mounted RGB cameras, 2 vehicle LiDARs, 17 infrastructure thermal cameras, and 12 infrastructure LiDARs. All sequences are annotated at a frequency of 10 Hz with 3D bounding boxes spanning 13 object classes, resulting in approximately 712k annotated instances across the dataset. We provide comprehensive evaluations using state-of-the-art cooperative perception methods and publicly release the codebase, dataset, HD map, and a digital twin of the complete data collection environment via https://github.com/thi-ad/UrbanIng-V2X.

Reinforcement Learning · Everything Else

Sangkyu Lee, Janghoon Han, Hosung Song, Stanley Jungkyu Choi, Honglak Lee, Youngjae Yu

Direct Preference Optimization (DPO) demonstrates the advantage of aligning a large language model with human preference using only an offline dataset. However, DPO has the limitation that the KL penalty, which prevents excessive deviation from the reference model, is static throughout the training process. Several methods claim to change this static KL penalty of DPO into a dynamic one, but no approach can adaptively assign different KL penalties for each preference pair. In this paper, we propose $\varepsilon$-Direct Preference Optimization ($\varepsilon$-DPO), which allows adaptive control of the KL penalty strength $\beta$ for each preference pair. Specifically, $\varepsilon$-DPO adaptively controls $\beta$ for each preference pair based on the monotonicity of logits as a preference model under the perturbation of $\beta$ during training. This is equivalent to adjusting the KL penalty by checking whether the change in training-time temperature can lead to better preference confidence as preference models by simply reusing the logit of the current policy and the reference policy. Experimental results show that the simple criterion of $\varepsilon$-DPO for KL penalty relaxation significantly improves DPO compared to most existing direct alignment algorithms on general chatbot benchmarks and reveal that this KL penalty control criterion can reflect confusion as a preference model and provide an efficient KL trade-off, highlighting the significance of instance-level adaptive KL penalty control in DPO.

Deep Learning · Everything Else

Reece Shuttleworth, Jacob Andreas, Antonio Torralba, Pratyusha Sharma

Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to effectively fine-tune LLMs with an extreme reduction in trainable parameters. But, \emph{are their learned solutions really equivalent?} We study how LoRA and full-finetuning change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that LoRA and full fine-tuning yield weight matrices whose singular value decompositions exhibit very different structure: weight matrices trained with LoRA have new, high-ranking singular vectors, which we call \emph{intruder dimensions}, while those trained with full fine-tuning do not. Further, we extend the finding that LoRA forgets less than full fine-tuning and find its forgetting is vastly localized to the intruder dimension -- by causally intervening on the intruder dimensions by changing their associated singular values post-fine-tuning, we show that they cause forgetting. Moreover, scaling them down significantly improves modeling of the pre-training distribution with a minimal drop in downstream task performance. Given this, we should expect accumulating intruder dimensions to be harmful and lead to more forgetting. This will be amplified during continual learning because of sequentially fine-tuning, and we show that LoRA models do accumulate intruder dimensions here tend to perform worse in this setting, emphasizing the practicality of our findings.

Deep Learning · Everything Else

Yiyang Gu, Bohan Wu, Qinghua Ran, Rong-Cheng Tu, Xiao Luo, Zhiping Xiao, Wei Ju, Dacheng Tao, Ming Zhang

This paper studies the problem of learning hash codes from noisy supervision, which is a practical yet challenging task. This problem is important in extensive real-world applications such as image retrieval and cross-modal retrieval. However, most of the existing methods focus on label denoising to address this problem, but ignore the geometric structure of the hash space, which is critical for learning stable hash codes. Towards this end, this paper proposes a novel framework named Semantic Geometry Shaping (SEGA) that explicitly refines the semantic geometry of hash space. Specifically, we first learn dynamic class prototypes as semantic anchors and cluster hash embeddings around these prototypes to keep structural stability. We then leverage both the energy of predicted distributions and structure-based divergence to estimate the uncertainty of instances and calibrate the supervision in a soft manner. Moreover, we introduce structure-aware interpolation to improve the class boundaries. To verify the effectiveness of our design, we give the theoretical analysis for the proposed framework. Experiments on a range of widely-used retrieval datasets justify the superiority of our SEGA over extensive strong baselines under noisy supervision.

Computer Vision · Everything Else

Yuan Wu, Zhiqiang Yan, Yigong Zhang, Xiang Li, Jian Yang

Occupancy prediction aims to estimate the 3D spatial distribution of occupied regions along with their corresponding semantic labels. Existing vision-based methods perform well on daytime benchmarks but struggle in nighttime scenarios due to limited visibility and challenging lighting conditions. To address these challenges, we propose LIAR, a novel framework that learns illumination-affined representations. LIAR first introduces Selective Low-light Image Enhancement (SLLIE), which leverages the illumination priors from daytime scenes to adaptively determine whether a nighttime image is genuinely dark or sufficiently well-lit, enabling more targeted global enhancement. Building on the illumination maps generated by SLLIE, LIAR further incorporates two illumination-aware components: 2D Illumination-guided Sampling (2D-IGS) and 3D Illumination-driven Projection (3D-IDP), to respectively tackle local underexposure and overexposure. Specifically, 2D-IGS modulates feature sampling positions according to illumination maps, assigning larger offsets to darker regions and smaller ones to brighter regions, thereby alleviating feature degradation in underexposed areas. Subsequently, 3D-IDP enhances semantic understanding in overexposed regions by constructing illumination intensity fields and supplying refined residual queries to the BEV context refinement process. Extensive experiments on both real and synthetic datasets demonstrate the superior performance of LIAR under challenging nighttime scenarios. The source code and pretrained models are available [here](https://github.com/yanzq95/LIAR).

Probabilistic Methods · Everything Else

Wen-Bo Du, Tian Qin, Tian-Zuo Wang, Zhi-Hua Zhou

In machine learning, a critical class of decision-making problems involves *Avoiding Undesired Future* (AUF): given a predicted undesired outcome, how can one make decision about actions to prevent it? Recently, the *rehearsal learning* framework has been proposed to address AUF problem. While existing methods offer reliable decisions for single-round success, this paper considers long-term settings that involve coordinating multiple future outcomes, which is often required in real-world tasks. Specifically, we generalize the AUF objective to characterize a long-term decision target that incorporates cross-temporal relations among variables. As directly optimizing the *AUF probability* $\mathbb{P}_{\operatorname{AUF}}$ over this objective remains challenging, we derive an explicit expression for the objective and further propose a quadratic programming (QP) reformulation that transforms the intractable probabilistic AUF optimization into a tractable one. Under mild assumptions, we show that solutions to the QP reformulation are equivalent to those of the original AUF optimization, based on which we develop two novel rehearsal learning methods for long-term decision-making: (i) a *greedy* method that maximizes the single-round $\mathbb{P}_{\operatorname{AUF}}$ at each step, and (ii) a *far-sighted* method that accounts for future consequences in each decision, yielding a higher overall $\mathbb{P}_{\operatorname{AUF}}$ through an $L/(L+1)$ variance reduction in the AUF objective. We further establish an $\mathcal{O}(1/\sqrt{N})$ excess risk bound for decisions based on estimated parameters, ensuring reliable practical applicability with finite data. Experiments validate the effectiveness of our approach.

Applications · Everything Else

Jinouwen Zhang, Junjie Ren, Ma Qianhong, Jianyu Wu, Aobo Yang, Yan Lu, Lu Chen, Hairun Xie, Jing Wang, Miao Zhang 等

Aircraft manufacturing is the jewel in the crown of industry, in which generating high-fidelity airfoil geometries with controllable and editable representations remains a fundamental challenge. Existing deep learning methods, which typically rely on predefined parametric representations (e.g., Bézier curves) or discrete point sets, face an inherent trade-off between expressive power and resolution adaptability. To tackle this challenge, we introduce FuncGenFoil, a novel function-space generative model that directly reconstructs airfoil geometries as function curves. Our method inherits the advantages of arbitrary-resolution sampling and smoothness from parametric functions, as well as the strong expressiveness of discrete point-based representations. Empirical evaluations demonstrate that FuncGenFoil improves upon state-of-the-art methods in airfoil generation, achieving a relative 74.4% reduction in label error and a 23.2% increase in diversity on the AF-200K dataset. Our results highlight the advantages of function-space modeling for aerodynamic shape optimization, offering a powerful and flexible framework for high-fidelity airfoil design.

Computer Vision · Everything Else

Hyunjin Kim, Kunho Kim, Adam Lee, Wonkwang Lee

We present GOATex, a diffusion-based method for 3D mesh texturing that generates high-quality textures for both exterior and interior surfaces. While existing methods perform well on visible regions, they inherently lack mechanisms to handle occluded interiors, resulting in incomplete textures and visible seams. To address this, we introduce an occlusion-aware texturing framework based on the concept of hit levels, which quantify the relative depth of mesh faces via multi-view ray casting. This allows us to partition mesh faces into ordered visibility layers, from outermost to innermost. We then apply a two-stage visibility control strategy that progressively reveals interior regions with structural coherence, followed by texturing each layer using a pretrained diffusion model. To seamlessly merge textures obtained across layers, we propose a soft UV-space blending technique that weighs each texture’s contribution based on view-dependent visibility confidence. Empirical results demonstrate that GOATex consistently outperforms existing methods, producing seamless, high-fidelity textures across both visible and occluded surfaces. Unlike prior works, GOATex operates entirely without costly fine-tuning of a pretrained diffusion model and allows separate prompting for exterior and interior mesh regions, enabling fine-grained control over layered appearances.

Theory · Everything Else

Beatrice Bertolotti, Matteo Russo, Chris Schwiegelshohn, Sudarshan Shyam

We study the sublinear multivariate mean estimation problem in $d$-dimensional Euclidean space. Specifically, we aim to find the mean $\mu$ of a ground point set $A$, which minimizes the sum of squared Euclidean distances of the points in $A$ to $\mu$. We first show that a multiplicative $(1+\varepsilon)$ approximation to $\mu$ can be found with probability $1-\delta$ using $O(\varepsilon^{-1}\log \delta^{-1})$ many independent uniform random samples, and provide a matching lower bound. Furthermore, we give two estimators with optimal sample complexity that can be computed in optimal running time for extracting a suitable approximate mean: 1. The coordinate-wise median of $\log \delta^{-1}$ sample means of sample size $\varepsilon^{-1}$. As a corollary, we also show improved convergence rates for this estimator for estimating means of multivariate distributions. 2. The geometric median of $\log \delta^{-1}$ sample means of sample size $\varepsilon^{-1}$. To compute a solution efficiently, we design a novel and simple gradient descent algorithm that is significantly faster for our specific setting than all other known algorithms for computing geometric medians. In addition, we propose an order statistics approach that is empirically competitive with these algorithms, has an optimal sample complexity and matches the running time up to lower order terms. We finally provide an extensive experimental evaluation among several estimators which concludes that the geometric-median-of-means-based approach is typically the most competitive in practice.