NeurIPS 2024 Papers

Conference on Neural Information Processing Systems

Decision breakdown

4,562papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    721.6%
  • Spotlight
    3828.4%
  • Poster
    4,06489.1%
  • Other / unlabeled
    441.0%

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Who Evaluates the Evaluations? Objectively Scoring Text-to-Image Prompt Coherence Metrics with T2IScoreScore (TS2)

Michael Saxon, Fatima Jahara, Mahsa Khoshnoodi, Yujie Lu, Aditya Sharma, William Yang Wang

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With advances in the quality of text-to-image (T2I) models has come interest in benchmarking their prompt faithfulness---the semantic coherence of generated images to the prompts they were conditioned on. A variety of T2I faithfulness metrics have been proposed, leveraging advances in cross-modal embeddings and vision-language models (VLMs). However, these metrics are not rigorously compared and benchmarked, instead presented with correlation to human Likert scores over a set of easy-to-discriminate images against seemingly weak baselines. We introduce T2IScoreScore, a curated set of semantic error graphs containing a prompt and a set of increasingly erroneous images. These allow us to rigorously judge whether a given prompt faithfulness metric can correctly order images with respect to their objective error count and significantly discriminate between different error nodes, using meta-metric scores derived from established statistical tests. Surprisingly, we find that the state-of-the-art VLM-based metrics (e.g., TIFA, DSG, LLMScore, VIEScore) we tested fail to significantly outperform simple (and supposedly worse) feature-based metrics like CLIPScore, particularly on a hard subset of naturally-occurring T2I model errors. TS2 will enable the development of better T2I prompt faithfulness metrics through more rigorous comparison of their conformity to expected orderings and separations under objective criteria.

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Sample Complexity Reduction via Policy Difference Estimation in Tabular Reinforcement Learning

Adhyyan Narang, Andrew Wagenmaker, Lillian J. Ratliff, Kevin Jamieson

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In this paper, we study the non-asymptotic sample complexity for the pure exploration problem in contextual bandits and tabular reinforcement learning (RL): identifying an $\epsilon$-optimal policy from a set of policies $\Pi$ with high probability. Existing work in bandits has shown that it is possible to identify the best policy by estimating only the *difference* between the behaviors of individual policies–which can have substantially lower variance than estimating the behavior of each policy directly—yet the best-known complexities in RL fail to take advantage of this, and instead estimate the behavior of each policy directly. Does it suffice to estimate only the differences in the behaviors of policies in RL? We answer this question positively for contextual bandits, but in the negative for tabular RL, showing a separation between contextual bandits and RL. However, inspired by this, we show that it *almost* suffices to estimate only the differences in RL: if we can estimate the behavior of a *single* reference policy, it suffices to only estimate how any other policy deviates from this reference policy. We develop an algorithm which instantiates this principle and obtains, to the best of our knowledge, the tightest known bound on the sample complexity of tabular RL.

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Non-Asymptotic Uncertainty Quantification in High-Dimensional Learning

Frederik Hoppe, Claudio Mayrink Verdun, Hannah Laus, Felix Krahmer, Holger Rauhut

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Uncertainty quantification (UQ) is a crucial but challenging task in many high-dimensional learning problems to increase the confidence of a given predictor. We develop a new data-driven approach for UQ in regression that applies both to classical optimization approaches such as the LASSO as well as to neural networks. One of the most notable UQ techniques is the debiased LASSO, which modifies the LASSO to allow for the construction of asymptotic confidence intervals by decomposing the estimation error into a Gaussian and an asymptotically vanishing bias component. However, in real-world problems with finite-dimensional data, the bias term is often too significant to disregard, resulting in overly narrow confidence intervals. Our work rigorously addresses this issue and derives a data-driven adjustment that corrects the confidence intervals for a large class of predictors by estimating the means and variances of the bias terms from training data, exploiting high-dimensional concentration phenomena. This gives rise to non-asymptotic confidence intervals, which can help avoid overestimating certainty in critical applications such as MRI diagnosis. Importantly, our analysis extends beyond sparse regression to data-driven predictors like neural networks, enhancing the reliability of model-based deep learning. Our findings bridge the gap between established theory and the practical applicability of such methods.

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Gradients of Functions of Large Matrices

Nicholas Krämer, Pablo Moreno-Muñoz, Hrittik Roy, Søren Hauberg

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Tuning scientific and probabilistic machine learning models - for example, partial differential equations, Gaussian processes, or Bayesian neural networks - often relies on evaluating functions of matrices whose size grows with the data set or the number of parameters. While the state-of-the-art for _evaluating_ these quantities is almost always based on Lanczos and Arnoldi iterations, the present work is the first to explain how to _differentiate_ these workhorses of numerical linear algebra efficiently. To get there, we derive previously unknown adjoint systems for Lanczos and Arnoldi iterations, implement them in JAX, and show that the resulting code can compete with Diffrax when it comes to differentiating PDEs, GPyTorch for selecting Gaussian process models and beats standard factorisation methods for calibrating Bayesian neural networks. All this is achieved without any problem-specific code optimisation. Find the code at [link redacted] and install the library with *pip install [redacted]*.

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A Careful Examination of Large Language Model Performance on Grade School Arithmetic

Hugh Zhang, Jeff Da, Dean Lee, Vaughn Robinson, Catherine Wu, William Song, Tiffany Zhao, Pranav Vishnu Raja, Charlotte Zhuang, Dylan Z Slack, Qin Lyu, Sean M. Hendryx, Russell Kaplan, Michele Lunati, Summer Yue

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Large language models (LLMs) have achieved impressive success on many benchmarks for mathematical reasoning. However, there is growing concern that some of this performance actually reflects dataset contamination, where data closely resembling benchmark questions leaks into the training data, instead of true reasoning ability. To investigate this claim rigorously, we commission Grade School Math 1000 (GSM1k). GSM1k is designed to mirror the style and complexity of the established GSM8k benchmark, the gold standard for measuring elementary mathematical reasoning. We ensure that the two benchmarks are comparable across important metrics such as human solve rates, number of steps in solution, answer magnitude, and more. When evaluating leading open- and closed-source LLMs on GSM1k, we observe accuracy drops of up to 8%, with several families of models showing evidence of systematic overfitting across almost all model sizes. Further analysis suggests a positive relationship (Spearman's r^2=0.36) between a model's probability of generating an example from GSM8k and its performance gap between GSM8k and GSM1k, suggesting that some models may have partially memorized GSM8k. Nevertheless, many models, especially those on the frontier, show minimal signs of overfitting, and all models broadly demonstrate generalization to novel math problems guaranteed to not be in their training data.

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Spider2-V: How Far Are Multimodal Agents From Automating Data Science and Engineering Workflows?

Ruisheng Cao, Fangyu Lei, Haoyuan Wu, Jixuan Chen, Yeqiao Fu, Hongcheng Gao, Xiong Xinzhuang, Hanchong Zhang, Wenjing Hu, Yuchen Mao, Tianbao Xie, Hongshen Xu, Danyang Zhang, Sida Wang, Ruoxi Sun, Pengcheng Yin, Caiming Xiong, Ansong Ni, Qian Liu, Victor Zhong, Lu Chen, Kai Yu, Tao Yu

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Data science and engineering workflows often span multiple stages, from warehousing to orchestration, using tools like BigQuery, dbt, and Airbyte. As vision language models (VLMs) advance in multimodal understanding and code generation, VLM-based agents could potentially automate these workflows by generating SQL queries, Python code, and GUI operations. This automation can improve the productivity of experts while democratizing access to large-scale data analysis. In this paper, we introduce Spider2-V, the first multimodal agent benchmark focusing on professional data science and engineering workflows, featuring 494 real-world tasks in authentic computer environments and incorporating 20 enterprise-level professional applications. These tasks, derived from real-world use cases, evaluate the ability of a multimodal agent to perform data-related tasks by writing code and managing the GUI in enterprise data software systems. To balance realistic simulation with evaluation simplicity, we devote significant effort to developing automatic configurations for task setup and carefully crafting evaluation metrics for each task. Furthermore, we supplement multimodal agents with comprehensive documents of these enterprise data software systems. Our empirical evaluation reveals that existing state-of-the-art LLM/VLM-based agents do not reliably automate full data workflows (14.0% success). Even with step-by-step guidance, these agents still underperform in tasks that require fine-grained, knowledge-intensive GUI actions (16.2%) and involve remote cloud-hosted workspaces (10.6%). We hope that Spider2-V paves the way for autonomous multimodal agents to transform the automation of data science and engineering workflow. Our code and data are available at https://spider2-v.github.io.

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Rethinking Exploration in Reinforcement Learning with Effective Metric-Based Exploration Bonus

Yiming Wang, Kaiyan Zhao, Furui Liu, Leong Hou U

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Enhancing exploration in reinforcement learning (RL) through the incorporation of intrinsic rewards, specifically by leveraging *state discrepancy* measures within various metric spaces as exploration bonuses, has emerged as a prevalent strategy to encourage agents to visit novel states. The critical factor lies in how to quantify the difference between adjacent states as *novelty* for promoting effective exploration. Nonetheless, existing methods that evaluate state discrepancy in the latent space under $L_1$ or $L_2$ norm often depend on count-based episodic terms as scaling factors for exploration bonuses, significantly limiting their scalability. Additionally, methods that utilize the bisimulation metric for evaluating state discrepancies face a theory-practice gap due to improper approximations in metric learning, particularly struggling with *hard exploration* tasks. To overcome these challenges, we introduce the **E**ffective **M**etric-based **E**xploration-bonus (EME). EME critically examines and addresses the inherent limitations and approximation inaccuracies of current metric-based state discrepancy methods for exploration, proposing a robust metric for state discrepancy evaluation backed by comprehensive theoretical analysis. Furthermore, we propose the diversity-enhanced scaling factor integrated into the exploration bonus to be dynamically adjusted by the variance of prediction from an ensemble of reward models, thereby enhancing exploration effectiveness in particularly challenging scenarios. Extensive experiments are conducted on hard exploration tasks within Atari games, Minigrid, Robosuite, and Habitat, which illustrate our method's scalability to various scenarios. The project website can be found at https://sites.google.com/view/effective-metric-exploration.

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Archaeoscape: Bringing Aerial Laser Scanning Archaeology to the Deep Learning Era

Yohann PERRON, Vladyslav Sydorov, Adam P. Wijker, Damian Evans, Christophe Pottier, Loic Landrieu

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Airborne Laser Scanning (ALS) technology has transformed modern archaeology by unveiling hidden landscapes beneath dense vegetation. However, the lack of expert-annotated, open-access resources has hindered the analysis of ALS data using advanced deep learning techniques. We address this limitation with Archaeoscape (available at https://archaeoscape.ai/data/2024), a novel large-scale archaeological ALS dataset spanning 888 km² in Cambodia with 31,141 annotated archaeological features from the Angkorian period. Archaeoscape is over four times larger than comparable datasets, and the first ALS archaeology resource with open-access data, annotations, and models. We benchmark several recent segmentation models to demonstrate the benefits of modern vision techniques for this problem and highlight the unique challenges of discovering subtle human-made structures under dense jungle canopies. By making Archaeoscape available in open access, we hope to bridge the gap between traditional archaeology and modern computer vision methods.

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Tetrahedron Splatting for 3D Generation

Chun Gu, Zeyu Yang, Zijie Pan, Xiatian Zhu, Li Zhang

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3D representation is essential to the significant advance of 3D generation with 2D diffusion priors. As a flexible representation, NeRF has been first adopted for 3D representation. With density-based volumetric rendering, it however suffers both intensive computational overhead and inaccurate mesh extraction. Using a signed distance field and Marching Tetrahedra, DMTet allows for precise mesh extraction and real-time rendering but is limited in handling large topological changes in meshes, leading to optimization challenges. Alternatively, 3D Gaussian Splatting (3DGS) is favored in both training and rendering efficiency while falling short in mesh extraction. In this work, we introduce a novel 3D representation, Tetrahedron Splatting (TeT-Splatting), that supports easy convergence during optimization, precise mesh extraction, and real-time rendering simultaneously. This is achieved by integrating surface-based volumetric rendering within a structured tetrahedral grid while preserving the desired ability of precise mesh extraction, and a tile-based differentiable tetrahedron rasterizer. Furthermore, we incorporate eikonal and normal consistency regularization terms for the signed distance field to improve generation quality and stability. Critically, our representation can be trained without mesh extraction, making the optimization process easier to converge. Our TeT-Splatting can be readily integrated in existing 3D generation pipelines, along with polygonal mesh for texture optimization. Extensive experiments show that our TeT-Splatting strikes a superior tradeoff among convergence speed, render efficiency, and mesh quality as compared to previous alternatives under varying 3D generation settings.

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Towards an Information Theoretic Framework of Context-Based Offline Meta-Reinforcement Learning

Lanqing Li, Hai Zhang, Xinyu Zhang, Shatong Zhu, Yang Yu, Junqiao Zhao, Pheng-Ann Heng

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As a marriage between offline RL and meta-RL, the advent of offline meta-reinforcement learning (OMRL) has shown great promise in enabling RL agents to multi-task and quickly adapt while acquiring knowledge safely. Among which, context-based OMRL (COMRL) as a popular paradigm, aims to learn a universal policy conditioned on effective task representations. In this work, by examining several key milestones in the field of COMRL, we propose to integrate these seemingly independent methodologies into a unified framework. Most importantly, we show that the pre-existing COMRL algorithms are essentially optimizing the same mutual information objective between the task variable $M$ and its latent representation $Z$ by implementing various approximate bounds. Such theoretical insight offers ample design freedom for novel algorithms. As demonstrations, we propose a supervised and a self-supervised implementation of $I(Z; M)$, and empirically show that the corresponding optimization algorithms exhibit remarkable generalization across a broad spectrum of RL benchmarks, context shift scenarios, data qualities and deep learning architectures. This work lays the information theoretic foundation for COMRL methods, leading to a better understanding of task representation learning in the context of reinforcement learning. Given its generality, we envision our framework as a promising offline pre-training paradigm of foundation models for decision making.

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ConvBench: A Multi-Turn Conversation Evaluation Benchmark with Hierarchical Ablation Capability for Large Vision-Language Models

Shuo Liu, Kaining Ying, Hao Zhang, Yue Yang, Yuqi Lin, Tianle Zhang, Chuanhao Li, Yu Qiao, Ping Luo, Wenqi Shao, Kaipeng Zhang

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Multi-turn visual conversation is an important ability of real-world AI assistants. However, the related evaluation benchmark is missed. This paper presents ConvBench, a multi-turn conversation benchmark with hierarchical capabilities ablation evaluation for Large Vision-Language Models (LVLMs). ConvBench comprises 577 curated multi-turn conversations, encompassing 215 tasks. These tasks are broad and open-ended, which resemble real-world user behaviors. ConvBench progressively examines the LVLMs' perception, reasoning, and creativity capabilities in each conversation and can decouple these capabilities in evaluations and thus perform reliable error attribution. Besides, considering the diversity of open-ended questions, we introduce an efficient and reliable automatic evaluation framework. Experimental results reveal that ConvBench is a significant challenge for current LVLMs, even for GPT4V, which achieves only a 39.51% score. Besides, we have some insightful findings, such as the weak perception of LVLMs inhibits authentic strengths in reasoning and creation. We believe our design of hierarchical capabilities, decoupling capabilities evaluation, and multi-turn conversation can blaze a new trail in LVLMs evaluation. Code and benchmark are released at https://github.com/shirlyliu64/ConvBench.

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Second-order forward-mode optimization of recurrent neural networks for neuroscience

Youjing Yu, Rui Xia, Qingxi Ma, Máté Lengyel, Guillaume Hennequin

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A common source of anxiety for the computational neuroscience student is the question “will my recurrent neural network (RNN) model finally learn that task?”. Unlike in machine learning where any architectural modification of an RNN (e.g. GRU or LSTM) is acceptable if it speeds up training, the RNN models trained as _models of brain dynamics_ are subject to plausibility constraints that fundamentally exclude the usual machine learning hacks. The “vanilla” RNNs commonly used in computational neuroscience find themselves plagued by ill-conditioned loss surfaces that complicate training and significantly hinder our capacity to investigate the brain dynamics underlying complex tasks. Moreover, some tasks may require very long time horizons which backpropagation cannot handle given typical GPU memory limits. Here, we develop SOFO, a second-order optimizer that efficiently navigates loss surfaces whilst _not_ requiring backpropagation. By relying instead on easily parallelized batched forward-mode differentiation, SOFO enjoys constant memory cost in time. Morever, unlike most second-order optimizers which involve inherently sequential operations, SOFO's effective use of GPU parallelism yields a per-iteration wallclock time essentially on par with first-order gradient-based optimizers. We show vastly superior performance compared to Adam on a number of RNN tasks, including a difficult double-reaching motor task and the learning of an adaptive Kalman filter algorithm trained over a long horizon.

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Algebraic Positional Encodings

Konstantinos Kogkalidis, Jean-Philippe Bernardy, Vikas Garg

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We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework implements a flexible mapping from the algebraic specification of a domain to a positional encoding scheme where positions are interpreted as orthogonal operators. This design preserves the structural properties of the source domain, thereby ensuring that the end-model upholds them. The framework can accommodate various structures, including sequences, grids and trees, but also their compositions. We conduct a series of experiments demonstrating the practical applicability of our method. Our results suggest performance on par with or surpassing the current state of the art, without hyper-parameter optimizations or ``task search'' of any kind. Code is available through https://aalto-quml.github.io/ape/.

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Scaling Proprioceptive-Visual Learning with Heterogeneous Pre-trained Transformers

Lirui Wang, Xinlei Chen, Jialiang Zhao, Kaiming He

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One of the roadblocks for training generalist robotic models today is heterogeneity. Previous robot learning methods often collect data to train with one specific embodiment for one task, which is expensive and prone to overfitting. This work studies the problem of learning policy representations through heterogeneous pre-training on robot data across different embodiments and tasks at scale. We propose Heterogeneous Pre-trained Transformers (HPT), which pre-train a large, shareable trunk of a policy neural network to learn a task and embodiment agnostic shared representation. This general architecture aligns the specific proprioception and vision inputs from distinct embodiments to a short sequence of tokens and then processes such tokens to map to control robots for different tasks. Leveraging the recent large-scale multi-embodiment real-world robotic datasets as well as simulation, deployed robots, and human video datasets, we investigate pre-training policies across heterogeneity. We conduct experiments to investigate the scaling behaviors of training objectives, to the extent of 52 datasets. HPTs outperform several baselines and enhance the fine-tuned policy performance by over 20% on unseen tasks in multiple simulator benchmarks and real-world settings. See the project website (liruiw.github.io/hpt) for code and videos.

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DreamCatcher: A Wearer-aware Multi-modal Sleep Event Dataset Based on Earables in Non-restrictive Environments

Zeyu Wang, Xiyuxing Zhang, Ruotong Yu, Yuntao Wang, Kenneth Christofferson, Jingru Zhang, Alex Mariakakis, Yuanchun Shi

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Poor quality sleep can be characterized by the occurrence of events ranging from body movement to breathing impairment. Widely available earbuds equipped with sensors (also known as earables) can be combined with a sleep event detection algorithm to offer a convenient alternative to laborious clinical tests for individuals suffering from sleep disorders. Although various solutions utilizing such devices have been proposed to detect sleep events, they ignore the fact that individuals often share sleeping spaces with roommates or couples. To address this issue, we introduce DreamCatcher, the first publicly available dataset for wearer-aware sleep event algorithm development on earables. DreamCatcher encompasses eight distinct sleep events, including synchronous dual-channel audio and motion data collected from 12 pairs (24 participants) totaling 210 hours (420 hour.person) with fine-grained label. We tested multiple benchmark models on three tasks related to sleep event detection, demonstrating the usability and unique challenge of DreamCatcher. We hope that the proposed DreamCatcher can inspire other researchers to further explore efficient wearer-aware human vocal activity sensing on earables. DreamCatcher is publicly available at https://github.com/thuhci/DreamCatcher.

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Recursive PAC-Bayes: A Frequentist Approach to Sequential Prior Updates with No Information Loss

Yi-Shan Wu, Yijie Zhang, Badr-Eddine Chérief-Abdellatif, Yevgeny Seldin

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PAC-Bayesian analysis is a frequentist framework for incorporating prior knowledge into learning. It was inspired by Bayesian learning, which allows sequential data processing and naturally turns posteriors from one processing step into priors for the next. However, despite two and a half decades of research, the ability to update priors sequentially without losing confidence information along the way remained elusive for PAC-Bayes. While PAC-Bayes allows construction of data-informed priors, the final confidence intervals depend only on the number of points that were not used for the construction of the prior, whereas confidence information in the prior, which is related to the number of points used to construct the prior, is lost. This limits the possibility and benefit of sequential prior updates, because the final bounds depend only on the size of the final batch. We present a novel and, in retrospect, surprisingly simple and powerful PAC-Bayesian procedure that allows sequential prior updates with no information loss. The procedure is based on a novel decomposition of the expected loss of randomized classifiers. The decomposition rewrites the loss of the posterior as an excess loss relative to a downscaled loss of the prior plus the downscaled loss of the prior, which is bounded recursively. As a side result, we also present a generalization of the split-kl and PAC-Bayes-split-kl inequalities to discrete random variables, which we use for bounding the excess losses, and which can be of independent interest. In empirical evaluation the new procedure significantly outperforms state-of-the-art.

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Thompson Sampling For Combinatorial Bandits: Polynomial Regret and Mismatched Sampling Paradox

Raymond Zhang, Richard Combes

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We consider Thompson Sampling (TS) for linear combinatorial semi-bandits and subgaussian rewards. We propose the first known TS whose finite-time regret does not scale exponentially with the dimension of the problem. We further show the mismatched sampling paradox: A learner who knows the rewards distributions and samples from the correct posterior distribution can perform exponentially worse than a learner who does not know the rewards and simply samples from a well-chosen Gaussian posterior. The code used to generate the experiments is available at https://github.com/RaymZhang/CTS-Mismatched-Paradox

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3DGS-Enhancer: Enhancing Unbounded 3D Gaussian Splatting with View-consistent 2D Diffusion Priors

Xi Liu, Chaoyi Zhou, Siyu Huang

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Novel-view synthesis aims to generate novel views of a scene from multiple input images or videos, and recent advancements like 3D Gaussian splatting (3DGS) have achieved notable success in producing photorealistic renderings with efficient pipelines. However, generating high-quality novel views under challenging settings, such as sparse input views, remains difficult due to insufficient information in under-sampled areas, often resulting in noticeable artifacts. This paper presents 3DGS-Enhancer, a novel pipeline for enhancing the representation quality of 3DGS representations. We leverage 2D video diffusion priors to address the challenging 3D view consistency problem, reformulating it as achieving temporal consistency within a video generation process. 3DGS-Enhancer restores view- consistent latent features of rendered novel views and integrates them with the input views through a spatial-temporal decoder. The enhanced views are then used to fine-tune the initial 3DGS model, significantly improving its rendering performance. Extensive experiments on large-scale datasets of unbounded scenes demonstrate that 3DGS-Enhancer yields superior reconstruction performance and high-fidelity rendering results compared to state-of-the-art methods. The project webpage is https://xiliu8006.github.io/3DGS-Enhancer-project.

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Diffusion Priors for Variational Likelihood Estimation and Image Denoising

Jun Cheng, Shan Tan

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Real-world noise removal is crucial in low-level computer vision. Due to the remarkable generation capabilities of diffusion models, recent attention has shifted towards leveraging diffusion priors for image restoration tasks. However, existing diffusion priors-based methods either consider simple noise types or rely on approximate posterior estimation, limiting their effectiveness in addressing structured and signal-dependent noise commonly found in real-world images. In this paper, we build upon diffusion priors and propose adaptive likelihood estimation and MAP inference during the reverse diffusion process to tackle real-world noise. We introduce an independent, non-identically distributed likelihood combined with the noise precision (inverse variance) prior and dynamically infer the precision posterior using variational Bayes during the generation process. Meanwhile, we rectify the estimated noise variance through local Gaussian convolution. The final denoised image is obtained by propagating intermediate MAP solutions that balance the updated likelihood and diffusion prior. Additionally, we explore the local diffusion prior inherent in low-resolution diffusion models, enabling direct handling of high-resolution noisy images. Extensive experiments and analyses on diverse real-world datasets demonstrate the effectiveness of our method. Code is available at https://github.com/HUST-Tan/DiffusionVI.

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Mean-Field Langevin Dynamics for Signed Measures via a Bilevel Approach

Guillaume Wang, Alireza Mousavi-Hosseini, Lénaïc Chizat

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Mean-field Langevin dynamics (MLFD) is a class of interacting particle methods that tackle convex optimization over probability measures on a manifold, which are scalable, versatile, and enjoy computational guarantees. However, some important problems -- such as risk minimization for infinite width two-layer neural networks, or sparse deconvolution -- are originally defined over the set of signed, rather than probability, measures. In this paper, we investigate how to extend the MFLD framework to convex optimization problems over signed measures. Among two known reductions from signed to probability measures -- the lifting and the bilevel approaches -- we show that the bilevel reduction leads to stronger guarantees and faster rates (at the price of a higher per-iteration complexity). In particular, we investigate the convergence rate of MFLD applied to the bilevel reduction in the low-noise regime and obtain two results. First, this dynamics is amenable to an annealing schedule, adapted from [Suzuki et al., 2023], that results in polynomial convergence rates to a fixed multiplicative accuracy. Second, we investigate the problem of learning a single neuron with the bilevel approach and obtain local exponential convergence rates that depend polynomially on the dimension and noise level (to compare with the exponential dependence that would result from prior analyses).

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