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%

Browse all papers

Complete Graphical Criterion for Sequential Covariate Adjustment in Causal Inference

Yonghan Jung, Min Woo Park, Sanghack Lee

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Covariate adjustment, also known as back-door adjustment, is a fundamental tool in causal inference. Although a sound and complete graphical identification criterion, known as the adjustment criterion (Shpitser, 2010), exists for static contexts, sequential contexts present challenges. Current practices, such as the sequential back-door adjustment (Pearl, 1995) or multi-outcome sequential back-door adjustment (Jung, 2020), are sound but incomplete; i.e., there are graphical scenarios where the causal effect is expressible via covariate adjustment, yet these criteria do not cover. In this paper, we exemplify this incompleteness and then present the *sequential adjustment criterion*, a sound and complete criterion for sequential covariate adjustment. We provide a constructive sequential adjustment criterion that identifies a set that satisfies the sequential adjustment criterion if and only if the causal effect can be expressed as a sequential covariate adjustment. Finally, we present an algorithm for identifying a *minimal* sequential covariate adjustment set, which optimizes efficiency by ensuring that no unnecessary vertices are included.

Poster
DreamClear: High-Capacity Real-World Image Restoration with Privacy-Safe Dataset Curation

Yuang Ai, Xiaoqiang Zhou, Huaibo Huang, Xiaotian Han, Zhengyu Chen, Quanzeng You, Hongxia Yang

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Image restoration (IR) in real-world scenarios presents significant challenges due to the lack of high-capacity models and comprehensive datasets. To tackle these issues, we present a dual strategy: GenIR, an innovative data curation pipeline, and DreamClear, a cutting-edge Diffusion Transformer (DiT)-based image restoration model. **GenIR**, our pioneering contribution, is a dual-prompt learning pipeline that overcomes the limitations of existing datasets, which typically comprise only a few thousand images and thus offer limited generalizability for larger models. GenIR streamlines the process into three stages: image-text pair construction, dual-prompt based fine-tuning, and data generation \& filtering. This approach circumvents the laborious data crawling process, ensuring copyright compliance and providing a cost-effective, privacy-safe solution for IR dataset construction. The result is a large-scale dataset of one million high-quality images. Our second contribution, **DreamClear**, is a DiT-based image restoration model. It utilizes the generative priors of text-to-image (T2I) diffusion models and the robust perceptual capabilities of multi-modal large language models (MLLMs) to achieve photorealistic restoration. To boost the model's adaptability to diverse real-world degradations, we introduce the Mixture of Adaptive Modulator (MoAM). It employs token-wise degradation priors to dynamically integrate various restoration experts, thereby expanding the range of degradations the model can address. Our exhaustive experiments confirm DreamClear's superior performance, underlining the efficacy of our dual strategy for real-world image restoration. Code and pre-trained models are available at: https://github.com/shallowdream204/DreamClear.

Poster
Transfer Learning for Diffusion Models

Yidong Ouyang, Liyan Xie, Hongyuan Zha, Guang Cheng

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Diffusion models, a specific type of generative model, have achieved unprecedented performance in recent years and consistently produce high-quality synthetic samples. A critical prerequisite for their notable success lies in the presence of a substantial number of training samples, which can be impractical in real-world applications due to high collection costs or associated risks. Consequently, various finetuning and regularization approaches have been proposed to transfer knowledge from existing pre-trained models to specific target domains with limited data. This paper introduces the Transfer Guided Diffusion Process (TGDP), a novel approach distinct from conventional finetuning and regularization methods. We prove that the optimal diffusion model for the target domain integrates pre-trained diffusion models on the source domain with additional guidance from a domain classifier. We further extend TGDP to a conditional version for modeling the joint distribution of data and its corresponding labels, together with two additional regularization terms to enhance the model performance. We validate the effectiveness of TGDP on both simulated and real-world datasets.

Poster
Classifier Clustering and Feature Alignment for Federated Learning under Distributed Concept Drift

Junbao Chen, Jingfeng Xue, Yong Wang, Zhenyan Liu, Lu Huang

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Data heterogeneity is one of the key challenges in federated learning, and many efforts have been devoted to tackling this problem. However, distributed concept drift with data heterogeneity, where clients may additionally experience different concept drifts, is a largely unexplored area. In this work, we focus on real drift, where the conditional distribution $P(\mathcal{Y}|\mathcal{X})$ changes. We first study how distributed concept drift affects the model training and find that local classifier plays a critical role in drift adaptation. Moreover, to address data heterogeneity, we study the feature alignment under distributed concept drift, and find two factors that are crucial for feature alignment: the conditional distribution $P(\mathcal{Y}|\mathcal{X})$ and the degree of data heterogeneity. Motivated by the above findings, we propose FedCCFA, a federated learning framework with classifier clustering and feature alignment. To enhance collaboration under distributed concept drift, FedCCFA clusters local classifiers at class-level and generates clustered feature anchors according to the clustering results. Assisted by these anchors, FedCCFA adaptively aligns clients' feature spaces based on the entropy of label distribution $P(\mathcal{Y})$, alleviating the inconsistency in feature space. Our results demonstrate that FedCCFA significantly outperforms existing methods under various concept drift settings. Code is available at https://github.com/Chen-Junbao/FedCCFA.

Poster
CogVLM: Visual Expert for Pretrained Language Models

Weihan Wang, Qingsong Lv, Wenmeng Yu, Wenyi Hong, Ji Qi, Yan Wang, Junhui Ji, Zhuoyi Yang, Lei Zhao, Song XiXuan, Jiazheng Xu, Keqin Chen, Bin Xu, Juanzi Li, Yuxiao Dong, Ming Ding, Jie Tang

Expand abstract

We introduce CogVLM, a powerful open-source visual language foundation model. Different from the popular \emph{shallow alignment} method which maps image features into the input space of language model, CogVLM bridges the gap between the frozen pretrained language model and image encoder by a trainable visual expert module in the attention and FFN layers. As a result, CogVLM enables a deep fusion of vision language features without sacrificing any performance on NLP tasks. CogVLM-17B achieves state-of-the-art performance on 17 classic cross-modal benchmarks, including 1) image captioning datasets: NoCaps, Flicker30k, 2) VQA datasets: OKVQA, TextVQA, OCRVQA, ScienceQA, 3) LVLM benchmarks: MM-Vet, MMBench, SEED-Bench, LLaVABench, POPE, MMMU, MathVista, 4) visual grounding datasets: RefCOCO, RefCOCO+, RefCOCOg, Visual7W. Codes and checkpoints are available at Github.

Poster
Understanding the Transferability of Representations via Task-Relatedness

Akshay Mehra, Yunbei Zhang, Jihun Hamm

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The growing popularity of transfer learning due to the availability of models pre-trained on vast amounts of data, makes it imperative to understand when the knowledge of these pre-trained models can be transferred to obtain high-performing models on downstream target tasks. However, the exact conditions under which transfer learning succeeds in a cross-domain cross-task setting are still poorly understood. To bridge this gap, we propose a novel analysis that analyzes the transferability of the representations of pre-trained models to downstream tasks in terms of their relatedness to a given reference task. Our analysis leads to an upper bound on transferability in terms of task-relatedness, quantified using the difference between the class priors, label sets, and features of the two tasks.Our experiments using state-of-the-art pre-trained models show the effectiveness of task-relatedness in explaining transferability on various vision and language tasks. The efficient computability of task-relatedness even without labels of the target task and its high correlation with the model's accuracy after end-to-end fine-tuning on the target task makes it a useful metric for transferability estimation. Our empirical results of using task-relatedness on the problem of selecting the best pre-trained model from a model zoo for a target task highlight its utility for practical problems.

Poster
Universal Rates of Empirical Risk Minimization

Steve Hanneke, Mingyue Xu

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The well-known $\textit{empirical risk minimization}$ (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm's performance is its so-called “learning curve”, that is, the decay of the expected error as a function of the input sample size. As the PAC model fails to explain the behavior of learning curves, recent research has explored an alternative universal learning model and has ultimately revealed a distinction between optimal universal and uniform learning rates (Bousquet et al., 2021). However, a basic understanding of such differences with a particular focus on the ERM principle has yet to be developed. In this paper, we consider the problem of universal learning by ERM in the realizable case and study the possible universal rates. Our main result is a fundamental $\textit{tetrachotomy}$: there are only four possible universal learning rates by ERM, namely, the learning curves of any concept class learnable by ERM decay either at $e^{-n}$, $1/n$, $\log{(n)}/n$, or arbitrarily slow rates. Moreover, we provide a complete characterization of which concept classes fall into each of these categories, via new complexity structures. We also develop new combinatorial dimensions which supply sharp asymptotically-valid constant factors for these rates, whenever possible.

Poster
Building Timeseries Dataset: Empowering Large-Scale Building Analytics

Arian Prabowo, Xiachong LIN, Imran Razzak, Hao Xue, Emily W. Yap, Matt Amos, Flora D. Salim

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Buildings play a crucial role in human well-being, influencing occupant comfort, health, and safety. Additionally, they contribute significantly to global energy consumption, accounting for one-third of total energy usage, and carbon emissions. Optimizing building performance presents a vital opportunity to combat climate change and promote human flourishing. However, research in building analytics has been hampered by the lack of accessible, available, and comprehensive real-world datasets on multiple building operations. In this paper, we introduce the Building TimeSeries (BTS) dataset. Our dataset covers three buildings over a three-year period, comprising more than ten thousand timeseries data points with hundreds of unique ontologies. Moreover, the metadata is standardized using the Brick schema. To demonstrate the utility of this dataset, we performed benchmarks on two tasks: timeseries ontology classification and zero-shot forecasting. These tasks represent an essential initial step in addressing challenges related to interoperability in building analytics. Access to the dataset and the code used for benchmarking are available here: https://github.com/cruiseresearchgroup/DIEF\_BTS

Poster
Diffusion Imitation from Observation

Bo-Ruei Huang, Chun-Kai Yang, Chun-Mao Lai, Dai-Jie Wu, Shao-Hua Sun

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Learning from Observation (LfO) aims to imitate experts by learning from state-only demonstrations without requiring action labels. Existing adversarial imitation learning approaches learn a generator agent policy to produce state transitions that are indistinguishable to a discriminator that learns to classify agent and expert state transitions. Despite its simplicity in formulation, these methods are often sensitive to hyperparameters and brittle to train. Motivated by the recent success of diffusion models in generative modeling, we propose to integrate a diffusion model into the adversarial imitation learning from observation framework. Specifically, we employ a diffusion model to capture expert and agent transitions by generating the next state, given the current state. Then, we reformulate the learning objective to train the diffusion model as a binary classifier and use it to provide ``realness'' rewards for policy learning. Our proposed framework, Diffusion Imitation from Observation (DIFO), demonstrates superior performance in various continuous control domains, including navigation, locomotion, manipulation, and games.

Poster
Graph neural networks and non-commuting operators

Mauricio Velasco, Kaiying O'Hare, Bernardo Rychtenberg, Soledad Villar

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Graph neural networks (GNNs) provide state-of-the-art results in a wide variety of tasks which typically involve predicting features at the vertices of a graph. They are built from layers of graph convolutions which serve as a powerful inductive bias for describing the flow of information among the vertices. Often, more than one data modality is available. This work considers a setting in which several graphs have the same vertex set and a common vertex-level learning task. This generalizes standard GNN models to GNNs with several graph operators that do not commute. We may call this model graph-tuple neural networks (GtNN). In this work, we develop the mathematical theory to address the stability and transferability of GtNNs using properties of non-commuting non-expansive operators. We develop a limit theory of graphon-tuple neural networks and use it to prove a universal transferability theorem that guarantees that all graph-tuple neural networks are transferable on convergent graph-tuple sequences. In particular, there is no non-transferable energy under the convergence we consider here. Our theoretical results extend well-known transferability theorems for GNNs to the case of several simultaneous graphs (GtNNs) and provide a strict improvement on what is currently known even in the GNN case. We illustrate our theoretical results with simple experiments on synthetic and real-world data. To this end, we derive a training procedure that provably enforces the stability of the resulting model.

Poster
DreamMesh4D: Video-to-4D Generation with Sparse-Controlled Gaussian-Mesh Hybrid Representation

Zhiqi Li, Yiming Chen, Peidong Liu

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Recent advancements in 2D/3D generative techniques have facilitated the generation of dynamic 3D objects from monocular videos. Previous methods mainly rely on the implicit neural radiance fields (NeRF) or explicit Gaussian Splatting as the underlying representation, and struggle to achieve satisfactory spatial-temporal consistency and surface appearance. Drawing inspiration from modern 3D animation pipelines, we introduce DreamMesh4D, a novel framework combining mesh representation with geometric skinning technique to generate high-quality 4D object from a monocular video. Instead of utilizing classical texture map for appearance, we bind Gaussian splats to triangle face of mesh for differentiable optimization of both the texture and mesh vertices. In particular, DreamMesh4D begins with a coarse mesh obtained through an image-to-3D generation procedure. Sparse points are then uniformly sampled across the mesh surface, and are used to build a deformation graph to drive the motion of the 3D object for the sake of computational efficiency and providing additional constraint. For each step, transformations of sparse control points are predicted using a deformation network, and the mesh vertices as well as the surface Gaussians are deformed via a novel geometric skinning algorithm. The skinning algorithm is a hybrid approach combining LBS (linear blending skinning) and DQS (dual-quaternion skinning), mitigating drawbacks associated with both approaches. The static surface Gaussians and mesh vertices as well as the dynamic deformation network are learned via reference view photometric loss, score distillation loss as well as other regularization losses in a two-stage manner. Extensive experiments demonstrate superior performance of our method in terms of both rendering quality and spatial-temporal consistency. Furthermore, our method is compatible with modern graphic pipelines, showcasing its potential in the 3D gaming and film industry.

Poster
Beating Adversarial Low-Rank MDPs with Unknown Transition and Bandit Feedback

Haolin Liu, Zakaria Mhammedi, Chen-Yu Wei, Julian Zimmert

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We consider regret minimization in low-rank MDPs with fixed transition and adversarial losses. Previous work has investigated this problem under either full-information loss feedback with unknown transitions (Zhao et al., 2024), or bandit loss feedback with known transitions (Foster et al., 2022). First, we improve the $poly(d, A, H)T^{5/6}$ regret bound of Zhao et al. (2024) to $poly(d, A, H)T^{2/3}$ for the full-information unknown transition setting, where $d$ is the rank of the transitions, $A$ is the number of actions, $H$ is the horizon length, and $T$ is the number of episodes. Next, we initiate the study on the setting with bandit loss feedback and unknown transitions. Assuming that the loss has a linear structure, we propose both model-based and model-free algorithms achieving $poly(d, A, H)T^{2/3}$ regret, though they are computationally inefficient. We also propose oracle-efficient model-free algorithms with $poly(d, A, H)T^{4/5}$ regret. We show that the linear structure is necessary for the bandit case—without structure on the reward function, the regret has to scale polynomially with the number of states. This is contrary to the full-information case (Zhao et al., 2024), where the regret can be independent of the number of states even for unstructured reward functions.

Poster
PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models

Fanxu Meng, Zhaohui Wang, Muhan Zhang

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To parameter-efficiently fine-tune (PEFT) large language models (LLMs), the low-rank adaptation (LoRA) method approximates the model changes $\Delta W \in \mathbb{R}^{m \times n}$ through the product of two matrices $A \in \mathbb{R}^{m \times r}$ and $B \in \mathbb{R}^{r \times n}$, where $r \ll \min(m, n)$, $A$ is initialized with Gaussian noise, and $B$ with zeros. LoRA **freezes the original model $W$** and **updates the "Noise \& Zero" adapter**, which may lead to slow convergence. To overcome this limitation, we introduce **P**r**i**ncipal **S**ingular values and **S**ingular vectors **A**daptation (PiSSA). PiSSA shares the same architecture as LoRA, but initializes the adaptor matrices $A$ and $B$ with the principal components of the original matrix $W$, and put the remaining components into a residual matrix $W^{res} \in \mathbb{R}^{m \times n}$ which is frozen during fine-tuning. Compared to LoRA, PiSSA **updates the principal components** while **freezing the "residual" parts**, allowing faster convergence and enhanced performance. Comparative experiments of PiSSA and LoRA across 11 different models, ranging from 184M to 70B, encompassing 5 NLG and 8 NLU tasks, reveal that PiSSA consistently outperforms LoRA under identical experimental setups. On the GSM8K benchmark, Gemma-7B fine-tuned with PiSSA achieves an accuracy of 77.7\%, surpassing LoRA's 74.53\% by 3.25\%. Due to the same architecture, PiSSA is also compatible with quantization to further reduce the memory requirement of fine-tuning. Compared to QLoRA, QPiSSA (PiSSA with 4-bit quantization) exhibits smaller quantization errors in the initial stages. Fine-tuning LLaMA-3-70B on GSM8K, QPiSSA attains an accuracy of 86.05\%, exceeding the performances of QLoRA at 81.73\%. Leveraging a fast SVD technique, PiSSA can be initialized in only a few seconds, presenting a negligible cost for transitioning from LoRA to PiSSA.

Spotlight
Inevitable Trade-off between Watermark Strength and Speculative Sampling Efficiency for Language Models

Zhengmian Hu, Heng Huang

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Large language models are probabilistic models, and the process of generating content is essentially sampling from the output distribution of the language model. Existing watermarking techniques inject watermarks into the generated content without altering the output quality. On the other hand, existing acceleration techniques, specifically speculative sampling, leverage a draft model to speed up the sampling process while preserving the output distribution. However, there is no known method to simultaneously accelerate the sampling process and inject watermarks into the generated content. In this paper, we investigate this direction and find that the integration of watermarking and acceleration is non-trivial. We prove a no-go theorem, which states that it is impossible to simultaneously maintain the highest watermark strength and the highest sampling efficiency. Furthermore, we propose two methods that maintain either the sampling efficiency or the watermark strength, but not both. Our work provides a rigorous theoretical foundation for understanding the inherent trade-off between watermark strength and sampling efficiency in accelerating the generation of watermarked tokens for large language models. We also conduct numerical experiments to validate our theoretical findings and demonstrate the effectiveness of the proposed methods.

Poster
The Sample-Communication Complexity Trade-off in Federated Q-Learning

Sudeep Salgia, Yuejie Chi

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We consider the problem of Federated Q-learning, where $M$ agents aim to collaboratively learn the optimal Q-function of an unknown infinite horizon Markov Decision Process with finite state and action spaces. We investigate the trade-off between sample and communication complexity for the widely used class of intermittent communication algorithms. We first establish the converse result, where we show that any Federated Q-learning that offers a linear speedup with respect to number of agents in sample complexity needs to incur a communication cost of at least $\Omega(\frac{1}{1-\gamma})$, where $\gamma$ is the discount factor. We also propose a new Federated Q-learning algorithm, called Fed-DVR-Q, which is the first Federated Q-learning algorithm to simultaneously achieve order-optimal sample and communication complexities. Thus, together these results provide a complete characterization of the sample-communication complexity trade-off in Federated Q-learning.

Oral
Lighting Every Darkness with 3DGS: Fast Training and Real-Time Rendering for HDR View Synthesis

Xin Jin, Pengyi Jiao, Zheng-Peng Duan, Xingchao Yang, Chongyi Li, Chun-Le Guo, Bo Ren

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Volumetric rendering-based methods, like NeRF, excel in HDR view synthesis from RAW images, especially for nighttime scenes. They suffer from long training times and cannot perform real-time rendering due to dense sampling requirements. The advent of 3D Gaussian Splatting (3DGS) enables real-time rendering and faster training. However, implementing RAW image-based view synthesis directly using 3DGS is challenging due to its inherent drawbacks: 1) in nighttime scenes, extremely low SNR leads to poor structure-from-motion (SfM) estimation in dis- tant views; 2) the limited representation capacity of the spherical harmonics (SH) function is unsuitable for RAW linear color space; and 3) inaccurate scene structure hampers downstream tasks such as refocusing. To address these issues, we propose LE3D (Lighting Every darkness with 3DGS). Our method proposes Cone Scatter Initialization to enrich the estimation of SfM and replaces SH with a Color MLP to represent the RAW linear color space. Additionally, we introduce depth distortion and near-far regularizations to improve the accuracy of scene structure for down- stream tasks. These designs enable LE3D to perform real-time novel view synthesis, HDR rendering, refocusing, and tone-mapping changes. Compared to previous vol- umetric rendering-based methods, LE3D reduces training time to 1% and improves rendering speed by up to 4,000 times for 2K resolution images in terms of FPS. Code and viewer can be found in https://srameo.github.io/projects/le3d.

Poster
Team-Fictitious Play for Reaching Team-Nash Equilibrium in Multi-team Games

Ahmed Said Dönmez, Yüksel Arslantaş, Muhammed O. Sayin

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Multi-team games, prevalent in robotics and resource management, involve team members striving for a joint best response against other teams. Team-Nash equilibrium (TNE) predicts the outcomes of such coordinated interactions. However, can teams of self-interested agents reach TNE? We introduce Team-Fictitious Play (Team-FP), a new variant of fictitious play where agents respond to the last actions of team members and the beliefs formed about other teams with some inertia in action updates. This design is essential in team coordination beyond the classical fictitious play dynamics. We focus on zero-sum potential team games (ZSPTGs) where teams can interact pairwise while the team members do not necessarily have identical payoffs. We show that Team-FP reaches near TNE in ZSPTGs with a quantifiable error bound. We extend Team-FP dynamics to multi-team Markov games for model-based and model-free cases. The convergence analysis tackles the challenge of non-stationarity induced by evolving opponent strategies based on the optimal coupling lemma and stochastic differential inclusion approximation methods. Our work strengthens the foundation for using TNE to predict the behavior of decentralized teams and offers a practical rule for team learning in multi-team environments. We provide extensive simulations of Team-FP dynamics and compare its performance with other widely studied dynamics such as smooth fictitious play and multiplicative weights update. We further explore how different parameters impact the speed of convergence.

Poster
LAVIB: A Large-scale Video Interpolation Benchmark

Alexandros Stergiou

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This paper introduces a LArge-scale Video Interpolation Benchmark (LAVIB) for the low-level video task of Video Frame Interpolation (VFI). LAVIB comprises a large collection of high-resolution videos sourced from the web through an automated pipeline with minimal requirements for human verification. Metrics are computed for each video's motion magnitudes, luminance conditions, frame sharpness, and contrast. The collection of videos and the creation of quantitative challenges based on these metrics are under-explored by current low-level video task datasets. In total, LAVIB includes 283K clips from 17K ultra-HD videos, covering 77.6 hours. Benchmark train, val, and test sets maintain similar video metric distributions. Further splits are also created for out-of-distribution (OOD) challenges, with train and test splits including videos of dissimilar attributes.

Poster
Robust Neural Contextual Bandit against Adversarial Corruptions

Yunzhe Qi, Yikun Ban, Arindam Banerjee, Jingrui He

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Contextual bandit algorithms aim to identify the optimal arm with the highest reward among a set of candidates, based on the accessible contextual information. Among these algorithms, neural contextual bandit methods have shown generally superior performances against linear and kernel ones, due to the representation power of neural networks. However, similar to other neural network applications, neural bandit algorithms can be vulnerable to adversarial attacks or corruptions on the received labels (i.e., arm rewards), which can lead to unexpected performance degradation without proper treatments. As a result, it is necessary to improve the robustness of neural bandit models against potential reward corruptions. In this work, we propose a novel neural contextual bandit algorithm named R-NeuralUCB, which utilizes a novel context-aware Gradient Descent (GD) training strategy to improve the robustness against adversarial reward corruptions. Under over-parameterized neural network settings, we provide regret analysis for R-NeuralUCB to quantify reward corruption impacts, without the commonly adopted arm separateness assumption in existing neural bandit works. We also conduct experiments against baselines on real data sets under different scenarios, in order to demonstrate the effectiveness of our proposed R-NeuralUCB.

Poster
Topological Generalization Bounds for Discrete-Time Stochastic Optimization Algorithms

Rayna Andreeva, Benjamin Dupuis, Rik Sarkar, Tolga Birdal, Umut Simsekli

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We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neural networks (DNNs). DNNs show remarkable generalization properties, yet the source of these capabilities remains elusive, defying the established statistical learning theory. Recent studies have revealed that properties of training trajectories can be indicative of generalization. Building on this insight, state-of-the-art methods have leveraged the topology of these trajectories, particularly their fractal dimension, to quantify generalization. Most existing works compute this quantity by assuming continuous- or infinite-time training dynamics, complicating the development of practical estimators capable of accurately predicting generalization without access to test data. In this paper, we respect the discrete-time nature of training trajectories and investigate the underlying topological quantities that can be amenable to topological data analysis tools. This leads to a new family of reliable topological complexity measures that provably bound the generalization error, eliminating the need for restrictive geometric assumptions. These measures are computationally friendly, enabling us to propose simple yet effective algorithms for computing generalization indices. Moreover, our flexible framework can be extended to different domains, tasks, and architectures. Our experimental results demonstrate that our new complexity measures exhibit a strong correlation with generalization error in industry-standard architectures such as transformers and deep graph networks. Our approach consistently outperforms existing topological bounds across a wide range of datasets, models, and optimizers, highlighting the practical relevance and effectiveness of our complexity measures.

Poster