NeurIPS 2023 论文列表

Conference on Neural Information Processing Systems

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On the Sublinear Regret of GP-UCB

Justin Whitehouse, Aaditya Ramdas, Steven Wu

展开摘要

In the kernelized bandit problem, a learner aims to sequentially compute the optimum of a function lying in a reproducing kernel Hilbert space given only noisy evaluations at sequentially chosen points. In particular, the learner aims to minimize regret, which is a measure of the suboptimality of the choices made. Arguably the most popular algorithm is the Gaussian Process Upper Confidence Bound (GP-UCB) algorithm, which involves acting based on a simple linear estimator of the unknown function. Despite its popularity, existing analyses of GP-UCB give a suboptimal regret rate, which fails to be sublinear for many commonly used kernels such as the Matern kernel. This has led to a longstanding open question: are existing regret analyses for GP-UCB tight, or can bounds be improved by using more sophisticated analytical techniques? In this work, we resolve this open question and show that GP-UCB enjoys nearly optimal regret. In particular, our results yield sublinear regret rates for the Matern kernel, improving over the state-of-the-art analyses and partially resolving a COLT open problem posed by Vakili et al. Our improvements rely on a key technical contribution --- regularizing kernel ridge estimators in proportion to the smoothness of the underlying kernel $k$. Applying this key idea together with a largely overlooked concentration result in separable Hilbert spaces (for which we provide an independent, simplified derivation), we are able to provide a tighter analysis of the GP-UCB algorithm.

Poster
Evolutionary Neural Architecture Search for Transformer in Knowledge Tracing

Shangshang Yang, Xiaoshan Yu, Ye Tian, Xueming Yan, Haiping Ma, Xingyi Zhang

展开摘要

Knowledge tracing (KT) aims to trace students' knowledge states by predicting whether students answer correctly on exercises. Despite the excellent performance of existing Transformer-based KT approaches, they are criticized for the manually selected input features for fusion and the defect of single global context modelling to directly capture students' forgetting behavior in KT, when the related records are distant from the current record in terms of time. To address the issues, this paper first considers adding convolution operations to the Transformer to enhance its local context modelling ability used for students' forgetting behavior, then proposes an evolutionary neural architecture search approach to automate the input feature selection and automatically determine where to apply which operation for achieving the balancing of the local/global context modelling. In the search space, the original global path containing the attention module in Transformer is replaced with the sum of a global path and a local path that could contain different convolutions, and the selection of input features is also considered. To search the best architecture, we employ an effective evolutionary algorithm to explore the search space and also suggest a search space reduction strategy to accelerate the convergence of the algorithm. Experimental results on the two largest and most challenging education datasets demonstrate the effectiveness of the architecture found by the proposed approach.

Poster
A Dual-Stream Neural Network Explains the Functional Segregation of Dorsal and Ventral Visual Pathways in Human Brains

Minkyu Choi, Kuan Han, Xiaokai Wang, Yizhen Zhang, Zhongming Liu

展开摘要

The human visual system uses two parallel pathways for spatial processing and object recognition. In contrast, computer vision systems tend to use a single feedforward pathway, rendering them less robust, adaptive, or efficient than human vision. To bridge this gap, we developed a dual-stream vision model inspired by the human eyes and brain. At the input level, the model samples two complementary visual patterns to mimic how the human eyes use magnocellular and parvocellular retinal ganglion cells to separate retinal inputs to the brain. At the backend, the model processes the separate input patterns through two branches of convolutional neural networks (CNN) to mimic how the human brain uses the dorsal and ventral cortical pathways for parallel visual processing. The first branch (WhereCNN) samples a global view to learn spatial attention and control eye movements. The second branch (WhatCNN) samples a local view to represent the object around the fixation. Over time, the two branches interact recurrently to build a scene representation from moving fixations. We compared this model with the human brains processing the same movie and evaluated their functional alignment by linear transformation. The WhereCNN and WhatCNN branches were found to differentially match the dorsal and ventral pathways of the visual cortex, respectively, primarily due to their different learning objectives, rather than their distinctions in retinal sampling or sensitivity to attention-driven eye movements. These model-based results lead us to speculate that the distinct responses and representations of the ventral and dorsal streams are more influenced by their distinct goals in visual attention and object recognition than by their specific bias or selectivity in retinal inputs. This dual-stream model takes a further step in brain-inspired computer vision, enabling parallel neural networks to actively explore and understand the visual surroundings.

Poster
Neural Image Compression: Generalization, Robustness, and Spectral Biases

Kelsey Lieberman, James Diffenderfer, Charles Godfrey, Bhavya Kailkhura

展开摘要

Recent advances in neural image compression (NIC) have produced models that are starting to outperform classic codecs. While this has led to growing excitement about using NIC in real-world applications, the successful adoption of any machine learning system in the wild requires it to generalize (and be robust) to unseen distribution shifts at deployment. Unfortunately, current research lacks comprehensive datasets and informative tools to evaluate and understand NIC performance in real-world settings. To bridge this crucial gap, first, this paper presents a comprehensive benchmark suite to evaluate the out-of-distribution (OOD) performance of image compression methods. Specifically, we provide CLIC-C and Kodak-C by introducing 15 corruptions to the popular CLIC and Kodak benchmarks. Next, we propose spectrally-inspired inspection tools to gain deeper insight into errors introduced by image compression methods as well as their OOD performance. We then carry out a detailed performance comparison of several classic codecs and NIC variants, revealing intriguing findings that challenge our current understanding of the strengths and limitations of NIC. Finally, we corroborate our empirical findings with theoretical analysis, providing an in-depth view of the OOD performance of NIC and its dependence on the spectral properties of the data. Our benchmarks, spectral inspection tools, and findings provide a crucial bridge to the real-world adoption of NIC. We hope that our work will propel future efforts in designing robust and generalizable NIC methods. Code and data will be made available at https://github.com/klieberman/ood_nic.

Poster
Data Quality in Imitation Learning

Suneel Belkhale, Yuchen Cui, Dorsa Sadigh

展开摘要

In supervised learning, the question of data quality and curation has been sidelined in recent years in favor of increasingly more powerful and expressive models that can ingest internet-scale data. However, in offline learning for robotics, we simply lack internet scale data, and so high quality datasets are a necessity. This is especially true in imitation learning (IL), a sample efficient paradigm for robot learning using expert demonstrations. Policies learned through IL suffer from state distribution shift at test time due to compounding errors in action prediction, which leads to unseen states that the policy cannot recover from. Instead of designing new algorithms to address distribution shift, an alternative perspective is to develop new ways of assessing and curating datasets. There is growing evidence that the same IL algorithms can have substantially different performance across different datasets. This calls for a formalism for defining metrics of "data quality" that can further be leveraged for data curation. In this work, we take the first step toward formalizing data quality for imitation learning through the lens of distribution shift: a high quality dataset encourages the policy to stay in distribution at test time. We propose two fundamental properties that are necessary for a high quality datasets: i) action divergence: the mismatch between the expert and learned policy at certain states; and ii) transition diversity: the noise present in the system for a given state and action. We investigate the combined effect of these two key properties in imitation learning theoretically, and we empirically analyze models trained on a variety of different data sources. We show that state diversity is not always beneficial, and we demonstrate how action divergence and transition diversity interact in practice.

Poster
On Differentially Private Sampling from Gaussian and Product Distributions

Badih Ghazi, Xiao Hu, Ravi Kumar, Pasin Manurangsi

展开摘要

We study the problem, where given a dataset of $n$ i.i.d. samples from an unknown distribution $P$, we seek to generate a sample from a distribution that is close to $P$ in total variation distance, under the constraint of differential privacy. We study the settings where $P$ is a multi-dimensional Gaussian distribution with different assumptions: known covariance, unknown bounded covariance, and unknown unbounded covariance. We present new differentially private sampling algorithms, and show that they achieve near-optimal sample complexity in the first two settings. Moreover, when $P$ is a product distribution on the binary hypercube, we obtain a pure-DP algorithm whereas only an approximate-DP algorithm (with slightly worse sample complexity) was previously known.

Poster
Dynamic Pricing and Learning with Bayesian Persuasion

Shipra Agrawal, Yiding Feng, Wei Tang

展开摘要

We consider a novel dynamic pricing and learning setting where in addition to setting prices of products in sequential rounds, the seller also ex-ante commits to ‘advertising schemes’. That is, in the beginning of each round the seller can decide what kind of signal they will provide to the buyer about the product’s quality upon realization. Using the popular Bayesian persuasion framework to model the effect of these signals on the buyers’ valuation and purchase responses, we formulate the problem of finding an optimal design of the advertising scheme along with a pricing scheme that maximizes the seller’s expected revenue. Without any apriori knowledge of the buyers’ demand function, our goal is to design an online algorithm that can use past purchase responses to adaptively learn the optimal pricing and advertising strategy. We study the regret of the algorithm when compared to the optimal clairvoyant price and advertising scheme. Our main result is a computationally efficient online algorithm that achieves an $O(T^{2/3}(m \log T )^{1/3})$ regret bound when the valuation function is linear in the product quality. Here $m$ is the cardinality of the discrete product quality domain and $T$ is the time horizon. This result requires some natural monotonicity and Lipschitz assumptions on the valuation function, but no Lipschitz or smoothness assumption on the buyers’ demand function. For constant $m$, our result matches the regret lower bound for dynamic pricing within logarithmic factors, which is a special case of our problem. We also obtain several improved results for the widely considered special case of additive valuations, including an $\tilde{O}(T^{2/3})$ regret bound independent of $m$ when $m\le T^{1/3}$.

Poster
RiskQ: Risk-sensitive Multi-Agent Reinforcement Learning Value Factorization

Siqi Shen, Chennan Ma, Chao Li, Weiquan Liu, Yongquan Fu, Songzhu Mei, Xinwang Liu, Cheng Wang

展开摘要

Multi-agent systems are characterized by environmental uncertainty, varying policies of agents, and partial observability, which result in significant risks. In the context of Multi-Agent Reinforcement Learning (MARL), learning coordinated and decentralized policies that are sensitive to risk is challenging. To formulate the coordination requirements in risk-sensitive MARL, we introduce the Risk-sensitive Individual-Global-Max (RIGM) principle as a generalization of the Individual-Global-Max (IGM) and Distributional IGM (DIGM) principles. This principle requires that the collection of risk-sensitive action selections of each agent should be equivalent to the risk-sensitive action selection of the central policy. Current MARL value factorization methods do not satisfy the RIGM principle for common risk metrics such as the Value at Risk (VaR) metric or distorted risk measurements. Therefore, we propose RiskQ to address this limitation, which models the joint return distribution by modeling quantiles of it as weighted quantile mixtures of per-agent return distribution utilities. RiskQ satisfies the RIGM principle for the VaR and distorted risk metrics. We show that RiskQ can obtain promising performance through extensive experiments. The source code of RiskQ is available in https://github.com/xmu-rl-3dv/RiskQ.

Poster
Differentiable Blocks World: Qualitative 3D Decomposition by Rendering Primitives

Tom Monnier, Jake Austin, Angjoo Kanazawa, Alexei A. Efros, Mathieu Aubry

展开摘要

Given a set of calibrated images of a scene, we present an approach that produces a simple, compact, and actionable 3D world representation by means of 3D primitives. While many approaches focus on recovering high-fidelity 3D scenes, we focus on parsing a scene into mid-level 3D representations made of a small set of textured primitives. Such representations are interpretable, easy to manipulate and suited for physics-based simulations. Moreover, unlike existing primitive decomposition methods that rely on 3D input data, our approach operates directly on images through differentiable rendering. Specifically, we model primitives as textured superquadric meshes and optimize their parameters from scratch with an image rendering loss. We highlight the importance of modeling transparency for each primitive, which is critical for optimization and also enables handling varying numbers of primitives. We show that the resulting textured primitives faithfully reconstruct the input images and accurately model the visible 3D points, while providing amodal shape completions of unseen object regions. We compare our approach to the state of the art on diverse scenes from DTU, and demonstrate its robustness on real-life captures from BlendedMVS and Nerfstudio. We also showcase how our results can be used to effortlessly edit a scene or perform physical simulations. Code and video results are available at https://www.tmonnier.com/DBW.

Poster
Faster approximate subgraph counts with privacy

Dung Nguyen, Mahantesh M Halappanavar, Venkatesh Srinivasan, Anil Vullikanti

展开摘要

One of the most common problems studied in the context of differential privacy for graph data is counting the number of non-induced embeddings of a subgraph in a given graph. These counts have very high global sensitivity. Therefore, adding noise based on powerful alternative techniques, such as smooth sensitivity and higher-order local sensitivity have been shown to give significantly better accuracy. However, all these alternatives to global sensitivity become computationally very expensive, and to date efficient polynomial time algorithms are known only for few selected subgraphs, such as triangles, $k$-triangles, and $k$-stars. In this paper, we show that good approximations to these sensitivity metrics can be still used to get private algorithms. Using this approach, we much faster algorithms for privately counting the number of triangles in real-world social networks, which can be easily parallelized. We also give a private polynomial time algorithm for counting any constant size subgraph using less noise than the global sensitivity; we show this can be improved significantly for counting paths in special classes of graphs.

Poster
MiliPoint: A Point Cloud Dataset for mmWave Radar

Han Cui, Shu Zhong, Jiacheng Wu, Zichao Shen, Naim Dahnoun, Yiren Zhao

展开摘要

Millimetre-wave (mmWave) radar has emerged as an attractive and cost-effective alternative for human activity sensing compared to traditional camera-based systems. mmWave radars are also non-intrusive, providing better protection for user privacy. However, as a Radio Frequency based technology, mmWave radars rely on capturing reflected signals from objects, making them more prone to noise compared to cameras. This raises an intriguing question for the deep learning community: Can we develop more effective point set-based deep learning methods for such attractive sensors? To answer this question, our work, termed MiliPoint, delves into this idea by providing a large-scale, open dataset for the community to explore how mmWave radars can be utilised for human activity recognition. Moreover, MiliPoint stands out as it is larger in size than existing datasets, has more diverse human actions represented, and encompasses all three key tasks in human activity recognition. We have also established a range of point-based deep neural networks such as DGCNN, PointNet++ and PointTransformer, on MiliPoint, which can serve to set the ground baseline for further development.

Poster
3D-IntPhys: Towards More Generalized 3D-grounded Visual Intuitive Physics under Challenging Scenes

Haotian Xue, Antonio Torralba, Joshua B. Tenenbaum, Daniel LK Yamins, Yunzhu Li, Hsiao-Yu Tung

展开摘要

Given a visual scene, humans have strong intuitions about how a scene can evolve over time under given actions. The intuition, often termed visual intuitive physics, is a critical ability that allows us to make effective plans to manipulate the scene to achieve desired outcomes without relying on extensive trial and error. In this paper, we present a framework capable of learning 3D-grounded visual intuitive physics models from videos of complex scenes with fluids. Our method is composed of a conditional Neural Radiance Field (NeRF)-style visual frontend and a 3D point-based dynamics prediction backend, using which we can impose strong relational and structural inductive bias to capture the structure of the underlying environment. Unlike existing intuitive point-based dynamics works that rely on the supervision of dense point trajectory from simulators, we relax the requirements and only assume access to multi-view RGB images and (imperfect) instance masks acquired using color prior. This enables the proposed model to handle scenarios where accurate point estimation and tracking are hard or impossible. We generate datasets including three challenging scenarios involving fluid, granular materials, and rigid objects in the simulation. The datasets do not include any dense particle information so most previous 3D-based intuitive physics pipelines can barely deal with that. We show our model can make long-horizon future predictions by learning from raw images and significantly outperforms models that do not employ an explicit 3D representation space. We also show that once trained, our model can achieve strong generalization in complex scenarios under extrapolate settings.

Poster
NU-MCC: Multiview Compressive Coding with Neighborhood Decoder and Repulsive UDF

Stefan Lionar, Xiangyu Xu, Min Lin, Gim Hee Lee

展开摘要

Remarkable progress has been made in 3D reconstruction from single-view RGB-D inputs. MCC is the current state-of-the-art method in this field, which achieves unprecedented success by combining vision Transformers with large-scale training. However, we identified two key limitations of MCC: 1) The Transformer decoder is inefficient in handling large number of query points; 2) The 3D representation struggles to recover high-fidelity details. In this paper, we propose a new approach called NU-MCC that addresses these limitations. NU-MCC includes two key innovations: a Neighborhood decoder and a Repulsive Unsigned Distance Function (Repulsive UDF). First, our Neighborhood decoder introduces center points as an efficient proxy of input visual features, allowing each query point to only attend to a small neighborhood. This design not only results in much faster inference speed but also enables the exploitation of finer-scale visual features for improved recovery of 3D textures. Second, our Repulsive UDF is a novel alternative to the occupancy field used in MCC, significantly improving the quality of 3D object reconstruction. Compared to standard UDFs that suffer from holes in results, our proposed Repulsive UDF can achieve more complete surface reconstruction. Experimental results demonstrate that NU-MCC is able to learn a strong 3D representation, significantly advancing the state of the art in single-view 3D reconstruction. Particularly, it outperforms MCC by 9.7% in terms of the F1-score on the CO3D-v2 dataset with more than 5x faster running speed.

Poster
Robust Multi-Agent Reinforcement Learning via Adversarial Regularization: Theoretical Foundation and Stable Algorithms

Alexander Bukharin, Yan Li, Yue Yu, Qingru Zhang, Zhehui Chen, Simiao Zuo, Chao Zhang, Songan Zhang, Tuo Zhao

展开摘要

Multi-Agent Reinforcement Learning (MARL) has shown promising results across several domains. Despite this promise, MARL policies often lack robustness and are therefore sensitive to small changes in their environment. This presents a serious concern for the real world deployment of MARL algorithms, where the testing environment may slightly differ from the training environment. In this work we show that we can gain robustness by controlling a policy’s Lipschitz constant, and under mild conditions, establish the existence of a Lipschitz and close-to-optimal policy. Motivated by these insights, we propose a new robust MARL framework, ERNIE, that promotes the Lipschitz continuity of the policies with respect to the state observations and actions by adversarial regularization. The ERNIE framework provides robustness against noisy observations, changing transition dynamics, and malicious actions of agents. However, ERNIE’s adversarial regularization may introduce some training instability. To reduce this instability, we reformulate adversarial regularization as a Stackelberg game. We demonstrate the effectiveness of the proposed framework with extensive experiments in traffic light control and particle environments. In addition, we extend ERNIE to mean-field MARL with a formulation based on distributionally robust optimization that outperforms its non-robust counterpart and is of independent interest. Our code is available at https://github.com/abukharin3/ERNIE.

Poster
Entropy-dissipation Informed Neural Network for McKean-Vlasov Type PDEs

Zebang Shen, Zhenfu Wang

展开摘要

The McKean-Vlasov equation (MVE) describes the collective behavior of particles subject to drift, diffusion, and mean-field interaction. In physical systems, the interaction term can be singular, i.e. it diverges when two particles collide. Notable examples of such interactions include the Coulomb interaction, fundamental in plasma physics, and the Biot-Savart interaction, present in the vorticity formulation of the 2D Navier-Stokes equation (NSE) in fluid dynamics. Solving MVEs that involve singular interaction kernels presents a significant challenge, especially when aiming to provide rigorous theoretical guarantees. In this work, we propose a novel approach based on the concept of entropy dissipation in the underlying system. We derive a potential function that effectively controls the KL divergence between a hypothesis solution and the ground truth. Building upon this theoretical foundation, we introduce the Entropy-dissipation Informed Neural Network (EINN) framework for solving MVEs. In EINN, we utilize neural networks (NN) to approximate the underlying velocity field and minimize the proposed potential function. By leveraging the expressive power of NNs, our approach offers a promising avenue for tackling the complexities associated with singular interactions. To assess the empirical performance of our method, we compare EINN with SOTA NN-based MVE solvers. The results demonstrate the effectiveness of our approach in solving MVEs across various example problems.

Poster
Direct Preference-based Policy Optimization without Reward Modeling

Gaon An, Junhyeok Lee, Xingdong Zuo, Norio Kosaka, Kyung-Min Kim, Hyun Oh Song

展开摘要

Preference-based reinforcement learning (PbRL) is an approach that enables RL agents to learn from preference, which is particularly useful when formulating a reward function is challenging. Existing PbRL methods generally involve a two-step procedure: they first learn a reward model based on given preference data and then employ off-the-shelf reinforcement learning algorithms using the learned reward model. However, obtaining an accurate reward model solely from preference information, especially when the preference is from human teachers, can be difficult. Instead, we propose a PbRL algorithm that directly learns from preference without requiring any reward modeling. To achieve this, we adopt a contrastive learning framework to design a novel policy scoring metric that assigns a high score to policies that align with the given preferences. We apply our algorithm to offline RL tasks with actual human preference labels and show that our algorithm outperforms or is on par with the existing PbRL methods. Notably, on high-dimensional control tasks, our algorithm surpasses offline RL methods that learn with ground-truth reward information. Finally, we show that our algorithm can be successfully applied to fine-tune large language models.

Poster
A Unified Approach to Domain Incremental Learning with Memory: Theory and Algorithm

Haizhou Shi, Hao Wang

展开摘要

Domain incremental learning aims to adapt to a sequence of domains with access to only a small subset of data (i.e., memory) from previous domains. Various methods have been proposed for this problem, but it is still unclear how they are related and when practitioners should choose one method over another. In response, we propose a unified framework, dubbed Unified Domain Incremental Learning (UDIL), for domain incremental learning with memory. Our UDIL **unifies** various existing methods, and our theoretical analysis shows that UDIL always achieves a tighter generalization error bound compared to these methods. The key insight is that different existing methods correspond to our bound with different **fixed** coefficients; based on insights from this unification, our UDIL allows **adaptive** coefficients during training, thereby always achieving the tightest bound. Empirical results show that our UDIL outperforms the state-of-the-art domain incremental learning methods on both synthetic and real-world datasets. Code will be available at https://github.com/Wang-ML-Lab/unified-continual-learning.

Poster
A Metadata-Driven Approach to Understand Graph Neural Networks

Ting Wei Li, Qiaozhu Mei, Jiaqi Ma

展开摘要

Graph Neural Networks (GNNs) have achieved remarkable success in various applications, but their performance can be sensitive to specific data properties of the graph datasets they operate on. Current literature on understanding the limitations of GNNs has primarily employed a \emph{model-driven} approach that leverage heuristics and domain knowledge from network science or graph theory to model the GNN behaviors, which is time-consuming and highly subjective. In this work, we propose a \emph{metadata-driven} approach to analyze the sensitivity of GNNs to graph data properties, motivated by the increasing availability of graph learning benchmarks. We perform a multivariate sparse regression analysis on the metadata derived from benchmarking GNN performance across diverse datasets, yielding a set of salient data properties. To validate the effectiveness of our data-driven approach, we focus on one identified data property, the degree distribution, and investigate how this property influences GNN performance through theoretical analysis and controlled experiments. Our theoretical findings reveal that datasets with more balanced degree distribution exhibit better linear separability of node representations, thus leading to better GNN performance. We also conduct controlled experiments using synthetic datasets with varying degree distributions, and the results align well with our theoretical findings. Collectively, both the theoretical analysis and controlled experiments verify that the proposed metadata-driven approach is effective in identifying critical data properties for GNNs.

Poster
Gradient-Based Feature Learning under Structured Data

Alireza Mousavi-Hosseini, Denny Wu, Taiji Suzuki, Murat A Erdogdu

展开摘要

Recent works have demonstrated that the sample complexity of gradient-based learning of single index models, i.e. functions that depend on a 1-dimensional projection of the input data, is governed by their information exponent. However, these results are only concerned with isotropic data, while in practice the input often contains additional structure which can implicitly guide the algorithm. In this work, we investigate the effect of a spiked covariance structure and reveal several interesting phenomena. First, we show that in the anisotropic setting, the commonly used spherical gradient dynamics may fail to recover the true direction, even when the spike is perfectly aligned with the target direction. Next, we show that appropriate weight normalization that is reminiscent of batch normalization can alleviate this issue. Further, by exploiting the alignment between the (spiked) input covariance and the target, we obtain improved sample complexity compared to the isotropic case. In particular, under the spiked model with a suitably large spike, the sample complexity of gradient-based training can be made independent of the information exponent while also outperforming lower bounds for rotationally invariant kernel methods.

Poster
On the Trade-off of Intra-/Inter-class Diversity for Supervised Pre-training

Jieyu Zhang, Bohan Wang, Zhengyu Hu, Pang Wei Koh, Alexander Ratner

展开摘要

Pre-training datasets are critical for building state-of-the-art machine learning models, motivating rigorous study on their impact on downstream tasks. In this work, we study the impact of the trade-off between the intra-class diversity (the number of samples per class) and the inter-class diversity (the number of classes) of a supervised pre-training dataset. Empirically, we found that with the size of the pre-training dataset fixed, the best downstream performance comes with a balance on the intra-/inter-class diversity. To understand the underlying mechanism, we show theoretically that the downstream performance depends monotonically on both types of diversity. Notably, our theory reveals that the optimal class-to-sample ratio (#classes / #samples per class) is invariant to the size of the pre-training dataset, which motivates an application of predicting the optimal number of pre-training classes. We demonstrate the effectiveness of this application by an improvement of around 2 points on the downstream tasks when using ImageNet as the pre-training dataset.

Poster