GenAI4ELab/papercli-papers huggingface dataset:
Accelerating Hamiltonian Monte Carlo via Chebyshev Integration Time
Authors: Jun-Kun Wang; Andre Wibisono
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: Hamiltonian Monte Carlo (HMC) is a popular method in sampling. While there are quite a few works of studying this method on various aspects, an interesting question is how to choose its integration time to achieve acceleration. In this work, we consider accelerating the process of sampling from a distribution $\pi(x) \propto \exp(-f(x))$ via HMC via time-varying integration time. When the potential $f$ is $L$-smooth and $m$-strongly convex, i.e. for sampling from a log-smooth and strongly log-concave target distribution $\pi$, it is known that under a constant integration time, the number of iterations that ideal HMC takes to get an $\epsilon$ Wasserstein-2 distance to the target $\pi$ is $O( \kappa \log \frac{1}{\epsilon} )$, where $\kappa := \frac{L}{m}$ is the condition number. We propose a scheme of time-varying integration time based on the roots of Chebyshev polynomials. We show that in the case of quadratic potential $f$, i.e. when the target $\pi$ is a Gaussian distribution, ideal HMC with this choice of integration time only takes $O( \sqrt{\kappa} \log \frac{1}{\epsilon} )$ number of iterations to reach Wasserstein-2 distance less than $\epsilon$; this improvement on the dependence on condition number is akin to acceleration in optimization. The design and analysis of HMC with the proposed integration time is built on the tools of Chebyshev polynomials. Experiments find the advantage of adopting our scheme of time-varying integration time even for sampling from distributions with smooth strongly convex potentials that are not quadratic.
Differentiable Logic Programming for Probabilistic Reasoning
Authors: Tuo Xu; Lei Zou
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: This paper studies inductive logic programming for probabilistic reasoning. The key problems, i.e. learning rule structures and learning rule weights, have been extensively studied with traditional discrete searching methods as well as recent neural-based approaches. In this paper, we present a new approach called Differentiable Logic Programming (DLP), which provides a flexible framework for learning first-order logical rules for reasoning. We propose a continuous version of optimization problem for learning high-quality rules as a proxy and generalize rule learning and forward chaining algorithms in a differentiable manner, which enables us to efficiently learn rule structures and weights via gradient-based methods. Theoretical analysis and empirical results show effectiveness of our approach.
Spatio-temporal Self-Attention for Egocentric 3D Pose Estimation
Authors: Jinman Park; Kimathi Kaai; Saad Hossain; Norikatsu Sumi; Sirisha Rambhatla; Paul W. Fieguth
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Vision-based ego-centric 3D human pose estimation (ego-HPE) is essential to support critical applications of xR-technologies. However, severe self-occlusions and strong distortion introduced by the fish-eye view from the head mounted camera, make ego-HPE extremely challenging. While current state-of-the-art (SOTA) methods try to address the distortion, they still suffer from large errors in the most critical joints (such as hands) due to self-occlusions. To this end, we propose a spatio-temporal transformer model that can attend to semantically rich feature maps obtained from popular convolutional backbones. Leveraging the complex spatio-temporal information encoded in ego-centric videos, we design a spatial concept called feature map tokens (FMT) which can attend to all the other spatial units in our spatio-temporal feature maps. Powered by this FMT-based transformer, we build Egocentric Spatio-Temporal Self-Attention Network (Ego-STAN), which uses heatmap-based representations and spatio-temporal attention specialized to address distortions and self-occlusions in ego-HPE.
Our quantitative evaluation on the contemporary sequential xR-EgoPose dataset, achieves a 38.2% improvement on the highest error joints against the SOTA ego-HPE model, while accomplishing a 22% decrease in the number of parameters. Finally, we also demonstrate the generalization capabilities of our model to real-world HPE tasks beyond ego-views.
Parametrizing Product Shape Manifolds by Composite Networks
Authors: Josua Sassen; Klaus Hildebrandt; Martin Rumpf; Benedikt Wirth
Venue: ICLR 2023 (ICLR 2023 notable top 25%)

Abstract: Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which raises the question if one can learn an efficient neural network approximation. We show that this is indeed possible for shape spaces with a special product structure, namely those smoothly approximable by a direct sum of low-dimensional manifolds. Our proposed architecture leverages this structure by separately learning approximations for the low-dimensional factors and a subsequent combination. After developing the approach as a general framework, we apply it to a shape space of triangular surfaces. Here, typical examples of data manifolds are given through datasets of articulated models and can be factorized, for example, by a Sparse Principal Geodesic Analysis (SPGA). We demonstrate the effectiveness of our proposed approach with experiments on synthetic data as well as manifolds extracted from data via SPGA.
Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification
Authors: Takashi Ishida; Ikko Yamane; Nontawat Charoenphakdee; Gang Niu; Masashi Sugiyama
Venue: ICLR 2023 (ICLR 2023 notable top 5%)

Abstract: There is a fundamental limitation in the prediction performance that a machine learning model can achieve due to the inevitable uncertainty of the prediction target. In classification problems, this can be characterized by the Bayes error, which is the best achievable error with any classifier. The Bayes error can be used as a criterion to evaluate classifiers with state-of-the-art performance and can be used to detect test set overfitting. We propose a simple and direct Bayes error estimator, where we just take the mean of the labels that show \emph{uncertainty} of the class assignments. Our flexible approach enables us to perform Bayes error estimation even for weakly supervised data. In contrast to others, our method is model-free and even instance-free. Moreover, it has no hyperparameters and gives a more accurate estimate of the Bayes error than several baselines empirically. Experiments using our method suggest that recently proposed deep networks such as the Vision Transformer may have reached, or is about to reach, the Bayes error for benchmark datasets. Finally, we discuss how we can study the inherent difficulty of the acceptance/rejection decision for scientific articles, by estimating the Bayes error of the ICLR papers from 2017 to 2023.
Jump-Start Reinforcement Learning
Authors: Ikechukwu Uchendu; Ted Xiao; Yao Lu; Banghua Zhu; Mengyuan Yan; Joséphine Simon; Matthew Bennice; Chuyuan Fu; Cong Ma; Jiantao Jiao; Sergey Levine; Karol Hausman
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Reinforcement learning (RL) provides a theoretical framework for continuously improving an agent’s behavior via trial and error. However, efficiently learning policies from scratch can be very difficult, particularly for tasks that present exploration challenges. In such settings, it might be desirable to initialize RL with an existing policy, offline data, or demonstrations. However, naively performing such initialization in RL often works poorly, especially for value-based methods. In this paper, we present a meta algorithm that can use offline data, demonstrations, or a pre-existing policy to initialize an RL policy, and is compatible with any RL approach. In particular, we propose Jump-Start Reinforcement Learning (JSRL), an algorithm that employs two policies to solve tasks: a guide-policy, and an exploration-policy. By using the guide-policy to form a curriculum of starting states for the exploration-policy, we are able to efficiently improve performance on a set of simulated robotic tasks. We show via experiments that it is able to significantly outperform existing imitation and reinforcement learning algorithms, particularly in the small-data regime. In addition, we provide an upper bound on the sample complexity of JSRL and show that with the help of a guide-policy, one can improve the sample complexity for non-optimism exploration methods from exponential in horizon to polynomial.
The Multiple Subnetwork Hypothesis: Enabling Multidomain Learning by Isolating Task-Specific Subnetworks in Feedforward Neural Networks
Authors: Jacob William Renn; Ian Sotnek; Benjamin Harvey; Brian Caffo
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Neural networks have seen an explosion of usage and research in the past decade, particularly within the domains of computer vision and natural language processing. However, only recently have advancements in neural networks yielded performance improvements beyond narrow applications and translated to expanded multitask models capable of generalizing across multiple data types and modalities. Simultaneously, it has been shown that neural networks are overparameterized to a high degree, and pruning techniques have proved capable of significantly reducing the number of active weights within the network while largely preserving performance. In this work, we identify a methodology and network representational structure which allows a pruned network to employ previously unused weights to learn subsequent tasks. We employ these methodologies on well-known benchmarking datasets for testing purposes and show that networks trained using our approaches are able to learn multiple tasks, which may be related or unrelated, in parallel or in sequence without sacrificing performance on any task or exhibiting catastrophic forgetting.
ERL-Re$^2$: Efficient Evolutionary Reinforcement Learning with Shared State Representation and Individual Policy Representation 
Authors: Jianye HAO; Pengyi Li; Hongyao Tang; YAN ZHENG; Xian Fu; Zhaopeng Meng
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: Deep Reinforcement Learning (Deep RL) and Evolutionary Algorithm (EA) are two major paradigms of policy optimization with distinct learning principles, i.e., gradient-based v.s. gradient-free. An appealing research direction is integrating Deep RL and EA to devise new methods by fusing their complementary advantages. However, existing works on combining Deep RL and EA have two common drawbacks:1) the RL agent and EA agents learn their policies individually, neglecting efficient sharing of useful common knowledge; 2) parameter-level policy optimization guarantees no semantic level of behavior evolution for the EA side. In this paper, we propose Evolutionary Reinforcement Learning with Two-scale State Representation and Policy Representation (ERL-Re$^2$), a novel solution to the aforementioned two drawbacks. The key idea of ERL-Re$^2$ is two-scale representation: all EA and RL policies share the same nonlinear state representation while maintaining individual linear policy representations. The state representation conveys expressive common features of the environment learned by all the agents collectively; the linear policy representation provides a favorable space for efficient policy optimization, where novel behavior-level crossover and mutation operations can be performed. Moreover, the linear policy representation allows convenient generalization of policy fitness with the help of Policy-extended Value Function Approximator (PeVFA), further improving the sample efficiency of fitness estimation. The experiments on a range of continuous control tasks show that ERL-Re$^2$ consistently outperforms advanced baselines and achieves the State Of The Art (SOTA). Our code is available on  https://github.com/yeshenpy/ERL-Re2.
Universal Mini-Batch Consistency for Set Encoding Functions
Authors: Jeffrey Ryan Willette; Bruno Andreis; Juho Lee; Sung Ju Hwang
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Previous works have established solid foundations for neural set functions, complete with architectures which preserve the necessary properties for operating on sets, such as invariance to permutations of the set elements. Subsequent work has highlighted the utility of Mini-Batch Consistency (MBC), the ability to sequentially process any permutation of a set partition scheme (e.g. streaming chunks of data) while maintaining consistency guarantees on the output, although there are limited options for MBC architectures. We propose a framework which can convert an arbitrary non-MBC model to one which satisfies MBC. In doing so, we allow all set functions to universally be considered in an MBC setting (UMBC). Additionally, we explore a Monte Carlo dropout strategy made possible by our framework which allows performing Monte Carlo dropout on streaming sets while never seeing the entire set at once. We validate UMBC with theoretical proofs, unit tests, and also provide qualitative/quantitative experiments on Gaussian data, clean and corrupted point cloud classification, and amortized clustering on ImageNet. Additionally, we investigate the probabilistic calibration of set-functions under test-time distributional shifts. Our results demonstrate the utility of universal mini-batch consistency, and we further discover that our dropout strategy improves uncertainty calibration.
Learning to Counter: Stochastic Feature-based Learning for Diverse Counterfactual Explanations
Authors: Vy Vo; Trung Le; Van Nguyen; He Zhao; Edwin V. Bonilla; Gholamreza Haffari; Dinh Phung
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: Interpretable machine learning seeks to understand the reasoning process of complex black-box systems that are long notorious for lack of explainability. One growing interpreting approach is through counterfactual explanations, which go beyond why a system arrives at a certain decision to further provide suggestions on what a user can do to alter the outcome. A counterfactual example must be able to counter the original prediction from the black-box classifier, while also satisfying various constraints for practical applications. These constraints exist at trade-offs between one and another presenting radical challenges to existing works. To this end, we propose a stochastic learning-based framework that effectively balances the counterfactual trade-offs. The framework consists of a generation and a feature selection module with complementary roles: the former aims to model the distribution of valid counterfactuals whereas the latter serves to enforce additional constraints in a way that allows for differentiable training and amortized optimization. We demonstrate the effectiveness of our method in generating actionable and plausible counterfactuals that are more diverse than the existing methods and particularly in a more efficient manner than counterparts of the same capacity.
PAC Reinforcement Learning for Predictive State Representations
Authors: Wenhao Zhan; Masatoshi Uehara; Wen Sun; Jason D. Lee
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: In this paper we study online Reinforcement Learning (RL) in partially observable dynamical systems. We focus on the Predictive State Representations (PSRs) model, which is an expressive model that captures other well-known models such as Partially Observable Markov Decision Processes (POMDP). PSR represents the states using a set of predictions of future observations and is defined entirely using observable quantities. We develop a novel model-based algorithm for PSRs that can learn a near optimal policy in sample complexity scaling polynomially with respect to all the relevant parameters of the systems. Our algorithm naturally works with function approximation to extend to systems with potentially large state and observation spaces. We show that given a realizable model class, the sample complexity of learning the near optimal policy only scales polynomially with respect to the statistical complexity of the model class, without any explicit polynomial dependence on the size of the state and observation spaces. Notably, our work is the first work that shows polynomial sample complexities to compete with the globally optimal policy in PSRs. Finally, we demonstrate how our general theorem can be directly used to derive sample complexity bounds for special models including $m$-step weakly revealing and $m$-step decodable tabular POMDPs, POMDPs with low-rank latent transition, and POMDPs with linear emission and latent transition.
A Statistical Framework for Personalized Federated Learning and Estimation: Theory, Algorithms, and Privacy
Authors: Kaan Ozkara; Antonious M. Girgis; Deepesh Data; Suhas Diggavi
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: A distinguishing characteristic of federated learning is that the (local) client data could have statistical heterogeneity. This heterogeneity has motivated the design of personalized learning, where individual (personalized) models are trained, through collaboration. There have been various personalization methods proposed in literature, with seemingly very different forms and methods ranging from use of a single global model for local regularization and model interpolation, to use of multiple global models for personalized clustering, etc. In this work, we begin with a statistical framework that  unifies several different algorithms as well as suggest new algorithms.  We apply our framework to personalized estimation, and connect it to the classical empirical Bayes' methodology. We develop novel private personalized estimation under this framework. We then use our statistical framework to propose new personalized learning algorithms, including AdaPeD based on information-geometry regularization, which numerically outperforms several known algorithms. We develop privacy for personalized learning methods with guarantees for user-level privacy and composition. We numerically evaluate the performance as well as the privacy for both the estimation and learning problems, demonstrating the advantages of our proposed methods.
CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations
Authors: Peter Yichen Chen; Jinxu Xiang; Dong Heon Cho; Yue Chang; G A Pershing; Henrique Teles Maia; Maurizio M Chiaramonte; Kevin Thomas Carlberg; Eitan Grinspun
Venue: ICLR 2023 (ICLR 2023 notable top 25%)

Abstract: The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce the dimensionality of discretized vector fields, our continuous reduced-order modeling (CROM) approach builds a low-dimensional embedding of the continuous vector fields themselves, not their discretization. We represent this reduced manifold using continuously differentiable neural fields, which may train on any and all available numerical solutions of the continuous system, even when they are obtained using diverse methods or discretizations. We validate our approach on an extensive range of PDEs with training data from voxel grids, meshes, and point clouds. Compared to prior discretization-dependent ROM methods, such as linear subspace proper orthogonal decomposition (POD) and nonlinear manifold neural-network-based autoencoders, CROM features higher accuracy, lower memory consumption, dynamically adaptive resolutions, and applicability to any discretization. For equal latent space dimension, CROM exhibits 79$\times$ and 49$\times$ better accuracy, and 39$\times$ and 132$\times$ smaller memory footprint, than POD and autoencoder methods, respectively. Experiments demonstrate 109$\times$ and 89$\times$ wall-clock speedups over unreduced models on CPUs and GPUs, respectively. Videos and codes are available on the project page: https://crom-pde.github.io
Improved Convergence of Differential Private SGD with Gradient Clipping
Authors: Huang Fang; Xiaoyun Li; Chenglin Fan; Ping Li
Venue: ICLR 2023 (ICLR 2023 poster)

Abstract: Differential private stochastic gradient descent (DP-SGD) with gradient clipping (DP-SGD-GC) is an effective optimization algorithm that can train machine learning models with a privacy guarantee. Despite the popularity of DP-SGD-GC, its convergence in unbounded domain without the Lipschitz continuous assumption is less-understood; existing analysis of DP-SGD-GC either impose additional assumptions or end up with an utility bound that involves an non-vanishing bias term. In this work, for smooth and unconstrained problems, we improve the current analysis and show that DP-SGD-GC can achieve a vanishing utility bound without any bias term. Furthermore, when the noise generated from subsampled gradients is light-tailed, we prove that DP-SGD-GC can achieve nearly the same utility bound as DP-SGD applies to the Lipschitz continuous objectives. As a by-product, we propose a new clipping technique, called value clipping, to mitigate the computational overhead caused by the classic gradient clipping. Experiments on standard benchmark datasets are conducted to support our analysis.
Convergence of Generative Deep Linear Networks Trained with Bures-Wasserstein Loss
Authors: Pierre Bréchet; Katerina Papagiannouli; Jing An; Guido Montufar
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: We consider a deep matrix factorization model of covariance matrices trained with the Bures-Wasserstein distance. While recent works have made important advances in the study of the optimization problem for overparametrized low-rank matrix approximation, much emphasis has been placed on discriminative settings and the square loss. In contrast, our model considers another interesting type of loss and connects with the generative setting. We characterize the critical points and minimizers of the Bures-Wasserstein distance over the space of rank-bounded matrices. For low-rank matrices the Hessian of this loss can blow up, which creates challenges to analyze convergence of optimizaton methods. We establish convergence results for gradient flow using a smooth perturbative version of the loss and convergence results for finite step size gradient descent under certain assumptions on the initial weights
Newton Losses: Efficiently Including Second-Order Information into Gradient Descent
Authors: Felix Petersen; Christian Borgelt; Tobias Sutter; Hilde Kuehne; Oliver Deussen
Venue: ICLR 2023 (Submitted to ICLR 2023)

Abstract: We present Newton losses, a method for incorporating second-order information of losses by approximating them with quadratic functions. The presented method is applied only to the loss function and allows training the neural network with gradient descent. As loss functions are usually substantially cheaper to compute than the neural network, Newton losses can be used at a relatively small additional cost. We find that they yield superior performance, especially when applied to non-convex and hard-to-optimize loss functions such as algorithmic losses, which have been popularized in recent research.