ICML 2023 Papers

This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an infinite hierarchy of non-convex problems via the lifting technique and the Burer-Monteiro factorization. This contrasts with the existing over-parametrization technique where the search rank is limited by the dimension of the matrix and it does not allow a rich over-parametrization of an arbitrary degree. We show that although the spurious solutions of the problem remain stationary points through the hierarchy, they will be transformed into strict saddle points (under some technical conditions) and can be escaped via local search methods. This is the first result in the literature showing that over-parametrization creates a negative curvature for escaping spurious solutions. We also derive a bound on how much over-parametrization is requited to enable the elimination of spurious solutions.

In this paper, we introduce the idea of decomposing the residuals of regression with respect to the data instances instead of features. This allows us to determine the effects of each individual instance on the model and each other, and in doing so makes for a model-agnostic method of identifying instances of interest. In doing so, we can also determine the appropriateness of the model and data in the wider context of a given study. The paper focuses on the possible applications that such a framework brings to the relatively unexplored field of instance analysis in the context of Explainable AI tasks.

We study the problem of imputing missing values in a dataset, which has important applications in many domains. The key to missing value imputation is to capture the data distribution with incomplete samples and impute the missing values accordingly. In this paper, by leveraging the fact that any two batches of data with missing values come from the same data distribution, we propose to impute the missing values of two batches of samples by transforming them into a latent space through deep invertible functions and matching them distributionally. To learn the transformations and impute the missing values simultaneously, a simple and well-motivated algorithm is proposed. Our algorithm has fewer hyperparameters to fine-tune and generates high-quality imputations regardless of how missing values are generated. Extensive experiments over a large number of datasets and competing benchmark algorithms show that our method achieves state-of-the-art performance.

Many compression techniques have been proposed to reduce the communication overhead of Federated Learning training procedures. However, these are typically designed for compressing model updates, which are expected to decay throughout training. As a result, such methods are inapplicable to downlink (i.e., from the parameter server to clients) compression in the cross-device setting, where heterogeneous clients *may appear only once* during training and thus must download the model parameters. Accordingly, we propose DoCoFL -- a new framework for downlink compression in the cross-device setting. Importantly, DoCoFL can be seamlessly combined with many uplink compression schemes, rendering it suitable for bi-directional compression. Through extensive evaluation, we show that DoCoFL offers significant bi-directional bandwidth reduction while achieving competitive accuracy to that of a baseline without any compression.

Latent variable models (LVMs) with discrete compositional latents are an important but challenging setting due to a combinatorially large number of possible configurations of the latents. A key tradeoff in modeling the posteriors over latents is between expressivity and tractable optimization. For algorithms based on expectation-maximization (EM), the E-step is often intractable without restrictive approximations to the posterior. We propose the use of GFlowNets, algorithms for sampling from an unnormalized density by learning a stochastic policy for sequential construction of samples, for this intractable E-step. By training GFlowNets to sample from the posterior over latents, we take advantage of their strengths as amortized variational inference algorithms for complex distributions over discrete structures. Our approach, GFlowNet-EM, enables the training of expressive LVMs with discrete compositional latents, as shown by experiments on non-context-free grammar induction and on images using discrete variational autoencoders (VAEs) without conditional independence enforced in the encoder.

A classic result in the theory of extensive-form games asserts that the set of strategies available to any perfect-recall player is strategically equivalent to a low-dimensional convex polytope, called the *sequence-form polytope*. Online convex optimization tools operating on this polytope are the current state-of-the-art for computing several notions of equilibria in games, and have been crucial in landmark applications of computational game theory. However, when optimizing over the *joint* strategy space of a *team* of players, one cannot use the sequence form to obtain a strategically-equivalent convex description of the strategy set of the team. In this paper, we provide new complexity results on the computation of optimal strategies for teams, and propose a new representation, coined *team belief DAG (TB-DAG)*, that describes team strategies as a convex set. The TB-DAG enjoys state-of-the-art parameterized complexity bounds, while at the same time enjoying the advantages of efficient regret minimization techniques. We show that TB-DAG can be exponentially smaller and can be computed exponentially faster than all other known representations, and that the converse is never true. Experimentally, we show that the TB-DAG, when paired with learning techniques, yields state of the art on a wide variety of benchmark team games.

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the *data separation function*. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to $1$ in the general case of arbitrary normalized dataset consisting of $n$ samples in $d$ dimension as $n/\sqrt{d}\rightarrow 0$. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes *kinetic optimal* as $n/\sqrt{d}\rightarrow 0$. We further support this theory with empirical experiments on ImageNet.

We initiate the study of proper losses for evaluating generative models in the discrete setting. Unlike traditional proper losses, we treat both the generative model and the target distribution as black-boxes, only assuming ability to draw i.i.d. samples. We define a loss to be black-box proper if the generative distribution that minimizes expected loss is equal to the target distribution. Using techniques from statistical estimation theory, we give a general construction and characterization of black-box proper losses: they must take a polynomial form, and the number of draws from the model and target distribution must exceed the degree of the polynomial. The characterization rules out a loss whose expectation is the cross-entropy between the target distribution and the model. By extending the construction to arbitrary sampling schemes such as Poisson sampling, however, we show that one can construct such a loss.

The use of deep neural networks in real-world applications require well-calibrated networks with confidence scores that accurately reflect the actual probability. However, it has been found that these networks often provide over-confident predictions, which leads to poor calibration. Recent efforts have sought to address this issue by focal loss to reduce over-confidence, but this approach can also lead to under-confident predictions. While different variants of focal loss have been explored, it is difficult to find a balance between over-confidence and under-confidence. In our work, we propose a new loss function by focusing on dual logits. Our method not only considers the ground truth logit, but also take into account the highest logit ranked after the ground truth logit. By maximizing the gap between these two logits, our proposed dual focal loss can achieve a better balance between over-confidence and under-confidence. We provide theoretical evidence to support our approach and demonstrate its effectiveness through evaluations on multiple models and datasets, where it achieves state-of-the-art performance. Code is available at https://github.com/Linwei94/DualFocalLoss

The learnware paradigm aims to build a learnware market containing numerous learnwares, each of which is a well-performing machine learning model with a corresponding specification to describe its functionality so that future users can identify useful models for reuse according to their own requirements. With the learnware paradigm, model developers can spontaneously submit models to the market without leaking data privacy, and users can leverage models in the market to accomplish different machine learning tasks without having to build models from scratch. Recent studies have attempted to realize the model specification through Reduced Kernel Mean Embedding (RKME). In this paper, we make an attempt to improve the effectiveness of RKME specification for heterogeneous label spaces, where the learnware market does not contain a model that has the same label space as the user's task, by considering a class-specific model specification explicitly, along with a class-wise learnware identification method. Both theoretical and empirical analyses show that our proposal can quickly and accurately find useful learnwares that satisfy users' requirements. Moreover, we find that for a specific task, reusing a small model identified via the specification performs better than directly reusing a pre-trained generic big model.

We present AIRS: **A**utomatic **I**ntrinsic **R**eward **S**haping that intelligently and adaptively provides high-quality intrinsic rewards to enhance exploration in reinforcement learning (RL). More specifically, AIRS selects shaping function from a predefined set based on the estimated task return in real-time, providing reliable exploration incentives and alleviating the biased objective problem. Moreover, we develop an intrinsic reward toolkit to provide efficient and reliable implementations of diverse intrinsic reward approaches. We test AIRS on various tasks of MiniGrid, Procgen, and DeepMind Control Suite. Extensive simulation demonstrates that AIRS can outperform the benchmarking schemes and achieve superior performance with simple architecture.

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.

Offline goal-conditioned RL (GCRL) offers a way to train general-purpose agents from fully offline datasets. In addition to being conservative within the dataset, the generalization ability to achieve unseen goals is another fundamental challenge for offline GCRL. However, to the best of our knowledge, this problem has not been well studied yet. In this paper, we study out-of-distribution (OOD) generalization of offline GCRL both theoretically and empirically to identify factors that are important. In a number of experiments, we observe that weighted imitation learning enjoys better generalization than pessimism-based offline RL method. Based on this insight, we derive a theory for OOD generalization, which characterizes several important design choices. We then propose a new offline GCRL method, Generalizable Offline goAl-condiTioned RL (GOAT), by combining the findings from our theoretical and empirical studies. On a new benchmark containing 9 independent identically distributed (IID) tasks and 17 OOD tasks, GOAT outperforms current state-of-the-art methods by a large margin.

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. In this paper we contribute to the understanding of such flows. We propose to approximate the backward scheme of Jordan, Kinderlehrer and Otto for computing such Wasserstein gradient flows as well as a forward scheme for so-called Wasserstein steepest descent flows by neural networks (NNs). Since we cannot restrict ourselves to absolutely continuous measures, we have to deal with transport plans and velocity plans instead of usual transport maps and velocity fields. Indeed, we approximate the disintegration of both plans by generative NNs which are learned with respect to appropriate loss functions. In order to evaluate the quality of both neural schemes, we benchmark them on the interaction energy. Here we provide analytic formulas for Wasserstein schemes starting at a Dirac measure and show their convergence as the time step size tends to zero. Finally, we illustrate our neural MMD flows by numerical examples.

Persistent homology is arguably the most successful technique in Topological Data Analysis. It combines homology, a topological feature of a data set, with persistence, which tracks the evolution of homology over different scales. The persistent Laplacian is a recent theoretical development that combines persistence with the combinatorial Laplacian, the higher-order extension of the well-known graph Laplacian. Crucially, the Laplacian encode both the homology of a data set, and some additional geometric information not captured by the homology. Here, we provide the first investigation into the efficacy of the persistence Laplacian as an embedding of data for downstream classification and regression tasks. We extend the persistent Laplacian to cubical complexes so it can be used on images, then evaluate its performance as an embedding method on the MNIST and MoleculeNet datasets, demonstrating that it consistently outperforms persistent homology across tasks.

Recent work has shown that leveraging learned predictions can improve the running time of algorithms for bipartite matching and similar combinatorial problems. In this work, we build on this idea to improve the performance of the widely used Ford-Fulkerson algorithm for computing maximum flows by seeding Ford-Fulkerson with predicted flows. Our proposed method offers strong theoretical performance in terms of the quality of the prediction. We then consider image segmentation, a common use-case of flows in computer vision, and complement our theoretical analysis with strong empirical results.

$k$-nearest neighbor classification is a popular non-parametric method because of desirable properties like automatic adaption to distributional scale changes. Unfortunately, it has thus far proved difficult to design active learning strategies for the training of local voting-based classifiers that naturally retain these desirable properties, and hence active learning strategies for $k$-nearest neighbor classification have been conspicuously missing from the literature. In this work, we introduce a simple and intuitive active learning algorithm for the training of $k$-nearest neighbor classifiers, the first in the literature which retains the concept of the $k$-nearest neighbor vote at prediction time. We provide consistency guarantees for a modified $k$-nearest neighbors classifier trained on samples acquired via our scheme, and show that when the conditional probability function $\mathbb{P}(Y=y|X=x)$ is sufficiently smooth and the Tsybakov noise condition holds, our actively trained classifiers converge to the Bayes optimal classifier at a faster asymptotic rate than passively trained $k$-nearest neighbor classifiers.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search direction at each iteration. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We demonstrate the efficacy of our approach on spatially discretized Poisson equations, which arise in computational fluid dynamics applications, with millions of degrees of freedom. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

The top-$k$ classification accuracy is a crucial metric in machine learning and is often used to evaluate the performance of deep neural networks. These networks are typically trained using the cross-entropy loss, which optimizes for top-$1$ classification and is considered optimal in the case of infinite data. However, in real-world scenarios, data is often noisy and limited, leading to the need for more robust losses. In this paper, we propose using the Weighted Sampling Without Replacement (WSWR) method as a learning objective for top-$k$ loss. While traditional methods for evaluating **WSWR-based top-$k$ loss** are computationally impractical, we show a novel connection between WSWR and Reinforcement Learning (RL) and apply well-established RL algorithms to estimate gradients. We compared our method with recently proposed top-$k$ losses in various regimes of noise and data size for the prevalent use case of $k = 5$. Our experimental results reveal that our method consistently outperforms all other methods on the top-$k$ metric for noisy datasets, has more robustness on extreme testing scenarios, and achieves competitive results on training with limited data.