ICLR 2021 论文列表

We propose Multi-Level Local SGD, a distributed stochastic gradient method for learning a smooth, non-convex objective in a multi-level communication network with heterogeneous workers. Our network model consists of a set of disjoint sub-networks, with a single hub and multiple workers; further, workers may have different operating rates. The hubs exchange information with one another via a connected, but not necessarily complete communication network. In our algorithm, sub-networks execute a distributed SGD algorithm, using a hub-and-spoke paradigm, and the hubs periodically average their models with neighboring hubs. We first provide a unified mathematical framework that describes the Multi-Level Local SGD algorithm. We then present a theoretical analysis of the algorithm; our analysis shows the dependence of the convergence error on the worker node heterogeneity, hub network topology, and the number of local, sub-network, and global iterations. We illustrate the effectiveness of our algorithm in a multi-level network with slow workers via simulation-based experiments.

A broad class of unsupervised deep learning methods such as Generative Adversarial Networks (GANs) involve training of overparameterized models where the number of parameters of the model exceeds a certain threshold. Indeed, most successful GANs used in practice are trained using overparameterized generator and discriminator networks, both in terms of depth and width. A large body of work in supervised learning have shown the importance of model overparameterization in the convergence of the gradient descent (GD) to globally optimal solutions. In contrast, the unsupervised setting and GANs in particular involve non-convex concave mini-max optimization problems that are often trained using Gradient Descent/Ascent (GDA). The role and benefits of model overparameterization in the convergence of GDA to a global saddle point in non-convex concave problems is far less understood. In this work, we present a comprehensive analysis of the importance of model overparameterization in GANs both theoretically and empirically. We theoretically show that in an overparameterized GAN model with a $1$-layer neural network generator and a linear discriminator, GDA converges to a global saddle point of the underlying non-convex concave min-max problem. To the best of our knowledge, this is the first result for global convergence of GDA in such settings. Our theory is based on a more general result that holds for a broader class of nonlinear generators and discriminators that obey certain assumptions (including deeper generators and random feature discriminators). Our theory utilizes and builds upon a novel connection with the convergence analysis of linear time-varying dynamical systems which may have broader implications for understanding the convergence behavior of GDA for non-convex concave problems involving overparameterized models. We also empirically study the role of model overparameterization in GANs using several large-scale experiments on CIFAR-10 and Celeb-A datasets. Our experiments show that overparameterization improves the quality of generated samples across various model architectures and datasets. Remarkably, we observe that overparameterization leads to faster and more stable convergence behavior of GDA across the board.

The largely successful method of training neural networks is to learn their weights using some variant of stochastic gradient descent (SGD). Here, we show that the solutions found by SGD can be further improved by ensembling a subset of the weights in late stages of learning. At the end of learning, we obtain back a single model by taking a spatial average in weight space. To avoid incurring increased computational costs, we investigate a family of low-dimensional late-phase weight models which interact multiplicatively with the remaining parameters. Our results show that augmenting standard models with late-phase weights improves generalization in established benchmarks such as CIFAR-10/100, ImageNet and enwik8. These findings are complemented with a theoretical analysis of a noisy quadratic problem which provides a simplified picture of the late phases of neural network learning.

The label shift problem refers to the supervised learning setting where the train and test label distributions do not match. Existing work addressing label shift usually assumes access to an unlabelled test sample. This sample may be used to estimate the test label distribution, and to then train a suitably re-weighted classifier. While approaches using this idea have proven effective, their scope is limited as it is not always feasible to access the target domain; further, they require repeated retraining if the model is to be deployed in multiple test environments. Can one instead learn a single classifier that is robust to arbitrary label shifts from a broad family? In this paper, we answer this question by proposing a model that minimises an objective based on distributionally robust optimisation (DRO). We then design and analyse a gradient descent-proximal mirror ascent algorithm tailored for large-scale problems to optimise the proposed objective. Finally, through experiments on CIFAR-100 and ImageNet, we show that our technique can significantly improve performance over a number of baselines in settings where label shift is present.

Invariant Causal Prediction (Peters et al., 2016) is a technique for out-of-distribution generalization which assumes that some aspects of the data distribution vary across the training set but that the underlying causal mechanisms remain constant. Recently, Arjovsky et al. (2019) proposed Invariant Risk Minimization (IRM), an objective based on this idea for learning deep, invariant features of data which are a complex function of latent variables; many alternatives have subsequently been suggested. However, formal guarantees for all of these works are severely lacking. In this paper, we present the first analysis of classification under the IRM objective—as well as these recently proposed alternatives—under a fairly natural and general model. In the linear case, we show simple conditions under which the optimal solution succeeds or, more often, fails to recover the optimal invariant predictor. We furthermore present the very first results in the non-linear regime: we demonstrate that IRM can fail catastrophically unless the test data is sufficiently similar to the training distribution—this is precisely the issue that it was intended to solve. Thus, in this setting we find that IRM and its alternatives fundamentally do not improve over standard Empirical Risk Minimization.

Neural networks are prone to learning shortcuts -- they often model simple correlations, ignoring more complex ones that potentially generalize better. Prior works on image classification show that instead of learning a connection to object shape, deep classifiers tend to exploit spurious correlations with low-level texture or the background for solving the classification task. In this work, we take a step towards more robust and interpretable classifiers that explicitly expose the task's causal structure. Building on current advances in deep generative modeling, we propose to decompose the image generation process into independent causal mechanisms that we train without direct supervision. By exploiting appropriate inductive biases, these mechanisms disentangle object shape, object texture, and background; hence, they allow for generating counterfactual images. We demonstrate the ability of our model to generate such images on MNIST and ImageNet. Further, we show that the counterfactual images can improve out-of-distribution robustness with a marginal drop in performance on the original classification task, despite being synthetic. Lastly, our generative model can be trained efficiently on a single GPU, exploiting common pre-trained models as inductive biases.

While successful for various computer vision tasks, deep neural networks have shown to be vulnerable to texture style shifts and small perturbations to which humans are robust. In this work, we show that the robustness of neural networks can be greatly improved through the use of random convolutions as data augmentation. Random convolutions are approximately shape-preserving and may distort local textures. Intuitively, randomized convolutions create an infinite number of new domains with similar global shapes but random local texture. Therefore, we explore using outputs of multi-scale random convolutions as new images or mixing them with the original images during training. When applying a network trained with our approach to unseen domains, our method consistently improves the performance on domain generalization benchmarks and is scalable to ImageNet. In particular, in the challenging scenario of generalizing to the sketch domain in PACS and to ImageNet-Sketch, our method outperforms state-of-art methods by a large margin. More interestingly, our method can benefit downstream tasks by providing a more robust pretrained visual representation.

Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. Mahloujifar et al. (2019) presented an empirical way to measure the concentration of a data distribution using samples, and employed it to find lower bounds on intrinsic robustness for several benchmark datasets. However, it remains unclear whether these lower bounds are tight enough to provide a useful approximation for the intrinsic robustness of a dataset. To gain a deeper understanding of the concentration of measure phenomenon, we first extend the Gaussian Isoperimetric Inequality to non-spherical Gaussian measures and arbitrary $\ell_p$-norms ($p \geq 2$). We leverage these theoretical insights to design a method that uses half-spaces to estimate the concentration of any empirical dataset under $\ell_p$-norm distance metrics. Our proposed algorithm is more efficient than Mahloujifar et al. (2019)'s, and experiments on synthetic datasets and image benchmarks demonstrate that it is able to find much tighter intrinsic robustness bounds. These tighter estimates provide further evidence that rules out intrinsic dataset concentration as a possible explanation for the adversarial vulnerability of state-of-the-art classifiers.

The recommendation system (RS) plays an important role in the content recommendation and retrieval scenarios. The core part of the system is the Ranking neural network, which is usually a bottleneck of whole system performance during online inference. In this work, we propose a unified model and embedding compression (UMEC) framework to hammer an efficient neural network-based recommendation system. Our framework jointly learns input feature selection and neural network compression together, and solve them as an end-to-end resource-constrained optimization problem using ADMM. Our method outperforms other baselines in terms of neural network Flops, sparse embedding feature size and the number of sparse embedding features. We evaluate our method on the public benchmark of DLRM, trained over the Kaggle Criteo dataset. The codes can be found at https://github.com/VITA-Group/UMEC.

Predicting the behaviors of Hamiltonian systems has been drawing increasing attention in scientific machine learning. However, the vast majority of the literature was focused on predicting separable Hamiltonian systems with their kinematic and potential energy terms being explicitly decoupled, while building data-driven paradigms to predict nonseparable Hamiltonian systems that are ubiquitous in fluid dynamics and quantum mechanics were rarely explored. The main computational challenge lies in the effective embedding of symplectic priors to describe the inherently coupled evolution of position and momentum, which typically exhibits intricate dynamics. To solve the problem, we propose a novel neural network architecture, Nonseparable Symplectic Neural Networks (NSSNNs), to uncover and embed the symplectic structure of a nonseparable Hamiltonian system from limited observation data. The enabling mechanics of our approach is an augmented symplectic time integrator to decouple the position and momentum energy terms and facilitate their evolution. We demonstrated the efficacy and versatility of our method by predicting a wide range of Hamiltonian systems, both separable and nonseparable, including chaotic vortical flows. We showed the unique computational merits of our approach to yield long-term, accurate, and robust predictions for large-scale Hamiltonian systems by rigorously enforcing symplectomorphism.

In this work, we examine the security of InstaHide, a scheme recently proposed by \cite{hsla20} for preserving the security of private datasets in the context of distributed learning. To generate a synthetic training example to be shared among the distributed learners, InstaHide takes a convex combination of private feature vectors and randomly flips the sign of each entry of the resulting vector with probability 1/2. A salient question is whether this scheme is secure in any provable sense, perhaps under a plausible complexity-theoretic assumption. The answer to this turns out to be quite subtle and closely related to the average-case complexity of a multi-task, missing-data version of the classic problem of phase retrieval that is interesting in its own right. Motivated by this connection, under the standard distributional assumption that the public/private feature vectors are isotropic Gaussian, we design an algorithm that can actually recover a private vector using only the public vectors and a sequence of synthetic vectors generated by InstaHide.

Using a high Update-To-Data (UTD) ratio, model-based methods have recently achieved much higher sample efficiency than previous model-free methods for continuous-action DRL benchmarks. In this paper, we introduce a simple model-free algorithm, Randomized Ensembled Double Q-Learning (REDQ), and show that its performance is just as good as, if not better than, a state-of-the-art model-based algorithm for the MuJoCo benchmark. Moreover, REDQ can achieve this performance using fewer parameters than the model-based method, and with less wall-clock run time. REDQ has three carefully integrated ingredients which allow it to achieve its high performance: (i) a UTD ratio $\gg 1$; (ii) an ensemble of Q functions; (iii) in-target minimization across a random subset of Q functions from the ensemble. Through carefully designed experiments, we provide a detailed analysis of REDQ and related model-free algorithms. To our knowledge, REDQ is the first successful model-free DRL algorithm for continuous-action spaces using a UTD ratio $\gg 1$.

We study the role that a finite timescale separation parameter $\tau$ has on gradient descent-ascent in non-convex, non-concave zero-sum games where the learning rate of player 1 is denoted by $\gamma_1$ and the learning rate of player 2 is defined to be $\gamma_2=\tau\gamma_1$. We provide a non-asymptotic construction of the finite timescale separation parameter $\tau^{\ast}$ such that gradient descent-ascent locally converges to $x^{\ast}$ for all $\tau \in (\tau^{\ast}, \infty)$ if and only if it is a strict local minmax equilibrium. Moreover, we provide explicit local convergence rates given the finite timescale separation. The convergence results we present are complemented by a non-convergence result: given a critical point $x^{\ast}$ that is not a strict local minmax equilibrium, we present a non-asymptotic construction of a finite timescale separation $\tau_{0}$ such that gradient descent-ascent with timescale separation $\tau\in (\tau_0, \infty)$ does not converge to $x^{\ast}$. Finally, we extend the results to gradient penalty regularization methods for generative adversarial networks and empirically demonstrate on CIFAR-10 and CelebA the significant impact timescale separation has on training performance.

Recent research has proposed neural architectures for solving combinatorial problems in structured output spaces. In many such problems, there may exist multiple solutions for a given input, e.g. a partially filled Sudoku puzzle may have many completions satisfying all constraints. Further, we are often interested in finding any "one" of the possible solutions, without any preference between them. Existing approaches completely ignore this solution multiplicity. In this paper, we argue that being oblivious to the presence of multiple solutions can severely hamper their training ability. Our contribution is two-fold. First, we formally define the task of learning one-of-many solutions for combinatorial problems in structured output spaces, which is applicable for solving several problems of interest such as N-Queens, and Sudoku. Second, we present a generic learning framework that adapts an existing prediction network for a combinatorial problem to handle solution multiplicity. Our framework uses a selection module, whose goal is to dynamically determine, for every input, the solution that is most effective for training the network parameters in any given learning iteration. We propose an RL based approach to jointly train the selection module with the prediction network. Experiments on three different domains, and using two different prediction networks, demonstrate that our framework significantly improves the accuracy in our setting, obtaining up to 21 pt gain over the baselines.

Post-hoc multi-class calibration is a common approach for providing high-quality confidence estimates of deep neural network predictions. Recent work has shown that widely used scaling methods underestimate their calibration error, while alternative Histogram Binning (HB) methods often fail to preserve classification accuracy. When classes have small prior probabilities, HB also faces the issue of severe sample-inefficiency after the conversion into K one-vs-rest class-wise calibration problems. The goal of this paper is to resolve the identified issues of HB in order to provide calibrated confidence estimates using only a small holdout calibration dataset for bin optimization while preserving multi-class ranking accuracy. From an information-theoretic perspective, we derive the I-Max concept for binning, which maximizes the mutual information between labels and quantized logits. This concept mitigates potential loss in ranking performance due to lossy quantization, and by disentangling the optimization of bin edges and representatives allows simultaneous improvement of ranking and calibration performance. To improve the sample efficiency and estimates from a small calibration set, we propose a shared class-wise (sCW) calibration strategy, sharing one calibrator among similar classes (e.g., with similar class priors) so that the training sets of their class-wise calibration problems can be merged to train the single calibrator. The combination of sCW and I-Max binning outperforms the state of the art calibration methods on various evaluation metrics across different benchmark datasets and models, using a small calibration set (e.g., 1k samples for ImageNet).

This paper is concerned with self-supervised learning for small models. The problem is motivated by our empirical studies that while the widely used contrastive self-supervised learning method has shown great progress on large model training, it does not work well for small models. To address this problem, we propose a new learning paradigm, named $\textbf{SE}$lf-Sup$\textbf{E}$rvised $\textbf{D}$istillation (${\large S}$EED), where we leverage a larger network (as Teacher) to transfer its representational knowledge into a smaller architecture (as Student) in a self-supervised fashion. Instead of directly learning from unlabeled data, we train a student encoder to mimic the similarity score distribution inferred by a teacher over a set of instances. We show that ${\large S}$EED dramatically boosts the performance of small networks on downstream tasks. Compared with self-supervised baselines, ${\large S}$EED improves the top-1 accuracy from 42.2% to 67.6% on EfficientNet-B0 and from 36.3% to 68.2% on MobileNet-v3-Large on the ImageNet-1k dataset.

Matrix factorization is a simple and natural test-bed to investigate the implicit regularization of gradient descent. Gunasekar et al. (2017) conjectured that gradient flow with infinitesimal initialization converges to the solution that minimizes the nuclear norm, but a series of recent papers argued that the language of norm minimization is not sufficient to give a full characterization for the implicit regularization. In this work, we provide theoretical and empirical evidence that for depth-2 matrix factorization, gradient flow with infinitesimal initialization is mathematically equivalent to a simple heuristic rank minimization algorithm, Greedy Low-Rank Learning, under some reasonable assumptions. This generalizes the rank minimization view from previous works to a much broader setting and enables us to construct counter-examples to refute the conjecture from Gunasekar et al. (2017). We also extend the results to the case where depth >= 3, and we show that the benefit of being deeper is that the above convergence has a much weaker dependence over initialization magnitude so that this rank minimization is more likely to take effect for initialization with practical scale.

A hallmark of human intelligence is the ability to construct self-contained chunks of knowledge and adequately reuse them in novel combinations for solving different yet structurally related problems. Learning such compositional structures has been a significant challenge for artificial systems, due to the combinatorial nature of the underlying search problem. To date, research into compositional learning has largely proceeded separately from work on lifelong or continual learning. We integrate these two lines of work to present a general-purpose framework for lifelong learning of compositional structures that can be used for solving a stream of related tasks. Our framework separates the learning process into two broad stages: learning how to best combine existing components in order to assimilate a novel problem, and learning how to adapt the set of existing components to accommodate the new problem. This separation explicitly handles the trade-off between the stability required to remember how to solve earlier tasks and the flexibility required to solve new tasks, as we show empirically in an extensive evaluation.

We present Wasserstein Embedding for Graph Learning (WEGL), a novel and fast framework for embedding entire graphs in a vector space, in which various machine learning models are applicable for graph-level prediction tasks. We leverage new insights on defining similarity between graphs as a function of the similarity between their node embedding distributions. Specifically, we use the Wasserstein distance to measure the dissimilarity between node embeddings of different graphs. Unlike prior work, we avoid pairwise calculation of distances between graphs and reduce the computational complexity from quadratic to linear in the number of graphs. WEGL calculates Monge maps from a reference distribution to each node embedding and, based on these maps, creates a fixed-sized vector representation of the graph. We evaluate our new graph embedding approach on various benchmark graph-property prediction tasks, showing state-of-the-art classification performance while having superior computational efficiency. The code is available at https://github.com/navid-naderi/WEGL.