ICLR 2020 论文列表

Deep neural networks (DNNs) have great expressive power, which can even memorize samples with wrong labels. It is vitally important to reiterate robustness and generalization in DNNs against label corruption. To this end, this paper studies the 0-1 loss, which has a monotonic relationship between empirical adversary (reweighted) risk (Hu et al. 2018). Although the 0-1 loss is robust to outliers, it is also difficult to optimize. To efficiently optimize the 0-1 loss while keeping its robust properties, we propose a very simple and efficient loss, i.e. curriculum loss (CL). Our CL is a tighter upper bound of the 0-1 loss compared with conventional summation based surrogate losses. Moreover, CL can adaptively select samples for stagewise training. As a result, our loss can be deemed as a novel perspective of curriculum sample selection strategy, which bridges a connection between curriculum learning and robust learning. Experimental results on noisy MNIST, CIFAR10 and CIFAR100 dataset validate the robustness of the proposed loss.

The selection of initial parameter values for gradient-based optimization of deep neural networks is one of the most impactful hyperparameter choices in deep learning systems, affecting both convergence times and model performance. Yet despite significant empirical and theoretical analysis, relatively little has been proved about the concrete effects of different initialization schemes. In this work, we analyze the effect of initialization in deep linear networks, and provide for the first time a rigorous proof that drawing the initial weights from the orthogonal group speeds up convergence relative to the standard Gaussian initialization with iid weights. We show that for deep networks, the width needed for efficient convergence to a global minimum with orthogonal initializations is independent of the depth, whereas the width needed for efficient convergence with Gaussian initializations scales linearly in the depth. Our results demonstrate how the benefits of a good initialization can persist throughout learning, suggesting an explanation for the recent empirical successes found by initializing very deep non-linear networks according to the principle of dynamical isometry.

We study the benefit of sharing representations among tasks to enable the effective use of deep neural networks in Multi-Task Reinforcement Learning. We leverage the assumption that learning from different tasks, sharing common properties, is helpful to generalize the knowledge of them resulting in a more effective feature extraction compared to learning a single task. Intuitively, the resulting set of features offers performance benefits when used by Reinforcement Learning algorithms. We prove this by providing theoretical guarantees that highlight the conditions for which is convenient to share representations among tasks, extending the well-known finite-time bounds of Approximate Value-Iteration to the multi-task setting. In addition, we complement our analysis by proposing multi-task extensions of three Reinforcement Learning algorithms that we empirically evaluate on widely used Reinforcement Learning benchmarks showing significant improvements over the single-task counterparts in terms of sample efficiency and performance.

In this work, we develop the theory for analyzing the generalization performance of recurrent neural networks. We first present a new generalization bound for recurrent neural networks based on matrix 1-norm and Fisher-Rao norm. The definition of Fisher-Rao norm relies on a structural lemma about the gradient of RNNs. This new generalization bound assumes that the covariance matrix of the input data is positive definite, which might limit its use in practice. To address this issue, we propose to add random noise to the input data and prove a generalization bound for training with random noise, which is an extension of the former one. Compared with existing results, our generalization bounds have no explicit dependency on the size of networks. We also discover that Fisher-Rao norm for RNNs can be interpreted as a measure of gradient, and incorporating this gradient measure not only can tighten the bound, but allows us to build a relationship between generalization and trainability. Based on the bound, we theoretically analyze the effect of covariance of features on generalization of RNNs and discuss how weight decay and gradient clipping in the training can help improve generalization.

It is well-known that overparametrized neural networks trained using gradient based methods quickly achieve small training error with appropriate hyperparameter settings. Recent papers have proved this statement theoretically for highly overparametrized networks under reasonable assumptions. These results either assume that the activation function is ReLU or they depend on the minimum eigenvalue of a certain Gram matrix. In the latter case, existing works only prove that this minimum eigenvalue is non-zero and do not provide quantitative bounds which require that this eigenvalue be large. Empirically, a number of alternative activation functions have been proposed which tend to perform better than ReLU at least in some settings but no clear understanding has emerged. This state of affairs underscores the importance of theoretically understanding the impact of activation functions on training. In the present paper, we provide theoretical results about the effect of activation function on the training of highly overparametrized 2-layer neural networks. A crucial property that governs the performance of an activation is whether or not it is smooth: • For non-smooth activations such as ReLU, SELU, ELU, which are not smooth because there is a point where either the first order or second order derivative is discontinuous, all eigenvalues of the associated Gram matrix are large under minimal assumptions on the data. • For smooth activations such as tanh, swish, polynomial, which have derivatives of all orders at all points, the situation is more complex: if the subspace spanned by the data has small dimension then the minimum eigenvalue of the Gram matrix can be small leading to slow training. But if the dimension is large and the data satisfies another mild condition, then the eigenvalues are large. If we allow deep networks, then the small data dimension is not a limitation provided that the depth is sufficient. We discuss a number of extensions and applications of these results.

We consider off-policy policy evaluation when the trajectory data are generated by multiple behavior policies. Recent work has shown the key role played by the state or state-action stationary distribution corrections in the infinite horizon context for off-policy policy evaluation. We propose estimated mixture policy (EMP), a novel class of partially policy-agnostic methods to accurately estimate those quantities. With careful analysis, we show that EMP gives rise to estimates with reduced variance for estimating the state stationary distribution correction while it also offers a useful induction bias for estimating the state-action stationary distribution correction. In extensive experiments with both continuous and discrete environments, we demonstrate that our algorithm offers significantly improved accuracy compared to the state-of-the-art methods.

The critical locus of the loss function of a neural network is determined by the geometry of the functional space and by the parameterization of this space by the network's weights. We introduce a natural distinction between pure critical points, which only depend on the functional space, and spurious critical points, which arise from the parameterization. We apply this perspective to revisit and extend the literature on the loss function of linear neural networks. For this type of network, the functional space is either the set of all linear maps from input to output space, or a determinantal variety, i.e., a set of linear maps with bounded rank. We use geometric properties of determinantal varieties to derive new results on the landscape of linear networks with different loss functions and different parameterizations. Our analysis clearly illustrates that the absence of "bad" local minima in the loss landscape of linear networks is due to two distinct phenomena that apply in different settings: it is true for arbitrary smooth convex losses in the case of architectures that can express all linear maps ("filling architectures") but it holds only for the quadratic loss when the functional space is a determinantal variety ("non-filling architectures"). Without any assumption on the architecture, smooth convex losses may lead to landscapes with many bad minima.

Deep networks run with low precision operations at inference time offer power and space advantages over high precision alternatives, but need to overcome the challenge of maintaining high accuracy as precision decreases. Here, we present a method for training such networks, Learned Step Size Quantization, that achieves the highest accuracy to date on the ImageNet dataset when using models, from a variety of architectures, with weights and activations quantized to 2-, 3- or 4-bits of precision, and that can train 3-bit models that reach full precision baseline accuracy. Our approach builds upon existing methods for learning weights in quantized networks by improving how the quantizer itself is configured. Specifically, we introduce a novel means to estimate and scale the task loss gradient at each weight and activation layer's quantizer step size, such that it can be learned in conjunction with other network parameters. This approach works using different levels of precision as needed for a given system and requires only a simple modification of existing training code.

An important research direction in machine learning has centered around developing meta-learning algorithms to tackle few-shot learning. An especially successful algorithm has been Model Agnostic Meta-Learning (MAML), a method that consists of two optimization loops, with the outer loop finding a meta-initialization, from which the inner loop can efficiently learn new tasks. Despite MAML's popularity, a fundamental open question remains -- is the effectiveness of MAML due to the meta-initialization being primed for rapid learning (large, efficient changes in the representations) or due to feature reuse, with the meta initialization already containing high quality features? We investigate this question, via ablation studies and analysis of the latent representations, finding that feature reuse is the dominant factor. This leads to the ANIL (Almost No Inner Loop) algorithm, a simplification of MAML where we remove the inner loop for all but the (task-specific) head of the underlying neural network. ANIL matches MAML's performance on benchmark few-shot image classification and RL and offers computational improvements over MAML. We further study the precise contributions of the head and body of the network, showing that performance on the test tasks is entirely determined by the quality of the learned features, and we can remove even the head of the network (the NIL algorithm). We conclude with a discussion of the rapid learning vs feature reuse question for meta-learning algorithms more broadly.

In this paper, we present an approach to learn recomposable motor primitives across large-scale and diverse manipulation demonstrations. Current approaches to decomposing demonstrations into primitives often assume manually defined primitives and bypass the difficulty of discovering these primitives. On the other hand, approaches in primitive discovery put restrictive assumptions on the complexity of a primitive, which limit applicability to narrow tasks. Our approach attempts to circumvent these challenges by jointly learning both the underlying motor primitives and recomposing these primitives to form the original demonstration. Through constraints on both the parsimony of primitive decomposition and the simplicity of a given primitive, we are able to learn a diverse set of motor primitives, as well as a coherent latent representation for these primitives. We demonstrate both qualitatively and quantitatively, that our learned primitives capture semantically meaningful aspects of a demonstration. This allows us to compose these primitives in a hierarchical reinforcement learning setup to efficiently solve robotic manipulation tasks like reaching and pushing. Our results may be viewed at https://sites.google.com/view/discovering-motor-programs.

Few-shot classification refers to learning a classifier for new classes given only a few examples. While a plethora of models have emerged to tackle it, we find the procedure and datasets that are used to assess their progress lacking. To address this limitation, we propose Meta-Dataset: a new benchmark for training and evaluating models that is large-scale, consists of diverse datasets, and presents more realistic tasks. We experiment with popular baselines and meta-learners on Meta-Dataset, along with a competitive method that we propose. We analyze performance as a function of various characteristics of test tasks and examine the models’ ability to leverage diverse training sources for improving their generalization. We also propose a new set of baselines for quantifying the benefit of meta-learning in Meta-Dataset. Our extensive experimentation has uncovered important research challenges and we hope to inspire work in these directions.

Recently mean field theory has been successfully used to analyze properties of wide, random neural networks. It gave rise to a prescriptive theory for initializing feed-forward neural networks with orthogonal weights, which ensures that both the forward propagated activations and the backpropagated gradients are near \(\ell_2\) isometries and as a consequence training is orders of magnitude faster. Despite strong empirical performance, the mechanisms by which critical initializations confer an advantage in the optimization of deep neural networks are poorly understood. Here we show a novel connection between the maximum curvature of the optimization landscape (gradient smoothness) as measured by the Fisher information matrix (FIM) and the spectral radius of the input-output Jacobian, which partially explains why more isometric networks can train much faster. Furthermore, given that orthogonal weights are necessary to ensure that gradient norms are approximately preserved at initialization, we experimentally investigate the benefits of maintaining orthogonality throughout training, and we conclude that manifold optimization of weights performs well regardless of the smoothness of the gradients. Moreover, we observe a surprising yet robust behavior of highly isometric initializations --- even though such networks have a lower FIM condition number \emph{at initialization}, and therefore by analogy to convex functions should be easier to optimize, experimentally they prove to be much harder to train with stochastic gradient descent. We conjecture the FIM condition number plays a non-trivial role in the optimization.

We consider the large-scale query-document retrieval problem: given a query (e.g., a question), return the set of relevant documents (e.g., paragraphs containing the answer) from a large document corpus. This problem is often solved in two steps. The retrieval phase first reduces the solution space, returning a subset of candidate documents. The scoring phase then re-ranks the documents. Critically, the retrieval algorithm not only desires high recall but also requires to be highly efficient, returning candidates in time sublinear to the number of documents. Unlike the scoring phase witnessing significant advances recently due to the BERT-style pre-training tasks on cross-attention models, the retrieval phase remains less well studied. Most previous works rely on classic Information Retrieval (IR) methods such as BM-25 (token matching + TF-IDF weights). These models only accept sparse handcrafted features and can not be optimized for different downstream tasks of interest. In this paper, we conduct a comprehensive study on the embedding-based retrieval models. We show that the key ingredient of learning a strong embedding-based Transformer model is the set of pre-training tasks. With adequately designed paragraph-level pre-training tasks, the Transformer models can remarkably improve over the widely-used BM-25 as well as embedding models without Transformers. The paragraph-level pre-training tasks we studied are Inverse Cloze Task (ICT), Body First Selection (BFS), Wiki Link Prediction (WLP), and the combination of all three.

Exploration in sparse reward environments remains one of the key challenges of model-free reinforcement learning. Instead of solely relying on extrinsic rewards provided by the environment, many state-of-the-art methods use intrinsic rewards to encourage exploration. However, we show that existing methods fall short in procedurally-generated environments where an agent is unlikely to visit a state more than once. We propose a novel type of intrinsic reward which encourages the agent to take actions that lead to significant changes in its learned state representation. We evaluate our method on multiple challenging procedurally-generated tasks in MiniGrid, as well as on tasks with high-dimensional observations used in prior work. Our experiments demonstrate that this approach is more sample efficient than existing exploration methods, particularly for procedurally-generated MiniGrid environments. Furthermore, we analyze the learned behavior as well as the intrinsic reward received by our agent. In contrast to previous approaches, our intrinsic reward does not diminish during the course of training and it rewards the agent substantially more for interacting with objects that it can control.

The universal approximation theorem, in one of its most general versions, says that if we consider only continuous activation functions σ, then a standard feedforward neural network with one hidden layer is able to approximate any continuous multivariate function f to any given approximation threshold ε, if and only if σ is non-polynomial. In this paper, we give a direct algebraic proof of the theorem. Furthermore we shall explicitly quantify the number of hidden units required for approximation. Specifically, if X in R^n is compact, then a neural network with n input units, m output units, and a single hidden layer with {n+d choose d} hidden units (independent of m and ε), can uniformly approximate any polynomial function f:X -> R^m whose total degree is at most d for each of its m coordinate functions. In the general case that f is any continuous function, we show there exists some N in O(ε^{-n}) (independent of m), such that N hidden units would suffice to approximate f. We also show that this uniform approximation property (UAP) still holds even under seemingly strong conditions imposed on the weights. We highlight several consequences: (i) For any δ > 0, the UAP still holds if we restrict all non-bias weights w in the last layer to satisfy |w| < δ. (ii) There exists some λ>0 (depending only on f and σ), such that the UAP still holds if we restrict all non-bias weights w in the first layer to satisfy |w|>λ. (iii) If the non-bias weights in the first layer are *fixed* and randomly chosen from a suitable range, then the UAP holds with probability 1.

We propose Dynamically Pruned Message Passing Networks (DPMPN) for large-scale knowledge graph reasoning. In contrast to existing models, embedding-based or path-based, we learn an input-dependent subgraph to explicitly model a sequential reasoning process. Each subgraph is dynamically constructed, expanding itself selectively under a flow-style attention mechanism. In this way, we can not only construct graphical explanations to interpret prediction, but also prune message passing in Graph Neural Networks (GNNs) to scale with the size of graphs. We take the inspiration from the consciousness prior proposed by Bengio to design a two-GNN framework to encode global input-invariant graph-structured representation and learn local input-dependent one coordinated by an attention module. Experiments show the reasoning capability in our model that is providing a clear graphical explanation as well as predicting results accurately, outperforming most state-of-the-art methods in knowledge base completion tasks.

Space partitions of $\mathbb{R}^d$ underlie a vast and important class of fast nearest neighbor search (NNS) algorithms. Inspired by recent theoretical work on NNS for general metric spaces (Andoni et al. 2018b,c), we develop a new framework for building space partitions reducing the problem to balanced graph partitioning followed by supervised classification. We instantiate this general approach with the KaHIP graph partitioner (Sanders and Schulz 2013) and neural networks, respectively, to obtain a new partitioning procedure called Neural Locality-Sensitive Hashing (Neural LSH). On several standard benchmarks for NNS (Aumuller et al. 2017), our experiments show that the partitions obtained by Neural LSH consistently outperform partitions found by quantization-based and tree-based methods as well as classic, data-oblivious LSH.

Inductive and unsupervised graph learning is a critical technique for predictive or information retrieval tasks where label information is difficult to obtain. It is also challenging to make graph learning inductive and unsupervised at the same time, as learning processes guided by reconstruction error based loss functions inevitably demand graph similarity evaluation that is usually computationally intractable. In this paper, we propose a general framework SEED (Sampling, Encoding, and Embedding Distributions) for inductive and unsupervised representation learning on graph structured objects. Instead of directly dealing with the computational challenges raised by graph similarity evaluation, given an input graph, the SEED framework samples a number of subgraphs whose reconstruction errors could be efficiently evaluated, encodes the subgraph samples into a collection of subgraph vectors, and employs the embedding of the subgraph vector distribution as the output vector representation for the input graph. By theoretical analysis, we demonstrate the close connection between SEED and graph isomorphism. Using public benchmark datasets, our empirical study suggests the proposed SEED framework is able to achieve up to 10% improvement, compared with competitive baseline methods.

The performance of graph neural nets (GNNs) is known to gradually decrease with increasing number of layers. This decay is partly attributed to oversmoothing, where repeated graph convolutions eventually make node embeddings indistinguishable. We take a closer look at two different interpretations, aiming to quantify oversmoothing. Our main contribution is PairNorm, a novel normalization layer that is based on a careful analysis of the graph convolution operator, which prevents all node embeddings from becoming too similar. What is more, PairNorm is fast, easy to implement without any change to network architecture nor any additional parameters, and is broadly applicable to any GNN. Experiments on real-world graphs demonstrate that PairNorm makes deeper GCN, GAT, and SGC models more robust against oversmoothing, and significantly boosts performance for a new problem setting that benefits from deeper GNNs. Code is available at https://github.com/LingxiaoShawn/PairNorm.