ICML 2020 论文列表

We investigate the ability of popular flow models to capture tail-properties of a target density by studying the increasing triangular maps used in these flow methods acting on a tractable source density. We show that the density quantile functions of the source and target density provide a precise characterization of the slope of transformation required to capture tails in a target density. We further show that any Lipschitz-continuous transport map acting on a source density will result in a density with similar tail properties as the source, highlighting the trade-off between the importance of choosing a complex source density and a sufficiently expressive transformation to capture desirable properties of a target density. Subsequently, we illustrate that flow models like Real-NVP, MAF, and Glow as implemented lack the ability to capture a distribution with non-Gaussian tails. We circumvent this problem by proposing tail-adaptive flows consisting of a source distribution that can be learned simultaneously with the triangular map to capture tail-properties of a target density. We perform several synthetic and real-world experiments to complement our theoretical findings.

Recent advancements in Generative Adversarial Networks (GANs) enable the generation of highly realistic images, raising concerns about their misuse for malicious purposes. Detecting these GAN-generated images (GAN-images) becomes increasingly challenging due to the significant reduction of underlying artifacts and specific patterns. The absence of such traces can hinder detection algorithms from identifying GAN-images and transferring knowledge to identify other types of GAN-images as well. In this work, we present the Transferable GAN-images Detection framework T-GD, a robust transferable framework for an effective detection of GAN-images. T-GD is composed of a teacher and a student model that can iteratively teach and evaluate each other to improve the detection performance. First, we train the teacher model on the source dataset and use it as a starting point for learning the target dataset. To train the student model, we inject noise by mixing up the source and target datasets, while constraining the weight variation to preserve the starting point. Our approach is a self-training method, but distinguishes itself from prior approaches by focusing on improving the transferability of GAN-image detection. T-GD achieves high performance on the source dataset by overcoming catastrophic forgetting and effectively detecting state-of-the-art GAN-images with only a small volume of data without any metadata information.

We introduce T-Basis, a novel concept for a compact representation of a set of tensors, each of an arbitrary shape, which is often seen in Neural Networks. Each of the tensors in the set is modeled using Tensor Rings, though the concept applies to other Tensor Networks. Owing its name to the T-shape of nodes in diagram notation of Tensor Rings, T-Basis is simply a list of equally shaped three-dimensional tensors, used to represent Tensor Ring nodes. Such representation allows us to parameterize the tensor set with a small number of parameters (coefficients of the T-Basis tensors), scaling logarithmically with each tensor’s size in the set and linearly with the dimensionality of T-Basis. We evaluate the proposed approach on the task of neural network compression and demonstrate that it reaches high compression rates at acceptable performance drops. Finally, we analyze memory and operation requirements of the compressed networks and conclude that T-Basis networks are equally well suited for training and inference in resource-constrained environments and usage on the edge devices. Project website: obukhov.ai/tbasis.

A Relational Markov Decision Process (RMDP) is a first-order representation to express all instances of a single probabilistic planning domain with possibly unbounded number of objects. Early work in RMDPs outputs generalized (instance-independent) first-order policies or value functions as a means to solve all instances of a domain at once. Unfortunately, this line of work met with limited success due to inherent limitations of the representation space used in such policies or value functions. Can neural models provide the missing link by easily representing more complex generalized policies, thus making them effective on all instances of a given domain? We present SymNet, the first neural approach for solving RMDPs that are expressed in the probabilistic planning language of RDDL. SymNet trains a set of shared parameters for an RDDL domain using training instances from that domain. For each instance, SymNet first converts it to an instance graph and then uses relational neural models to compute node embeddings. It then scores each ground action as a function over the first-order action symbols and node embeddings related to the action. Given a new test instance from the same domain, SymNet architecture with pre-trained parameters scores each ground action and chooses the best action. This can be accomplished in a single forward pass without any retraining on the test instance, thus implicitly representing a neural generalized policy for the whole domain. Our experiments on nine RDDL domains from IPPC demonstrate that SymNet policies are significantly better than random and sometimes even more effective than training a state-of-the-art deep reactive policy from scratch.

Supervised learning requires the specification of a loss function to minimise. While the theory of admissible losses from both a computational and statistical perspective is well-developed, these offer a panoply of different choices. In practice, this choice is typically made in an \emph{ad hoc} manner. In hopes of making this procedure more principled, the problem of \emph{learning the loss function} for a downstream task (e.g., classification) has garnered recent interest. However, works in this area have been generally empirical in nature. In this paper, we revisit the {\sc SLIsotron} algorithm of Kakade et al. (2011) through a novel lens, derive a generalisation based on Bregman divergences, and show how it provides a principled procedure for learning the loss. In detail, we cast {\sc SLIsotron} as learning a loss from a family of composite square losses. By interpreting this through the lens of \emph{proper losses}, we derive a generalisation of {\sc SLIsotron} based on Bregman divergences. The resulting {\sc BregmanTron} algorithm jointly learns the loss along with the classifier. It comes equipped with a simple guarantee of convergence for the loss it learns, and its set of possible outputs comes with a guarantee of agnostic approximability of Bayes rule. Experiments indicate that the {\sc BregmanTron} significantly outperforms the {\sc SLIsotron}, and that the loss it learns can be minimized by other algorithms for different tasks, thereby opening the interesting problem of \emph{loss transfer} between domains.

Low rank matrix factorization is a fundamental building block in machine learning, used for instance to summarize gene expression profile data or word-document counts. To be robust to outliers and differences in scale across features, a matrix factorization step is usually preceded by ad-hoc feature normalization steps, such as tf-idf scaling or data whitening. We propose in this work to learn these normalization operators jointly with the factorization itself. More precisely, given a $d\times n$ matrix $X$ of $d$ features measured on $n$ individuals, we propose to learn the parameters of quantile normalization operators that can operate row-wise on the values of $X$ and/or of its factorization $UV$ to improve the quality of the low-rank representation of $X$ itself. This optimization is facilitated by the introduction of a new differentiable quantile normalization operator built using optimal transport, providing new results on top of existing work by Cuturi et al. (2019). We demonstrate the applicability of these techniques on synthetic and genomics datasets.

We give the first superpolynomial lower bounds for learning one-layer neural networks with respect to the Gaussian distribution for a broad class of algorithms. In the regression setting, we prove that gradient descent run on any classifier with respect to square loss will fail to achieve small test error in polynomial time. Prior work held only for gradient descent run with small batch sizes and sufficiently smooth classifiers. For classification, we give a stronger result, namely that any statistical query (SQ) algorithm will fail to achieve small test error in polynomial time. Our lower bounds hold for commonly used activations such as ReLU and sigmoid. The core of our result relies on a novel construction of a simple family of neural networks that are exactly orthogonal with respect to all spherically symmetric distributions.

In min-min optimization or max-min optimization, one has to compute the gradient of a function defined as a minimum. In most cases, the minimum has no closed-form, and an approximation is obtained via an iterative algorithm. There are two usual ways of estimating the gradient of the function: using either an analytic formula obtained by assuming exactness of the approximation, or automatic differentiation through the algorithm. In this paper, we study the asymptotic error made by these estimators as a function of the optimization error. We find that the error of the automatic estimator is close to the square of the error of the analytic estimator, reflecting a super-efficiency phenomenon. The convergence of the automatic estimator greatly depends on the convergence of the Jacobian of the algorithm. We analyze it for gradient descent and stochastic gradient descent and derive convergence rates for the estimators in these cases. Our analysis is backed by numerical experiments on toy problems and on Wasserstein barycenter computation. Finally, we discuss the computational complexity of these estimators and give practical guidelines to chose between them.

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with varying levels of supervision in the training data (i.e., the proportion of input-output examples of the desired low-dimensional mapping) and orthonormality of the vectors defining the learned operator. This flexible family of problems connects standard, unsupervised subspace fitting that enforces strict orthonormality with a corresponding regression task that is fully supervised and does not constrain the linear operator structure. This class of problems is defined over a supervision-orthonormality plane, where each coordinate induces a problem instance with a unique pair of supervision level and softness of orthonormality constraints. We explore this plane and show that the generalization errors of the corresponding subspace fitting problems follow double descent trends as the settings become more supervised and less orthonormally constrained.

We present the first sublinear memory sketch that can be queried to find the nearest neighbors in a dataset. Our online sketching algorithm compresses an N element dataset to a sketch of size $O(N^b \log^3 N)$ in $O(N^{(b+1)} \log^3 N)$ time, where $b < 1$. This sketch can correctly report the nearest neighbors of any query that satisfies a stability condition parameterized by $b$. We achieve sublinear memory performance on stable queries by combining recent advances in locality sensitive hash (LSH)-based estimators, online kernel density estimation, and compressed sensing. Our theoretical results shed new light on the memory-accuracy tradeoff for nearest neighbor search, and our sketch, which consists entirely of short integer arrays, has a variety of attractive features in practice. We evaluate the memory-recall tradeoff of our method on a friend recommendation task in the Google plus social media network. We obtain orders of magnitude better compression than the random projection based alternative while retaining the ability to report the nearest neighbors of practical queries.

Many AI problems, in robotics and other domains, are goal-directed, essentially seeking a trajectory leading to some goal state. Reinforcement learning (RL), building on Bellman’s optimality equation, naturally optimizes for a single goal, yet can be made goal-directed by augmenting the state with the goal. Instead, we propose a new RL framework, derived from a dynamic programming equation for the all pairs shortest path (APSP) problem, which naturally solves goal-directed queries. We show that this approach has computational benefits for both standard and approximate dynamic programming. Interestingly, our formulation prescribes a novel protocol for computing a trajectory: instead of predicting the next state given its predecessor, as in standard RL, a goal-conditioned trajectory is constructed by first predicting an intermediate state between start and goal, partitioning the trajectory into two. Then, recursively, predicting intermediate points on each sub-segment, until a complete trajectory is obtained. We call this trajectory structure a sub-goal tree. Building on it, we additionally extend the policy gradient methodology to recursively predict sub-goals, resulting in novel goal-based algorithms. Finally, we apply our method to neural motion planning, where we demonstrate significant improvements compared to standard RL on navigating a 7-DoF robot arm between obstacles.

Accurate and reliable prediction of hospital admission location is important due to resource-constraints and space availability in a clinical setting, particularly when dealing with patients who come from the emergency department. In this work we propose a student-teacher network via reinforcement learning to deal with this specific problem. A representation of the weights of the student network is treated as the state and is fed as an input to the teacher network. The teacher network’s action is to select the most appropriate batch of data to train the student network on from a training set sorted according to entropy. By validating on three datasets, not only do we show that our approach outperforms state-of-the-art methods on tabular data and performs competitively on image recognition, but also that novel curricula are learned by the teacher network. We demonstrate experimentally that the teacher network can actively learn about the student network and guide it to achieve better performance than if trained alone.

We consider a deep ReLU / Leaky ReLU student network trained from the output of a fixed teacher network of the same depth, with Stochastic Gradient Descent (SGD). The student network is \emph{over-realized}: at each layer $l$, the number $n_l$ of student nodes is more than that ($m_l$) of teacher. Under mild conditions on dataset and teacher network, we prove that when the gradient is small at every data sample, each teacher node is \emph{specialized} by at least one student node \emph{at the lowest layer}. For two-layer network, such specialization can be achieved by training on any dataset of \emph{polynomial} size $\mathcal{O}( K^{5/2} d^3 \epsilon^{-1})$. until the gradient magnitude drops to $\mathcal{O}(\epsilon/K^{3/2}\sqrt{d})$. Here $d$ is the input dimension, $K = m_1 + n_1$ is the total number of neurons in the lowest layer of teacher and student. Note that we require a specific form of data augmentation and the sample complexity includes the additional data generated from augmentation. To our best knowledge, we are the first to give polynomial sample complexity for student specialization of training two-layer (Leaky) ReLU networks with finite depth and width in teacher-student setting, and finite complexity for the lowest layer specialization in multi-layer case, without parametric assumption of the input (like Gaussian). Our theory suggests that teacher nodes with large fan-out weights get specialized first when the gradient is still large, while others are specialized with small gradient, which suggests inductive bias in training. This shapes the stage of training as empirically observed in multiple previous works. Experiments on synthetic and CIFAR10 verify our findings. The code is released in \url{https://github.com/facebookresearch/luckmatters}.

Annotating datasets is one of the main costs in nowadays supervised learning. The goal of weak supervision is to enable models to learn using only forms of labelling which are cheaper to collect, as partial labelling. This is a type of incomplete annotation where, for each datapoint, supervision is cast as a set of labels containing the real one. The problem of supervised learning with partial labelling has been studied for specific instances such as classification, multi-label, ranking or segmentation, but a general framework is still missing. This paper provides a unified framework based on structured prediction and on the concept of \emph{infimum loss} to deal with partial labelling over a wide family of learning problems and loss functions. The framework leads naturally to explicit algorithms that can be easily implemented and for which proved statistical consistency and learning rates. Experiments confirm the superiority of the proposed approach over commonly used baselines.

Linear quadratic regulator (LQR) is one of the most popular frameworks to tackle continuous Markov decision process tasks. With its fundamental theory and tractable optimal policy, LQR has been revisited and analyzed in recent years, in terms of reinforcement learning scenarios such as the model-free or model-based setting. In this paper, we introduce the Structured Policy Iteration (S-PI) for LQR, a method capable of deriving a structured linear policy. Such a structured policy with (block) sparsity or low-rank can have significant advantages over the standard LQR policy: more interpretable, memory-efficient, and well-suited for the distributed setting. In order to derive such a policy, we first cast a regularized LQR problem when the model is known. Then, our Structured Policy Iteration (S-PI) algorithm, which takes a policy evaluation step and a policy improvement step in an iterative manner, can solve this regularized LQR efficiently. We further extend the S-PI algorithm to the model-free setting where a smoothing procedure is adopted to estimate the gradient. In both the known-model and model-free setting, we prove convergence analysis under the proper choice of parameters. Finally, the experiments demonstrate the advantages of S-PI in terms of balancing the LQR performance and level of structure by varying the weight parameter.

Bandit learning algorithms typically involve the balance of exploration and exploitation. However, in many practical applications, worst-case scenarios needing systematic exploration are seldom encountered. In this work, we consider a smoothed setting for structured linear contextual bandits where the adversarial contexts are perturbed by Gaussian noise and the unknown parameter $\theta^*$ has structure, e.g., sparsity, group sparsity, low rank, etc. We propose simple greedy algorithms for both the single- and multi-parameter (i.e., different parameter for each context) settings and provide a unified regret analysis for $\theta^*$ with any assumed structure. The regret bounds are expressed in terms of geometric quantities such as Gaussian widths associated with the structure of $\theta^*$. We also obtain sharper regret bounds compared to earlier work for the unstructured $\theta^*$ setting as a consequence of our improved analysis. We show there is implicit exploration in the smoothed setting where a simple greedy algorithm works.

We study reward maximisation in a wide class of structured stochastic multi-armed bandit problems, where the mean rewards of arms satisfy some given structural constraints, e.g. linear, unimodal, sparse, etc. Our aim is to develop methods that are \emph{flexible} (in that they easily adapt to different structures), \emph{powerful} (in that they perform well empirically and/or provably match instance-dependent lower bounds) and \emph{efficient} in that the per-round computational burden is small. We develop asymptotically optimal algorithms from instance-dependent lower-bounds using iterative saddle-point solvers. Our approach generalises recent iterative methods for pure exploration to reward maximisation, where a major challenge arises from the estimation of the sub-optimality gaps and their reciprocals. Still we manage to achieve all the above desiderata. Notably, our technique avoids the computational cost of the full-blown saddle point oracle employed by previous work, while at the same time enabling finite-time regret bounds. Our experiments reveal that our method successfully leverages the structural assumptions, while its regret is at worst comparable to that of vanilla UCB.

We address the problem of any-code completion - generating a missing piece of source code in a given program without any restriction on the vocabulary or structure. We introduce a new approach to any-code completion that leverages the strict syntax of programming languages to model a code snippet as a tree - structural language modeling (SLM). SLM estimates the probability of the program’s abstract syntax tree (AST) by decomposing it into a product of conditional probabilities over its nodes. We present a neural model that computes these conditional probabilities by considering all AST paths leading to a target node. Unlike previous techniques that have severely restricted the kinds of expressions that can be generated in this task, our approach can generate arbitrary code in any programming language. Our model significantly outperforms both seq2seq and a variety of structured approaches in generating Java and C# code. Our code, data, and trained models are available at http://github.com/tech-srl/slm-code-generation/. An online demo is available at http://AnyCodeGen.org.

Deep models, while being extremely flexible and accurate, are surprisingly vulnerable to “small, imperceptible” perturbations known as adversarial attacks. While the majority of existing attacks focus on measuring perturbations under the $\ell_p$ metric, Wasserstein distance, which takes geometry in pixel space into account, has long been known to be a suitable metric for measuring image quality and has recently risen as a compelling alternative to the $\ell_p$ metric in adversarial attacks. However, constructing an effective attack under the Wasserstein metric is computationally much more challenging and calls for better optimization algorithms. We address this gap in two ways: (a) we develop an exact yet efficient projection operator to enable a stronger projected gradient attack; (b) we show that the Frank-Wolfe method equipped with a suitable linear minimization oracle works extremely fast under Wasserstein constraints. Our algorithms not only converge faster but also generate much stronger attacks. For instance, we decrease the accuracy of a residual network on CIFAR-10 to $3.4%$ within a Wasserstein perturbation ball of radius $0.005$, in contrast to $65.6%$ using the previous Wasserstein attack based on an \emph{approximate} projection operator. Furthermore, employing our stronger attacks in adversarial training significantly improves the robustness of adversarially trained models.