ICLR 2021 论文列表

Thompson Sampling (TS) is one of the most effective algorithms for solving contextual multi-armed bandit problems. In this paper, we propose a new algorithm, called Neural Thompson Sampling, which adapts deep neural networks for both exploration and exploitation. At the core of our algorithm is a novel posterior distribution of the reward, where its mean is the neural network approximator, and its variance is built upon the neural tangent features of the corresponding neural network. We prove that, provided the underlying reward function is bounded, the proposed algorithm is guaranteed to achieve a cumulative regret of $O(T^{1/2})$, which matches the regret of other contextual bandit algorithms in terms of total round number $T$. Experimental comparisons with other benchmark bandit algorithms on various data sets corroborate our theory.

From the perspectives of expressive power and learning, this work compares multi-layer Graph Neural Networks (GNNs) with a simplified alternative that we call Graph-Augmented Multi-Layer Perceptrons (GA-MLPs), which first augments node features with certain multi-hop operators on the graph and then applies learnable node-wise functions. From the perspective of graph isomorphism testing, we show both theoretically and numerically that GA-MLPs with suitable operators can distinguish almost all non-isomorphic graphs, just like the Weisfeiler-Lehman (WL) test and GNNs. However, by viewing them as node-level functions and examining the equivalence classes they induce on rooted graphs, we prove a separation in expressive power between GA-MLPs and GNNs that grows exponentially in depth. In particular, unlike GNNs, GA-MLPs are unable to count the number of attributed walks. We also demonstrate via community detection experiments that GA-MLPs can be limited by their choice of operator family, whereas GNNs have higher flexibility in learning.

We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many applications, including biology, genomics, computer systems and linguistics. A line of research spanning the last decade resulted in algorithms that estimate the support up to $ \pm \varepsilon n$ from a sample of size $O(\log^2(1/\varepsilon) \cdot n/\log n)$, where $n$ is the data set size. Unfortunately, this bound is known to be tight, limiting further improvements to the complexity of this problem. In this paper we consider estimation algorithms augmented with a machine-learning-based predictor that, given any element, returns an estimation of its frequency. We show that if the predictor is correct up to a constant approximation factor, then the sample complexity can be reduced significantly, to $$ \ \log (1/\varepsilon) \cdot n^{1-\Theta(1/\log(1/\varepsilon))}. $$ We evaluate the proposed algorithms on a collection of data sets, using the neural-network based estimators from {Hsu et al, ICLR'19} as predictors. Our experiments demonstrate substantial (up to 3x) improvements in the estimation accuracy compared to the state of the art algorithm.

Flow-based models are powerful tools for designing probabilistic models with tractable density. This paper introduces Convex Potential Flows (CP-Flow), a natural and efficient parameterization of invertible models inspired by the optimal transport (OT) theory. CP-Flows are the gradient map of a strongly convex neural potential function. The convexity implies invertibility and allows us to resort to convex optimization to solve the convex conjugate for efficient inversion. To enable maximum likelihood training, we derive a new gradient estimator of the log-determinant of the Jacobian, which involves solving an inverse-Hessian vector product using the conjugate gradient method. The gradient estimator has constant-memory cost, and can be made effectively unbiased by reducing the error tolerance level of the convex optimization routine. Theoretically, we prove that CP-Flows are universal density approximators and are optimal in the OT sense. Our empirical results show that CP-Flow performs competitively on standard benchmarks of density estimation and variational inference.

We study the problem of predicting and controlling the future state distribution of an autonomous agent. This problem, which can be viewed as a reframing of goal-conditioned reinforcement learning (RL), is centered around learning a conditional probability density function over future states. Instead of directly estimating this density function, we indirectly estimate this density function by training a classifier to predict whether an observation comes from the future. Via Bayes' rule, predictions from our classifier can be transformed into predictions over future states. Importantly, an off-policy variant of our algorithm allows us to predict the future state distribution of a new policy, without collecting new experience. This variant allows us to optimize functionals of a policy's future state distribution, such as the density of reaching a particular goal state. While conceptually similar to Q-learning, our work lays a principled foundation for goal-conditioned RL as density estimation, providing justification for goal-conditioned methods used in prior work. This foundation makes hypotheses about Q-learning, including the optimal goal-sampling ratio, which we confirm experimentally. Moreover, our proposed method is competitive with prior goal-conditioned RL methods.

Deep generative models have made important progress towards modeling complex, high dimensional data via learning latent representations. Their usefulness is nevertheless often limited by a lack of control over the generative process or a poor understanding of the latent representation. To overcome these issues, attention is now focused on discovering latent variables correlated to the data properties and ways to manipulate these properties. This paper presents the new Property controllable VAE (PCVAE), where a new Bayesian model is proposed to inductively bias the latent representation using explicit data properties via novel group-wise and property-wise disentanglement. Each data property corresponds seamlessly to a latent variable, by innovatively enforcing invertible mutual dependence between them. This allows us to move along the learned latent dimensions to control specific properties of the generated data with great precision. Quantitative and qualitative evaluations confirm that the PCVAE outperforms the existing models by up to 28% in capturing and 65% in manipulating the desired properties.

Inspired by human learning, researchers have proposed ordering examples during training based on their difficulty. Both curriculum learning, exposing a network to easier examples early in training, and anti-curriculum learning, showing the most difficult examples first, have been suggested as improvements to the standard i.i.d. training. In this work, we set out to investigate the relative benefits of ordered learning. We first investigate the implicit curricula resulting from architectural and optimization bias and find that samples are learned in a highly consistent order. Next, to quantify the benefit of explicit curricula, we conduct extensive experiments over thousands of orderings spanning three kinds of learning: curriculum, anti-curriculum, and random-curriculum -- in which the size of the training dataset is dynamically increased over time, but the examples are randomly ordered. We find that for standard benchmark datasets, curricula have only marginal benefits, and that randomly ordered samples perform as well or better than curricula and anti-curricula, suggesting that any benefit is entirely due to the dynamic training set size. Inspired by common use cases of curriculum learning in practice, we investigate the role of limited training time budget and noisy data in the success of curriculum learning. Our experiments demonstrate that curriculum, but not anti-curriculum or random ordering can indeed improve the performance either with limited training time budget or in the existence of noisy data.

Traditional off-policy actor-critic Reinforcement Learning (RL) algorithms learn value functions of a single target policy. However, when value functions are updated to track the learned policy, they forget potentially useful information about old policies. We introduce a class of value functions called Parameter-Based Value Functions (PBVFs) whose inputs include the policy parameters. They can generalize across different policies. PBVFs can evaluate the performance of any policy given a state, a state-action pair, or a distribution over the RL agent's initial states. First we show how PBVFs yield novel off-policy policy gradient theorems. Then we derive off-policy actor-critic algorithms based on PBVFs trained by Monte Carlo or Temporal Difference methods. We show how learned PBVFs can zero-shot learn new policies that outperform any policy seen during training. Finally our algorithms are evaluated on a selection of discrete and continuous control tasks using shallow policies and deep neural networks. Their performance is comparable to state-of-the-art methods.

We introduce a modern Hopfield network with continuous states and a corresponding update rule. The new Hopfield network can store exponentially (with the dimension of the associative space) many patterns, retrieves the pattern with one update, and has exponentially small retrieval errors. It has three types of energy minima (fixed points of the update): (1) global fixed point averaging over all patterns, (2) metastable states averaging over a subset of patterns, and (3) fixed points which store a single pattern. The new update rule is equivalent to the attention mechanism used in transformers. This equivalence enables a characterization of the heads of transformer models. These heads perform in the first layers preferably global averaging and in higher layers partial averaging via metastable states. The new modern Hopfield network can be integrated into deep learning architectures as layers to allow the storage of and access to raw input data, intermediate results, or learned prototypes. These Hopfield layers enable new ways of deep learning, beyond fully-connected, convolutional, or recurrent networks, and provide pooling, memory, association, and attention mechanisms. We demonstrate the broad applicability of the Hopfield layers across various domains. Hopfield layers improved state-of-the-art on three out of four considered multiple instance learning problems as well as on immune repertoire classification with several hundreds of thousands of instances. On the UCI benchmark collections of small classification tasks, where deep learning methods typically struggle, Hopfield layers yielded a new state-of-the-art when compared to different machine learning methods. Finally, Hopfield layers achieved state-of-the-art on two drug design datasets. The implementation is available at: \url{https://github.com/ml-jku/hopfield-layers}

Designing an unsupervised image denoising approach in practical applications is a challenging task due to the complicated data acquisition process. In the real-world case, the noise distribution is so complex that the simplified additive white Gaussian (AWGN) assumption rarely holds, which significantly deteriorates the Gaussian denoisers' performance. To address this problem, we apply a deep neural network that maps the noisy image into a latent space in which the AWGN assumption holds, and thus any existing Gaussian denoiser is applicable. More specifically, the proposed neural network consists of the encoder-decoder structure and approximates the likelihood term in the Bayesian framework. Together with a Gaussian denoiser, the neural network can be trained with the input image itself and does not require any pre-training in other datasets. Extensive experiments on real-world noisy image datasets have shown that the combination of neural networks and Gaussian denoisers improves the performance of the original Gaussian denoisers by a large margin. In particular, the neural network+BM3D method significantly outperforms other unsupervised denoising approaches and is competitive with supervised networks such as DnCNN, FFDNet, and CBDNet.

The goal of continual learning (CL) is to learn a sequence of tasks without suffering from the phenomenon of catastrophic forgetting. Previous work has shown that leveraging memory in the form of a replay buffer can reduce performance degradation on prior tasks. We hypothesize that forgetting can be further reduced when the model is encouraged to remember the \textit{evidence} for previously made decisions. As a first step towards exploring this hypothesis, we propose a simple novel training paradigm, called Remembering for the Right Reasons (RRR), that additionally stores visual model explanations for each example in the buffer and ensures the model has ``the right reasons'' for its predictions by encouraging its explanations to remain consistent with those used to make decisions at training time. Without this constraint, there is a drift in explanations and increase in forgetting as conventional continual learning algorithms learn new tasks. We demonstrate how RRR can be easily added to any memory or regularization-based approach and results in reduced forgetting, and more importantly, improved model explanations. We have evaluated our approach in the standard and few-shot settings and observed a consistent improvement across various CL approaches using different architectures and techniques to generate model explanations and demonstrated our approach showing a promising connection between explainability and continual learning. Our code is available at \url{https://github.com/SaynaEbrahimi/Remembering-for-the-Right-Reasons}.

We propose greedy and local search algorithms for rank-constrained convex optimization, namely solving $\underset{\mathrm{rank}(A)\leq r^*}{\min}\, R(A)$ given a convex function $R:\mathbb{R}^{m\times n}\rightarrow \mathbb{R}$ and a parameter $r^*$. These algorithms consist of repeating two steps: (a) adding a new rank-1 matrix to $A$ and (b) enforcing the rank constraint on $A$. We refine and improve the theoretical analysis of Shalev-Shwartz et al. (2011), and show that if the rank-restricted condition number of $R$ is $\kappa$, a solution $A$ with rank $O(r^*\cdot \min\{\kappa \log \frac{R(\mathbf{0})-R(A^*)}{\epsilon}, \kappa^2\})$ and $R(A) \leq R(A^*) + \epsilon$ can be recovered, where $A^*$ is the optimal solution. This significantly generalizes associated results on sparse convex optimization, as well as rank-constrained convex optimization for smooth functions. We then introduce new practical variants of these algorithms that have superior runtime and recover better solutions in practice. We demonstrate the versatility of these methods on a wide range of applications involving matrix completion and robust principal component analysis.

This paper studies learning logic rules for reasoning on knowledge graphs. Logic rules provide interpretable explanations when used for prediction as well as being able to generalize to other tasks, and hence are critical to learn. Existing methods either suffer from the problem of searching in a large search space (e.g., neural logic programming) or ineffective optimization due to sparse rewards (e.g., techniques based on reinforcement learning). To address these limitations, this paper proposes a probabilistic model called RNNLogic. RNNLogic treats logic rules as a latent variable, and simultaneously trains a rule generator as well as a reasoning predictor with logic rules. We develop an EM-based algorithm for optimization. In each iteration, the reasoning predictor is updated to explore some generated logic rules for reasoning. Then in the E-step, we select a set of high-quality rules from all generated rules with both the rule generator and reasoning predictor via posterior inference; and in the M-step, the rule generator is updated with the rules selected in the E-step. Experiments on four datasets prove the effectiveness of RNNLogic.

Contrastive visual pretraining based on the instance discrimination pretext task has made significant progress. Notably, recent work on unsupervised pretraining has shown to surpass the supervised counterpart for finetuning downstream applications such as object detection and segmentation. It comes as a surprise that image annotations would be better left unused for transfer learning. In this work, we investigate the following problems: What makes instance discrimination pretraining good for transfer learning? What knowledge is actually learned and transferred from these models? From this understanding of instance discrimination, how can we better exploit human annotation labels for pretraining? Our findings are threefold. First, what truly matters for the transfer is low-level and mid-level representations, not high-level representations. Second, the intra-category invariance enforced by the traditional supervised model weakens transferability by increasing task misalignment. Finally, supervised pretraining can be strengthened by following an exemplar-based approach without explicit constraints among the instances within the same category.

We consider the problem of distributed mean estimation (DME), in which $n$ machines are each given a local $d$-dimensional vector $\mathbf x_v \in \mathbb R^d$, and must cooperate to estimate the mean of their inputs $\mathbf \mu = \frac 1n\sum_{v = 1}^n \mathbf x_v$, while minimizing total communication cost. DME is a fundamental construct in distributed machine learning, and there has been considerable work on variants of this problem, especially in the context of distributed variance reduction for stochastic gradients in parallel SGD. Previous work typically assumes an upper bound on the norm of the input vectors, and achieves an error bound in terms of this norm. However, in many real applications, the input vectors are concentrated around the correct output $\mathbf \mu$, but $\mathbf \mu$ itself has large norm. In such cases, previous output error bounds perform poorly. In this paper, we show that output error bounds need not depend on input norm. We provide a method of quantization which allows distributed mean estimation to be performed with solution quality dependent only on the distance between inputs, not on input norm, and show an analogous result for distributed variance reduction. The technique is based on a new connection with lattice theory. We also provide lower bounds showing that the communication to error trade-off of our algorithms is asymptotically optimal. As the lattices achieving optimal bounds under $\ell_2$-norm can be computationally impractical, we also present an extension which leverages easy-to-use cubic lattices, and is loose only up to a logarithmic factor in $d$. We show experimentally that our method yields practical improvements for common applications, relative to prior approaches.

Kernelized Stein discrepancy (KSD), though being extensively used in goodness-of-fit tests and model learning, suffers from the curse-of-dimensionality. We address this issue by proposing the sliced Stein discrepancy and its scalable and kernelized variants, which employs kernel-based test functions defined on the optimal one-dimensional projections. When applied to goodness-of-fit tests, extensive experiments show the proposed discrepancy significantly outperforms KSD and various baselines in high dimensions. For model learning, we show its advantages by training an independent component analysis when compared with existing Stein discrepancy baselines. We further propose a novel particle inference method called sliced Stein variational gradient descent (S-SVGD) which alleviates the mode-collapse issue of SVGD in training variational autoencoders.

Instrumental variable (IV) regression is a standard strategy for learning causal relationships between confounded treatment and outcome variables from observational data by using an instrumental variable, which affects the outcome only through the treatment. In classical IV regression, learning proceeds in two stages: stage 1 performs linear regression from the instrument to the treatment; and stage 2 performs linear regression from the treatment to the outcome, conditioned on the instrument. We propose a novel method, deep feature instrumental variable regression (DFIV), to address the case where relations between instruments, treatments, and outcomes may be nonlinear. In this case, deep neural nets are trained to define informative nonlinear features on the instruments and treatments. We propose an alternating training regime for these features to ensure good end-to-end performance when composing stages 1 and 2, thus obtaining highly flexible feature maps in a computationally efficient manner. DFIV outperforms recent state-of-the-art methods on challenging IV benchmarks, including settings involving high dimensional image data. DFIV also exhibits competitive performance in off-policy policy evaluation for reinforcement learning, which can be understood as an IV regression task.

Our work is concerned with the generation and targeted design of RNA, a type of genetic macromolecule that can adopt complex structures which influence their cellular activities and functions. The design of large scale and complex biological structures spurs dedicated graph-based deep generative modeling techniques, which represents a key but underappreciated aspect of computational drug discovery. In this work, we investigate the principles behind representing and generating different RNA structural modalities, and propose a flexible framework to jointly embed and generate these molecular structures along with their sequence in a meaningful latent space. Equipped with a deep understanding of RNA molecular structures, our most sophisticated encoding and decoding methods operate on the molecular graph as well as the junction tree hierarchy, integrating strong inductive bias about RNA structural regularity and folding mechanism such that high structural validity, stability and diversity of generated RNAs are achieved. Also, we seek to adequately organize the latent space of RNA molecular embeddings with regard to the interaction with proteins, and targeted optimization is used to navigate in this latent space to search for desired novel RNA molecules.

In recent years, Generative Adversarial Networks have become ubiquitous in both research and public perception, but how GANs convert an unstructured latent code to a high quality output is still an open question. In this work, we investigate regression into the latent space as a probe to understand the compositional properties of GANs. We find that combining the regressor and a pretrained generator provides a strong image prior, allowing us to create composite images from a collage of random image parts at inference time while maintaining global consistency. To compare compositional properties across different generators, we measure the trade-offs between reconstruction of the unrealistic input and image quality of the regenerated samples. We find that the regression approach enables more localized editing of individual image parts compared to direct editing in the latent space, and we conduct experiments to quantify this independence effect. Our method is agnostic to the semantics of edits, and does not require labels or predefined concepts during training. Beyond image composition, our method extends to a number of related applications, such as image inpainting or example-based image editing, which we demonstrate on several GANs and datasets, and because it uses only a single forward pass, it can operate in real-time. Code is available on our project page: https://chail.github.io/latent-composition/.