Optimization Variance: Exploring Generalization Properties of DNNs

Unlike the conventional wisdom in statistical learning theory, the test error of a deep neural network (DNN) often demonstrates double descent: as the model complexity increases, it first follows a classical U-shaped curve and then shows a second descent. Through bias-variance decomposition, recent studies revealed that the bell-shaped variance is the major cause of model-wise double descent (when the DNN is widened gradually). This paper investigates epoch-wise double descent, i.e., the test error of a DNN also shows double descent as the number of training epoches increases. By extending the bias-variance analysis to epoch-wise double descent of the zero-one loss, we surprisingly find that the variance itself, without the bias, varies consistently with the test error. Inspired by this result, we propose a novel metric, optimization variance (OV), to measure the diversity of model updates caused by the stochastic gradients of random training batches drawn in the same iteration. OV can be estimated using samples from the training set only but correlates well with the (unknown) \emph{test} error, and hence early stopping may be achieved without using a validation set.

Scene-aware Generative Network for Human Motion Synthesis

We revisit human motion synthesis, a task useful in various real world applications, in this paper. Whereas a number of methods have been developed previously for this task, they are often limited in two aspects: focusing on the poses while leaving the location movement behind, and ignoring the impact of the environment on the human motion. In this paper, we propose a new framework, with the interaction between the scene and the human motion taken into account. Considering the uncertainty of human motion, we formulate this task as a generative task, whose objective is to generate plausible human motion conditioned on both the scene and the human initial position. This framework factorizes the distribution of human motions into a distribution of movement trajectories conditioned on scenes and that of body pose dynamics conditioned on both scenes and trajectories. We further derive a GAN based learning approach, with discriminators to enforce the compatibility between the human motion and the contextual scene as well as the 3D to 2D projection constraints. We assess the effectiveness of the proposed method on two challenging datasets, which cover both synthetic and real world environments.

Leveraging Non-uniformity in First-order Non-convex Optimization

Classical global convergence results for first-order methods rely on uniform smoothness and the \L{}ojasiewicz inequality. Motivated by properties of objective functions that arise in machine learning, we propose a non-uniform refinement of these notions, leading to \emph{Non-uniform Smoothness} (NS) and \emph{Non-uniform \L{}ojasiewicz inequality} (N\L{}). The new definitions inspire new geometry-aware first-order methods that are able to converge to global optimality faster than the classical $\Omega(1/t^2)$ lower bounds. To illustrate the power of these geometry-aware methods and their corresponding non-uniform analysis, we consider two important problems in machine learning: policy gradient optimization in reinforcement learning (PG), and generalized linear model training in supervised learning (GLM). For PG, we find that normalizing the gradient ascent method can accelerate convergence to $O(e^{-t})$ while incurring less overhead than existing algorithms. For GLM, we show that geometry-aware normalized gradient descent can also achieve a linear convergence rate, which significantly improves the best known results. We additionally show that the proposed geometry-aware descent methods escape landscape plateaus faster than standard gradient descent. Experimental results are used to illustrate and complement the theoretical findings.

Unsupervised 3D Shape Completion through GAN Inversion

Most 3D shape completion approaches rely heavily on partial-complete shape pairs and learn in a fully supervised manner. Despite their impressive performances on in-domain data, when generalizing to partial shapes in other forms or real-world partial scans, they often obtain unsatisfactory results due to domain gaps. In contrast to previous fully supervised approaches, in this paper we present ShapeInversion, which introduces Generative Adversarial Network (GAN) inversion to shape completion for the first time. ShapeInversion uses a GAN pre-trained on complete shapes by searching for a latent code that gives a complete shape that best reconstructs the given partial input. In this way, ShapeInversion no longer needs paired training data, and is capable of incorporating the rich prior captured in a well-trained generative model. On the ShapeNet benchmark, the proposed ShapeInversion outperforms the SOTA unsupervised method, and is comparable with supervised methods that are learned using paired data. It also demonstrates remarkable generalization ability, giving robust results for real-world scans and partial inputs of various forms and incompleteness levels. Importantly, ShapeInversion naturally enables a series of additional abilities thanks to the involvement of a pre-trained GAN, such as producing multiple valid complete shapes for an ambiguous partial input, as well as shape manipulation and interpolation.

Revisiting Skeleton-based Action Recognition

Human skeleton, as a compact representation of human action, has received increasing attention in recent years. Many skeleton-based action recognition methods adopt graph convolutional networks (GCN) to extract features on top of human skeletons. Despite the positive results shown in previous works, GCN-based methods are subject to limitations in robustness, interoperability, and scalability. In this work, we propose PoseC3D, a new approach to skeleton-based action recognition, which relies on a 3D heatmap stack instead of a graph sequence as the base representation of human skeletons. Compared to GCN-based methods, PoseC3D is more effective in learning spatiotemporal features, more robust against pose estimation noises, and generalizes better in cross-dataset settings. Also, PoseC3D can handle multiple-person scenarios without additional computation cost, and its features can be easily integrated with other modalities at early fusion stages, which provides a great design space to further boost the performance. On four challenging datasets, PoseC3D consistently obtains superior performance, when used alone on skeletons and in combination with the RGB modality.

Visually Informed Binaural Audio Generation without Binaural Audios

Stereophonic audio, especially binaural audio, plays an essential role in immersive viewing environments. Recent research has explored generating visually guided stereophonic audios supervised by multi-channel audio collections. However, due to the requirement of professional recording devices, existing datasets are limited in scale and variety, which impedes the generalization of supervised methods in real-world scenarios. In this work, we propose PseudoBinaural, an effective pipeline that is free of binaural recordings. The key insight is to carefully build pseudo visual-stereo pairs with mono data for training. Specifically, we leverage spherical harmonic decomposition and head-related impulse response (HRIR) to identify the relationship between spatial locations and received binaural audios. Then in the visual modality, corresponding visual cues of the mono data are manually placed at sound source positions to form the pairs. Compared to fully-supervised paradigms, our binaural-recording-free pipeline shows great stability in cross-dataset evaluation and achieves comparable performance under subjective preference. Moreover, combined with binaural recordings, our method is able to further boost the performance of binaural audio generation under supervised settings.

On the Optimality of Batch Policy Optimization Algorithms

Batch policy optimization considers leveraging existing data for policy construction before interacting with an environment. Although interest in this problem has grown significantly in recent years, its theoretical foundations remain under-developed. To advance the understanding of this problem, we provide three results that characterize the limits and possibilities of batch policy optimization in the finite-armed stochastic bandit setting. First, we introduce a class of confidence-adjusted index algorithms that unifies optimistic and pessimistic principles in a common framework, which enables a general analysis. For this family, we show that any confidence-adjusted index algorithm is minimax optimal, whether it be optimistic, pessimistic or neutral. Our analysis reveals that instance-dependent optimality, commonly used to establish optimality of on-line stochastic bandit algorithms, cannot be achieved by any algorithm in the batch setting. In particular, for any algorithm that performs optimally in some environment, there exists another environment where the same algorithm suffers arbitrarily larger regret. Therefore, to establish a framework for distinguishing algorithms, we introduce a new weighted-minimax criterion that considers the inherent difficulty of optimal value prediction. We demonstrate how this criterion can be used to justify commonly used pessimistic principles for batch policy optimization.

Nearly Horizon-Free Offline Reinforcement Learning

We revisit offline reinforcement learning on episodic time-homogeneous tabular Markov Decision Processes with $S$ states, $A$ actions and planning horizon $H$. Given the collected $N$ episodes data with minimum cumulative reaching probability $d_m$, we obtain the first set of nearly $H$-free sample complexity bounds for evaluation and planning using the empirical MDPs: 1.For the offline evaluation, we obtain an $\tilde{O}\left(\sqrt{\frac{1}{Nd_m}} \right)$ error rate, which matches the lower bound and does not have additional dependency on $\poly\left(S,A\right)$ in higher-order term, that is different from previous works~\citep{yin2020near,yin2020asymptotically}. 2.For the offline policy optimization, we obtain an $\tilde{O}\left(\sqrt{\frac{1}{Nd_m}} + \frac{S}{Nd_m}\right)$ error rate, improving upon the best known result by \cite{cui2020plug}, which has additional $H$ and $S$ factors in the main term. Furthermore, this bound approaches the $\Omega\left(\sqrt{\frac{1}{Nd_m}}\right)$ lower bound up to logarithmic factors and a high-order term. To the best of our knowledge, these are the first set of nearly horizon-free bounds in offline reinforcement learning.

DeepStyle: User Style Embedding for Authorship Attribution of Short Texts

Authorship attribution (AA), which is the task of finding the owner of a given text, is an important and widely studied research topic with many applications. Recent works have shown that deep learning methods could achieve significant accuracy improvement for the AA task. Nevertheless, most of these proposed methods represent user posts using a single type of feature (e.g., word bi-grams) and adopt a text classification approach to address the task. Furthermore, these methods offer very limited explainability of the AA results. In this paper, we address these limitations by proposing DeepStyle, a novel embedding-based framework that learns the representations of users' salient writing styles. We conduct extensive experiments on two real-world datasets from Twitter and Weibo. Our experiment results show that DeepStyle outperforms the state-of-the-art baselines on the AA task.

Towards Automatic Evaluation of Dialog Systems: A Model-Free Off-Policy Evaluation Approach

Reliable automatic evaluation of dialogue systems under an interactive environment has long been overdue. An ideal environment for evaluating dialog systems, also known as the Turing test, needs to involve human interaction, which is usually not affordable for large-scale experiments. Though researchers have attempted to use metrics (e.g., perplexity, BLEU) in language generation tasks or some model-based reinforcement learning methods (e.g., self-play evaluation) for automatic evaluation, these methods only show a very weak correlation with the actual human evaluation in practice. To bridge such a gap, we propose a new framework named ENIGMA for estimating human evaluation scores based on recent advances of off-policy evaluation in reinforcement learning. ENIGMA only requires a handful of pre-collected experience data, and therefore does not involve human interaction with the target policy during the evaluation, making automatic evaluations feasible. More importantly, ENIGMA is model-free and agnostic to the behavior policies for collecting the experience data (see details in Section 2), which significantly alleviates the technical difficulties of modeling complex dialogue environments and human behaviors. Our experiments show that ENIGMA significantly outperforms existing methods in terms of correlation with human evaluation scores.