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In this article, the optimal sample complexity of learning the underlying interaction/dependencies of a Linear Dynamical System (LDS) over a Directed Acyclic Graph (DAG) is studied. The sample complexity of learning a DAG's structure is well-studied for static systems, where the samples of nodal states are independent and identically distributed (i.i.d.). However, such a study is less explored for DAGs with dynamical systems, where the nodal states are temporally correlated. We call such a DAG underlying an LDS as \emph{dynamical} DAG (DDAG). In particular, we consider a DDAG where the nodal dynamics are driven by unobserved exogenous noise sources that are wide-sense stationary (WSS) in time but are mutually uncorrelated, and have the same {power spectral density (PSD)}. Inspired by the static settings, a metric and an algorithm based on the PSD matrix of the observed time series are proposed to reconstruct the DDAG. The equal noise PSD assumption can be relaxed such that identifiability conditions for DDAG reconstruction are not violated. For the LDS with WSS (sub) Gaussian exogenous noise sources, it is shown that the optimal sample complexity (or length of state trajectory) needed to learn the DDAG is $n=\Theta(q\log(p/q))$, where $p$ is the number of nodes and $q$ is the maximum number of parents per node. To prove the sample complexity upper bound, a concentration bound for the PSD estimation is derived, under two different sampling strategies. A matching min-max lower bound using generalized Fano's inequality also is provided, thus showing the order optimality of the proposed algorithm.

Medical image data are often limited due to the expensive acquisition and annotation process. Hence, training a deep-learning model with only raw data can easily lead to overfitting. One solution to this problem is to augment the raw data with various transformations, improving the model's ability to generalize to new data. However, manually configuring a generic augmentation combination and parameters for different datasets is non-trivial due to inconsistent acquisition approaches and data distributions. Therefore, automatic data augmentation is proposed to learn favorable augmentation strategies for different datasets while incurring large GPU overhead. To this end, we present a novel method, called Dynamic Data Augmentation (DDAug), which is efficient and has negligible computation cost. Our DDAug develops a hierarchical tree structure to represent various augmentations and utilizes an efficient Monte-Carlo tree searching algorithm to update, prune, and sample the tree. As a result, the augmentation pipeline can be optimized for each dataset automatically. Experiments on multiple Prostate MRI datasets show that our method outperforms the current state-of-the-art data augmentation strategies.

A mainstream type of current self-supervised learning methods pursues a general-purpose representation that can be well transferred to downstream tasks, typically by optimizing on a given pretext task such as instance discrimination. In this work, we argue that existing pretext tasks inevitably introduce biases into the learned representation, which in turn leads to biased transfer performance on various downstream tasks. To cope with this issue, we propose Maximum Entropy Coding (MEC), a more principled objective that explicitly optimizes on the structure of the representation, so that the learned representation is less biased and thus generalizes better to unseen downstream tasks. Inspired by the principle of maximum entropy in information theory, we hypothesize that a generalizable representation should be the one that admits the maximum entropy among all plausible representations. To make the objective end-to-end trainable, we propose to leverage the minimal coding length in lossy data coding as a computationally tractable surrogate for the entropy, and further derive a scalable reformulation of the objective that allows fast computation. Extensive experiments demonstrate that MEC learns a more generalizable representation than previous methods based on specific pretext tasks. It achieves state-of-the-art performance consistently on various downstream tasks, including not only ImageNet linear probe, but also semi-supervised classification, object detection, instance segmentation, and object tracking. Interestingly, we show that existing batch-wise and feature-wise self-supervised objectives could be seen equivalent to low-order approximations of MEC. Code and pre-trained models are available at //github.com/xinliu20/MEC.

Transformer is a promising neural network learner, and has achieved great success in various machine learning tasks. Thanks to the recent prevalence of multimodal applications and big data, Transformer-based multimodal learning has become a hot topic in AI research. This paper presents a comprehensive survey of Transformer techniques oriented at multimodal data. The main contents of this survey include: (1) a background of multimodal learning, Transformer ecosystem, and the multimodal big data era, (2) a theoretical review of Vanilla Transformer, Vision Transformer, and multimodal Transformers, from a geometrically topological perspective, (3) a review of multimodal Transformer applications, via two important paradigms, i.e., for multimodal pretraining and for specific multimodal tasks, (4) a summary of the common challenges and designs shared by the multimodal Transformer models and applications, and (5) a discussion of open problems and potential research directions for the community.

Multimodal learning helps to comprehensively understand the world, by integrating different senses. Accordingly, multiple input modalities are expected to boost model performance, but we actually find that they are not fully exploited even when the multimodal model outperforms its uni-modal counterpart. Specifically, in this paper we point out that existing multimodal discriminative models, in which uniform objective is designed for all modalities, could remain under-optimized uni-modal representations, caused by another dominated modality in some scenarios, e.g., sound in blowing wind event, vision in drawing picture event, etc. To alleviate this optimization imbalance, we propose on-the-fly gradient modulation to adaptively control the optimization of each modality, via monitoring the discrepancy of their contribution towards the learning objective. Further, an extra Gaussian noise that changes dynamically is introduced to avoid possible generalization drop caused by gradient modulation. As a result, we achieve considerable improvement over common fusion methods on different multimodal tasks, and this simple strategy can also boost existing multimodal methods, which illustrates its efficacy and versatility. The source code is available at \url{//github.com/GeWu-Lab/OGM-GE_CVPR2022}.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Deep learning has become the dominant approach in coping with various tasks in Natural LanguageProcessing (NLP). Although text inputs are typically represented as a sequence of tokens, there isa rich variety of NLP problems that can be best expressed with a graph structure. As a result, thereis a surge of interests in developing new deep learning techniques on graphs for a large numberof NLP tasks. In this survey, we present a comprehensive overview onGraph Neural Networks(GNNs) for Natural Language Processing. We propose a new taxonomy of GNNs for NLP, whichsystematically organizes existing research of GNNs for NLP along three axes: graph construction,graph representation learning, and graph based encoder-decoder models. We further introducea large number of NLP applications that are exploiting the power of GNNs and summarize thecorresponding benchmark datasets, evaluation metrics, and open-source codes. Finally, we discussvarious outstanding challenges for making the full use of GNNs for NLP as well as future researchdirections. To the best of our knowledge, this is the first comprehensive overview of Graph NeuralNetworks for Natural Language Processing.

When learning tasks over time, artificial neural networks suffer from a problem known as Catastrophic Forgetting (CF). This happens when the weights of a network are overwritten during the training of a new task causing forgetting of old information. To address this issue, we propose MetA Reusable Knowledge or MARK, a new method that fosters weight reusability instead of overwriting when learning a new task. Specifically, MARK keeps a set of shared weights among tasks. We envision these shared weights as a common Knowledge Base (KB) that is not only used to learn new tasks, but also enriched with new knowledge as the model learns new tasks. Key components behind MARK are two-fold. On the one hand, a metalearning approach provides the key mechanism to incrementally enrich the KB with new knowledge and to foster weight reusability among tasks. On the other hand, a set of trainable masks provides the key mechanism to selectively choose from the KB relevant weights to solve each task. By using MARK, we achieve state of the art results in several popular benchmarks, surpassing the best performing methods in terms of average accuracy by over 10% on the 20-Split-MiniImageNet dataset, while achieving almost zero forgetfulness using 55% of the number of parameters. Furthermore, an ablation study provides evidence that, indeed, MARK is learning reusable knowledge that is selectively used by each task.

There has been appreciable progress in unsupervised network representation learning (UNRL) approaches over graphs recently with flexible random-walk approaches, new optimization objectives and deep architectures. However, there is no common ground for systematic comparison of embeddings to understand their behavior for different graphs and tasks. In this paper we theoretically group different approaches under a unifying framework and empirically investigate the effectiveness of different network representation methods. In particular, we argue that most of the UNRL approaches either explicitly or implicit model and exploit context information of a node. Consequently, we propose a framework that casts a variety of approaches -- random walk based, matrix factorization and deep learning based -- into a unified context-based optimization function. We systematically group the methods based on their similarities and differences. We study the differences among these methods in detail which we later use to explain their performance differences (on downstream tasks). We conduct a large-scale empirical study considering 9 popular and recent UNRL techniques and 11 real-world datasets with varying structural properties and two common tasks -- node classification and link prediction. We find that there is no single method that is a clear winner and that the choice of a suitable method is dictated by certain properties of the embedding methods, task and structural properties of the underlying graph. In addition we also report the common pitfalls in evaluation of UNRL methods and come up with suggestions for experimental design and interpretation of results.

The potential of graph convolutional neural networks for the task of zero-shot learning has been demonstrated recently. These models are highly sample efficient as related concepts in the graph structure share statistical strength allowing generalization to new classes when faced with a lack of data. However, knowledge from distant nodes can get diluted when propagating through intermediate nodes, because current approaches to zero-shot learning use graph propagation schemes that perform Laplacian smoothing at each layer. We show that extensive smoothing does not help the task of regressing classifier weights in zero-shot learning. In order to still incorporate information from distant nodes and utilize the graph structure, we propose an Attentive Dense Graph Propagation Module (ADGPM). ADGPM allows us to exploit the hierarchical graph structure of the knowledge graph through additional connections. These connections are added based on a node's relationship to its ancestors and descendants and an attention scheme is further used to weigh their contribution depending on the distance to the node. Finally, we illustrate that finetuning of the feature representation after training the ADGPM leads to considerable improvements. Our method achieves competitive results, outperforming previous zero-shot learning approaches.