Graph convolutional networks (GCNs) have gained popularity due to high performance achievable on several downstream tasks including node classification. Several architectural variants of these networks have been proposed and investigated with experimental studies in the literature. Motivated by a recent work on simplifying GCNs, we study the problem of designing other variants and propose a framework to compose networks using building blocks of GCN. The framework offers flexibility to compose and evaluate different networks using feature and/or label propagation networks, linear or non-linear networks, with each composition having different computational complexity. We conduct a detailed experimental study on several benchmark datasets with many variants and present observations from our evaluation. Our empirical experimental results suggest that several newly composed variants are useful alternatives to consider because they are as competitive as, or better than the original GCN.

We propose learning discrete structured representations from unlabeled data by maximizing the mutual information between a structured latent variable and a target variable. Calculating mutual information is intractable in this setting. Our key technical contribution is an adversarial objective that can be used to tractably estimate mutual information assuming only the feasibility of cross entropy calculation. We develop a concrete realization of this general formulation with Markov distributions over binary encodings. We report critical and unexpected findings on practical aspects of the objective such as the choice of variational priors. We apply our model on document hashing and show that it outperforms current best baselines based on discrete and vector quantized variational autoencoders. It also yields highly compressed interpretable representations.

Previous work on symmetric group equivariant neural networks generally only considered the case where the group acts by permuting the elements of a single vector. In this paper we derive formulae for general permutation equivariant layers, including the case where the layer acts on matrices by permuting their rows and columns simultaneously. This case arises naturally in graph learning and relation learning applications. As a specific case of higher order permutation equivariant networks, we present a second order graph variational encoder, and show that the latent distribution of equivariant generative models must be exchangeable. We demonstrate the efficacy of this architecture on the tasks of link prediction in citation graphs and molecular graph generation.

In multi-label learning, the issue of missing labels brings a major challenge. Many methods attempt to recovery missing labels by exploiting low-rank structure of label matrix. However, these methods just utilize global low-rank label structure, ignore both local low-rank label structures and label discriminant information to some extent, leaving room for further performance improvement. In this paper, we develop a simple yet effective discriminant multi-label learning (DM2L) method for multi-label learning with missing labels. Specifically, we impose the low-rank structures on all the predictions of instances from the same labels (local shrinking of rank), and a maximally separated structure (high-rank structure) on the predictions of instances from different labels (global expanding of rank). In this way, these imposed low-rank structures can help modeling both local and global low-rank label structures, while the imposed high-rank structure can help providing more underlying discriminability. Our subsequent theoretical analysis also supports these intuitions. In addition, we provide a nonlinear extension via using kernel trick to enhance DM2L and establish a concave-convex objective to learn these models. Compared to the other methods, our method involves the fewest assumptions and only one hyper-parameter. Even so, extensive experiments show that our method still outperforms the state-of-the-art methods.

Here, we propose an unsupervised fuzzy rule-based dimensionality reduction method primarily for data visualization. It considers the following important issues relevant to dimensionality reduction-based data visualization: (i) preservation of neighborhood relationships, (ii) handling data on a non-linear manifold, (iii) the capability of predicting projections for new test data points, (iv) interpretability of the system, and (v) the ability to reject test points if required. For this, we use a first-order Takagi-Sugeno type model. We generate rule antecedents using clusters in the input data. In this context, we also propose a new variant of the Geodesic c-means clustering algorithm. We estimate the rule parameters by minimizing an error function that preserves the inter-point geodesic distances (distances over the manifold) as Euclidean distances on the projected space. We apply the proposed method on three synthetic and three real-world data sets and visually compare the results with four other standard data visualization methods. The obtained results show that the proposed method behaves desirably and performs better than or comparable to the methods compared with. The proposed method is found to be robust to the initial conditions. The predictability of the proposed method for test points is validated by experiments. We also assess the ability of our method to reject output points when it should. Then, we extend this concept to provide a general framework for learning an unsupervised fuzzy model for data projection with different objective functions. To the best of our knowledge, this is the first attempt to manifold learning using unsupervised fuzzy modeling.

This paper makes a first step towards compatible and hence reusable network components. Rather than training networks for different tasks independently, we adapt the training process to produce network components that are compatible across tasks. We propose and compare several different approaches to accomplish compatibility. Our experiments on CIFAR-10 show that: (i) we can train networks to produce compatible features, without degrading task accuracy compared to training networks independently; (ii) the degree of compatibility is highly dependent on where we split the network into a feature extractor and a classification head; (iii) random initialization has a large effect on compatibility; (iv) we can train incrementally: given previously trained components, we can train new ones which are also compatible with them. This work is part of a larger goal to increase network reusability: we envision that compatibility will enable solving new tasks by mixing and matching suitable components.

Flow-based generative models are an important class of exact inference models that admit efficient inference and sampling for image synthesis. Owing to the efficiency constraints on the design of the flow layers, e.g. split coupling flow layers in which approximately half the pixels do not undergo further transformations, they have limited expressiveness for modeling long-range data dependencies compared to autoregressive models that rely on conditional pixel-wise generation. In this work, we improve the representational power of flow-based models by introducing channel-wise dependencies in their latent space through multi-scale autoregressive priors (mAR). Our mAR prior for models with split coupling flow layers (mAR-SCF) can better capture dependencies in complex multimodal data. The resulting model achieves state-of-the-art density estimation results on MNIST, CIFAR-10, and ImageNet. Furthermore, we show that mAR-SCF allows for improved image generation quality, with gains in FID and Inception scores compared to state-of-the-art flow-based models.

Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is currently one of the most widely used due to its speed and simplicity. Yet, there are few theoretical guarantee to recover the underlying partitions of the graph for general models. This paper therefore presents a variant of spectral clustering, called 1-spectral clustering, performed on a new random model closely related to stochastic block model. Its goal is to promote a sparse eigenbasis solution of a 1 minimization problem revealing the natural structure of the graph. The effectiveness and the robustness to small noise perturbations of our technique is confirmed through a collection of simulated and real data examples.

There exist several inherent trade-offs in designing a fair model, such as those between the model's predictive performance and fairness, or even among different notions of fairness. In practice, exploring these trade-offs requires significant human and computational resources. We propose a diagnostic that enables practitioners to explore these trade-offs without training a single model. Our work hinges on the observation that many widely-used fairness definitions can be expressed via the fairness-confusion tensor, an object obtained by splitting the traditional confusion matrix according to protected data attributes. Optimizing accuracy and fairness objectives directly over the elements in this tensor yields a data-dependent yet model-agnostic way of understanding several types of trade-offs. We further leverage this tensor-based perspective to generalize existing theoretical impossibility results to a wider range of fairness definitions. Finally, we demonstrate the usefulness of the proposed diagnostic on synthetic and real datasets.

Normalization layers and activation functions are critical components in deep neural networks that frequently co-locate with each other. Instead of designing them separately, we unify them into a single computation graph, and evolve its structure starting from low-level primitives. Our layer search algorithm leads to the discovery of EvoNorms, a set of new normalization-activation layers that go beyond existing design patterns. Several of these layers enjoy the property of being independent from the batch statistics. Our experiments show that EvoNorms not only excel on a variety of image classification models including ResNets, MobileNets and EfficientNets, but also transfer well to Mask R-CNN for instance segmentation and BigGAN for image synthesis, outperforming BatchNorm and GroupNorm based layers by a significant margin in many cases.