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Topological Data Analysis (TDA) provides novel approaches that allow us to analyze the geometrical shapes and topological structures of a dataset. As one important application, TDA can be used for data visualization and dimension reduction. We follow the framework of circular coordinate representation, which allows us to perform dimension reduction and visualization for high-dimensional datasets on a torus using persistent cohomology. In this paper, we propose a method to adapt the circular coordinate framework to take into account the roughness of circular coordinates in change-point and high-dimensional applications. We use a generalized penalty function instead of an $L_{2}$ penalty in the traditional circular coordinate algorithm. We provide simulation experiments and real data analysis to support our claim that circular coordinates with generalized penalty will detect the change in high-dimensional datasets under different sampling schemes while preserving the topological structures.

This paper addresses the problem of finding interpretable directions in the latent space of pre-trained Generative Adversarial Networks (GANs) to facilitate controllable image synthesis. Such interpretable directions correspond to transformations that can affect both the style and geometry of the synthetic images. However, existing approaches that utilise linear techniques to find these transformations often fail to provide an intuitive way to separate these two sources of variation. To address this, we propose to a) perform a multilinear decomposition of the tensor of intermediate representations, and b) use a tensor-based regression to map directions found using this decomposition to the latent space. Our scheme allows for both linear edits corresponding to the individual modes of the tensor, and non-linear ones that model the multiplicative interactions between them. We show experimentally that we can utilise the former to better separate style- from geometry-based transformations, and the latter to generate an extended set of possible transformations in comparison to prior works. We demonstrate our approach's efficacy both quantitatively and qualitatively compared to the current state-of-the-art.

We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection metric. In sharp contrast with the behavior of linear block codes, we show that the typical non-linear code in the Hamming metric of cardinality $q^{n-d+1}$ is far from having minimum distance $d$, i.e., from being MDS. We also give more precise results about the asymptotic proportion of block codes with good distance properties within the set of codes having a certain cardinality. We then establish the analogous results for subspace codes with the injection metric, showing also an application to the theory of partial spreads in finite geometry.

Drug Discovery is a fundamental and ever-evolving field of research. The design of new candidate molecules requires large amounts of time and money, and computational methods are being increasingly employed to cut these costs. Machine learning methods are ideal for the design of large amounts of potential new candidate molecules, which are naturally represented as graphs. Graph generation is being revolutionized by deep learning methods, and molecular generation is one of its most promising applications. In this paper, we introduce a sequential molecular graph generator based on a set of graph neural network modules, which we call MG^2N^2. At each step, a node or a group of nodes is added to the graph, along with its connections. The modular architecture simplifies the training procedure, also allowing an independent retraining of a single module. Sequentiality and modularity make the generation process interpretable. The use of graph neural networks maximizes the information in input at each generative step, which consists of the subgraph produced during the previous steps. Experiments of unconditional generation on the QM9 and Zinc datasets show that our model is capable of generalizing molecular patterns seen during the training phase, without overfitting. The results indicate that our method is competitive, and outperforms challenging baselines for unconditional generation.

Modeling generative process of growing graphs has wide applications in social networks and recommendation systems, where cold start problem leads to new nodes isolated from existing graph. Despite the emerging literature in learning graph representation and graph generation, most of them can not handle isolated new nodes without nontrivial modifications. The challenge arises due to the fact that learning to generate representations for nodes in observed graph relies heavily on topological features, whereas for new nodes only node attributes are available. Here we propose a unified generative graph convolutional network that learns node representations for all nodes adaptively in a generative model framework, by sampling graph generation sequences constructed from observed graph data. We optimize over a variational lower bound that consists of a graph reconstruction term and an adaptive Kullback-Leibler divergence regularization term. We demonstrate the superior performance of our approach on several benchmark citation network datasets.

The ability to generate natural language sequences from source code snippets has a variety of applications such as code summarization, documentation, and retrieval. Sequence-to-sequence (seq2seq) models, adopted from neural machine translation (NMT), have achieved state-of-the-art performance on these tasks by treating source code as a sequence of tokens. We present ${\rm {\scriptsize CODE2SEQ}}$: an alternative approach that leverages the syntactic structure of programming languages to better encode source code. Our model represents a code snippet as the set of compositional paths in its abstract syntax tree (AST) and uses attention to select the relevant paths while decoding. We demonstrate the effectiveness of our approach for two tasks, two programming languages, and four datasets of up to $16$M examples. Our model significantly outperforms previous models that were specifically designed for programming languages, as well as state-of-the-art NMT models. An interactive online demo of our model is available at //code2seq.org. Our code, data and trained models are available at //github.com/tech-srl/code2seq.

Generating realistic images from scene graphs asks neural networks to be able to reason about object relationships and compositionality. As a relatively new task, how to properly ensure the generated images comply with scene graphs or how to measure task performance remains an open question. In this paper, we propose to harness scene graph context to improve image generation from scene graphs. We introduce a scene graph context network that pools features generated by a graph convolutional neural network that are then provided to both the image generation network and the adversarial loss. With the context network, our model is trained to not only generate realistic looking images, but also to better preserve non-spatial object relationships. We also define two novel evaluation metrics, the relation score and the mean opinion relation score, for this task that directly evaluate scene graph compliance. We use both quantitative and qualitative studies to demonstrate that our pro-posed model outperforms the state-of-the-art on this challenging task.

Generating structural query language (SQL) queries from natural language is a long-standing open problem. Answering a natural language question about a database table requires modeling complex interactions between the columns of the table and the question. In this paper, we apply the synthesizing approach to solve this problem. Based on the structure of SQL queries, we break down the model to three sub-modules and design specific deep neural networks for each of them. Taking inspiration from the similar machine reading task, we employ the bidirectional attention mechanisms and character-level embedding with convolutional neural networks (CNNs) to improve the result. Experimental evaluations show that our model achieves the state-of-the-art results in WikiSQL dataset.

When a recurrent neural network language model is used for caption generation, the image information can be fed to the neural network either by directly incorporating it in the RNN -- conditioning the language model by `injecting' image features -- or in a layer following the RNN -- conditioning the language model by `merging' image features. While both options are attested in the literature, there is as yet no systematic comparison between the two. In this paper we empirically show that it is not especially detrimental to performance whether one architecture is used or another. The merge architecture does have practical advantages, as conditioning by merging allows the RNN's hidden state vector to shrink in size by up to four times. Our results suggest that the visual and linguistic modalities for caption generation need not be jointly encoded by the RNN as that yields large, memory-intensive models with few tangible advantages in performance; rather, the multimodal integration should be delayed to a subsequent stage.

Modeling and generating graphs is fundamental for studying networks in biology, engineering, and social sciences. However, modeling complex distributions over graphs and then efficiently sampling from these distributions is challenging due to the non-unique, high-dimensional nature of graphs and the complex, non-local dependencies that exist between edges in a given graph. Here we propose GraphRNN, a deep autoregressive model that addresses the above challenges and approximates any distribution of graphs with minimal assumptions about their structure. GraphRNN learns to generate graphs by training on a representative set of graphs and decomposes the graph generation process into a sequence of node and edge formations, conditioned on the graph structure generated so far. In order to quantitatively evaluate the performance of GraphRNN, we introduce a benchmark suite of datasets, baselines and novel evaluation metrics based on Maximum Mean Discrepancy, which measure distances between sets of graphs. Our experiments show that GraphRNN significantly outperforms all baselines, learning to generate diverse graphs that match the structural characteristics of a target set, while also scaling to graphs 50 times larger than previous deep models.