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We summarize our recent results on the large N renormalization group (RG) approach to matrix models for discretized two-dimensional quantum gravity. We derive exact RG equations by solving the reparametrization identities, which reduce…

Graphs serve as generic tools to encode the underlying relational structure of data. Often this graph is not given, and so the task of inferring it from nodal observations becomes important. Traditional approaches formulate a convex inverse…

This paper investigates multilevel initialization strategies for training very deep neural networks with a layer-parallel multigrid solver. The scheme is based on the continuous interpretation of the training problem as a problem of optimal…

Rich semantic relations are important in a variety of visual recognition problems. As a concrete example, group activity recognition involves the interactions and relative spatial relations of a set of people in a scene. State of the art…

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…

Recurrent Neural Networks (RNNs) offer fast inference on long sequences but are hard to optimize and slow to train. Deep state-space models (SSMs) have recently been shown to perform remarkably well on long sequence modeling tasks, and have…

To take full advantage of experimental facilities such as FRIB for applications to nuclear astrophysics, nuclear structure, and explorations of neutrinos and fundamental symmetries, we need a better understanding of the interplay of…

By bridging deep networks and physics, the programme of geometrization of deep networks was proposed as a framework for the interpretability of deep learning systems. Following this programme we can apply two key ideas of physics, the…

Network representation learning (NRL) is an effective graph analytics technique and promotes users to deeply understand the hidden characteristics of graph data. It has been successfully applied in many real-world tasks related to network…

Learning on large graphs presents significant challenges, with traditional Message Passing Neural Networks suffering from computational and memory costs scaling linearly with the number of edges. We introduce the Intersecting Block Graph…

Algorithm unfolding or unrolling is the technique of constructing a deep neural network (DNN) from an iterative algorithm. Unrolled DNNs often provide better interpretability and superior empirical performance over standard DNNs in signal…

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…

It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what…

Deep neural networks have been shown to be highly miscalibrated. often they tend to be overconfident in their predictions. It poses a significant challenge for safety-critical systems to utilise deep neural networks (DNNs), reliably. Many…

The Dirichlet Belief Network~(DirBN) has been recently proposed as a promising approach in learning interpretable deep latent representations for objects. In this work, we leverage its interpretable modelling architecture and propose a deep…

Recent work in Information Retrieval (IR) using Deep Learning models has yielded state of the art results on a variety of IR tasks. Deep neural networks (DNN) are capable of learning ideal representations of data during the training…

Object rearranging is one of the most common deformable manipulation tasks, where the robot needs to rearrange a deformable object into a goal configuration. Previous studies focus on designing an expert system for each specific task by…

Deep neural networks have proven remarkably effective at solving many classification problems, but have been criticized recently for two major weaknesses: the reasons behind their predictions are uninterpretable, and the predictions…

The proliferation of large-scale and structurally complex data has spurred the integration of machine learning methods into statistical modeling. Recurrent neural networks (RNNs), a foundational class of models for time-dependent data, can…

The graph neural network (GNN) has demonstrated its superior performance in various applications. The working mechanism behind it, however, remains mysterious. GNN models are designed to learn effective representations for graph-structured…