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This survey article is concerned with the application of lattice rules to Deep Neural Networks (DNNs), lattice rules being a family of quasi-Monte Carlo methods. They have demonstrated effectiveness in various contexts for high-dimensional…

We build a rigorous bridge between deep networks (DNs) and approximation theory via spline functions and operators. Our key result is that a large class of DNs can be written as a composition of max-affine spline operators (MASOs), which…

We address the problem of vehicle self-localization from multi-modal sensor information and a reference map. The map is generated off-line by extracting landmarks from the vehicle's field of view, while the measurements are collected…

In this paper, we study the polynomial optimization problem of multi-forms over the intersection of the multi-spheres and the nonnegative orthants. This class of problems is NP-hard in general, and includes the problem of finding the best…

Existing analyses of optimization in deep learning are either continuous, focusing on (variants of) gradient flow, or discrete, directly treating (variants of) gradient descent. Gradient flow is amenable to theoretical analysis, but is…

In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…

Closeness is a widely-studied centrality measure. Since it requires all pairwise distances, computing closeness for all nodes is infeasible for large real-world networks. However, for many applications, it is only necessary to find the k…

Using deep neural nets as function approximator for reinforcement learning tasks have recently been shown to be very powerful for solving problems approaching real-world complexity. Using these results as a benchmark, we discuss the role…

In this work, we propose an effective scheme (called DP-Net) for compressing the deep neural networks (DNNs). It includes a novel dynamic programming (DP) based algorithm to obtain the optimal solution of weight quantization and an…

Supervised training of deep neural nets typically relies on minimizing cross-entropy. However, in many domains, we are interested in performing well on metrics specific to the application. In this paper we propose a direct loss minimization…

We propose doubly nested network(DNNet) where all neurons represent their own sub-models that solve the same task. Every sub-model is nested both layer-wise and channel-wise. While nesting sub-models layer-wise is straight-forward with…

Deep neural networks (DNNs) have been increasingly deployed on and integrated with edge devices, such as mobile phones, drones, robots and wearables. To run DNN inference directly on edge devices (a.k.a. edge inference) with a satisfactory…

Deep Neural Networks (DNNs) are used in a wide variety of applications. However, as in any software application, DNN-based apps are afflicted with bugs. Previous work observed that DNN bug fix patterns are different from traditional bug fix…

The optimal scheduling of interfering links in a dense wireless network with full frequency reuse is a challenging task. The traditional method involves first estimating all the interfering channel strengths then optimizing the scheduling…

In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in…

Diagnosis and risk stratification of cancer and many other diseases require the detection of genomic breakpoints as a prerequisite of calling copy number alterations (CNA). This, however, is still challenging and requires time-consuming…

The Bilevel Optimization Problem is a hierarchical optimization problem with two agents, a leader and a follower. The leader make their own decisions first, and the followers make the best choices accordingly. The leader knows the…

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal…

Deep neural networks have proven to be particularly effective in visual and audio recognition tasks. Existing models tend to be computationally expensive and memory intensive, however, and so methods for hardware-oriented approximation have…

The success of deep learning depends on finding an architecture to fit the task. As deep learning has scaled up to more challenging tasks, the architectures have become difficult to design by hand. This paper proposes an automated method,…