State of Compact Architecture Search For Deep Neural Networks

The design of compact deep neural networks is a crucial task to enable widespread adoption of deep neural networks in the real-world, particularly for edge and mobile scenarios. Due to the time-consuming and challenging nature of manually designing compact deep neural networks, there has been significant recent research interest into algorithms that automatically search for compact network architectures. A particularly interesting class of compact architecture search algorithms are those that are guided by baseline network architectures. Such algorithms have been shown to be significantly more computationally efficient than unguided methods. In this study, we explore the current state of compact architecture search for deep neural networks through both theoretical and empirical analysis of four different state-of-the-art compact architecture search algorithms: i) group lasso regularization, ii) variational dropout, iii) MorphNet, and iv) Generative Synthesis. We examine these methods in detail based on a number of different factors such as efficiency, effectiveness, and scalability. Furthermore, empirical evaluations are conducted to compare the efficacy of these compact architecture search algorithms across three well-known benchmark datasets. While by no means an exhaustive exploration, we hope that this study helps provide insights into the interesting state of this relatively new area of research in terms of diversity and real, tangible gains already achieved in architecture design improvements. Furthermore, the hope is that this study would help in pushing the conversation forward towards a deeper theoretical and empirical understanding where the research community currently stands in the landscape of compact architecture search for deep neural networks, and the practical challenges and considerations in leveraging such approaches for operational usage.

Seeing Convolution Through the Eyes of Finite Transformation Semigroup Theory: An Abstract Algebraic Interpretation of Convolutional Neural Networks

Researchers are actively trying to gain better insights into the representational properties of convolutional neural networks for guiding better network designs and for interpreting a network's computational nature. Gaining such insights can be an arduous task due to the number of parameters in a network and the complexity of a network's architecture. Current approaches of neural network interpretation include Bayesian probabilistic interpretations and information theoretic interpretations. In this study, we take a different approach to studying convolutional neural networks by proposing an abstract algebraic interpretation using finite transformation semigroup theory. Specifically, convolutional layers are broken up and mapped to a finite space. The state space of the proposed finite transformation semigroup is then defined as a single element within the convolutional layer, with the acting elements defined by surrounding state elements combined with convolution kernel elements. Generators of the finite transformation semigroup are defined to complete the interpretation. We leverage this approach to analyze the basic properties of the resulting finite transformation semigroup to gain insights on the representational properties of convolutional neural networks, including insights into quantized network representation. Such a finite transformation semigroup interpretation can also enable better understanding outside of the confines of fixed lattice data structures, thus useful for handling data that lie on irregular lattices. Furthermore, the proposed abstract algebraic interpretation is shown to be viable for interpreting convolutional operations within a variety of convolutional neural network architectures.

PolyNeuron: Automatic Neuron Discovery via Learned Polyharmonic Spline Activations

Automated deep neural network architecture design has received a significant amount of recent attention. However, this attention has not been equally shared by one of the fundamental building blocks of a deep neural network, the neurons. In this study, we propose PolyNeuron, a novel automatic neuron discovery approach based on learned polyharmonic spline activations. More specifically, PolyNeuron revolves around learning polyharmonic splines, characterized by a set of control points, that represent the activation functions of the neurons in a deep neural network. A relaxed variant of PolyNeuron, which we term PolyNeuron-R, loosens the constraints imposed by PolyNeuron to reduce the computational complexity for discovering the neuron activation functions in an automated manner. Experiments show both PolyNeuron and PolyNeuron-R lead to networks that have improved or comparable performance on multiple network architectures (LeNet-5 and ResNet-20) using different datasets (MNIST and CIFAR10). As such, automatic neuron discovery approaches such as PolyNeuron is a worthy direction to explore.