Efficient Processing of Deep Neural Networks. Vivienne Sze

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      Figure 1.1: Deep learning in the context of artificial intelligence.

      Within AI is a large sub-field called machine learning, which was defined in 1959 by Arthur Samuel [12] as “the field of study that gives computers the ability to learn without being explicitly programmed.” That means a single program, once created, will be able to learn how to do some intelligent activities outside the notion of programming. This is in contrast to purpose-built programs whose behavior is defined by hand-crafted heuristics that explicitly and statically define their behavior.

      The advantage of an effective machine learning algorithm is clear. Instead of the laborious and hit-or-miss approach of creating a distinct, custom program to solve each individual problem in a domain, a single machine learning algorithm simply needs to learn, via a process called training, to handle each new problem.

      Within the machine learning field, there is an area that is often referred to as brain-inspired computation. Since the brain is currently the best “machine” we know of for learning and solving problems, it is a natural place to look for inspiration. Therefore, a brain-inspired computation is a program or algorithm that takes some aspects of its basic form or functionality from the way the brain works. This is in contrast to attempts to create a brain, but rather the program aims to emulate some aspects of how we understand the brain to operate.

      Although scientists are still exploring the details of how the brain works, it is generally believed that the main computational element of the brain is the neuron. There are approximately 86 billion neurons in the average human brain. The neurons themselves are connected by a number of elements entering them, called dendrites, and an element leaving them, called an axon, as shown in Figure 1.2. The neuron accepts the signals entering it via the dendrites, performs a computation on those signals, and generates a signal on the axon. These input and output signals are referred to as activations. The axon of one neuron branches out and is connected to the dendrites of many other neurons. The connections between a branch of the axon and a dendrite is called a synapse. There are estimated to be 10¹⁴ to 10¹⁵ synapses in the average human brain.

      Figure 1.2: Connections to a neuron in the brain. xi, wi, f (.), and b are the activations, weights, nonlinear function, and bias, respectively. (Figure adapted from [4].)

      A key characteristic of the synapse is that it can scale the signal (xi) crossing it, as shown in Figure 1.2. That scaling factor can be referred to as a weight (wi), and the way the brain is believed to learn is through changes to the weights associated with the synapses. Thus, different weights result in different responses to an input. One aspect of learning can be thought of as the adjustment of weights in response to a learning stimulus, while the organization (what might be thought of as the program) of the brain largely does not change. This characteristic makes the brain an excellent inspiration for a machine-learning-style algorithm.

Within the brain-inspired computing paradigm, there is a subarea called spiking computing. In this subarea, inspiration is taken from the fact that the communication on the dendrites and axons are spike-like pulses and that the information being conveyed is not just based on a spike’s amplitude. Instead, it also depends on the time the pulse arrives and that the computation that happens in the neuron is a function of not just a single value but the width of pulse and the timing relationship between different pulses. The IBM TrueNorth project is an example of work that was inspired by the spiking of the brain [13]. In contrast to spiking computing, another subarea of brain-inspired computing is called neural networks, which is the focus of this book.²

      Figure 1.3: Simple neural network example and terminology. (Figure adapted from [4].)

1.1.2 NEURAL NETWORKS AND DEEP NEURAL NETWORKS

Neural networks take their inspiration from the notion that a neuron’s computation involves a weighted sum of the input values. These weighted sums correspond to the value scaling performed by the synapses and the combining of those values in the neuron. Furthermore, the neuron does not directly output that weighted sum because the expressive power of the cascade of neurons involving only linear operations is just equal to that of a single neuron, which is very limited. Instead, there is a functional operation within the neuron that is performed on the combined inputs. This operation appears to be a nonlinear function that causes a neuron to generate an output only if its combined inputs cross some threshold. Thus, by analogy, neural networks apply a nonlinear function to the weighted sum of the input values.³ These nonlinear functions are inspired by biological functions, but are not meant to emulate the brain. We look at some of those nonlinear functions in Section 2.3.3.

      Figure 1.3a shows a diagram of a three-layer (non-biological) neural network. The neurons in the input layer receive some values, compute their weighted sums followed by the nonlinear function, and propagate the outputs to the neurons in the middle layer of the network, which is also frequently called a “hidden layer.” A neural network can have more than one hidden layer, and the outputs from the hidden layers ultimately propagate to the output layer, which computes the final outputs of the network to the user. To align brain-inspired terminology with neural networks, the outputs of the neurons are often referred to as activations, and the synapses are often referred to as weights, as shown in Figure 1.3a. We will use the activation/weight nomenclature in this book.

      Figure 1.4: Example of image classification using deep neural networks. (Figure adapted from [15].) Note that the features go from low level to high level as we go deeper into the network.

      Figure 1.3b shows an example of the computation at layer 1: , where Wij, xi, and yj are the weights, input activations, and output activations, respectively, and f(.) is a nonlinear function described in Section 2.3.3. The bias term bj is omitted from Figure 1.3b for simplicity. In this book, we will use the color green to denote weights, blue to denote activations, and red to denote weighted sums (or partial sums, which are further accumulated to become the final weighted sums).

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