A Low-power, Mixed-mode Neural Network Classifier for Robust Scene Classification

Analog Gaussian Function Circuit: Architectures, Operating Principles and Applications

“…In most cases, digital or other analog circuits are attached around a partially tunable Gaussian or Gaussian-like function circuit (Figure 28) to improve the tunability of the Gaussian function curve's three characteristics (height, mean value and variance). The extra components include multiplexers (MUX) [11,81] and/or switches [15,[82][83][84][85] and other digital circuitry (mixed-mode architectures [86]) [82][83][84], series of resistors [19,87,88], DACs [22,28,87] or Analog to Digital converters (ADC) [22], multipliers [28,31,33,87] or tunable current mirrors [89,90], OTAs [91][92][93][94] or other amplifiers [12,87], common mode feedback circuits (CMFB) [22,95], squarers [33], exponentiators [87], current-controlled current-conveyor second generation (CCII) circuits [90], minimum value circuits [96] and additional current correlators [97]. Four representative examples are provided in Figures 29-32.…”

“…... Each implementation uses the extra components differently, but the general concept regarding the added extra components is to enhance the operation of a simple Gaussian function core, for example, to provide variance tunability to the circuit. In particular, multiplexers and switches are used to select the appropriate value from multiple parallel outputs in order to achieve the tunability in the variance [11,15,[81][82][83][84][85]. In a similar manner, the series of resistors alter the Gaussian function output by changing the total resistance value [19,87,88].…”

“…In Table 7, we summarize some common characteristics of the system level implementations, presented along with the Gaussian function circuit. The proposed ML systems are RBF NNs [11,12,14,16,24,28,61,81,94,101], a general design flow is shown in Figure 37 or other NNs, like a Multi-layer Perceptron (MLP)/RBF network (RBFN) [15] or a Gaussian RBF NN (GRBF NN) [87], Support Vector Machine (SVM) [41,62], regression (SVR) [4] or domain description (SVDD) [42] algorithms, pattern-matching classifiers [66,68], vector quantizers [64,99], a Deep ML (DML) engine [45], a similarity evaluation circuit [67] and an SOM [39]. A typical example of an Analog-hardware implementation of the SVM algorithm is shown in Figure 38.…”

“…Gaussian function circuits are used for the implementation of two functions that are useful for many ML algorithms: (a) kernel density (b) distance computation. Most of the applications are designed for an input dimensionality lower than 65 dimensions, with some not specifying an upper boundary [15,24,64,87], being able to categorize high definition images. Additionally, the simulation level as well as the circuit area for the layout and chip implementations (or for [39] an estimation), if provided, can be found in Table 7.…”

“…Since the first Gaussian function circuit (also called the Bump circuit) was introduced by Delbruck (Delbruck's Simple Bump) in 1991 [1,2] (shown in Figure 1), many research groups have focused on improving this architecture and/or incorporating it in various fields [3][4][5][6][7][8][9][10][11][12][13][14]. Some of the implementations are used for Machine Learning (ML) applications [15,16], neuromorphic systems [17,18], smart sensors [19,20] and fuzzy or neuro-fuzzy systems [21,22]. Gaussian function circuits are specific analog circuits that provide an output current, which is a typical Gaussian function [23] or a bell-shaped curve [24].…”