On the Relationship Between the Generalized Equality Classifier and ART 2 Neural Networks

In this paper, we introduce the Generalized Equality Classifier (GEC) for use as an unsupervised clustering algorithm in categorizing analog data. GEC is based on a formal definition of inexact equality originally developed for voting in fault tolerant software applications. GEC is defined using a metric space framework. The only parameter in GEC is a scalar threshold which defines the approximate equality of two patterns. Here, we compare the characteristics of GEC to the ART2-A algorithm (Carpenter, Grossberg, and Rosen, 1991). In particular, we show that GEC with the Hamming distance performs the same optimization as ART2. Moreover, GEC has lower computational requirements than AR12 on serial machines

Random deep neural networks are biased towards simple functions

We prove that the binary classifiers of bit strings generated by random wide deep neural networks with ReLU activation function are biased towards simple functions. The simplicity is captured by the following two properties. For any given input bit string, the average Hamming distance of the closest input bit string with a different classification is at least sqrt(n / (2{\pi} log n)), where n is the length of the string. Moreover, if the bits of the initial string are flipped randomly, the average number of flips required to change the classification grows linearly with n. These results are confirmed by numerical experiments on deep neural networks with two hidden layers, and settle the conjecture stating that random deep neural networks are biased towards simple functions. This conjecture was proposed and numerically explored in [Valle P\'erez et al., ICLR 2019] to explain the unreasonably good generalization properties of deep learning algorithms. The probability distribution of the functions generated by random deep neural networks is a good choice for the prior probability distribution in the PAC-Bayesian generalization bounds. Our results constitute a fundamental step forward in the characterization of this distribution, therefore contributing to the understanding of the generalization properties of deep learning algorithms

Nearest Labelset Using Double Distances for Multi-label Classification

Multi-label classification is a type of supervised learning where an instance may belong to multiple labels simultaneously. Predicting each label independently has been criticized for not exploiting any correlation between labels. In this paper we propose a novel approach, Nearest Labelset using Double Distances (NLDD), that predicts the labelset observed in the training data that minimizes a weighted sum of the distances in both the feature space and the label space to the new instance. The weights specify the relative tradeoff between the two distances. The weights are estimated from a binomial regression of the number of misclassified labels as a function of the two distances. Model parameters are estimated by maximum likelihood. NLDD only considers labelsets observed in the training data, thus implicitly taking into account label dependencies. Experiments on benchmark multi-label data sets show that the proposed method on average outperforms other well-known approaches in terms of Hamming loss, 0/1 loss, and multi-label accuracy and ranks second after ECC on the F-measure

Binary object recognition system on FPGA with bSOM

Tri-state Self Organizing Map (bSOM), which takes binary inputs and maintains tri-state weights, has been used for classification rather than clustering in this paper. The major contribution here is the demonstration of the potential use of the modified bSOM in security surveillance, as a recognition system on FPGA