A transport equation approach for deep neural networks with quenched random weights

We consider a multi-layer Sherrington-Kirkpatrick spin-glass as a model for deep restricted Boltzmann machines with quenched random weights and solve for its free energy in the thermodynamic limit by means of Guerra's interpolating techniques under the RS and 1RSB ansatz. In particular, we recover the expression already known for the replica-symmetric case. Further, we drop the restriction constraint by introducing intra-layer connections among spins and we show that the resulting system can be mapped into a modular Hopfield network, which is also addressed via the same techniques up to the first step of replica symmetry breaking.

Predictive Constructions Based on Measure-Valued Pólya Urn Processes

Measure-valued Pólya urn processes (MVPP) are Markov chains with an additive structure that serve as an extension of the generalized k-color Pólya urn model towards a continuum of possible colors. We prove that, for any MVPP (μn)n≥0 on a Polish space X, the normalized sequence (μn/μn(X))n≥0 agrees with the marginal predictive distributions of some random process (Xn)n≥1. Moreover, μn=μn−1+RXn, n≥1, where x↦Rx is a random transition kernel on X; thus, if μn−1 represents the contents of an urn, then Xn denotes the color of the ball drawn with distribution μn−1/μn−1(X) and RXn—the subsequent reinforcement. In the case RXn=WnδXn, for some non-negative random weights W1,W2,…, the process (Xn)n≥1 is better understood as a randomly reinforced extension of Blackwell and MacQueen’s Pólya sequence. We study the asymptotic properties of the predictive distributions and the empirical frequencies of (Xn)n≥1 under different assumptions on the weights. We also investigate a generalization of the above models via a randomization of the law of the reinforcement.

Important Milestones in the Study of Neural Networks with Random Weights

Neural networks with partially random weights are currently not really an independent field of research. However, the first works on random neural networks date back to the 1990s and in the last three decades there have been important new works in which random weights have been used and which are promising in that they give surprisingly good results when compared to approaches in which all weights are trained. These works, however, come from very different subareas of neural networks: Random Feedforward Neural Networks, Random Recurrent Neural Networks and Random ConvNets. In this paper, I analyze the most important works from these three areas and thereby follow a chronological order. I also work out the core result of each work. As a result, the reader can get a quick overview of this field of research.<br>

Important Milestones in the Study of Neural Networks with Random Weights

Neural networks with partially random weights are currently not really an independent field of research. However, the first works on random neural networks date back to the 1990s and in the last three decades there have been important new works in which random weights have been used and which are promising in that they give surprisingly good results when compared to approaches in which all weights are trained. These works, however, come from very different subareas of neural networks: Random Feedforward Neural Networks, Random Recurrent Neural Networks and Random ConvNets. In this paper, I analyze the most important works from these three areas and thereby follow a chronological order. I also work out the core result of each work. As a result, the reader can get a quick overview of this field of research.<br>

Tomato pest classification using deep convolutional neural network with transfer learning, fine tuning and scratch learning

Pests are major threat to economic growth of a country. Application of pesticide is the easiest way to control the pest infection. However, excessive utilization of pesticide is hazardous to environment. The recent advances in deep learning have paved the way for early detection and improved classification of pest in tomato plants which will benefit the farmers. This paper presents a comprehensive analysis of 11 state-of-the-art deep convolutional neural network (CNN) models with three configurations: transfers learning, fine-tuning and scratch learning. The training in transfer learning and fine tuning initiates from pre-trained weights whereas random weights are used in case of scratch learning. In addition, the concept of data augmentation has been explored to improve the performance. Our dataset consists of 859 tomato pest images from 10 categories. The results demonstrate that the highest classification accuracy of 94.87% has been achieved in the transfer learning approach by DenseNet201 model with data augmentation.

Multiobjective Site Selection Model for Emergency Shelter Facilities in Urban Areas

Industrial and economic development is primarily applied to densely populated urban areas. If a sudden disaster occurs in such areas, the consequences can be severe. Shelter facility location affects the implementation of postdisaster relief work. This study explored residents’ perceived utility of evacuation time, their risk utility for road blocking, and the cost factors associated with constructing shelter facilities in the context of governance. A location model for emergency shelter facilities in cities was established on the basis of the aforementioned factors. Because the resolution of the random-weighted genetic algorithm (RWGA) is susceptible to influence from random weights, a robustness random-weighted method (RRWM) was developed. The validity and feasibility of the location model were examined through numerical analysis. Finally, the convergence of the RRWM was analyzed and compared with that of the RWGA and a single-objective genetic algorithm. The results revealed that the proposed algorithm exhibited satisfactory performance and can assist in evaluation and decision-making related to the selection of urban shelter facility locations.

Allocating hot standbys to randomly weighted k-out-of-n: G systems

In industrial engineering applications, randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems can model many reliability systems whose components may contribute unequally and randomly to the systems’ performance. This paper investigates optimal allocations of hot standbys for [Formula: see text]-out-of-[Formula: see text]: G systems with random weights. First, optimal allocation policies are presented by maximizing the total capacity according to the usual stochastic ordering and the expectation ordering when the system is constituted by independent and heterogeneous components accompanied with independent random weights. Second, we investigate hot standbys allocation for randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems with right [left] tail weakly stochastic arrangement increasing random weights in the sense of the usual stochastic ordering [increasing concave ordering]. Simulation studies are provided to illustrate our theoretical findings as well. These established results can provide useful guidance for system designers on how to introduce hot standbys in randomly weighted [Formula: see text]-out-of-[Formula: see text]: G systems in order to enhance their total capacities.