Computer Engineering Commons^™

Orthogonal Bases Are The Best: A Theorem Justifying Bruno Apolloni's Heuristic Neural Network Idea, Jaime Nava, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main problems with neural networks is that they are often very slow in learning the desired dependence. To speed up neural networks, Bruno Apolloni proposed to othogonalize neurons during training, i.e., to select neurons whose output functions are orthogonal to each other. In this paper, we use symmetries to provide a theoretical explanation for this heuristic idea.

Towards Neural-Based Understanding Of The Cauchy Deviate Method For Processing Interval And Fuzzy Uncertainty, Vladik Kreinovich, Hung T. Nguyen

Departmental Technical Reports (CS)

One of the most efficient techniques for processing interval and fuzzy data is a Monte-Carlo type technique of Cauchy deviates that uses Cauchy distributions. This technique is mathematically valid, but somewhat counterintuitive. In this paper, following the ideas of Paul Werbos, we provide a natural neural network explanation for this technique.

Sensitivity Analysis Of Neural Control, Chin-Wang Tao, Hung T. Nguyen, J. T. Yao, Vladik Kreinovich

Departmental Technical Reports (CS)

We provide explicit formulas that describe how sensitive the resulting signal of a neural network is to the measurement errors with which we measure the inputs.

Computational Geometry And Artifical Neural Networks: A Hybrid Approach To Optimal Sensor Placement For Aerospace Nde, Roberto A. Osegueda, Carlos M. Ferregut, Mary J. George, Jose M. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

The ideal design of an airplane should include built-in sensors that are pre-blended in the perfect aerodynamic shape. Each built-in sensor is expensive to blend in and requires continuous maintenance and data processing, so we would like to use as few sensors as possible. The ideal formulation of the corresponding optimization problem is, e.g., to minimize the average detection error for fault locations. However, there are two obstacles to this ideal formulation:

--First, this ideal formulation requires that we know the probabilities of different fault locations etc., and there are usually not enough statistics to determine these probabilities.

--Second, even …

Sensor Placement For Aerospace Non-Destructive Evaluation (Nde): Optimization Under Fuzzy Uncertainty, Roberto A. Osegueda, Carlos M. Ferregut, Mary J. George, Jose M. Gutierrez, Vladik Kreinovich

Departmental Technical Reports (CS)

No abstract provided.