The softassign quadratic assignment algorithm has recently emerged as an effective strategy for a variety of optimization problems inpattern recognition and combinatorial optimization. While the effectiveness of the algorithm was demonstrated in thousands of simulations, there was no known proof of convergence. Here, we provide a proof of convergence for the most general form of the algorithm.

We examine the issue of evaluation of model specific parameters in a modified VC-formalism. Two examples are analyzed: the 2-dimensional homogeneous perceptron and the I-dimensional higher order neuron. Both models are solved theoretically, and their learning curves are compared against true learning curves. It is shown that the formalism has the potential to generate a variety of learning curves, including ones displaying ''phase transitions."

Over the last few years the Fourier Transform (FT) representation of boolean functions has been an instrumental tool in the computational learning theory community. It has been used mainly to demonstrate the learnability of various classes of functions with respect to the uniform distribution.

A set of labeled training samples is provided, and a network must be obtained which is then expected to correctly classify previously unseen inputs. In this context, a central problem is to estimate the amount of training data needed to guarantee satisfactory learning performance. To study this question, it is necessary to first formalize the notion of learning from examples. One such formalization is based on the paradigm of probably approximately correct (PAC) learning, due to Valiant (1984). In this framework, one starts by fitting some function /, chosen from a predetermined class F, to the given training data. The class F is often called the "hypothesis class", and for purposes of this discussion it will be assumed that the functions in F take binary values {O, I} and are defined on a common domain X.

We examine the issue of evaluation of model specific parameters in a modified VC-formalism. Two examples are analyzed: the 2-dimensional homogeneous perceptron and the I-dimensional higher order neuron. Both models are solved theoretically, and their learning curves are compared against true learning curves. It is shown that the formalism has the potential to generate a variety of learning curves, including ones displaying ''phase transitions."

Over the last few years the Fourier Transform (FT) representation of boolean functions has been an instrumental tool in the computational learning theory community. It has been used mainly to demonstrate the learnability of various classes of functions with respect to the uniform distribution.

A set of labeled training samples is provided, and a network must be obtained which is then expected to correctly classify previously unseen inputs. In this context, a central problem is to estimate the amount of training data needed to guarantee satisfactory learning performance. To study this question, it is necessary to first formalize the notion of learning from examples. One such formalization is based on the paradigm of probably approximately correct (PAC) learning, due to Valiant (1984). In this framework, one starts by fitting some function /, chosen from a predetermined class F, to the given training data. The class F is often called the "hypothesis class", and for purposes of this discussion it will be assumed that the functions in F take binary values {O, I} and are defined on a common domain X.

We examine the issue of evaluation of model specific parameters in a modified VC-formalism. Two examples are analyzed: the 2-dimensional homogeneous perceptron and the I-dimensional higher order neuron. Both models are solved theoretically, and their learning curves are compared againsttrue learning curves. It is shown that the formalism has the potential to generate a variety of learning curves, including ones displaying ''phase transitions."

A set of labeled training samples is provided, and a network must be obtained which is then expected to correctly classify previously unseen inputs. In this context, a central problem is to estimate the amount of training data needed to guarantee satisfactory learning performance. To study this question, it is necessary to first formalize the notion of learning from examples. One such formalization is based on the paradigm of probably approximately correct (PAC) learning, due to Valiant (1984). In this framework, one starts by fitting some function /, chosen from a predetermined class F, to the given training data. The class F is often called the "hypothesis class", and for purposes of this discussion it will be assumed that the functions in F take binary values {O, I} and are defined on a common domain X.

We investigate the computational power of a formal model for networks ofspiking neurons, both for the assumption of an unlimited timing precision, and for the case of a limited timing precision. We also prove upper and lower bounds for the number of examples that are needed to train such networks.