Refereed full papers (journals, book chapters, international conferences)

1991

@article{KrH1991,
	vgclass =	{refpap},
	vgproject =	{nn},
	author =	{Anders Krogh and John A. Hertz},
	title =	{Dynamics of Generalization in Linear Perceptrons},
	journal =	{Advances in Neural Information Processing Systems},
	volume =	{3},
	pages =	{897--903},
	year =	{1991},
	abstract =	{We study the evolution of the generalization ability of a
	simple perceptron with $N$ inputs which learns to imitate a ``teacher
	perceptron''. The system is trained on $p = \alpha N$ binary example
	inputs and the generalization ability measured by testing for agreement
	with the teacher on all $2^N$ possible binary input patterns. The
	dynamics may be solved analytically and exhibits a phase transition
	from imperfect to perfect generalization at $\alpha=1$. Except at this
	point the generalization ability approaches its asymptotic value
	exponentially, with critical slowing down near the transition; the
	relaxation time is $\propto {\left(1-\sqrt{\alpha}\right)}^{-2}$. Right
	at the critical point, the approach to perfect generalization follows a
	power law $\propto t^{-\frac{1}{2}}$. In the presence of noise, the
	generalization ability is degraded by an amount $\propto
	{\left(\sqrt{\alpha} - 1\right)}^{-1}$ just above $\alpha = 1$.},
}