We demonstrate that the problem of training neural networks with small (average) squared error is computationally intractable. Consider a data set of M points (Xi, Yi), i = 1,2, ... , M, where Xi are input vectors from Rd, Yi are real outputs (Yi E R). For a network 10 in some class F of neural networks, (11M) L~l (fO(Xi)Yi)2)1/2 inlfEF(l/ M) "2:f!1 (f(Xi) YJ2)1/2 is the (avarage) relative erro...

In this paper, a systematic compensation approach is presented to efficiently design the approximate squaring function with a simple combinational logic circuit. Also, a set of recursive Boolean equations for general outputs is derived such that the logic circuit can be rapidly designed and reused for various bit-width inputs. In logic implementation, our design approach possesses less circuit ...

By analysis of historical data of the ionosphere, it is suggested to apply grey theory to ionospheric short-term forecasting, grey range information entropy is defined to determine the optimum grey length of the sample sequence, the prediction model based on residual error is constructed, and the observation data of multiple ionospheric observation stations in China are adopted for test. The pr...

This paper describes recent improvements to SPLICE, Stereo-based Piecewise Linear Compensation for Environments, which produces an estimate of cepstrum of undistorted speech given the observed cepstrum of distorted speech. For distributed speech recognition applications, SPLICE can be placed at the server, thus limiting the processing that would take place at the client. We evaluated this algor...

We present a novel framework for depth based optic cup boundary extraction from a single 2D color fundus photograph per eye. Multiple depth estimates from shading, color and texture gradients in the image are correlated with Optical Coherence Tomography (OCT) based depth using a coupled sparse dictionary, trained on image-depth pairs. Finally, a Markov Random Field is formulated on the depth ma...