The principle of maximizing mutual information is applied to learning overcomplete and recurrent representations. The underlying model consists ofa network of input units driving a larger number of output units with recurrent interactions. In the limit of zero noise, the network is deterministic andthe mutual information can be related to the entropy of the output units.

H.Kurino, M.Nakagawa, K.W.Lee, T.Nakamura, Y.Yamada, K.T.Park and M.Koyanagi Dept. of Machine Intelligence and Systems Engineering, Tohoku University 01, Aza-Aramaki, Aoba-ku, Sendai 980-8579, Japan kurino@sd.mech.tohoku.ac.jp Abstract The smart VISIOn chip has a large potential for application in general purpose high speed image processing systems. In order to fabricate smart vision chips including photo detector compactly, we have proposed the application of three dimensional LSI technology for smart vision chips. Three dimensional technology has great potential to realize new neuromorphic systems inspired by not only the biological function but also the biological structure. In this paper, we describe our three dimensional LSI technology for neuromorphic circuits and the design of smart vision chips. 1 Introduction Recently, the demand for very fast image processing systems with real time operation capability has significantly increased. Conventional image processing systems based on the system level integration of a camera and a digital processor, do not have the potential for application in general purpose consumer electronic products.

Output coding is a general method for solving multiclass problems by reducing them to multiple binary classification problems. Previous research onoutput coding has employed, almost solely, predefined discrete codes. We describe an algorithm that improves the performance of output codes by relaxing them to continuous codes. The relaxation procedure is cast as an optimization problem and is reminiscent of the quadratic program for support vector machines. We describe experiments with the proposed algorithm, comparing it to standard discrete output codes. The experimental results indicate that continuous relaxations of output codes often improve the generalization performance, especially for short codes.

We introduce a novel algorithm, termed PPA (Performance Prediction Algorithm), that quantitatively measures the contributions of elements of a neural system to the tasks it performs. The algorithm identifies the neurons or areas which participate in a cognitive or behavioral task, given data about performance decrease in a small set of lesions. It also allows the accurate prediction of performances due to multi-element lesions. The effectiveness of the new algorithm is demonstrated in two models of recurrent neural networks with complex interactions among the elements. Thealgorithm is scalable and applicable to the analysis of large neural networks. Given the recent advances in reversible inactivation techniques, it has the potential to significantly contribute to the understanding ofthe organization of biological nervous systems, and to shed light on the long-lasting debate about local versus distributed computation inthe brain.

We analyze Gallager codes by employing a simple mean-field approximation thatdistorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decodingalgorithm as an extremization of a proper free-energy. We find a thermodynamic phase transition that coincides with information theoreticalupper-bounds and explain the practical code performance in terms of the free-energy landscape.

In this paper we will discuss a variational mean-field theory and its application to BNs, sigmoidal BNs in particular. We present a variational derivation of the mean-field theory, proposed by Plefka[2].

The resulting combinatorial problem - finding the best agreement half-space over an input sample - is NP hard to approximate to within some constant factor. We suggest a way to circumvent this theoretical bound by introducing a new measure of success for such algorithms. An algorithm is ILmargin successful if the agreement ratio of the half-space it outputs is as good as that of any half-space once training points that are inside the ILmargins of its separating hyper-plane are disregarded. We prove crisp computational complexity resultswith respect to this success measure: On one hand, for every positive IL, there exist efficient (poly-time) ILmargin successful learningalgorithms. On the other hand, we prove that unless P NP, there is no algorithm that runs in time polynomial in the sample size and in 1/IL that is ILmargin successful for all IL O. 1 Introduction We consider the computational complexity of learning linear perceptrons for arbitrary (Le.non -separable) data sets.

We introduce a new, nonparametric and principled, distance based clustering method. This method combines a pairwise based approach witha vector-quantization method which provide a meaningful interpretation to the resulting clusters. The idea is based on turning the distance matrix into a Markov process and then examine the decay of mutual-information during the relaxation of this process. The clusters emerge as quasi-stable structures during thisrelaxation, and then are extracted using the information bottleneck method.

We analyze the bit error probability of multiuser demodulators for directsequence binaryphase-shift-keying (DSIBPSK) CDMA channel with additive gaussian noise. The problem of multiuser demodulation is cast into the finite-temperature decoding problem, and replica analysis is applied toevaluate the performance of the resulting MPM (Marginal Posterior Mode)demodulators, which include the optimal demodulator and the MAP demodulator as special cases. An approximate implementation ofdemodulators is proposed using analog-valued Hopfield model as a naive mean-field approximation to the MPM demodulators, and its performance is also evaluated by the replica analysis. Results of the performance evaluationshows effectiveness of the optimal demodulator and the mean-field demodulator compared with the conventional one, especially inthe cases of small information bit rate and low noise level. 1 Introduction The CDMA (Code-Division-Multiple-Access) technique [1] is important as a fundamental technology of digital communications systems, such as cellular phones. The important applications includerealization of spread-spectrum multipoint-to-point communications systems, in which multiple users share the same communication channel.

In this paper, we derive a second order mean field theory for directed graphical probability models. By using an information theoretic argument itis shown how this can be done in the absense of a partition function. This method is a direct generalisation of the well-known TAP approximation for Boltzmann Machines. In a numerical example, it is shown that the method greatly improves the first order mean field approximation. Fora restricted class of graphical models, so-called single overlap graphs, the second order method has comparable complexity to the first order method. For sigmoid belief networks, the method is shown to be particularly fast and effective.