Related papers: A multifractal phase-space analysis of perceptrons…
Random input patterns induce a partition of the coupling space of feed-forward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the…
Random input patterns induce a partition of the coupling space of a perceptron into cells labeled by their output sequences. Learning some data with a maximal error rate leads to clusters of neighboring cells. By analyzing the internal…
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
We extend our study of phase transitions in the generalization behaviour of multilayer perceptrons with non-overlapping receptive fields to the problem of the influence of noise, concerning e.g. the input units and/or the couplings between…
We investigate the influence of different kinds of structure on the learning behaviour of a perceptron performing a classification task defined by a teacher rule. The underlying pattern distribution is permitted to have spatial…
A learning algorithm for multilayer perceptrons is presented which is based on finding the principal components of a correlation matrix computed from the example inputs and their target outputs. For large networks our procedure needs far…
The optimal capacity of graded-response perceptrons storing biased and spatially correlated patterns with non-monotonic input-output relations is studied. It is shown that only the structure of the output patterns is important for the…
Information processing in certain neuronal networks in the brain can be considered as a map of binary vectors, where ones (spikes) and zeros (no spikes) of input neurons are transformed into spikes and no spikes of output neurons. A simple…
In this article, starting from a Gibbs capacity, we build a new random capacity by applying two simple operators, the first one introducing some redundancy and the second one performing a random sampling. Depending on the values of the two…
An unsupervised learning procedure based on maximizing the mutual information between the outputs of two networks receiving different but statistically dependent inputs is analyzed (Becker and Hinton, Nature, 355, 92, 161). For a generic…
A perceptron is trained by a random bit sequence. In comparison to the corresponding classification problem, the storage capacity decreases to alpha_c=1.70\pm 0.02 due to correlations between input and output bits. The numerical results are…
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…
We consider the generalization problem for a perceptron with binary synapses, implementing the Stochastic Belief-Propagation-Inspired (SBPI) learning algorithm which we proposed earlier, and perform a mean-field calculation to obtain a…
We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A…
Multifractal analysis (MFA) provides a framework for the global characterization of image textures by describing the spatial fluctuations of their local regularity based on the multifractal spectrum. Several works have shown the interest of…
A popular theory of perceptual processing holds that the brain learns both a generative model of the world and a paired recognition model using variational Bayesian inference. Most hypotheses of how the brain might learn these models assume…
We investigate the generalization ability of a perceptron with non-monotonic transfer function of a reversed-wedge type in on-line mode. This network is identical to a parity machine, a multilayer network. We consider several learning…
We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the…
In this paper, we introduce the gated perceptron, an enhancement of the conventional perceptron, which incorporates an additional input computed as the product of the existing inputs. This allows the perceptron to capture non-linear…
On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous…