Related papers: On-line learning through simple perceptron with a …

A perceptron with N random weights can store of the order of N patterns by removing a fraction of the weights without changing their strengths. The critical storage capacity as a function of the concentration of the remaining bonds for…

We derive the Gardner storage capacity for associative networks of threshold linear units, and show that with Hebbian learning they can operate closer to such Gardner bound than binary networks, and even surpass it. This is largely achieved…

Perceptron is a classic online algorithm for learning a classification function. In this paper, we provide a novel extension of the perceptron algorithm to the learning to rank problem in information retrieval. We consider popular listwise…

Using the cavity method we consider the learning of noisy teacher-generated examples by a nonlinear student perceptron. For insufficient examples and weak weight decay, the activation distribution of the training examples exhibits a gap for…

Recently, we proposed to transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average, and use separate shortcut connections to model the linear dependencies instead. We…

We study supervised learning and generalisation in coupled perceptrons trained on-line using two learning scenarios. In the first scenario the teacher and the student are independent networks and both are represented by an Ashkin-Teller…

We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based…

In this paper we are concerned with the learnability of nonlocal interaction kernels for first order systems modeling certain social interactions, from observations of realizations of their dynamics. This paper is the first of a series on…

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…

The binary perceptron problem asks us to find a sign vector in the intersection of independently chosen random halfspaces with intercept $-\kappa$. We analyze the performance of the canonical discrepancy minimization algorithms of…

In this paper, we propose a quasi-Newton method for solving smooth and monotone nonlinear equations, including unconstrained minimization and minimax optimization as special cases. For the strongly monotone setting, we establish two global…

We have recently shown that the statistical properties of goal directed reaching in human subjects depends on recent experience in a way that is consistent with the presence of adaptive Bayesian priors (Verstynen and Sabes, 2011). We also…

In order to design haptic icons or build a haptic vocabulary, we require a set of easily distinguishable haptic signals to avoid perceptual ambiguity, which in turn requires a way to accurately estimate the perceptual (dis)similarity of…

We present an exact solution for the dynamics of on-line Hebbian learning in neural networks, with restricted and unrealizable training sets. In contrast to other studies on learning with restricted training sets, unrealizability is here…

The classical perceptron rule provides a varying upper bound on the maximum margin, namely the length of the current weight vector divided by the total number of updates up to that time. Requiring that the perceptron updates its internal…

We study the problem of {\em properly} learning large margin halfspaces in the agnostic PAC model. In more detail, we study the complexity of properly learning $d$-dimensional halfspaces on the unit ball within misclassification error…

A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning…

On-line learning of a hierarchical learning model is studied by a method from statistical mechanics. In our model a student of a simple perceptron learns from not a true teacher directly, but ensemble teachers who learn from the true…

Perceptrons have been known for a long time as a promising tool within the neural networks theory. The analytical treatment for a special class of perceptrons started in seminal work of Gardner \cite{Gar88}. Techniques initially employed to…

We study and provide exposition to several phenomena that are related to the perceptron's compression. One theme concerns modifications of the perceptron algorithm that yield better guarantees on the margin of the hyperplane it outputs.…