相关论文: On-Line Learning with Restricted Training Sets: An…
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…
We apply a general theory describing the dynamics of supervised learning in layered neural networks in the regime where the size p of the training set is proportional to the number of inputs N, as developed in a previous paper, to several…
On-line learning of a rule given by an N-dimensional Ising perceptron, is considered for the case when the student is constrained to take values in a discrete state space of size $L^N$. For L=2 no on-line algorithm can achieve a finite…
We analyze the generalization performance of a student in a model composed of nonlinear perceptrons: a true teacher, ensemble teachers, and the student. We calculate the generalization error of the student analytically or numerically using…
Continual Learning aims to bring machine learning into a more realistic scenario, where tasks are learned sequentially and the i.i.d. assumption is not preserved. Although this setting is natural for biological systems, it proves very…
We study the problem of learning robust classifiers where the classifier will receive a perturbed input. Unlike robust PAC learning studied in prior work, here the clean data and its label are also adversarially chosen. We formulate this…
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…
Representation learning from complex data typically involves models with a large number of parameters, which in turn require large amounts of data samples. In neural network models, model complexity grows with the number of inputs to each…
It has been demonstrated that one of the most striking features of the nervous system, the so called 'plasticity' (i.e high adaptability at different structural levels) is primarily based on Hebbian learning which is a collection of…
Hebbian learning is a key principle underlying learning in biological neural networks. We relate a Hebbian spike-timing-dependent plasticity rule to noisy gradient descent with respect to a non-convex loss function on the probability…
The "fire together, wire together" Hebbian model is a central principle for learning in neuroscience, but surprisingly, it has found limited applicability in modern machine learning. In this paper, we take a first step towards bridging this…
We study the dynamics of on-line learning in large perceptrons, for the case of training sets with a structural bias of the input vectors, by deriving exact and closed macroscopic dynamical laws using non-equilibrium statistical mechanical…
Biological systems have to build models from their sensory data that allow them to efficiently process previously unseen inputs. Here, we study a neural network learning a linearly separable rule using examples provided by a teacher. We…
A recurrent neural net is described that learns a set of patterns in the presence of noise. The learning rule is of Hebbian type, and, if noise would be absent during the learning process, the resulting final values of the weights would…
We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability…
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…
We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability…
The learning dynamics of on-line independent component analysis is analysed in the limit of large data dimension. We study a simple Hebbian learning algorithm that can be used to separate out a small number of non-Gaussian components from a…
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…
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…