Learning on a General Network

This paper generalizes the back-propagation method to a general network containing feedback connections. The network model considered consists of interconnected groups of neurons, where each group could be fully interconnected (it could have feedback connections, with possibly asymmetric weights), but no loops between the groups are allowed. A stochastic descent algorithm is applied, under a certain inequality constraint on each intra-group weight matrix which ensures for the network to possess a unique equilibrium state for every input

Weight Priors for Learning Identity Relations

Learning abstract and systematic relations has been an open issue in neural network learning for over 30 years. It has been shown recently that neural networks do not learn relations based on identity and are unable to generalize well to unseen data. The Relation Based Pattern (RBP) approach has been proposed as a solution for this problem. In this work, we extend RBP by realizing it as a Bayesian prior on network weights to model the identity relations. This weight prior leads to a modified regularization term in otherwise standard network learning. In our experiments, we show that the Bayesian weight priors lead to perfect generalization when learning identity based relations and do not impede general neural network learning. We believe that the approach of creating an inductive bias with weight priors can be extended easily to other forms of relations and will be beneficial for many other learning tasks

Contrastive learning and neural oscillations

The concept of Contrastive Learning (CL) is developed as a family of possible learning algorithms for neural networks. CL is an extension of Deterministic Boltzmann Machines to more general dynamical systems. During learning, the network oscillates between two phases. One phase has a teacher signal and one phase has no teacher signal. The weights are updated using a learning rule that corresponds to gradient descent on a contrast function that measures the discrepancy between the free network and the network with a teacher signal. The CL approach provides a general unified framework for developing new learning algorithms. It also shows that many different types of clamping and teacher signals are possible. Several examples are given and an analysis of the landscape of the contrast function is proposed with some relevant predictions for the CL curves. An approach that may be suitable for collective analog implementations is described. Simulation results and possible extensions are briefly discussed together with a new conjecture regarding the function of certain oscillations in the brain. In the appendix, we also examine two extensions of contrastive learning to time-dependent trajectories

Collaborative Learning of Stochastic Bandits over a Social Network

We consider a collaborative online learning paradigm, wherein a group of agents connected through a social network are engaged in playing a stochastic multi-armed bandit game. Each time an agent takes an action, the corresponding reward is instantaneously observed by the agent, as well as its neighbours in the social network. We perform a regret analysis of various policies in this collaborative learning setting. A key finding of this paper is that natural extensions of widely-studied single agent learning policies to the network setting need not perform well in terms of regret. In particular, we identify a class of non-altruistic and individually consistent policies, and argue by deriving regret lower bounds that they are liable to suffer a large regret in the networked setting. We also show that the learning performance can be substantially improved if the agents exploit the structure of the network, and develop a simple learning algorithm based on dominating sets of the network. Specifically, we first consider a star network, which is a common motif in hierarchical social networks, and show analytically that the hub agent can be used as an information sink to expedite learning and improve the overall regret. We also derive networkwide regret bounds for the algorithm applied to general networks. We conduct numerical experiments on a variety of networks to corroborate our analytical results.Comment: 14 Pages, 6 Figure

The Fast and the Flexible: training neural networks to learn to follow instructions from small data

Learning to follow human instructions is a long-pursued goal in artificial intelligence. The task becomes particularly challenging if no prior knowledge of the employed language is assumed while relying only on a handful of examples to learn from. Work in the past has relied on hand-coded components or manually engineered features to provide strong inductive biases that make learning in such situations possible. In contrast, here we seek to establish whether this knowledge can be acquired automatically by a neural network system through a two phase training procedure: A (slow) offline learning stage where the network learns about the general structure of the task and a (fast) online adaptation phase where the network learns the language of a new given speaker. Controlled experiments show that when the network is exposed to familiar instructions but containing novel words, the model adapts very efficiently to the new vocabulary. Moreover, even for human speakers whose language usage can depart significantly from our artificial training language, our network can still make use of its automatically acquired inductive bias to learn to follow instructions more effectively