Hippocampal region CA3 contains strong recurrent exci-tation mediated by synapses of the longitudinal associa-tion fibers. These recurrent excitatory connections may play a dominant role in determining the information pro-cessing characteristics of this region. However, they result in feedback dynamics that may cause both runaway excit-atory activity and runaway synaptic modification. Previous models of recurrent excitation have prevented unbounded activity using biologically unrealistic techniques. Here, the activation of feedback inhibition is shown to prevent un-bounded activity, allowing stable activity states during re-call and learning. In the model, cholinergic suppression of synaptic transmission at excitatory feedback synapses is shown to determine the extent to which activity depends upon new features of the afferent input versus components

Models of unsupervised correlation-based (Hebbian) synaptic plasticity are typically unstable: either all synapses grow until each reaches the maximum allowed strength, or all synapses decay to zero strength. A common method of avoiding these outcomes is to use a constraint that conserves or limits the total synaptic strength over a cell. We study the dynamical effects of such constraints. Two methods of enforcing a constraint are distinguished, multiplicative and subtractive. For otherwise linear learning rules, multiplicative enforcement of a constraint results in dynamics that converge to the principal eigenvector of the operator determining unconstrained synaptic development. Subtractive enforcement, in contrast, typically leads to a final state in which almost all synaptic strengths reach either the maximum or minimum allowed value. This final state is often dominated by weight configurations other than the principal eigenvector of the unconstrained operator. Multiplica...

Coarse codes are widely used throughout the brain to encode sensory and motor variables. Methods designed to interpret these codes, such as population vector analysis, are either inefficient (the variance of the estimate is much larger than the smallest possible variance) or biologically implausible, like maximum likelihood. Moreover, these methods attempt to compute a scalar or vector estimate of the encoded variable. Neurons are faced with a similar estimation problem. They must read out the responses of the presynaptic neurons, but, by contrast, they typically encode the variable with a further population code rather than as a scalar. We show how a nonlinear recurrent network can be used to perform estimation in a near-optimal way while keeping the estimate in a coarse code format. This work suggests that lateral connections in the cortex may be involved in cleaning up uncorrelated noise among neurons representing similar variables.

This paper describes research done at the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for the Laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-89- J-3202, and in part by the National Science Foundation grant MIP-9001651. The author is also supported by a G.Y. Chu Fellowship

We study the war of attrition and the all-pay auction when players ’ signals are affiliated and symmetrically distributed. We (a) find sufficient conditions for the existence of symmetric monotonicequilibrium bidding strategies; and (b) examine the performance of these auction forms in terms of the expected revenue accruing to the seller. Under our conditions the war of attrition raises greater expected revenue than all other other known sealed bid auction forms. 1

Motivated partly by the resurgence of neural computation research, and partly by advances in device technology, there has been a recent increase of interest in analog, continuous-time computation. However, while special-case algorithms and devices are being developed, relatively little work exists on the general theory of continuous-time models of computation. In this paper, we survey the existing models and results in this area, and point to some of the open research questions. 1 Introduction After a long period of oblivion, interest in analog computation is again on the rise. The immediate cause for this new wave of activity is surely the success of the neural networks "revolution", which has provided hardware designers with several new numerically based, computationally interesting models that are structurally sufficiently simple to be implemented directly in silicon. (For designs and actual implementations of neural models in VLSI, see e.g. [30, 45]). However, the more fundamental...

This paper discusses the discrete analogue of the gradient of a function and shows how discrete gradients can be used in the numerical integration of ordinary differential equations (ODE's). Given an ODE and one or more first integrals (i.e., constants of the motion) and/or Lyapunov functions, it is shown that the ODE can be rewritten as a `linear-gradient system.' Discrete gradients are used to construct discrete approximations to the ODE which preserve the first integrals and Lyapunov functions exactly. The method applies to all Hamiltonian, Poisson, and gradient systems, and also to many dissipative systems (those with a known first integral or Lyapunov function).

This article reviews the application of various notions from the theory of dynamical systems to the analysis of numerical approximation of initial value problems over long time intervals. Standard error estimates comparing individual trajectories are of no direct use in this context since the error constant typically grows like the exponential of the time interval under consideration. Instead of comparing trajectories, the effect of discretization on various sets which are invariant under the evolution of the underlying differential equation is studied. Such invariant sets are crucial in determining long time dynamics. The particular invariant sets which are studied are equilibrium points, together with their unstable manifolds and local phase portraits, periodic solutions, quasi-periodic solutions and strange attractors. Particular attention is paid to the development of a unified theory and to the development of an existence theory for invariant sets of the underlying differential equation which may be used directly to construct an analogous existence theory (and hence a simple approximation theory) for the numerical method. To appear in Acta Numerica 1994, Cambridge University Press CONTENTS

Languages are transmitted from person to person and generation to generation via a process of iterated learning: people learn a language from other people who once learned that language themselves. We analyze the consequences of iterated learning for learning algorithms based on the principles of Bayesian inference, assuming that learners compute a posterior distribution over languages by combining a prior (representing their inductive biases) with the evidence provided by linguistic data. We show that when learners sample languages from this posterior distribution, iterated learning converges to a distribution over languages that is determined entirely by the prior. Under these conditions, iterated learning is a form of Gibbs sampling, a widely-used Markov chain Monte Carlo algorithm. The consequences of iterated learning are more complicated when learners choose the language with maximum posterior probability, being affected by both the prior of the learners and the amount of information transmitted between generations. We show that in this case, iterated learning corresponds to another statistical inference algorithm, a variant of the expectation-maximization (EM) algorithm. These results clarify the role of iterated learning in explanations of linguistic universals and provide a formal connection between constraints on language acquisition and the languages that come to be spoken, suggesting that information transmitted via iterated learning will ultimately come to mirror the minds of the learners.

This paper presents a theory that enables to interpret natural processes as special purpose analog computers. Since physical systems are naturally described in continuous time, a definition of computational complexity for continuous time systems is required. In analogy with the classical discrete theory we develop fundamentals of computational complexity for dynamical systems, discrete or continuous in time, on the basis of an intrinsic time scale of the system. Dissipative dynamical systems are classified into the computational complexity classes P d , Co-RP d , NP d