Defining Time in a Minimal Hippocampal CA3 Model by Matching Time-span of Associative Synaptic Modification and Input Pattern Duration Kurt E. Mitman 1 , Patryk A. Laurent 1 , William B Levy 2 Department of Neurosurgery 2 , College of Arts and Sciences 1 , University of Virginia P.O. Box 800420, Charlottesville, VA 22908 Abstract – This paper quantifies the time shifting of neuronal codes in a sparse, randomly connected neural network model of hippocampal region CA3. As this network is trained to learn a sequence, the neurons that encode portions of this sequence characteristically fire earlier and earlier over the course of training. Here we systematically investigate the effects of the N- methyl-D-aspartate(NMDA)-governed time-span of synaptic associativity on this shifting process and how this time-span interacts with the duration of each successive external input. The results show that there is an interaction between this synaptic time-span and externally applied pattern duration such that the early shifting effect approaches a maximum asymptotically and that this maximum is very nearly produced when the e-fold decay time-span of synaptic associativity is matched to the duration of individual input patterns. The performance of this model as a sequence prediction device varies with the time-span selected. If too long a time-span is used, overly strong attractors evolve and destroy the sequence prediction ability of the network. Local context cell firing − the learned repetitive firing of neurons that code for a specific subsequence − also varies in duration with these two parameters. Importantly, if the associative time-span is matched to the longevity of each individual external pattern and if time-shifting and local context length are normalized by this same external pattern duration, then time-shifting and local context length are constant across simulations with different parameters. This constancy supports the idea that real time can be mapped into a network of McCulloch-Pitts neurons that lack a time scale for excitation and resetting. I. INTRODUCTION The sequence learning, recoding theory of hippocampal function [1] depends heavily on a temporally asymmetric rule governing associative synaptic modification. This temporal asymmetry plays a critical role for a special kind of sequence completion: it allows learning that produces timely predictions [2]. That is, it enables the network to meet an important requirement − use an early part of a sequence to generate the rest of the sequence before the rest of the sequence occurs. The asymmetric associative temporal characteristic of synaptic modification arises from the on- and off-rate properties of the NMDA receptor [3]. The recoding process itself has been predicted as time- shifting to earlier firings [1,4] resulting in a somewhat loosely overlapping code (see “rough-counting” in [1]). In this way a sequence of neural firing resembles an incrementing, shifting binary counter when the neurons are visualized via re- ordering by the temporal order in which they fire. In terms of biology, the earlier or backwards shifting of firing in the model is similar to that recently demonstrated in vivo [5] where it was complemented by a negative skew in the activity of a large portion of the neurons [6]. The combination of earlier-shifting of firing with the formation and lengthening of place-cell type firing results in a neural code for the present input which becomes increasingly similar to the future patterns. This similarity is what allows timely predictions [1]. When the model learns a nonspatial task, cell firing resembling place cells occurs, and these neurons are called local context neurons because they identify a particular subsequence of a longer sequence. The average duration of such place-cell type firings is denoted E[L], the average local context length. When training the model to learn cognitive tasks, an intermediate to high value of E[L] correlates with good performance (e.g., [7,8] ). However, if E[L] becomes excessively large, the network state can be drawn into a noisy attractor, which could prevent the appropriate sequence recall. This motivates us to study E[L] as a function of parameters such as the time constant of synaptic associativity. As an expected result, we find that E[L] increases with increasing values of the time constant of associativity. A central finding of this paper is a matching between the time-span of associative modification and the duration of the inputs (stutter length) to the network. We show that this matching produces a compromise between the predictive component of the neuronal codes developed during learning and performance. Specifically increasing the LTP time-span beyond this compromise does in fact marginally increase the predictive component of the neuronal codes, but it also degrades performance and the robustness of the codes. That is, too large of a time-span can cause the formation of performance-destroying stable attractors. The other important observation here concerns the mapping of time between computational cycles of the simulations and real time. By ratioing against input pattern longevity (stutter length), the neuronal codes developed by training are constant across parametric changes of the NMDA receptor off-rate time constant that maps the model into real time. Thus, the longevity of neuronal firings and the time shifts measured are also mapped into real time. II. METHODS A. The Model 0-7803-7898-9/03/$17.00 ©2003 IEEE 1631