The firing rate maps of hippocampal place cells recorded in a freely moving rat are viewed as a set of approximate radial basis functions over the (2-D) environment of the rat. It is proposed that these firing fields are constructed during exploration from 'sensory inputs' (tuning curve responses to the distance of cues from the rat) and used by cells downstream to construct firing rate maps that approximate any desired surface over the environment. It is shown that, when a rat moves freely in an open field, the phase of firing of a place cell (with respect to the EEG 0 rhythm) contains information as to the relative position of its firing field from the rat. A model of hippocampal function is presented in which the firing rate maps of cells downstream of the hippocampus provide a 'population vector' encoding the instantaneous direction of the rat from a previously encountered reward site, enabling navigation to it. A neuronal simulation, involving reinforcement only at the goal location, provides good agreement with single cell recording from the hippocampal region, and can navigate to reward sites in open fields using sensory input from environmental cues. The system requires only brief exploration, performs latent learning, and can return to a goal location after encountering it only once.

The problem of predicting the position of a freely foraging rat based on the ensemble firing patterns of place cells recorded from the CA1 region of its hippocampus is used to develop a two-stage statistical paradigm for neural spike train decoding. In the first,or encoding stage,place cell spiking activity is modeled as an inhomogeneous Poisson process whose instantaneous rate is a function of the animal’s position in space and phase of its theta rhythm. The animal’s path is modeled as a Gaussian random walk. In the second,or decoding stage,a Bayesian statistical paradigm is used to derive a nonlinear recursive causal filter algorithm for predicting the position of the animal from the place cell ensemble firing patterns. The algebra of the decoding algorithm defines an explicit map of the discrete spike trains into the position prediction. The confidence regions for the position predictions quantify spike train infor-

such as the orientation of a line in the visual field or the location of Two main goals for reconstruction are approached in this the body in space are coded as activity levels in populations of neurons. Reconstruction or decoding is an inverse problem in which paper. The first goal is technical and is exemplified by the the physical variables are estimated from observed neural activity. population vector method applied to motor cortical activities Reconstruction is useful first in quantifying how much information during various reaching tasks (Georgopoulos et al. 1986, 1989; about the physical variables is present in the population and, second, Schwartz 1994) and the template matching method applied to in providing insight into how the brain might use distributed represen- disparity selective cells in the visual cortex (Lehky and Sejnowtations in solving related computational problems such as visual ob- ski 1990) and hippocampal place cells during rapid learning of ject recognition and spatial navigation. Two classes of reconstruction place fields in a novel environment (Wilson and McNaughton methods, namely, probabilistic or Bayesian methods and basis func- 1993). In these examples, reconstruction extracts information tion methods, are discussed. They include important existing methods from noisy neuronal population activity and transforms it to a

We present a theoretical framework for understanding the roles of the hippocampus and neocortex in learning and memory. This framework incorporates a theme found in many theories of hippocampal function, that the hippocampus is responsible for developing conjunctive representations binding together stimulus elements into a unitary rep- resentation that can later be recalled from partial input cues. This idea appears problematic, however, because it is contradicted by the fact that hippocampally lesioned rats can learn nonlinear discrimination problems that require conjunctive representations. Our framework accommodates this finding by establishing a principled division of labor between the cortex and hippocampus, where the cortex is responsible for slow learning that integrates over multiple experiences to extract generalities, while the hippocampus performs rapid learning of the arbitrary contents of individual experiences. This framework shows that nonlinear discrimination problems are not good tests of hippocampal function, and suggests that tasks involving rapid, incidental conjunctive learning are better. We implement this framework in a computational neural network model, and show that it can account for a wide range of data in animal learning, thus validating our theoretical ideas, and providing a number of insights and predictions about these learning phenomena.

We present a general encoding-decoding framework for interpreting the activity of a population of units. A standard population code interpretation method, the Poisson model, starts from a description as to how a single value of an underlying quantity can generate the activities of each unit in the population. In casting it in the encoding-decoding framework, we find that this model is too restrictive to describe fully the activities of units in population codes in higher processing areas, such as the medial temporal area. Under a more powerful model, the population activity can convey information not only about a single value of some quantity but also about its whole distribution, including its variance, and perhaps even the certainty the system has in the actual presence in the world of the entity generating this quantity. We propose a novel method for forming such probabilistic interpretations of population codes and compare it to the existing method.

. A computational model of hippocampal activity during spatial cognition and navigation tasks is presented. The spatial representation in our model of the rat hippocampus is built on-line during exploration via two processing streams. An allothetic vision-based representation is built by unsupervised Hebbian learning extracting spatio-temporal properties of the environment from visual input. An idiothetic representation is learned based on internal movement-related information provided by path integration. On the level of the hippocampus, allothetic and idiothetic representations are integrated to yield a stable representation of the environment by a population of localized overlapping CA3-CA1 place fields. The hippocampal spatial representation is used as a basis for goal-oriented spatial behavior. We focus on the neural pathway connecting the hippocampus to the nucleus accumbens. Place cells drive a population of locomotor action neurons in the nucleus accumbens. Reward-based learnin...

Using experimental facts about long-term potentiation (LTP) and hippocampal place cells, we model how a spatial map of the environment can be created in the rat hippocampus. Sequential firing of place cells during exploration induces, in the model, a pattern of LTP between place cells that shifts the location coded by their ensemble activity away from the actual location of the animal. These shifts provide a navigational map that, in a simulation of the Morris maze, can guide the animal toward its goal. The model demonstrates how behaviorally generated modifications of synaptic strengths can be read out to affect subsequent behavior. Our results also suggest a way that navigational maps can be constructed from experimental recordings of hippocampal place cells. *Current address: Dept. of Brain and Cognitive Sciences, MIT E25-236, 45 Carlton St., Cambridge, MA 02139. Blockade of long term potentiation (LTP) and hippocampal lesions drastically impair

Multiple factors simultaneously affect the spiking activity of individual neurons. Determining the effects and relative importance of these factors is a challenging problem in neurophysiology. We propose a statistical framework based on the point process likelihood function to relate a neuron’s spiking probability to three typical covariates: the neuron’s own spiking history, concurrent ensemble activity and extrinsic covariates such as stimuli or behavior. The framework uses parametric models of the conditional intensity function to define a neuron’s spiking probability in terms of the covariates. The discrete time likelihood function for point processes is used to carry out model fitting and model analysis. We show that, by modeling the logarithm of the conditional intensity function as a linear combination of functions of the covariates, the discrete time point process likelihood function is readily analyzed in the generalized linear model (GLM) framework. We illustrate our approach for both GLM and non-GLM likelihood functions using simulated data and multivariate single unit

Measuring agreement between a statistical model and a spike train data series, that is, evaluating goodness of fit, is crucial for establishing the model’s validity prior to using it to make inferences about a particular neural system. Assessing goodness-of-fit is a challenging problem for point process neural spike train models, especially for histogram-based models such as perstimulus time histograms (PSTH) and rate functions estimated by spike train smoothing. The time-rescaling theorem is a wellknown result in probability theory, which states that any point process with an integrable conditional intensity function may be transformed into a Poisson process with unit rate. We describe how the theorem may be used to develop goodness-of-fit tests for both parametric and histogram-based point process models of neural spike trains. We apply these tests in two examples: a comparison of PSTH, inhomogeneous Poisson, and inhomogeneous Markov interval models of neural spike trains from the sup-

ABSTRACT: This paper presents a model of how hippocampal place cells might be used for spatial navigation in two watermaze tasks: the standard reference memory task and a delayed matching-to-place task. In the reference memory task, the escape platform occupies a single location and rats gradually learn relatively direct paths to the goal over the course of days, in each of which they perform a fixed number of trials. In the delayed matching-to-place task, the escape platform occupies a novel location on each day, and rats gradually acquire one-trial learning, i.e., direct paths on the second trial of each day. The model uses a local, incremental, and statistically efficient connectionist algorithm called temporal difference learning in two distinct components. The first is a reinforcement-based ‘‘actor-critic’ ’ network that is a general model of classical and instrumental conditioning. In this case, it is applied to navigation, using place cells to provide information about state. By itself, the actor-critic can learn the reference memory task, but this learning is inflexible to changes to the platform location. We argue that one-trial learning in the delayed matching-to-place task demands a goal-independent representation of space. This is provided by the second component of the model: a network that uses temporal difference learning and selfmotion information to acquire consistent spatial coordinates in the environment. Each component of the model is necessary at a different stage of the task; the actor-critic provides a way of transferring control to the component that performs best. The model successfully captures gradual acquisition in both tasks, and, in particular, the ultimate development of one-trial learning in the delayed matching-to-place task. Place cells report a form of stable, allocentric information that is well-suited to the various kinds of learning in the model. Hippocampus 2000;10:1–16.