A minimal synaptic architecture is proposed for how the brain might perform path integration by computing the next internal representation of self-location from the current representation and from the perceived velocity of motion. In the model, a place-cell assembly called a “chart ” contains a twodimensional attractor set called an “attractor map ” that can be used to represent coordinates in any arbitrary environment, once associative binding has occurred between chart locations and sensory inputs. In hippocampus, there are different spatial relations among place fields in different environments and behavioral contexts. Thus, the same units may participate in many charts, and it is shown that the number of uncorrelated charts that can be encoded in the same recurrent network is potentially quite large. According to this theory, the firing of a given place cell is primarily a cooperative effect of the activity of its

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

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.

In the past decade, a large number of robots has been built that explicitly implement biological navigation behaviours. We review these biomimetic approaches using a framework that allows for a common description of biological and technical navigation behaviour. The review shows that biomimetic systems make significant contributions to two fields of research: First, they provide a real world test of models of biological navigation behaviour; second, they make new navigation mechanisms available for technical applications, most notably in the field of indoor robot navigation. While simpler insect navigation behaviours have been implemented quite successfully, the more complicated way-finding capabilities of vertebrates still pose a challenge to current systems. ©2000 Elsevier Science B.V. All rights reserved.

We analyze a model of navigational map formation based on correlation-based, temporally asymmetric potentiation and depression of synapses between hippocampal place cells. We show that synaptic modification during random exploration of an environment shifts the location encoded by place cell activity in such a way that it indicates the direction from any location to a fixed target avoiding walls and other obstacles. Multiple maps to different targets can be simultaneously stored if we introduce target-dependent modulation of place cell activity. Once maps to a number of target locations in a given environment have been stored, novel maps to previously unknown target locations are automatically constructed by interpolation between existing maps.

Our model of the spatial and temporal aspects of place cell firing, and their role in rat navigation is reviewed. The model provides a can- didate mechanism, at the level of individual cells, by which place cell information concerning self-localization could be used to guide navi- gation to previously visited reward sites. The model embodies specific predictions regarding the formation of place fields, the phase coding of place cell firing with respect to the hippocampal theta rhythm, and the formation of neuronal population vectors downstream from the place cells that code for the directions of goals during navigation. Re- cent experiments regarding the spatial distribution of place cell firing have confirmed our initial modeling hypothesis, that place fields are formed from Gaussian tuning curve inputs coding for the distances from environmental features, and enabled us to further specify the functional form of these inputs. Other recent experiments regarding the temporal distribution of place cell firing in 2-dimensional environ- ments have confirmed our predictions based on the temporal aspects of place cell firing on linear tracks. Directions for further experiments and refinements to the model are outlined for the future.

Strong constraints on the neural mechanisms underlying the formation of place fields in the rodent hippocampus come from the systematic changes in spatial activity patterns that are consequent on systematic environmental manipulations. We describe an attractor network model of area CA3 in which local, recurrent, excitatory, and inhibitory interactions generate appropriate place cell representations from location- and directionspecific activity in the entorhinal cortex. In the model, familiarity with the environment, as reflected by activity in neuromodulatory systems, influences the efficacy and plasticity of the recurrent and feedforward inputs to CA3. In unfamiliar, novel, environments, mossy fiber inputs impose activity patterns on CA3, and the recurrent collaterals and the perforant path inputs are subject to graded Hebbian plasticity. The hippocampus is known to be involved in spatial learning and memory in rodents. Some of the most convincing evidence for this is the presence of place cells in areas CA3 and CA1 of the hippocampus (O’Keefe and Dostrovsky, 1971; O’Keefe, 1976) and of many other types of spatially selective cells in neighboring areas

while these previous studies provided a novel connection between NMDA-dependent long-term potentiation RIKEN-MIT Neuroscience Research Center (LTP) and changes in the average receptive field proper-Department of Brain and Cognitive Sciences ties, such as size and specificity, the present work ex-Department of Biology plores the relationship between LTP and the structure Massachusetts Institute of Technology of a receptive field, which can be detected within a single

A model of place-cell firing is presented that makes quantitative predictions about specific place cells' spatial receptive fields following changes to the rat's environment. A place cell's firing rate is modeled as a function of the rat's location by the thresholded sum of the firing rates of a number of putative cortical inputs. These inputs are tuned to respond whenever an environmental boundary is at a particular distance and allocentric direction from the rat. The initial behavior of a place cell in any environment is simply determined by its set of inputs and its threshold; learning is not necessary. The model is shown to produce a good fit to the firing of individual place cells, and populations of place cells across environments of differing shape. The cells' behavior can be predicted for novel environments of arbitrary size and shape, or for manipulations such as introducing a barrier. The model can be extended to make behavioral predictions regarding spatial memory. Hippocampus 2000;10:369--379. 2000 Wiley-Liss, Inc.

There is evidence, beginning with Cheng (1986), that mobile animals may use the geometry of surrounding areas to reorient following disorientation. Gallistel (1990) proposed that geometry is used to compute the major or minor axes of space and suggested that such information might form an encapsulated cognitive module. Research reviewed here, conducted on a wide variety of species since the initial discovery of the use of geometry and the formulation of the modularity claim, has supported some aspects of the approach, while casting doubt on others. Three possible processing models are presented that vary in the way in which (and the extent to which) they instantiate the modularity claim. The extant data do not permit us to discriminate among them. We propose a modified concept of modularity for which an empirical program of research is more tractable.