The authors draw together the results of a series of detailed computational studies and show how they are contributing to the development of a theory of hippocampal function. A new part of the theory introduced here is a quantitative analysis of how backprojections from the hippocampus to the neocortex could lead to the recall of recent memories. The theory is then compared with other theories of hippocampal function. First, what is computed by the hippocampus is considered. The hypothesis the authors advocate, on the basis of the effects of damage to the hippocampus and neuronal activity recorded in it, is that it is involved in the formation of new memories by acting as an intermediate-term buffer store for information about episodes, particularly for spatial, but probably also for some nonspatial, information. The authors analyze how the hippocampus could perform this function, by producing a computational theory of how it operates, based on neuroanatomical and neurophysiological information about the different neuronal systems con-tained within the hippocampus. Key hypotheses are that the CA3 pyramidal cells operate as a single autoassociation network to store new episodic information as it arrives via a number of specialized preprocessing stages from many association areas of the cerebral cortex, and that the dentate

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.

The CA3 network in the hippocampus may operate as an autoassociator, in which declarative memories, known to be dependent on hippocampal processing, could be stored, and subsequently retrieved, using modifiable synaptic efficacies in the CA3 recurrent collateral system. On the basis of this hypothesis, the authors explore the computational relevance of the extrinsic afferents. to the CA3 network. A quantitative statistical analysis of the information that may be relayed by such afferent connections reveals the need for two distinct systems of input synapses. The synapses of the first system need to be strong (but not associatively modifiable) in order to force, during learning, the CA3 cells into a pattern of activity relatively independent of any inputs being received from the recurrent collaterals, and which thus reflects sizable amounts of new information. It is proposed that the mossy fiber system performs this function. A second system, with a large number of associatively modifiable synapses on each receiving cell, is needed in order to relay a signal specific enough to initiate the retrieval process. This may be identified, we propose, with the perforant path input to CA3. Key words: hippocampus, autoassociative memory, attractor neural networks, associative synapses, information storage

The differentiation between the CA3 and CA1 fields of the mammalian hippocampus is one of the salient traits that set it apart from the organization of the homologue medial wall in reptiles and birds. CA3 is widely thought to function as an autoassociator, but what do we need CA1 for? Based on evidence for a specific role of CA1 in temporal processing, I have explored the hypothesis that the differentiation between CA3 and CA1 may help solve a computational conflict. The conflict is between pattern completion, or integrating current sensory information on the basis of memory, and prediction, or moving from one pattern to the next in a stored sequence. CA3 would take care of the former, while CA1 would concentrate on the latter. I have found the hypothesis to be only weakly supported by neural network simulations. The conflict indeed exists, but the crucial parameter that regulates it appears to be simply the degree of firing frequency adaptation in pyramidal cells. The differentiation between the architectures of CA3 and CA1 has a minor effect on temporal prediction, while it does significantly increase the information content of hippocampal outputs. There may therefore be just a plain quantitative advantage in differentiating the connectivity of the two fields. Moreover, different degrees of adaptation in CA3 and CA1 cells were not found to lead to better performance, further undermining the notion of a functional dissociation.

This paper introduced an information theoretic formalism similar to that of Nadal and Parga (1993) to the analysis. As will become apparent, this approach to network analysis appears to be particularly powerful, and is certain to find diverse application in the future. Once the rudiments of a structural framework have been erected, it is possible to begin to add to the fabric of the theory -- to begin to consider the effect of additional details of biology that were not in themselves necessary to its structural basis. This is where the contribution of the work described in this chapter lies. The analysis described in (Treves, 1995) assumed, for the purposes of simplicity of analysis, that the distribution of patterns of firing of CA3 pyramidal neurons was binary (and for one case ternary), although it considered threshold-linear (and thus analogue) model neurons. Here we shall consider in more detail the effect on information transmission of the possible graded nature of neuronal signalling. Another simple assumption made was that the pattern of convergence (the number of connections each CA1 neuron receives from CA3 neurons) of the Schaffer collaterals was either uniform, or alternatively bi-layered. The real situation is slightly more complex, and a better approximation of it is considered here. 2 A model of the Schaffer collaterals

Hippocampal region CA1 seems from comparative studies to be particularly important in the primate brain, in addition to being crucial to memory function. Thus, it is an extremely appropriate place to begin a quantitative investigation of the information representation and transmission capabilities of cerebral neural networks. In this study, a mathematical model of the Schaffer collateral projection from CA3 to CA1 is described. From the model, the amount of information that can be conveyed by the Schaffer collaterals is calculated, i.e., the information that a pattern of firing in CA1 conveys about a pattern of firing in CA3, because of the connections between them. The calculation is performed analytically for an arbitrary probability distribution describing the pattern of CA3 firing and then solved numerically for particular input distributions. The effect of a number of issues on the information conveyed is examined.

Abstract. Within the theory that describes the hippocampus as a device for the on-line storage of complex memories, the crucial autoassociative operations are ascribed mainly to the recurrent CA3 network. The CA3to-CAI connections may still be important, both in completing information retrieval and in re-expanding, with minimal information loss, the highly compressed representation retrieved in CA3. To quantify these effects, I have defined a suitably realistic formal model of the relevant circuitry, and evaluated its performance in the sense of information theory. Analytical estimates, calculated with mean-field, replica and saddle-point techniques, of the amount of information present in the model CAI output, reveal how such performance depends on different parameters characterising these connections. In particular, nearly all the stored information can be preserved if the model Schaffer collaterals are endowed with an optimal degree of Hebbian plasticity, matching that of the CA3 recurrent collaterals. Keywords: associative memory, hippocampus, CAI field, information theory