Noise in attractor networks in the brain produced by graded firing rate representations

Attractor cortical neurodynamics, schizophrenia, and depression

The local recurrent collateral connections between cortical neurons provide a basis for attractor neural networks for memory, attention, decision-making, and thereby for many aspects of human behavior. In schizophrenia, a reduction of the firing rates of cortical neurons, caused for example by reduced NMDA receptor function or reduced spines on neurons, can lead to instability of the high firing rate attractor states that normally implement short-term memory and attention in the prefrontal cortex, contributing to the cognitive symptoms. Reduced NMDA receptor function in the orbitofrontal cortex by reducing firing rates may produce negative symptoms, by reducing reward, motivation, and emotion. Reduced functional connectivity between some brain regions increases the temporal variability of the functional connectivity, contributing to the reduced stability and more loosely associative thoughts. Further, the forward projections have decreased functional connectivity relative to the back projections in schizophrenia, and this may reduce the effects of external bottom-up inputs from the world relative to internal top-down thought processes. Reduced cortical inhibition, caused by a reduction of GABA neurotransmission, can lead to instability of the spontaneous firing states of cortical networks, leading to a noise-induced jump to a high firing rate attractor state even in the absence of external inputs, contributing to the positive symptoms of schizophrenia. In depression, the lateral orbitofrontal cortex non-reward attractor network system is over-connected and has increased sensitivity to non-reward, providing a new approach to understanding depression. This is complemented by under-sensitivity and under-connectedness of the medial orbitofrontal cortex reward system in depression.

Pattern separation, completion, and categorisation in the hippocampus and neocortex

The mechanisms for pattern completion and pattern separation are described in the context of a theory of hippocampal function in which the hippocampal CA3 system operates as a single attractor or autoassociation network to enable rapid, one-trial, associations between any spatial location (place in rodents, or spatial view in primates) and an object or reward, and to provide for completion of the whole memory during recall from any part. The factors important in the pattern completion in CA3 and also a large number of independent memories stored in CA3 include: a sparse distributed representation, representations that are independent due to the randomizing effect of the mossy fibres, heterosynaptic long-term depression as well as long-term potentiation in the recurrent collateral synapses, and diluted connectivity to minimize the number of multiple synapses between any pair of CA3 neurons which otherwise distort the basins of attraction. Recall of information from CA3 is implemented by the entorhinal cortex perforant path synapses to CA3 cells, which in acting as a pattern associator allow some pattern generalization. Pattern separation is performed in the dentate granule cells using competitive learning to convert grid-like entorhinal cortex firing to place-like fields, and in the dentate to CA3 connections that have diluted connectivity. Recall to the neocortex is achieved by a reverse hierarchical series of pattern association networks implemented by the hippocampo-cortical backprojections, each one of which performs some pattern generalization, to retrieve a complete pattern of cortical firing in higher-order cortical areas. New results on competitive networks show which factors contribute to their ability to perform pattern separation, pattern clustering, and pattern categorisation, and how these apply in different hippocampal and neocortical systems.

Diluted connectivity in pattern association networks facilitates the recall of information from the hippocampus to the neocortex

The recall of information stored in the hippocampus involves a series of corticocortical backprojections via the entorhinal cortex, parahippocampal gyrus, and one or more neocortical stages. Each stage is considered to be a pattern association network, with the retrieval cue at each stage the firing of neurons in the previous stage. The leading factor that determines the capacity of this multistage pattern association backprojection pathway is the number of connections onto any one neuron, which provides a quantitative basis for why there are as many backprojections between adjacent stages in the hierarchy as forward projections. The issue arises of why this multistage backprojection system uses diluted connectivity. One reason is that a multistage backprojection system with expansion of neuron numbers at each stage enables the hippocampus to address during recall the very large numbers of neocortical neurons, which would otherwise require hippocampal neurons to make very large numbers of synapses if they were directly onto neocortical neurons. The second reason is that as shown here, diluted connectivity in the backprojection pathways reduces the probability of more than one connection onto a receiving neuron in the backprojecting pathways, which otherwise reduces the capacity of the system, that is the number of memories that can be recalled from the hippocampus to the neocortex. For similar reasons, diluted connectivity is advantageous in pattern association networks in other brain systems such as the orbitofrontal cortex and amygdala; for related reasons, in autoassociation networks in, for example, the hippocampal CA3 and the neocortex; and for the different reason that diluted connectivity facilitates the operation of competitive networks in forward-connected cortical systems.

Networks for memory, perception, and decision-making, and beyond to how the syntax for language might be implemented in the brain

Neural principles that provide a foundation for memory, perception, and decision-making include place coding with sparse distributed representations, associative synaptic modification, and attractor networks in which the storage capacity is in the order of the number of associatively modifiable recurrent synapses on any one neuron. Based on those and further principles of cortical computation, hypotheses are explored in which syntax is encoded in the cortex using sparse distributed place coding. Each cortical module 2-3 mm in diameter is proposed to be formed of a local attractor neuronal network with a capacity in the order of 10,000 words (e.g. subjects, verbs or objects depending on the module). Such a system may form a deep language-of-thought layer. For the information to be communicated to other people, the modules in which the neurons are firing which encode the syntactic role, as well as which neurons are firing to specify the words, must be communicated. It is proposed that one solution to this (used in English) is temporal order encoding, for example subject-verb-object. It is shown with integrate-and-fire simulations that this order encoding could be implemented by weakly forward-coupled subject-verb-object modules. A related system can decode a temporal sequence. This approach based on known principles of cortical computation needs to be extended to investigate further whether it could form a biological foundation for the implementation of language in the brain. This article is part of a Special Issue entitled SI: Brain and Memory.

The mechanisms for pattern completion and pattern separation in the hippocampus

The mechanisms for pattern completion and pattern separation are described in the context of a theory of hippocampal function in which the hippocampal CA3 system operates as a single attractor or autoassociation network to enable rapid, one-trial, associations between any spatial location (place in rodents, or spatial view in primates) and an object or reward, and to provide for completion of the whole memory during recall from any part. The factors important in the pattern completion in CA3 together with a large number of independent memories stored in CA3 include a sparse distributed representation which is enhanced by the graded firing rates of CA3 neurons, representations that are independent due to the randomizing effect of the mossy fibers, heterosynaptic long-term depression as well as long-term potentiation in the recurrent collateral synapses, and diluted connectivity to minimize the number of multiple synapses between any pair of CA3 neurons which otherwise distort the basins of attraction. Recall of information from CA3 is implemented by the entorhinal cortex perforant path synapses to CA3 cells, which in acting as a pattern associator allow some pattern generalization. Pattern separation is performed in the dentate granule cells using competitive learning to convert grid-like entorhinal cortex firing to place-like fields. Pattern separation in CA3, which is important for completion of any one of the stored patterns from a fragment, is provided for by the randomizing effect of the mossy fiber synapses to which neurogenesis may contribute, by the large number of dentate granule cells each with a sparse representation, and by the sparse independent representations in CA3. Recall to the neocortex is achieved by a reverse hierarchical series of pattern association networks implemented by the hippocampo-cortical backprojections, each one of which performs some pattern generalization, to retrieve a complete pattern of cortical firing in higher-order cortical areas.

A quantitative theory of the functions of the hippocampal CA3 network in memory

A quantitative computational theory of the operation of the hippocampal CA3 system as an autoassociation or attractor network used in episodic memory system is described. In this theory, the CA3 system operates as a single attractor or autoassociation network to enable rapid, one-trial, associations between any spatial location (place in rodents, or spatial view in primates) and an object or reward, and to provide for completion of the whole memory during recall from any part. The theory is extended to associations between time and object or reward to implement temporal order memory, also important in episodic memory. The dentate gyrus (DG) performs pattern separation by competitive learning to produce sparse representations suitable for setting up new representations in CA3 during learning, producing for example neurons with place-like fields from entorhinal cortex grid cells. The dentate granule cells produce by the very small number of mossy fiber (MF) connections to CA3 a randomizing pattern separation effect important during learning but not recall that separates out the patterns represented by CA3 firing to be very different from each other, which is optimal for an unstructured episodic memory system in which each memory must be kept distinct from other memories. The direct perforant path (pp) input to CA3 is quantitatively appropriate to provide the cue for recall in CA3, but not for learning. Tests of the theory including hippocampal subregion analyses and hippocampal NMDA receptor knockouts are described, and support the theory.

Computational models of decision making: integration, stability, and noise

Decision making demands the accumulation of sensory evidence over time. Questions remain about how this occurs, but recent years have seen progress on several fronts. The first concerns when optimal accumulation of evidence coincides with the simplest method of accumulating neural activity: summation over time. The second involves what computations the brain might perform when summation is difficult due to imprecision in neural circuits or is suboptimal due to uncertainty or variability in how evidence arrives. Finally, the third concerns sources of noise in decision circuits. Empirical studies have better constrained the extent of this noise, and modeling work is helping to clarify its possible origins.

Cortical attractor network dynamics with diluted connectivity

The connectivity of the cerebral cortex is diluted, with the probability of excitatory connections between even nearby pyramidal cells rarely more than 0.1, and in the hippocampus 0.04. To investigate the extent to which this diluted connectivity affects the dynamics of attractor networks in the cerebral cortex, we simulated an integrate-and-fire attractor network taking decisions between competing inputs with diluted connectivity of 0.25 or 0.1, and with the same number of synaptic connections per neuron for the recurrent collateral synapses within an attractor population as for full connectivity. The results indicated that there was less spiking-related noise with the diluted connectivity in that the stability of the network when in the spontaneous state of firing increased, and the accuracy of the correct decisions increased. The decision times were a little slower with diluted than with complete connectivity. Given that the capacity of the network is set by the number of recurrent collateral synaptic connections per neuron, on which there is a biological limit, the findings indicate that the stability of cortical networks, and the accuracy of their correct decisions or memory recall operations, can be increased by utilizing diluted connectivity and correspondingly increasing the number of neurons in the network, with little impact on the speed of processing of the cortex. Thus diluted connectivity can decrease cortical spiking-related noise. In addition, we show that the Fano factor for the trial-to-trial variability of the neuronal firing decreases from the spontaneous firing state value when the attractor network makes a decision. This article is part of a Special Issue entitled "Neural Coding".

Neural and computational mechanisms of postponed decisions

We consider the mechanisms that enable decisions to be postponed for a period after the evidence has been provided. Using an information theoretic approach, we show that information about the forthcoming action becomes available from the activity of neurons in the medial premotor cortex in a sequential decision-making task after the second stimulus is applied, providing the information for a decision about whether the first or second stimulus is higher in vibrotactile frequency. The information then decays in a 3-s delay period in which the neuronal activity declines before the behavioral response can be made. The information then increases again when the behavioral response is required. We model this neuronal activity using an attractor decision-making network in which information reflecting the decision is maintained at a low level during the delay period, and is then selectively restored by a nonspecific input when the response is required. One mechanism for the short-term memory is synaptic facilitation, which can implement a mechanism for postponed decisions that can be correct even when there is little neuronal firing during the delay period before the postponed decision. Another mechanism is graded firing rates by different neurons in the delay period, with restoration by the nonspecific input of the low-rate activity from the higher-rate neurons still firing in the delay period. These mechanisms can account for the decision making and for the memory of the decision before a response can be made, which are evident in the activity of neurons in the medial premotor cortex.