Article

# Stimulus-dependent suppression of chaos in recurrent neural networks.

Lewis-Sigler Institute for Integrative Genomics, Icahn 262, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review E (Impact Factor: 2.31). 07/2010; 82(1 Pt 1):011903. DOI: 10.1103/PHYSREVE.82.011903 Source: PubMed

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**ABSTRACT:**Goal-directed decision making in biological systems is broadly based on associations between conditional and unconditional stimuli. This can be further classified as classical conditioning (correlation-based learning) and operant conditioning (reward-based learning). A number of computational and experimental studies have well established the role of the basal ganglia in reward-based learning, where as the cerebellum plays an important role in developing specific conditioned responses. Although viewed as distinct learning systems, recent animal experiments point towards their complementary role in behavioral learning, and also show the existence of substantial two-way communication between these two brain structures. Based on this notion of co-operative learning, in this paper we hypothesize that the basal ganglia and cerebellar learning systems work in parallel and interact with each other. We envision that such an interaction is influenced by reward modulated heterosynaptic plasticity (RMHP) rule at the thalamus, guiding the overall goal directed behavior. Using a recurrent neural network actor-critic model of the basal ganglia and a feed-forward correlation-based learning model of the cerebellum, we demonstrate that the RMHP rule can effectively balance the outcomes of the two learning systems. This is tested using simulated environments of increasing complexity with a four-wheeled robot in a foraging task in both static and dynamic configurations. Although modeled with a simplified level of biological abstraction, we clearly demonstrate that such a RMHP induced combinatorial learning mechanism, leads to stabler and faster learning of goal-directed behaviors, in comparison to the individual systems. Thus in this paper we provide a computational model for adaptive combination of the basal ganglia and cerebellum learning systems by way of neuromodulated plasticity for goal-directed decision making in biological and bio-mimetic organisms.Frontiers in Neural Circuits 09/2014; 8(126). · 2.95 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Johnson-Lindenstrauss (JL) matrices implemented by sparse random synaptic connections are thought to be a prime candidate for how convergent pathways in the brain compress information. However, to date, there is no complete mathematical support for such implementations given the constraints of real neural tissue. The fact that neurons are either excitatory or inhibitory implies that every so implementable JL matrix must be sign consistent (i.e., all entries in a single column must be either all nonnegative or all nonpositive), and the fact that any given neuron connects to a relatively small subset of other neurons implies that the JL matrix should be sparse. We construct sparse JL matrices that are sign consistent and prove that our construction is essentially optimal. Our work answers a mathematical question that was triggered by earlier work and is necessary to justify the existence of JL compression in the brain and emphasizes that inhibition is crucial if neurons are to perform efficient, correlation-preserving compression.Proceedings of the National Academy of Sciences 11/2014; · 9.81 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. For many models of these networks, a striking feature is that their dynamics are chaotic and thus, are sensitive to small perturbations. How does this chaos manifest in the neural code? Specifically, how variable are the spike patterns that such a network produces in response to an input signal? To answer this, we derive a bound for a general measure of variability-spike-train entropy. This leads to important insights on the variability of multi-cell spike pattern distributions in large recurrent networks of spiking neurons responding to fluctuating inputs. The analysis is based on results from random dynamical systems theory and is complemented by detailed numerical simulations. We find that the spike pattern entropy is an order of magnitude lower than what would be extrapolated from single cells. This holds despite the fact that network coupling becomes vanishingly sparse as network size grows-a phenomenon that depends on "extensive chaos," as previously discovered for balanced networks without stimulus drive. Moreover, we show how spike pattern entropy is controlled by temporal features of the inputs. Our findings provide insight into how neural networks may encode stimuli in the presence of inherently chaotic dynamics.Frontiers in Computational Neuroscience 10/2014; 8:123. · 2.23 Impact Factor

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