Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Learning to Discriminate Through Long-Term Changes of Dynamical Synaptic Transmission

Short-term synaptic plasticity is modulated by long-term synaptic changes. There is, however, no general agreement on the computational role of this interaction. Here, we derive a learning rule for the release probability and the maximal synaptic conductance in a circuit model with combined recurrent and feedforward connections that allows learning to discriminate among natural inputs. Short-term synaptic plasticity thereby provides a nonlinear expansion of the input space of a linear classifier, whereas the random recurrent network serves to decorrelate the expanded input space. Computer simulations reveal that the twofold increase in the number of input dimensions through short-term synaptic plasticity improves the performance of a standard perceptron up to 100%. The distributions of release probabilities and maximal synaptic conductances at the capacity limit strongly depend on the balance between excitation and inhibition. The model also suggests a new computational interpretation of spikes evoked by stimuli outside the classical receptive field. These neuronal activitiesmay reflect decorrelation of the expanded stimulus space by intracortical synaptic connections

A Digital Neuromorphic Architecture Efficiently Facilitating Complex Synaptic Response Functions Applied to Liquid State Machines

Information in neural networks is represented as weighted connections, or synapses, between neurons. This poses a problem as the primary computational bottleneck for neural networks is the vector-matrix multiply when inputs are multiplied by the neural network weights. Conventional processing architectures are not well suited for simulating neural networks, often requiring large amounts of energy and time. Additionally, synapses in biological neural networks are not binary connections, but exhibit a nonlinear response function as neurotransmitters are emitted and diffuse between neurons. Inspired by neuroscience principles, we present a digital neuromorphic architecture, the Spiking Temporal Processing Unit (STPU), capable of modeling arbitrary complex synaptic response functions without requiring additional hardware components. We consider the paradigm of spiking neurons with temporally coded information as opposed to non-spiking rate coded neurons used in most neural networks. In this paradigm we examine liquid state machines applied to speech recognition and show how a liquid state machine with temporal dynamics maps onto the STPU-demonstrating the flexibility and efficiency of the STPU for instantiating neural algorithms.Comment: 8 pages, 4 Figures, Preprint of 2017 IJCN