Introducing numerical bounds to improve event-based neural network simulation

Although the spike-trains in neural networks are mainly constrained by the neural dynamics itself, global temporal constraints (refractoriness, time precision, propagation delays, ..) are also to be taken into account. These constraints are revisited in this paper in order to use them in event-based simulation paradigms. We first review these constraints, and discuss their consequences at the simulation level, showing how event-based simulation of time-constrained networks can be simplified in this context: the underlying data-structures are strongly simplified, while event-based and clock-based mechanisms can be easily mixed. These ideas are applied to punctual conductance-based generalized integrate-and-fire neural networks simulation, while spike-response model simulations are also revisited within this framework. As an outcome, a fast minimal complementary alternative with respect to existing simulation event-based methods, with the possibility to simulate interesting neuron models is implemented and experimented.Comment: submitte

Distributed Online Big Data Classification Using Context Information

Distributed, online data mining systems have emerged as a result of applications requiring analysis of large amounts of correlated and high-dimensional data produced by multiple distributed data sources. We propose a distributed online data classification framework where data is gathered by distributed data sources and processed by a heterogeneous set of distributed learners which learn online, at run-time, how to classify the different data streams either by using their locally available classification functions or by helping each other by classifying each other's data. Importantly, since the data is gathered at different locations, sending the data to another learner to process incurs additional costs such as delays, and hence this will be only beneficial if the benefits obtained from a better classification will exceed the costs. We model the problem of joint classification by the distributed and heterogeneous learners from multiple data sources as a distributed contextual bandit problem where each data is characterized by a specific context. We develop a distributed online learning algorithm for which we can prove sublinear regret. Compared to prior work in distributed online data mining, our work is the first to provide analytic regret results characterizing the performance of the proposed algorithm

Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations

Although double-precision floating-point arithmetic currently dominates high-performance computing, there is increasing interest in smaller and simpler arithmetic types. The main reasons are potential improvements in energy efficiency and memory footprint and bandwidth. However, simply switching to lower-precision types typically results in increased numerical errors. We investigate approaches to improving the accuracy of reduced-precision fixed-point arithmetic types, using examples in an important domain for numerical computation in neuroscience: the solution of Ordinary Differential Equations (ODEs). The Izhikevich neuron model is used to demonstrate that rounding has an important role in producing accurate spike timings from explicit ODE solution algorithms. In particular, fixed-point arithmetic with stochastic rounding consistently results in smaller errors compared to single precision floating-point and fixed-point arithmetic with round-to-nearest across a range of neuron behaviours and ODE solvers. A computationally much cheaper alternative is also investigated, inspired by the concept of dither that is a widely understood mechanism for providing resolution below the least significant bit (LSB) in digital signal processing. These results will have implications for the solution of ODEs in other subject areas, and should also be directly relevant to the huge range of practical problems that are represented by Partial Differential Equations (PDEs).Comment: Submitted to Philosophical Transactions of the Royal Society

Adaptive Backstepping Controller Design for Stochastic Jump Systems

In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques