arXiv subjects

Ron Meir

Publications and source records attributed to Ron Meir.

46 records · Page 3Linked to original sources

arXiv2014

Spiking input-output relation for general biophysical neuron models

Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new processes are constantly being discovered, biophysical neuron models increasingly become "too complex to be useful" yet "too simple to be realistic". A fundamental open question in theoretical neuroscience pertains to how this deadlock may be resolved. In order to tackle this problem, we first define the notion of a "excitable neuron model". Then we analytically derive the input-output relation of such neuronal models, relating input spike trains to output spikes based on known biophysical properties. Thus we obtain closed-form expressions for the mean firing rates, all second order statistics (input-state-output correlation and spectra) and construct optimal linear estimators for the neuronal response and internal state. These results are guaranteed to hold, given a few generic assumptions, for any stochastic biophysical neuron model (with an arbitrary number of slow kinetic processes) under general sparse stimulation. This solution suggests that the common simplifying approach that ignores much of the complexity of the neuron might actually be unnecessary and even deleterious in some cases. Specifically, the stochasticity of ion channels and the temporal sparseness of inputs is exactly what rendered our analysis tractable, allowing us to incorporate slow kinetics.

q-bio.NC↗

arXiv2014

The neuron's response at extended timescales

Many systems are modulated by unknown slow processes. This hinders analysis in highly non-linear systems, such as excitable systems. We show that for such systems, if the input matches the sparse `spiky' nature of the output, the spiking input-output relation can be derived. We use this relation to reproduce and interpret the irregular and complex 1/f response observed in isolated neurons stimulated over days. We decompose the neuronal response into contributions from its long history of internal noise and its short (few minutes) history of inputs, quantifying memory, noise and stability.

q-bio.NC↗

arXiv2013

Mean Field Bayes Backpropagation: scalable training of multilayer neural networks with binary weights

Significant success has been reported recently using deep neural networks for classification. Such large networks can be computationally intensive, even after training is over. Implementing these trained networks in hardware chips with a limited precision of synaptic weights may improve their speed and energy efficiency by several orders of magnitude, thus enabling their integration into small and low-power electronic devices. With this motivation, we develop a computationally efficient learning algorithm for multilayer neural networks with binary weights, assuming all the hidden neurons have a fan-out of one. This algorithm, derived within a Bayesian probabilistic online setting, is shown to work well for both synthetic and real-world problems, performing comparably to algorithms with real-valued weights, while retaining computational tractability.

stat.ML↗

arXiv2013

Slow dynamics of neuronal excitability under pulse stimulation

Neurons fire irregularly on multiple timescales when stimulated with a periodic pulse train. This raises two questions: Does this irregularity imply significant intrinsic stochasticity? Can existing neuron models be readily extended to describe behavior at long timescales? We show here that for commonly studied neuronal models, dynamics is not chaotic and can only produce stable and periodic firing patterns. This is done by transforming the neuron model to an analytically tractable piecewise linear discrete map. Thus we answer "yes" and "no" to the above questions, respectively.

q-bio.CB↗

arXiv2012

Dynamic State Estimation Based on Poisson Spike Trains: Towards a Theory of Optimal Encoding

Neurons in the nervous system convey information to higher brain regions by the generation of spike trains. An important question in the field of computational neuroscience is how these sensory neurons encode environmental information in a way which may be simply analyzed by subsequent systems. Many aspects of the form and function of the nervous system have been understood using the concepts of optimal population coding. Most studies, however, have neglected the aspect of temporal coding. Here we address this shortcoming through a filtering theory of inhomogeneous Poisson processes. We derive exact relations for the minimal mean squared error of the optimal Bayesian filter and by optimizing the encoder, obtain optimal codes for populations of neurons. We also show that a class of non-Markovian, smooth stimuli are amenable to the same treatment, and provide results for the filtering and prediction error which hold for a general class of stochastic processes. This sets a sound mathematical framework for a population coding theory that takes temporal aspects into account. It also formalizes a number of studies which discussed temporal aspects of coding using time-window paradigms, by stating them in terms of correlation times and firing rates. We propose that this kind of analysis allows for a systematic study of temporal coding and will bring further insights into the nature of the neural code.

q-bio.NC↗

arXiv2012

An exact reduction of the master equation to a strictly stable system with an explicit expression for the stationary distribution

The evolution of a continuous time Markov process with a finite number of states is usually calculated by the Master equation - a linear differential equations with a singular generator matrix. We derive a general method for reducing the dimensionality of the Master equation by one by using the probability normalization constraint, thus obtaining a affine differential equation with a (non-singular) stable generator matrix. Additionally, the reduced form yields a simple explicit expression for the stationary probability distribution, which is usually derived implicitly. Finally, we discuss the application of this method to stochastic differential equations.

q-bio.QM↗

arXiv2010

Neuronal Response Clamp

Since the first recordings made of evoked action potentials it has become apparent that the responses of individual neurons to ongoing physiologically relevant input, are highly variable. This variability is manifested in non-stationary behavior of practically every observable neuronal response feature. Here we introduce the Neuronal Response Clamp, a closed-loop technique enabling full control over two important single neuron activity variables: response probability and stimulus-spike latency. The technique is applicable over extended durations (up to several hours), and is effective even on the background of ongoing neuronal network activity. The Response Clamp technique is a powerful tool, extending the voltage-clamp and dynamic-clamp approaches to the neuron's functional level, namely - its spiking behavior.

q-bio.NC↗

arXiv2010

History dependent dynamics in a generic model of ion channels - an analytic study

Recent experiments have demonstrated that the timescale of adaptation of single neurons and ion channel populations to stimuli slows down as the length of stimulation increases; in fact, no upper bound on temporal time-scales seems to exist in such systems. Furthermore, patch clamp experiments on single ion channels have hinted at the existence of large, mostly unobservable, inactivation state spaces within a single ion channel. This raises the question of the relation between this multitude of inactivation states and the observed behavior. In this work we propose a minimal model for ion channel dynamics which does not assume any specific structure of the inactivation state space. The model is simple enough to render an analytical study possible. This leads to a clear and concise explanation of the experimentally observed exponential history-dependent relaxation in sodium channels in a voltage clamp setting, and shows that their recovery rate from slow inactivation must be voltage dependent. Furthermore, we predict that history-dependent relaxation cannot be created by overly sparse spiking activity. While the model was created with ion channel populations in mind, its simplicity and genericalness render it a good starting point for modeling similar effects in other systems, and for scaling up to higher levels such as single neurons which are also known to exhibit multiple time scales.

q-bio.SC↗

arXiv2010

MSE-based analysis of optimal tuning functions predicts phenomena observed in sensory neurons

Biological systems display impressive capabilities in effectively responding to environmental signals in real time. There is increasing evidence that organisms may indeed be employing near optimal Bayesian calculations in their decision-making. An intriguing question relates to the properties of optimal encoding methods, namely determining the properties of neural populations in sensory layers that optimize performance, subject to physiological constraints. Within an ecological theory of neural encoding/decoding, we show that optimal Bayesian performance requires neural adaptation which reflects environmental changes. Specifically, we predict that neuronal tuning functions possess an optimal width, which increases with prior uncertainty and environmental noise, and decreases with the decoding time window. Furthermore, even for static stimuli, we demonstrate that dynamic sensory tuning functions, acting at relatively short time scales, lead to improved performance. Interestingly, the narrowing of tuning functions as a function of time was recently observed in several biological systems. Such results set the stage for a functional theory which may explain the high reliability of sensory systems, and the utility of neuronal adaptation occurring at multiple time scales.

q-bio.NC↗

arXiv2009

Delayed Feedback Control Requires an Internal Forward Model

Biological motor control provides highly effective solutions to difficult control problems in spite of the complexity of the plant and the significant delays in sensory feedback . Such delays are expected to lead to non trivial stability issues and lack of robustness of control solutions. However, such difficulties are not observed in biological systems under normal operating conditions. Based on early suggestions in the control literature, a possible solution to this conundrum has been the suggestion that the motor system contains within itself a forward model of the plant (e.g., the arm), which allows the system to `simulate' and predict the effect of applying a control signal. In this work we formally define the notion of a forward model for deterministic control problems, and provide simple conditions that imply its existence for tasks involving delayed feedback control. As opposed to previous work which dealt mostly with linear plants and quadratic cost functions, our results apply to rather generic control systems, showing that any controller (biological or otherwise) which solves a set of tasks, \emph{must} contain within itself a forward plant model. We suggest that our results provide strong theoretical support for the necessity of forward models in many delayed control problems, implying that they are not only useful, but rather, mandatory, under general conditions.

math.OC↗