# A Black-box Model for Neurons

## Summary (1 min read)

### Introduction

- Neurons are the basic information processing structures in the brain.
- There is a vast literature on modeling of such intrinsic features, see for instance [3] for a thorough treatment.
- A plethora of experiments has since been devoted to provide specific models by identifying and quantifying the ionic channels, giving rise to very precise biophysical models now available to the computational neuroscience community.
- Thus, the problem of identification and cell classification from voltage traces is fundamental to experimental neuroscience, see [5] where the problem of detection, time-estimation, and cell classification is treated in order to sort neural action potentials.
- The identification method decreases the number of used functions in Wavenet by combining localized and global scope functions instead of only localized functions.

### III. THE NETWORK CHARACTERISTICS

- Great advances were made in the last years in analysis and identification of dynamical systems using non-linear models originated from artificial intelligence.
- Mathematically, they are complex models, whose structure is empirically determined.
- Network structure parameters and training method are determined by error and trial or Heuristic.
- In the multiresolution frame, the approximation of a function f(x) is made through its projections to shifted and compressed versions of a basic function, known as “wavelet mother”.
- Training data are initially approximated with activation functions (scale functions), whose support is equal to the problem domain support (global scope functions), different from the originally proposed wavenet, which uses localized functions only.

### A. Dynamical system identification

- The authors deal with the identification of the neuronal voltage traces of the Morris-Lecar model proposed in [1].
- The steps followed in the identification process were: 1) Acquisition of data group for fitting (Training Patterns): data were obtained solving system 2.
- As a measure criterion, the smaller quadratic error with the smaller number of variables was considered.
- 3) The validation trough dynamic prediction, which corresponds to the prediction of an arbitrary number of steps forward.
- In relation to the other points, only the information of the perturbation variable is used, as external information, and a feedback of the output variables is performed.

### B. Simulation results

- The neural network was trained by defining the Iapp current as an independent variable.
- Iapp is defined as a piecewise constant signal with 50 levels randomly defined with a uniform distribution.
- The value of the constant changes every 2000 integration steps .
- The solutions of the differential equations the model and the neural network prediction are depicted (actually overlapped) in the next figures.
- As it can be verified from the results presented, the prediction in both subthreshold and trigger conditions is satisfactory.

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##### References

29,130 citations

### "A Black-box Model for Neurons" refers background in this paper

...Nevertheless, systems identification can be very tiring, due to the great number of network structure parameters (number of hidden layers, number of neurons per layer) and training method (weights, initial selection, learning factor determination, moment rate and stopping criteria) [7]....

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...RBFN have only one hidden layer, whose neurons use activation functions, generally with compact support and defined around centers [7]....

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### "A Black-box Model for Neurons" refers methods in this paper

...A signal in the multiresolution frame is represented as the sum of successive approximations, done from projections of this signal in spaces defined in wavelets theory [9], [10]....

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