- source
- (Lechner et al. 2020)
- tags
- Neural networks

## Summary

This article introduces a type of RNN called Neural Circuit
Policies (NCP). This architecture is said to be inspired from the
wiring diagram of the *C. elegans* nematode.

The main building block is a Recurrent neural network called liquid time constant (LTC) introduced in (Hasani et al. 2020).

### LTC Neurons

These neurons are bio-inspired. For a given neuron in state x_i(t), the continuous temporal evolution is described by an ODE: \[ \dot{x}_i = - \left(\frac{1}{\tau_i} + \frac{w_{ij}}{C_{m_i}} \sigma_i(x_j) \right) x_i + \left( \frac{x_{\text{leak}_i}}{\tau_i}+ \frac{w_{ij}}{C_{m_i}} \sigma_i(x_j) E_{ij} \right) \]

where \(w_{ij}\) is a synaptic weight from neuron \(i\) to \(j\), \(C_{m_i}\) is the membrane capacitance of the neuron \(i\), and \(\sigma_i(x_j(t)) = 1/\left( 1 + e^{-\gamma_{ij}(x_j-\mu_{ij})}\right)\). \(x_{\text{leak}_i}\) is called the resting potential and \(E_ij\) is a reversal synaptic potential.

More details about the biological analogy for those quantities are given in (Hasani et al. 2020; Lechner et al. 2020).

### Results

The authors reports good results on a car steering task compared to many RNN architectures, although not much better than LSTMs. The main advantages of this method according to the authors are:

- Better noise robustness
- Better interpret-ability
- Less parameters needed

## Comments

I was excited about this paper because it seemed to have found a way to train very small neural networks with an alternative learning mechanism, maybe akin to reservoir computing. However it appears to be based on the same principles as traditional supervised learning. The main innovation of this paper would therefore be the architecture it proposes, which I may not understand very deeply due to lack of knowledge in neuroscience.

## Bibliography

Hasani, Ramin, Mathias Lechner, Alexander
Amini, Daniela Rus, and Radu Grosu. 2020. “Liquid Time-Constant
Networks.” *arXiv:2006.04439 [Cs, Stat]*, September.

Lechner, Mathias, Ramin Hasani, Alexander
Amini, Thomas A. Henzinger, Daniela Rus, and Radu Grosu. 2020.
“Neural Circuit Policies Enabling Auditable Autonomy.” *Nature
Machine Intelligence* 2 (10):642–52.