C. Jarne

Mariano Caruso, Cecilia Jarne

Recurrent Neural Networks (RNNs) are widely used to model neural activity in Computational Neuroscience. Here, we explore the mathematical foundations of three fundamental procedures that can be implemented: temporal rescaling, discretisation, and linearisation. These techniques provide crucial tools for characterising the behaviour of RNNs, offering insights into their temporal dynamics, facilitating practical computational implementation, and allowing for linear approximations for analysis. We discuss the flexible order in which these procedures can be applied, emphasising their importance in modelling and analysing RNNs for neuroscience and formally prove that these three operations commute pairwise. We also explicitly describe the conditions under which these procedures can be considered interchangeable. Our findings directly inform the design of biologically plausible $\mathtt{RNN}$ models for simulating neural dynamics observed in decision-making circuits and motor control, where temporal scaling and stability are critical for matching experimental recordings. {Furthermore, we show that this exact commutativity guarantees the structural preservation of the network's controllability, preventing the emergence of inaccessible state-spaces under numerical discretisation or temporal rescaling.

Cecilia Jarne

Training neural networks to perform different tasks is relevant across various disciplines. In particular, Recurrent Neural Networks (RNNs) are of great interest in Computational Neuroscience. Open-source frameworks dedicated to Machine Learning, such as Tensorflow and Keras have produced significant changes in the development of technologies that we currently use. This work aims to make a significant contribution by comprehensively investigating and describing the implementation of a temporal processing task, specifically a 3-bit Flip Flop memory. We delve into the entire modelling process, encompassing equations, task parametrization, and software development. The obtained networks are meticulously analyzed to elucidate dynamics, aided by an array of visualization and analysis tools. Moreover, the provided code is versatile enough to facilitate the modelling of diverse tasks and systems. Furthermore, we present how memory states can be efficiently stored in the vertices of a cube in the dimensionally reduced space, supplementing previous results with a distinct approach.

Cecilia Jarne

Signal amplitude envelope allows to obtain information of the signal features for different applications. It is widely used to pre-process sound and other signals of physiological origin in human or animal studies. In order to obtain signal envelope, a fast and simple algorithm is proposed based on peak detection. The procedure presented here is quite straightforward and can be used in different applications of time series analysis. It can be applied in signals with different origin and frequency content. This algorithm presented is implemented based on python libraries. An open source code is also provided. Aspects on the parameter selection are discussed to adapt the same method for different applications. Also traditional methods are revisited and compared with the one proposed here.