arXiv subjects

Cecilia Jarne

Publications and source records attributed to Cecilia Jarne.

8 recordsLinked to original sources

arXiv2026

Analysing Rescaling, Discretisation, and Linearisation in RNNs for Neural System Modelling

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.

cs.NE↗

arXiv2023

Exploring Flip Flop memories and beyond: training recurrent neural networks with key insights

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.

cs.LG↗

arXiv2023

Exploring weight initialization, diversity of solutions, and degradation in recurrent neural networks trained for temporal and decision-making tasks

Recurrent Neural Networks (RNNs) are frequently used to model aspects of brain function and structure. In this work, we trained small fully-connected RNNs to perform temporal and flow control tasks with time-varying stimuli. Our results show that different RNNs can solve the same task by converging to different underlying dynamics and also how the performance gracefully degrades as either network size is decreased, interval duration is increased, or connectivity damage is increased. For the considered tasks, we explored how robust the network obtained after training can be according to task parameterization. In the process, we developed a framework that can be useful to parameterize other tasks of interest in computational neuroscience. Our results are useful to quantify different aspects of the models, which are normally used as black boxes and need to be understood in order to model the biological response of cerebral cortex areas.

q-bio.NC↗

arXiv2023

Recurrent Neural Networks as Electrical Networks, a formalization

Since the 1980s, and particularly with the Hopfield model, recurrent neural networks or RNN became a topic of great interest. The first works of neural networks consisted of simple systems of a few neurons that were commonly simulated through analogue electronic circuits. The passage from the equations to the circuits was carried out directly without justification and subsequent formalisation. The present work shows a way to formally obtain the equivalence between an analogue circuit and a neural network and formalizes the connection between both systems. We also show which are the properties that these electrical networks must satisfy. We can have confidence that the representation in terms of circuits is mathematically equivalent to the equations that represent the network.

cs.NE↗

arXiv2023

Effect in the spectra of eigenvalues and dynamics of RNNs trained with Excitatory-Inhibitory constraint

In order to comprehend and enhance models that describes various brain regions is important to study the dynamics of trained recurrent neural networks. Including Dales law in such models usually presents several challenges. However, this is an important aspect that allows computational models to better capture the characteristics of the brain. Here we present a framework to train networks using such constraint. Then we have used it to train them in simple decision making tasks. We characterized the eigenvalue distributions of the recurrent weight matrices of such networks. Interestingly, we discovered that the non-dominant eigenvalues of the recurrent weight matrix are distributed in a circle with a radius less than 1 for those whose initial condition before training was random normal and in a ring for those whose initial condition was random orthogonal. In both cases, the radius does not depend on the fraction of excitatory and inhibitory units nor the size of the network. Diminution of the radius, compared to networks trained without the constraint, has implications on the activity and dynamics that we discussed here.

q-bio.NC↗

arXiv2022

Different eigenvalue distributions encode the same temporal tasks in recurrent neural networks

Different brain areas, such as the cortex and, more specifically, the prefrontal cortex, show great recurrence in their connections, even in early sensory areas. {Several approaches and methods based on trained networks have been proposed to model and describe these regions. It is essential to understand the dynamics behind the models because they are used to build different hypotheses about the functioning of brain areas and to explain experimental results. The main contribution here is the description of the dynamics through the classification and interpretation carried out with a set of numerical simulations. This study sheds light on the multiplicity of solutions obtained for the same tasks and shows the link between the spectra of linearized trained networks and the dynamics of the counterparts. The patterns in the distribution of the eigenvalues of the recurrent weight matrix were studied and properly related to the dynamics in each task.

q-bio.NC↗

arXiv2018

A method to align time series segments based on envelope features as anchor points

In the time series analysis field, there is not a unique recipe for studying signal similarities. On the other hand, averaging signals of the same nature is an essential tool in the analysis of different kinds of data. Here we propose a method to align and average segments of time series with similar patterns. A simple implementation based on \textit{python} code is provided for the procedure. The analysis was inspired by the study of canary sound syllables, but it is possible to apply it in semi periodic signals of different nature and not necessarily related to sounds.

eess.SP↗

arXiv2018

A heuristic approach to obtain signal envelope with a simple software implementation

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.

cs.SD↗