Interpreting Recurrent Neural Networks Behaviour via Excitable Network Attractors

Abstract

Introduction: Machine learning provides fundamental tools both for scientific research and for the development of technologies with significant impact on society. It provides methods that facilitate the discovery of regularities in data and that give predictions without explicit knowledge of the rules governing a system. However, a price is paid for exploiting such flexibility: machine learning methods are typically black-boxes where it is difficult to fully understand what the machine is doing or how it is operating. This poses constraints on the applicability and explainability of such methods. Methods: Our research aims to open the black-box of recurrent neural networks, an important family of neural networks used for processing sequential data. We propose a novel methodology that provides a mechanistic interpretation of behaviour when solving a computational task. Our methodology uses mathematical constructs called excitable network attractors, which are invariant sets in phase space composed of stable attractors and excitable connections between them. Results and Discussion: As the behaviour of recurrent neural networks depends both on training and on inputs to the system, we introduce an algorithm to extract network attractors directly from the trajectory of a neural network while solving tasks. Simulations conducted on a controlled benchmark task confirm the relevance of these attractors for interpreting the behaviour of recurrent neural networks, at least for tasks that involve learning a finite number of stable states and transitions between them.as reservoir computing [32,33]. Echo state networks (ESNs) [21,30] constitute an important example of reservoir computing, where a recurrent layer (called a reservoir) is composed of a large number of neurons with randomly initialised connections that are not fine-tuned via gradient-based optimisation mechanisms. The main idea behind ESNs is to exploit the rich dynamics generated by the reservoir with an output layer, the read-out that is optimised to solve a specific task. Problem statement and research hypothesisThe high-dimensional and non-linear nature of RNNs complicates interpretability of their internal dynamics, which are characterised by complex, input-dependent spatio-temporal patterns of activity [47,55]. This poses constraints on understanding the behaviour of RNNs: they are usually viewed as black-boxes from which it is hard to extract useful knowledge about their inner workings. As highlighted by recent research efforts [10,24,40], similar interpretability issues affect many other machine learning methods. Furthermore, an increasing societal need to develop accountability and explainability of decision making by AI [17] is driving the development of methodologies for explaining the behaviour of such methods.Our aim in this paper is to develop effective models that capture the essential dynamical behaviour of RNNs on computational tasks as input-driven responses of a dynamical system, while neglecting microscopic details of the RNN dynamics in phase...

Echo State Networks with Self-Normalizing Activations on the Hyper-Sphere

“…Here, we analyze the ability of the proposed model (2) to retain memory of past inputs in the state. In order to perform such analysis, we define a measure of network's memory that quantifies the impact of past inputs on current state x n .…”

“…For linear and nonlinear networks, the input scaling (a constant scaling factor of the input signal) is fixed to 1 and the SR equals ρ = 0.95. For the proposed model (2), the input scaling is chosen to be 0.01, while the SR is ρ = 15. For the sake of simplicity, in what follows we refer to ESNs resulting from the use of (2) as "spherical reservoir".…”

Neuronal Sequence Models for Bayesian Online Inference

“…In a similar approach, recent theoretical work on the behavior of RNNs has introduced the concept of excitable network attractors, which are characterized by stable states of a system connected by excitable connections (Ceni et al, 2019). The conceptual idea of orbits between fixed points may further be implemented in different ways.…”

Evolutionary aspects of reservoir computing

“…For a review on RC training (including issues of reservoir design discussed in the next section) see [54] and other works [55,56]. Also, the computational capacity of RC can be boosted if a (trainable) feedback is added from the linear readouts to the reservoir [57][58][59][60][61]. This allows for more agile context-dependent computations and longerterm memory [57].…”