Using Directional Fibers to Locate Fixed Points of Recurrent Neural Networks

Katz, Garrett E.; Reggia, James A.

doi:10.1109/tnnls.2017.2733544

Cited by 9 publications

(3 citation statements)

References 18 publications

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“…These fixed points, along with local linearizations of the RNN dynamics about those fixed points, provide a mechanistic description of how the network implements a computation. Identifying the fixed points of an RNN requires optimization tools that have previously been tailored for specific, "vanilla" or Hopfield-like RNN architectures (Sussillo & Barak, 2013, Katz & Reggia (2018). These approaches rely on hard-coded analytic derivatives (e.g., of the hyperbolic tangent function) and thus can be cumbersome for complicated models (e.g., gated architectures), for studies that involve multiple different models, or when frequent architectural changes are required during the development of a model.…”

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confidence: 99%

FixedPointFinder: A Tensorflow toolbox for identifying and characterizing fixed points in recurrent neural networks

Golub¹,

Sussillo²

2018

JOSS

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confidence: 99%

FixedPointFinder: A Tensorflow toolbox for identifying and characterizing fixed points in recurrent neural networks

Golub¹,

Sussillo²

2018

JOSS

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“…The optimisation algorithm we have used to find fixed points is based on Sussillo and Barak [55]; see [16] for an open-source Tensorflow toolbox for finding fixed points in arbitrary RNN architectures and [25] for an alternative method to identify fixed points. The key idea is to define a scalar function whose minima correspond to fixed points of the ESN dynamics.…”

Section: Finding Fixed Points Of the Dynamicsmentioning

confidence: 99%

Interpreting Recurrent Neural Networks Behaviour via Excitable Network Attractors

2019

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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...

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“…This viewpoint has already been used to understand the difficulties for RNNs to capture longer time dependencies (Bengio, Frasconi, & Simard, 1993;Doya, 1993). In particular, recent work has highlighted the important role played by fixed points in RNN state spaces, that are defined as hidden states that updates to themself for a given input (Katz & Reggia, 2017;Sussillo & Barak, 2013). This line of work has argued that locating such fixed points efficiently could provide insights into RNN dynamics and input-output properties.…”

Section: Introductionmentioning

confidence: 99%

Warming up recurrent neural networks to maximise reachable multistability greatly improves learning

Lambrechts,

De Geeter,

Vecoven

et al. 2023

Neural Networks

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Using Directional Fibers to Locate Fixed Points of Recurrent Neural Networks

Cited by 9 publications

References 18 publications

FixedPointFinder: A Tensorflow toolbox for identifying and characterizing fixed points in recurrent neural networks

FixedPointFinder: A Tensorflow toolbox for identifying and characterizing fixed points in recurrent neural networks

Interpreting Recurrent Neural Networks Behaviour via Excitable Network Attractors

Warming up recurrent neural networks to maximise reachable multistability greatly improves learning

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