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Causal networks in simulated neural systems

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Abstract

Neurons engage in causal interactions with one another and with the surrounding body and environment. Neural systems can therefore be analyzed in terms of causal networks, without assumptions about information processing, neural coding, and the like. Here, we review a series of studies analyzing causal networks in simulated neural systems using a combination of Granger causality analysis and graph theory. Analysis of a simple target-fixation model shows that causal networks provide intuitive representations of neural dynamics during behavior which can be validated by lesion experiments. Extension of the approach to a neurorobotic model of the hippocampus and surrounding areas identifies shifting causal pathways during learning of a spatial navigation task. Analysis of causal interactions at the population level in the model shows that behavioral learning is accompanied by selection of specific causal pathways—“causal cores”—from among large and variable repertoires of neuronal interactions. Finally, we argue that a causal network perspective may be useful for characterizing the complex neural dynamics underlying consciousness.

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Notes

  1. Many applications in neurophysiology make use of a frequency-domain version of Granger causality (Geweke 1982; Kaminski et al. 2001). However, because in this paper we analyze simulation models without oscillatory dynamics, we remain in the (simpler) time domain.

  2. The fitness function was F = t fix  + 0.25(35 − d̄), where t fix denotes the proportion of time for which the target was fixated and d̄ the mean offset between H and G (the environment was a toroidal square plane with side length 100).

  3. The analyzed time series varied in length from 450 to 4,994 time-steps. Robustness to different lengths was assessed by reanalyzing causal interactions after dividing each time series into two parts; results were qualitatively identical (see (Seth and Edelman 2007) for details).

  4. Recursive complexity refers to the balance between differentiation and integration across different levels of description. The phenomenal structure of consciousness appears to be recursive inasmuch as individual features of conscious scenes are themselves Gestalts which share organizational properties with the conscious scene as a whole.

  5. Because Granger causality is based on linear regression it assumes a continuous signal, but neural systems at the level of spikes are discontinuous. A straightforward adaptation of the technique is to convolve spikes with a continuous function (e.g., a half-Gaussian) in order to generate a continuous signal. A more principled but more complex alternative is to substitute linear regression modelling with a point-process prediction algorithm (Okatan et al. 2005; Nykamp 2007).

  6. J. Feng, personal communication.

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Acknowledgment

The research described in this paper was largely carried out while the author was at The Neurosciences Institute, La Jolla, California, with support from the Neurosciences Research Foundation. Many thanks to my colleagues there and in particular to Jeffrey L. Krichmar and Gerald M. Edelman who were instrumental in enabling this work. I am also grateful for the comments of two anonymous reviewers.

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  1. Department of Informatics, University of Sussex, Brighton, BN1 9QJ, UK

    Anil K. Seth

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Seth, A.K. Causal networks in simulated neural systems. Cogn Neurodyn 2, 49–64 (2008). https://doi.org/10.1007/s11571-007-9031-z

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