Dynamics of Evolving Feed-Forward Neural Networks and Their Topological Invariants
- 2.1k Downloads
The evolution of a simulated feed-forward neural network with recurrent excitatory connections and inhibitory forward connections is studied within the framework of algebraic topology. The dynamics includes pruning and strengthening of the excitatory connections. The invariants that we define are based on the connectivity structure of the underlying graph and its directed clique complex. The computation of this complex and of its Euler characteristic are related with the dynamical evolution of the network. As the network evolves dynamically, its network topology changes because of the pruning and strengthening of the onnections and algebraic topological invariants can be computed at different time steps providing a description of the process. We observe that the initial values of the topological invariant computed on the network before it evolves can predict the intensity of the activity.
KeywordsGraph theory Network invariant Directed clique complex Recurrent neural dynamics Synfire chain Synaptic plasticity
This work was partially supported by the Swiss National Science Foundation grant CR13I1-138032.
- 5.Csardi, G., Nepusz, T.: The igraph software package for complex network research. InterJ. Complex Syst. 1695 (2006). http://igraph.org
- 6.Dłotko, P., Hess, K., Levi, R., Nolte, M., Reimann, M., Scolamiero, M., Turner, K., Muller, E., Markram, H.: Topological analysis of the connectome of digital reconstructions of neural microcircuits. arXiv preprint arXiv:1601.01580 (2016)
- 8.Giusti, C., Ghrist, R., Bassett, D.S.: Two’s company, three (or more) is a simplex: algebraic-topological tools for understanding higher-order structure in neural data. arXiv preprint arXiv:1601.01704 (2016)
- 12.Litvak, V., Sompolinsky, H., Segev, I., Abeles, M.: On the transmission of rate code in long feedforward networks with excitatoryinhibitory balance. J. Neurosci. 23(7), 3006–3015 (2003)Google Scholar
- 15.Prut, Y., Vaadia, E., Bergman, H., Haalman, I., Slovin, H., Abeles, M.: Spatiotemporal structure of cortical activity: properties and behavioral relevance. J. Neurophysiol. 79(6), 2857–2874 (1998)Google Scholar
- 16.Tange, O.: GNU parallel - the command-line power tool: login. USENIX Mag. 36(1), 42–47 (2011)Google Scholar