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Katz GE, Reggia JA. Using Directional Fibers to Locate Fixed Points of Recurrent Neural Networks. IEEE Trans Neural Netw Learn Syst. 2017;29(8):3636-3646doi: 10.1109/TNNLS.2017.2733544.
Katz, G. E., & Reggia, J. A. (2018). Using Directional Fibers to Locate Fixed Points of Recurrent Neural Networks. IEEE transactions on neural networks and learning systems, 29(8), 3636-3646. https://doi.org/10.1109/TNNLS.2017.2733544
Katz, Garrett E, and Reggia, James A. "Using Directional Fibers to Locate Fixed Points of Recurrent Neural Networks." IEEE transactions on neural networks and learning systems vol. 29,8 (2018): 3636-3646. doi: https://doi.org/10.1109/TNNLS.2017.2733544
Katz GE, Reggia JA. Using Directional Fibers to Locate Fixed Points of Recurrent Neural Networks. IEEE Trans Neural Netw Learn Syst. 2018 Aug;29(8):3636-3646. doi: 10.1109/TNNLS.2017.2733544. Epub 2017 Aug 24. PMID: 28858815.
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IEEE Trans Neural Netw Learn Syst. 2018 Aug;29(8):3636-3646. doi: 10.1109/TNNLS.2017.2733544. Epub 2017 Aug 24.

Using Directional Fibers to Locate Fixed Points of Recurrent Neural Networks.

IEEE transactions on neural networks and learning systems

Garrett E Katz, James A Reggia

PMID: 28858815 DOI: 10.1109/TNNLS.2017.2733544

Abstract

We introduce mathematical objects that we call "directional fibers," and show how they enable a new strategy for systematically locating fixed points in recurrent neural networks. We analyze this approach mathematically and use computer experiments to show that it consistently locates many fixed points in many networks with arbitrary sizes and unconstrained connection weights. Comparison with a traditional method shows that our strategy is competitive and complementary, often finding larger and distinct sets of fixed points. We provide theoretical groundwork for further analysis and suggest next steps for developing the method into a more powerful solver.

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