Selection Criteria for Neuromanifolds of Stochastic Dynamics

  • Nihat AyEmail author
  • Guido Montúfar
  • Johannes Rauh
Conference paper


We present ways of defining neuromanifolds – models of stochastic matrices – that are compatible with the maximization of an objective function such as the expected reward in reinforcement learning theory. Our approach is based on information geometry and aims to reduce the number of model parameters with the hope to improve gradient learning processes.


Extreme Point Reinforcement Learning Exponential Family Hamilton Path Deterministic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    S. Amari. Natural Gradient Works Efficiently in Learning. Neural Comput., 10(2) (1998) 251–276.CrossRefGoogle Scholar
  2. 2.
    S. Amari, K. Kurata, H. Nagaoka. Information Geometry of Boltzmann machines. IEEE T. Neural Networks, 3(2) (1992) 260–271.CrossRefGoogle Scholar
  3. 3.
    N. Ay, T. Wennekers. Dynamical Properties of Strongly Interacting Markov Chains. Neural Networks 16 (2003) 1483–1497.PubMedCrossRefGoogle Scholar
  4. 4.
    G. Lebanon. Axiomatic geometry of conditional models. IEEE Transactions on Information Theory, 51(4) (2005) 1283–1294.CrossRefGoogle Scholar
  5. 5.
    G. Montúfar, N. Ay. Refinements of Universal Approximation Results for DBNs and RBMs. Neural Comput. 23(5) (2011) 1306–1319.PubMedCrossRefGoogle Scholar
  6. 6.
    R. Sutton, A. Barto. Reinforcement Learning. MIT Press (1998).Google Scholar
  7. 7.
    R. Sutton, D. McAllester, S. Singh, Y. Mansour. Policy Gradient Methods for Reinforcement Learning with Function Approximation. Adv. in NIPS 12 (2000) 1057–1063.Google Scholar
  8. 8.
    K.G. Zahedi, N. Ay, R. Der. Higher Coordination With Less Control – A Result of Information Maximization in the Sensorimotor Loop. Adaptive Behavior 18 (3–4) (2010), 338–355.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Santa Fe InstituteSanta FeUSA

Personalised recommendations