Hyperplane Arrangements Separating Arbitrary Vertex Classes in n-Cubes. - Walter Wenzel; Nihat Ay; Frank Pasemann (Adv. Appl. Math., 2000)

Locality of Global Stochastic Interaction in Directed Acyclic Networks. - Nihat Ay (Neural Comput., 2002)

Dually Flat Manifolds and Global Information Geometry. - Nihat Ay; Wilderich Tuschmann (Open Syst. Inf. Dyn., 2002)

Temporal infomax leads to almost deterministic dynamical systems. - Nihat Ay; Thomas Wennekers (Neurocomputing, 2003)

Temporal Infomax on Markov chains with input leads to finite state automata. - Thomas Wennekers; Nihat Ay (Neurocomputing, 2003)

Dynamical properties of strongly interacting Markov chains. - Nihat Ay; Thomas Wennekers (Neural Networks, 2003)

Spatial and temporal stochastic interaction in neuronal assemblies. - Thomas Wennekers; Nihat Ay (Theory Biosci., 2003)

Stochastic interaction in associative nets. - Thomas Wennekers; Nihat Ay (Neurocomputing, 2005)

Finite State Automata Resulting from Temporal Information Maximization and a Temporal Learning Rule. - Thomas Wennekers; Nihat Ay (Neural Comput., 2005)

A temporal learning rule in recurrent systems supports high spatio-temporal stochastic interactions. - Thomas Wennekers; Nihat Ay (Neurocomputing, 2006)

Maximizing multi-information. - Nihat Ay; Andreas Knauf (Kybernetika, 2006)

High-resolution multiple-unit EEG in cat auditory cortex reveals large spatio-temporal stochastic interactions. - Thomas Wennekers; Nihat Ay; Péter András 001 (Biosyst., 2007)

Geometric robustness theory and biological networks. - Nihat Ay; David C. Krakauer (Theory Biosci., 2007)

Predictive information and emergent cooperativity in a chain of mobile robots. - Ralf Der; Frank Güttler; Nihat Ay (ALIFE, 2008)

Information Flows in Causal Networks. - Nihat Ay; Daniel Polani (Adv. Complex Syst., 2008)

Autonomy: An information theoretic perspective. - Nils Bertschinger; Eckehard Olbrich; Nihat Ay; Jürgen Jost (Biosyst., 2008)

Non-sufficient Memories That Are Sufficient for Prediction. - Wolfgang Löhr; Nihat Ay (Complex (1), 2009)

On the Generative Nature of Prediction. - Wolfgang Löhr; Nihat Ay (Adv. Complex Syst., 2009)

Higher coordination with less control - A result of information maximisation in the sensori-motor loop - Keyan Zahedi; Nihat Ay; Ralf Der (CoRR, 2009)

A refinement of the common cause principle. - Nihat Ay (Discret. Appl. Math., 2009)

Hierarchical Models, Marginal Polytopes, and Linear Codes. - Thomas Kahle; Walter Wenzel; Nihat Ay (Kybernetika, 2009)

Higher Coordination With Less Control - A Result of Information Maximization in the Sensorimotor Loop. - Keyan Zahedi; Nihat Ay; Ralf Der (Adapt. Behav., 2010)

Effective complexity and its relation to logical depth. - Nihat Ay; Markus Müller; Arleta Szkola (IEEE Trans. Inf. Theory, 2010)

Expressive Power and Approximation Errors of Restricted Boltzmann Machines. - Guido Montúfar; Johannes Rauh; Nihat Ay (NIPS, 2011)

Effective Complexity of Stationary Process Realizations. - Nihat Ay; Markus Müller; Arleta Szkola (Entropy, 2011)

Support sets in exponential families and oriented matroid theory. - Johannes Rauh; Thomas Kahle; Nihat Ay (Int. J. Approx. Reason., 2011)

Refinements of Universal Approximation Results for Deep Belief Networks and Restricted Boltzmann Machines. - Guido Montúfar; Nihat Ay (Neural Comput., 2011)

On solution sets of information inequalities. - Nihat Ay; Walter Wenzel (Kybernetika, 2012)

Process Dimension of Classical and Non-Commutative Processes. - Wolfgang Löhr; Arleta Szkola; Nihat Ay (Open Syst. Inf. Dyn., 2012)

Information-driven self-organization: the dynamical system approach to autonomous robot behavior. - Nihat Ay; Holger Bernigau; Ralf Der; Mikhail Prokopenko (Theory Biosci., 2012)

Guided self-organization: perception-action loops of embodied systems. - Nihat Ay; Ralf Der; Mikhail Prokopenko (Theory Biosci., 2012)

Maximal Information Divergence from Statistical Models Defined by Neural Networks. - Guido Montúfar; Johannes Rauh; Nihat Ay (GSI, 2013)

"More Is Different" in Functional Magnetic Resonance Imaging: A Review of Recent Data Analysis Techniques. - Gabriele Lohmann; Johannes Stelzer; Jane Neumann; Nihat Ay; Robert Turner (Brain Connect., 2013)

Linear combination of one-step predictive information with an external reward in an episodic policy gradient setting: a critical analysis. - Keyan Zahedi; Georg Martius; Nihat Ay (CoRR, 2013)

Information driven self-organization of complex robotic behaviors - Georg Martius; Ralf Der; Nihat Ay (CoRR, 2013)

Quantifying Morphological Computation. - Keyan Zahedi; Nihat Ay (Entropy, 2013)

Comparison between Different Methods of Level Identification. - Oliver Pfante; Nils Bertschinger; Eckehard Olbrich; Nihat Ay; Jürgen Jost (Adv. Complex Syst., 2014)

A Framework for Cheap Universal Approximation in Embodied Systems. - Guido Montúfar; Nihat Ay; Keyan Ghazi-Zahedi (CoRR, 2014)

Expressive Power of Conditional Restricted Boltzmann Machines for Sensorimotor Control. - Guido Montúfar; Nihat Ay; Keyan Zahedi (CoRR, 2014)

Quantifying Unique Information. - Nils Bertschinger; Johannes Rauh; Eckehard Olbrich; Jürgen Jost; Nihat Ay (Entropy, 2014)

On the Fisher Metric of Conditional Probability Polytopes. - Guido Montúfar; Johannes Rauh; Nihat Ay (Entropy, 2014)

Discriminating between causal structures in Bayesian Networks given partial observations. - Philipp Moritz; Jörg Reichardt; Nihat Ay (Kybernetika, 2014)

Robustness, canalyzing functions and systems design. - Johannes Rauh; Nihat Ay (Theory Biosci., 2014)

Standard Divergence in Manifold of Dual Affine Connections. - Shun-ichi Amari; Nihat Ay (GSI, 2015)

Invariant Geometric Structures on Statistical Models. - Lorenz Schwachhöfer; Nihat Ay; Jürgen Jost; Hông Vân Lê 001 (GSI, 2015)

Evaluating Morphological Computation in Muscle and DC-motor Driven Models of Human Hopping. - Keyan Ghazi-Zahedi; Daniel F. B. Haeufle; Guido Montúfar; Syn Schmitt; Nihat Ay (CoRR, 2015)

Geometry and Determinism of Optimal Stationary Control in Partially Observable Markov Decision Processes. - Guido Montúfar; Keyan Ghazi-Zahedi; Nihat Ay (CoRR, 2015)

Information Geometry on Complexity and Stochastic Interaction. - Nihat Ay (Entropy, 2015)

A Novel Approach to Canonical Divergences within Information Geometry. - Nihat Ay; Shun-ichi Amari (Entropy, 2015)

Information-Theoretic Inference of Common Ancestors. - Bastian Steudel; Nihat Ay (Entropy, 2015)

Hierarchical Quantification of Synergy in Channels. - Paolo Perrone; Nihat Ay (Frontiers Robotics AI, 2015)

Geometry and expressive power of conditional restricted Boltzmann machines. - Guido Montúfar; Nihat Ay; Keyan Ghazi-Zahedi (J. Mach. Learn. Res., 2015)

Geometric Design Principles for Brains of Embodied Agents. - Nihat Ay (Künstliche Intell., 2015)

Maximizing the Divergence from a Hierarchical Model of Quantum States. - Stephan Weis; Andreas Knauf; Nihat Ay; Ming-Jing Zhao (Open Syst. Inf. Dyn., 2015)

A Theory of Cheap Control in Embodied Systems. - Guido Montúfar; Keyan Ghazi-Zahedi; Nihat Ay (PLoS Comput. Biol., 2015)

The Umwelt of an embodied agent - a measure-theoretic definition. - Nihat Ay; Wolfgang Löhr (Theory Biosci., 2015)

The Umwelt of an Embodied Agent - A Measure-Theoretic Definition. - Nihat Ay; Wolfgang Löhr (CoRR, 2016)

Information Theoretically Aided Reinforcement Learning for Embodied Agents. - Guido Montúfar; Keyan Ghazi-Zahedi; Nihat Ay (CoRR, 2016)

Iterative Scaling Algorithm for Channels. - Paolo Perrone; Nihat Ay (CoRR, 2016)

Evaluating Morphological Computation in Muscle and DC-Motor Driven Models of Hopping Movements. - Keyan Ghazi-Zahedi; Daniel F. B. Haeufle; Guido Montúfar; Syn Schmitt; Nihat Ay (Frontiers Robotics AI, 2016)

Morphological Computation: Synergy of Body and Brain. - Keyan Ghazi-Zahedi; Carlotta Langer; Nihat Ay (Entropy, 2017)

Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines. - Maxinder S. Kanwal; Joshua A. Grochow; Nihat Ay (Entropy, 2017)

Divergence Functions in Information Geometry. - Domenico Felice; Nihat Ay (GSI, 2019)

A Numerical Efficiency Analysis of a Common Ancestor Condition. - Luca Carlini; Nihat Ay; Christiane Görgen (MACIS, 2019)

Canonical Divergence for Flat α-Connections: Classical and Quantum. - Domenico Felice; Nihat Ay (Entropy, 2019)

Canonical Divergence for Measuring Classical and Quantum Complexity. - Domenico Felice; Stefano Mancini; Nihat Ay (Entropy, 2019)

On the Locality of the Natural Gradient for Deep Learning. - Nihat Ay (CoRR, 2020)

Confounding Ghost Channels and Causality: A New Approach to Causal Information Flows. - Nihat Ay (CoRR, 2020)

Natural Wake-Sleep Algorithm. - Csongor Várady; Riccardo Volpi; Luigi Malagò; Nihat Ay (CoRR, 2020)

Complexity as Causal Information Integration. - Carlotta Langer; Nihat Ay (Entropy, 2020)

Information decomposition based on cooperative game theory. - Nihat Ay; Daniel Polani; Nathaniel Virgo (Kybernetika, 2020)

Special issue in memory of František Matúš. - Nihat Ay; Milan Studený (Kybernetika, 2020)

Ingredients for robustness. - Nihat Ay (Theory Biosci., 2020)

The information theory of individuality. - David C. Krakauer; Nils Bertschinger; Eckehard Olbrich; Jessica C. Flack; Nihat Ay (Theory Biosci., 2020)

Parametrisation Independence of the Natural Gradient in Overparametrised Systems. - Jesse van Oostrum; Nihat Ay (GSI, 2021)

How Morphological Computation shapes Integrated Information in Embodied Agents. - Carlotta Langer; Nihat Ay (CoRR, 2021)

Invariance Properties of the Natural Gradient in Overparametrised Systems. - Jesse van Oostrum; Johannes Müller; Nihat Ay (CoRR, 2022)

Learning to Predict Requires Integrated Information. - Carlotta Langer; Nihat Ay (CoRR, 2022)

Natural Reweighted Wake-Sleep. - Csongor Várady; Riccardo Volpi; Luigi Malagò; Nihat Ay (Neural Networks, 2022)

On the Fisher-Rao Gradient of the Evidence Lower Bound. - Nihat Ay; Jesse van Oostrum (CoRR, 2023)

Outsourcing Control Requires Control Complexity. - Carlotta Langer; Nihat Ay (Artif. Life, 2024)

A Concise Mathematical Description of Active Inference in Discrete Time. - Jesse van Oostrum; Carlotta Langer; Nihat Ay (CoRR, 2024)

Analyzing Multimodal Integration in the Variational Autoencoder from an Information-Theoretic Perspective. - Carlotta Langer; Yasmin Kim Georgie; Ilja Porohovoj; Verena Vanessa Hafner; Nihat Ay (CoRR, 2024)

Inversion of Bayesian networks. - Jesse van Oostrum; Peter van Hintum; Nihat Ay (Int. J. Approx. Reason., 2024)

Convergence Properties of Natural Gradient Descent for Minimizing KL Divergence. - Adwait Datar; Nihat Ay (Trans. Mach. Learn. Res., 2025)

Torsion of α-connections on the density manifold. - Nihat Ay; Lorenz Schwachhöfer (CoRR, 2025)