Polynomial Theory of Complex Systems

By A. G. Ivakhnenko, Yu V Koppa, I. Tymchenko, N. O. Ivakhnenko, A. Mucciardi. 1970

Subfields: Statistical Learning Theory, Network Science & Complex Systems

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Statistical Learning Theory

In Network Science & Complex Systems

Citations in the corpus

Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving (2019, methodology): “Multiplicative states have been used in neural networks before (Ivakhnenko and Lapa, 1965; Ivakhnenko, 1971).”
Deep learning in neural networks: An overview (2014, methodology): “The units of GMDH nets may have polynomial activation functions implementing Kolmogorov–Gabor polynomials (more general than other widely used NN activation functions, Section 2).”
On Learning to Think: Algorithmic Information Theory for Novel Combinations of Reinforcement Learning Controllers and Recurrent Neural World Models (2015, methodology): “As the history grows, to find an M with small bitsM + bitsH , step 4 uses sequential network construction: it regularly changes M ’s size by adding or pruning units and connections [111, 112, 8, 168, 59, 107, 304, 176, 141, 92, 143, 204, 53, 296, 106, 31, 57, 185, 283].”
One Big Net For Everything (2018, background): “5.6.3] can be used to further compress ONE, possibly shrinking it by pruning neurons and connections, as proposed already in 1965 for deep learning multilayer perceptrons [27, 26, 77].”
Lets keep it simple, Using simple architectures to outperform deeper and more complex architectures (2016, background): “Designing more effective networks was desirable and attempted from the advent of neural networks Fukushima (1979; 1980); Ivakhnenko (1971).”
Characterization and Optimization of Mechanical Properties of ABS Parts Manufactured by the Fused Deposition Modelling Process (2014, methodology): “The framework for modeling chosen for this applied research is based on the Group Method for Data Handling (GMDH) introduced by Ivakhnenko (details are found in [18, 22, 23]) as a means of identifying nonlinear relations between input and output variables.”
Neural networks for pattern recognition (1995, background): “We can generalize this idea to higher orders than just quadratic, and to several input variables (Ivakhnenko, 1971; Barron and Barron, 1988).”