Kolmogorov's theorem and multilayer neural networks
Neural Networks
On the Size of Weights for Threshold Gates
SIAM Journal on Discrete Mathematics
Computational aspects of Kolmogorov's superposition theorem
Neural Networks
On the realization of a Kolmogorov network
Neural Computation
Approximative versions of Kolmogorov's superposition theorem, proved constructively
Journal of Computational and Applied Mathematics
A numerical implementation of Kolmogorov's superpositions
Neural Networks
A numerical implementation of Komogorov's superpositions II
Neural Networks
Analog versus digital: extrapolating from electronics to neurobiology
Neural Computation
Deeper Sparsely Nets can be Optimal
Neural Processing Letters
Scalable hybrid computation with spikes
Neural Computation
On the Training of a Kolmogorov Network
ICANN '02 Proceedings of the International Conference on Artificial Neural Networks
On Kolmogorov's Superpositions and Boolean Functions
SBRN '98 Proceedings of the Vth Brazilian Symposium on Neural Networks
A Threshold Logic Synthesis Tool for RTD Circuits
DSD '04 Proceedings of the Digital System Design, EUROMICRO Systems
A Novel Highly Reliable Low-Power Nano Architecture When von Neumann Augments Kolmogorov
ASAP '04 Proceedings of the Application-Specific Systems, Architectures and Processors, 15th IEEE International Conference
Multiple-Valued Logic its Status and its Future
IEEE Transactions on Computers
Kolmogorov's theorem is relevant
Neural Computation
Representation properties of networks: Kolmogorov's theorem is irrelevant
Neural Computation
A universal mapping for kolmogorov's superposition theorem
Neural Networks
Constructive threshold logic addition: a synopsis of the last decade
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
Capacity of multilevel threshold devices
IEEE Transactions on Information Theory
Threshold network synthesis and optimization and its application to nanotechnologies
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
VLSI implementations of threshold logic-a comprehensive survey
IEEE Transactions on Neural Networks
A Communication Approach to the Superposition Problem
Fundamenta Informaticae - Hardest Boolean Functions and O.B. Lupanov
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Based on explicit numerical constructions for Kolmogorov's superpositions (KS) linear size circuits are possible. Because classical Boolean as well as threshold logic implementations require exponential size in the worst case, it follows that size-optimal solutions for arbitrary Boolean functions (BFs) should rely (at least partly) on KS. In this paper, we will present previous theoretical results while examining the particular case of 3-input BFs in detail. This shows that there is still room for improvement on the synthesis of BFs. Such size reductions (which can be achieved systematically) could help alleviate the challenging power consumption problem, and advocate for the design of Kolmogorov-inspired gates, as well as for the development of the theory, the algorithms, and the CAD tools that would allow taking advantage of such optimal combinations of different logic styles.