This book presents a self-contained introduction to techniques from field theory applied to stochastic and collective dynamics in neuronal networks. These powerful analytical techniques, which are well established in other fields of physics, are the basis of current developments and offer solutions to ...
This book highlights a comprehensive introduction to the fundamental statistical mechanics underneath the inner workings of neural networks. The book discusses in details important concepts and techniques including the cavity method, the mean-field theory, replica techniques, the Nishimori condition, variatio...
The Hopfield model of a neural network is studied near its saturation, i.e., when the number p of stored patterns increases with the size of the network N, as p = αN. The mean-field theory for this system is described in detail. The system possesses, at low α, both a spin-...
A theory of representation learning in deep neural networks gives a deep generalisation of kernel methods. Preprint at https://arxiv.org/abs/2108.13097 (2023). Cho, Y. & Saul, L. Kernel methods for deep learning. In Advances in Neural Information Processing Systems (eds Bengio, Y. et al....
The first edition, published in 1973, has become a classic reference in the field. Now with the second edition, readers will find information on key new topics such as neural networks and statistical pattern recognition, the theory of ma... RO Duda,PE Hart,DG Stork - 《En Broeck the Sta...
The concept of VC dimension is involved in two central results in statistical learning theory: the first identifies finite VC dimension as a necessary condition for long run convergence, while the second shows how a preference for lower VC dimension can improve “the rate of convergence.” Popper...
But I disagree with his (or his editor’s)claim thatthe t test is “the most important statistical method in science.” Sure, the t test has been used a lot, and it’s important for historical reasons, and it’s a mathematical or statistical breakthrough to use distribution theory to ...
New hybrid system of machine learning and statistical pattern recognition for a 3D visibility network Intelligent systems are an excellent tool to use for solving complex problems in the field of industrial applications. We use the mathematical method of fr... M. Babi,K Skala,D Kumar,... - ...
The number of network science applications across many different fields has been rapidly increasing. Surprisingly, the development of theory and domain-specific applications often occur in isolation, risking an effective disconnect between theoretical an
Experts (which I am in probability and statistics, but not in geometry, number theory, etc.) can see for miles; non-experts are walking around in the tall grass and can’t see past their next step. The current system of scholarly journal review is absolutely nuts. The vast majority of ...