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Graph Theory articles

Semantic Dimensions in English Word Embeddings

by Peter de Blanc + ChatGPT Deep Research 4 months ago
00
#Cognitive Science #Semantic Dimensions #Natural Language Processing more...
Introduction Word embeddings represent word meanings as points in a high-dimensional continuous space. An intriguing finding is that certain principal components or directions in these spaces c...

Applications of Combinatorial Game Theory

by Peter de Blanc + ChatGPT o1 pro 5 months ago
11
#Topology #Algebra #Transfinite Induction more...
Combinatorial Game Theory (CGT) is more than just analyzing recreational games like Nim or Go – it has introduced concepts and tools that have influenced other areas of mathematics. Below we survey bo...

Boltzmann Machines as Ising Models

by Peter de Blanc + ChatGPT o1 pro 5 months ago
00
#Neural Networks #Ising Models #Statistical Mechanics more...
First, let us state the problem precisely: You have a Boltzmann machine whose visible/hidden units x_i take values in \{0,1\} . Its energy function is of the form E(\mathbf{x}) \;...