RNNs, or Recurrent Neural Networks, are an important theoretical tool in both machine learning and computational neuroscience. In today’s world dominated by transformers, many may have forgotten about RNNs. However, RNNs remain a fundamental type of neural network and will surely play a role in the era of large models. First, let’s look at the … Read more
Canonical transformations are classical methods used by physicists, mechanical engineers, and astronomers to handle Hamiltonian systems. By finding suitable variable substitutions, canonical transformations can simplify, or even completely solve the dynamics of Hamiltonian systems. For instance, in the 19th century, French scientist Charles Delaunay published approximately 1800 pages of analytical derivations attempting to simplify the … Read more