A good theory of mathematical beauty is more practical than any current observation, as new
predictions about physical reality can be self-consistently verified. This belief applies to the …

We develop a theory to analyze how structure in connectivity shapes the high-dimensional,
internally generated activity of nonlinear recurrent neural networks. Using two …

Understanding neural dynamics is a central topic in machine learning, non-linear physics,
and neuroscience. However, the dynamics are non-linear, stochastic and particularly non …

The study of adaptive dynamics, involving many degrees of freedom on two separated
timescales, one for fast changes of state variables and another for the slow adaptation of …

High dimensional dynamics play a vital role in brain function, ecological systems, and neuro-
inspired machine learning. Where and how these dynamics are confined in the phase space …

Generative diffusion models apply the concept of Langevin dynamics in physics to machine
learning, attracting a lot of interest from engineering, statistics, and physics, but a complete …

In realistic neural circuits, both neurons and synapses are coupled in dynamics with
separate time scales. The circuit functions are intimately related to these coupled dynamics …

With an increasing amount of observations on the dynamics of many complex systems, it is
required to reveal the underlying mechanisms behind these complex dynamics, which is …

The dynamical evolution of a neural network during training has been an incredibly
fascinating subject of study. First principal derivation of generic evolution of variables in …

One of the central problems in many-body physics, both classical and quantum, is the
relations between different notions of chaos. Ergodicity, mixing, operator growth, the …