Definition
Plain language
A number that tells you how much a particular pattern persists or fades when you apply an operator repeatedly.
As stated in the literature
A scalar lambda such that an operator's action on its eigenvector is multiplication by lambda; magnitudes near one indicate persistent modes, near zero indicate transients.
Also called: eigenvalues
Why it matters: Eigenvalues govern stability and long-range behavior in everything from recurrent networks to diffusion processes, making them essential for understanding why some architectures train and others diverge.
For example, a recurrent system whose dominant eigenvalue is just below one will slowly fade its initial state, while one above one will blow it up.
Heard on the show
“Suppose an eigenvalue of the Jacobian creeps up toward one.”Episode 041 — When the Iteration Teaches the Model to Skip the Iteration