Word
hessian
Phoneticshes·sian
US/ˈhɛʃən/
UK/hˈɛʃən/
Definition
n. a mathematical grid of second derivatives that shows the curvature or steepness of an optimization landscape.
n. a square matrix of second-order partial derivatives of a scalar-valued function, describing the local curvature of the loss surface in optimization.
Examples
“Checking the eigenvalues of the Hessian reveals whether a point is a valley bottom or a saddle.”
“Second-order optimizers use the Hessian to take smarter steps toward the minimum of the loss function.”
“Analyzing the eigenspectrum of the Hessian matrix reveals flat directions in parameter space that correlate strongly with superior test generalization.”
Examples
simple
“Checking the eigenvalues of the Hessian reveals whether a point is a valley bottom or a saddle.”
contextual
“Second-order optimizers use the Hessian to take smarter steps toward the minimum of the loss function.”
complex
“Analyzing the eigenspectrum of the Hessian matrix reveals flat directions in parameter space that correlate strongly with superior test generalization.”
Real-World Examples
“We present PYHESSIAN, a new scalable framework that enables fast computation of Hessian (i.e., second-order derivative) information for deep neural networks.” Etymology
Named after German mathematician Ludwig Otto Hesse (1811–1874) by English mathematician James Joseph Sylvester in 1851.
Etymology adapted from Wiktionary, available under CC BY-SA 4.0.
Domains
Scan code
englishreference.com/q/hessian