Taylor Expansion
A mathematical tool for locally approximating a function with polynomials. The first-order expansion corresponds to the linear approximation used in gradient descent, while the second-order expansion introduces curvature and corresponds to second-order optimization methods such as Newton's method.
Timeline (last 90 days)
First-order Taylor expansion corresponds to the linear approximation of gradient descent, while second-order expansion introduces curvature information and corresponds to second-order optimization methods such as Newton's method.
Taylor expansion is an analysis tool rather than a training algorithm, and "training networks with Taylor expansion" is a confusion of terms.
The second-order Taylor expansion approximates exp(x) as 1 + x + x²/2, where (q^T k)² can be written in the form (q⊙q)^T (k⊙k) to maintain linear time complexity.
All Facts (3)
First-order Taylor expansion corresponds to the linear approximation of gradient descent, while second-order expansion introduces curvature information and corresponds to second-order optimization methods such as Newton's method.
50%UnverifiedTaylor expansion is an analysis tool rather than a training algorithm, and "training networks with Taylor expansion" is a confusion of terms.
50%UnverifiedThe second-order Taylor expansion approximates exp(x) as 1 + x + x²/2, where (q^T k)² can be written in the form (q⊙q)^T (k⊙k) to maintain linear time complexity.
50%