Adjoint state method

The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. It has applications in geophysics, seismic imaging and more in neural networks; the adjoint state space is chosen to simplify the physical interpretation of equation constraints. It may take the form of a Hilbert space. Adjoint state techniques allow the use of integration by parts, resulting in a form which explicitly contains the physically interesting quantity. An adjoint state equation is introduced, including a new unknown variable; the adjoint method formulates the gradient of a function towards its parameters in a constraint optimization form. By using the dual form of this constraint optimization problem, it can be used to calculate the gradient fast. A nice property is that the number of computations is independent of the number of parameters for which you want the gradient; the adjoint method is derived from the dual problem and is used e.g. in the Landweber iteration method.

The name adjoint state method refers to the dual form of the problem, where the adjoint matrix A ∗ = A ¯ T is used. When the initial problem consists of calculating the product s T x and x must satisfy A x = b, the dual problem can be realized as calculating the product r T b, where r must satisfy A ∗ r = s, and r is called the adjoint state vector. Backpropagation Adjoint equation A well written explanation by Errico: What is an adjoint Model? Another well written explanation with worked examples, written by Bradley More technical explanation: A review of the adjoint-state method for computing the gradient of a functional with geophysical applications MIT course Deriving the adjoint state method from different fields: MIT notes

The Panther!

The Panther! is an album by saxophonist Dexter Gordon, recorded in 1970 and released on the Prestige label. Lindsay Planer of Allmusic states, "Dexter Gordon entered the 1970s -- as well as his career's quarter-century mark -- on a definite upstroke with the sly, sexy -- and above else -- stylish platter The Panther!" All compositions by Dexter Gordon except as indicated "The Panther" - 6:29 "Body and Soul" - 11:01 "Valse Robin" - 5:56 "Mrs. Miniver" - 7:38 "The Christmas Song" - 5:23 "The Blues Walk" - 7:21 Dexter Gordon - tenor saxophone Tommy Flanagan - piano Larry Ridley - bass Alan Dawson - drums