Broadcasted Function Pullback Vjp Rule

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Broadcasted Function - Pullback/vJp rule Profile
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How do you backpropagate the cotangent (or gradient) information over the nonlinear activation Linear System Solvers are vital to all scientific computing. For example, you need them for incompressibility projection in ... The video showcases how to the derive the primitive High-Dimensional nonlinear root finding problems appear in the numerical solution of PDEs, in optimization algorithms, deep ... The scalar root-finding is a simple example for which we can leverage the implicit Matrix-Matrix multiplication is an essential linear algebra operation that underpins Scientific Computing (CFD, FEM etc.)

Deriving the L2 loss is typically the first step in backpropagation for Neural Networks when applied to regression problems (as ... The matrix-vector product is the essential operation for feed-forward Neural Networks. In order to perform deep learning, we need ... How to forwardly propagate tangent information over the nonlinear activation The softmax is the last layer in deep networks used for classification, but how do you backpropagate over it? What primitive

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Nonlinear System Solve - Pullback/vJp rule
Scalar Root-Finding - Pullback/vJp rule
Scalar Multiplication - Pullback/vJp rule
Matrix-Matrix Product - Pullback/vJp rule
L2 Loss (Least Squares) - Pullback/vJp rule
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Matrix-Vector product - Pullback/vJp rule
Broadcasted Function - Pushforward/Jvp rule
Softmax - Pullback/vJp rule

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Last Updated: June 18, 2026

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Softmax - Pullback/vJp rule

The softmax is the last layer in deep networks used for classification, but how do you backpropagate over it? What...