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Bijective Transformation
Invertible mathematical function that establishes a one-to-one correspondence between two spaces, essential for preserving the exact density computation property in flows.
Jacobian Determinant
Determinant of the Jacobian matrix of a transformation, used to apply the change of variables formula in the computation of transformed probability densities.
Invertible Neural Network
Neural network architecture designed to be perfectly invertible, enabling bidirectional computation of activations and gradients without information loss.
Density Estimation
Problem consisting of estimating the underlying probability density function from observed samples, solved precisely by normalizing flows.
Autoregressive Flow
Normalizing flow where the transformation of each dimension conditionally depends on previous dimensions, enabling sequential modeling of dependencies.
Triangular Matrix
Matrix structure (upper or lower) used in certain flows to guarantee efficient computation of the Jacobian determinant equal to the product of diagonal elements.
LU Decomposition
Matrix factorization decomposing a matrix into the product of a lower triangular matrix (L) and an upper triangular matrix (U), used to parameterize invertible matrices efficiently.
Masked Autoregressive Flow (MAF)
Autoregressive flow using masks to impose a directional dependency structure, with sequential sampling but possible parallel evaluation.
Inverse Autoregressive Flow (IAF)
Variant of MAF reversing the direction of dependency to enable fast parallel sampling at the cost of slower sequential evaluation.