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Main | | | | |
| Resources | | | |
| https://course.fast.ai/Resources/book.html | | | |
| https://github.com/fastai/fastbook | | | https://www.youtube.com/playlist?list=PL_iWQOsE6TfVmKkQHucjPAoRtIJYt8a5A |
| Glossary | | | |
| addition | addition is defined for matrices with the same shape (dimension size) | | |
| associativity | matrix multiplication is associative | | |
| broadcasting | deep learning convention of adding a vector repeatedly to a matrix | | |
| commutivity | matrix multiplication is not commutative | | |
| determinant | | | |
| distributive | matrix multiplication is distributive | | |
| dot product | matrix product of two equal dimension vectors | | |
| element-wise product | also known as the Hadamard product, simple multiplication of individual elements of matrices | | |
| identity matrix | the identity matrix is a matrix that does not change any vector when we multiply that vector by that matrix. All main diagnoal entries in an identity matrix are 1, and all other values are zero | | |
| linear combination | | | |
| matrix | a 2D array of numbers | | |
| matrix inverse | the matrix inverse of A, A^-1, is defined as A(A^-1) = I_n | | |
| matrix product | defined as the sum of A_i,k * B_k,j for all k | | |
| multiplication | multiplication is defined for a matrix and a scalar, multiplying two matrices is only defined for A_i,j if B_j,k, with product C_i,k. see matrix product. | | |
| scalar | mathematical object, often a real/integer in a single dimension | | |
| span | | | |
| stochastic differential equation (SDE) | | | |
| tensor | a multi-dimensional array of numbers | | |
| transpose | mirror image of a matrix across its main diagnoal, defined as A(T)_i,j = A_j,i. the transpose of (AB) is B^t*A^t | | |
| vector | a one-dimensional array of numbers | | |
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| Forward diffusion process where X_t is sample condition on X_t-1 using a Gaussian distribution with mean ((1 - B_t)^0.5)*x_t-1 and variance B_t | | | |
| B_t is usually predefined and fixed, T is total number of diffusion steps. | | | |
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| Reverse generative process (denoising) has denoising distribution of P_theta*(x_t-1 | x_t), a Gaussian whose mean is | | | |
| defined using a trainable neural network mu_theta(x_t, t), with variance preset | | | |
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| example of fixed forward SDE, transforms sample into noise | | | |