Flow-based generative model: Difference between revisions

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For <math>n=2</math>, <math>a>0</math> and <math>\mathbf A</math> positive definite, then <math>f_\text{cal}</math> and <math>f_\text{gcal}</math> are equivalent in the sense that in both cases, <math>\log\frac{p_1}{p_2}\mapsto\log\frac{q_1}{q_2}</math> is a straight line, the (positive) slope and offset of which are functions of the transform parameters. For <math>n>2,</math> <math>f_\text{gcal}</math> ''does'' generalize <math>f_\text{cal}</math>.
 
It must however be noted that chaining mutliplemultiple <math>f_\text{gcal}</math> flow transformations does ''not'' give a further generalization, because:
:<math>
f_\text{gcal}(\cdot\,;\mathbf A_1,\mathbf c_1) \circ