Flow with What You Know: An Introduction to Flow-Based Models
2 points
14 days ago
| 1 comment
| drscotthawley.github.io
| HN
billconan
14 days ago
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I can't understand the use of the 4th-order Runge-Kutta integration, if the underneath flow field simply does a linear interpolation? I thought Runge-Kutta is beneficial only when the flow field is "curved".
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blackbear_
14 days ago
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Linear interpolation is only used during training to generate intermediate samples and their trajectories, and there indeed you don't need any integration. But during inference you use the velocity predicted by the model at each point in space and time, and integrate that to find the path followed by a point, which is then usually non linear.
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billconan
13 days ago
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if the training goal is to mimic the linear interpolation behavior, then I don't understand why during inference, the behavior "is usually non linear".
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blackbear_
12 days ago
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The model isn't actually learning to mimic linear interpolation. Source and target points are sampled randomly, and linear interpolation is used to randomly choose a midpoint, then the model is trained to predict that the velocity at the midpoint points towards the target. But during training this selection of source, target and midpoint is randomly repeated thousands of times, so for the same spatial location the model will see many examples all going in different directions. Eventually this randomness will average out and the model will learn to predict this average, which happens to be the "true" velocity field at that point. Since this velocity field is usually non linear, the model will learn a behavior that is non linear as well.
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