Adding a little noise at every step turns any data into one round cloud.
- Drag the step t: where do the three clusters go?
- Trace three points: does any remember its cluster?
- At step 1000: compare the variance with pure noise.
Each point takes a random walk; together they spread like heat, but in the space of the data, not on the grid of an image.
Generating starts from pure noise and removes a little predicted noise per step.
- Press Generate: watch pure noise flow into the clusters.
- One big step: where do all the best guesses land?
- Same start, new noise: same clusters at the end?
Guidance steers the points to a target; a large weight pushes them past it.
Around the target, four times larger
Mean of the points past the centre, for every weight w
- Pick a target cluster: where do the points end?
- Raise the weight w: where does the mean go?
- Compare with the tiles: does w = 3 overshoot?
Target cluster
The lecture's network generates new tiles; only the solver tells their conductivity.
kxx from the solver, for every generated tile
- No target: do the new tiles look like tiles?
- Aim at kxx = 4: what shape do the tiles take?
- Raise w to 3: what does the solver say?
Target: kxx = 4 at half inclusions
Generated is not validated: check the statistics, the physics (here the solver) and for copies.
More options
Table: the 20 tiles
| Tile | Generated | Share of inclusions | kxx, solver |
|---|
How it is computed
Points, noise schedule and noise predictor follow the lecture's Python (compute.py). The tiles and their conductivities were computed for the lecture (the network trained with PyTorch on the graphics processor of a laptop, the solver in Python) and are stored in this page.