The rings turned out too easy? Try harder data — two twisted spirals.

Write a new file spiral.py that:

1. generates 1 000 points from two spiral arms. For each point:

   y      = a random class, 0 or 1
   t      = a random number in [0, 3π]
   angle  = t + π · y          # the second arm is turned by half a revolution
   radius = t / (3π)
   point  = (radius · cos(angle), radius · sin(angle)) + 0.02 · noise
   

2. trains three models on the same data (seed 42, batch 32, Adam lr = 0.01, 100 epochs): LinearClassifier(2, 2), MLP(2, (16,), 2) and MLP(2, (32, 32), 2);

3. prints each one's parameter count and training accuracy.

Use your model.py and train.py; fit prints a line per epoch — silence it with contextlib.redirect_stdout(io.StringIO()).

My machine:

linear             6 parameters  train accuracy 63.7%
mlp (16,)         82 parameters  train accuracy 97.0%
mlp (32, 32)    1218 parameters  train accuracy 99.6%

A few things to notice:

• The linear model gets 63.7 % here, not 50 % — spirals are not circles and a line can "cut off" part of them. Still, most points are wrong.
• From 6 numbers to 82 is a huge jump (+33 points). From 82 to 1 218 it is barely +2.6.
• Try (16,) with other seeds and see how much 97.0 % "jumps". One number is not yet a conclusion.

My generator is not necessarily identical to yours (it depends on the order in which you call torch.rand and torch.randn), so your numbers may differ by a few points. If the linear model gives 50–70 % and the MLP > 95 % — all is well.