Unbreak tutorials CI: pin katex + fastapi, keep Cayley init on SO(3)

[atalman]

Three fixes for the tutorials CI. Together with #3960 (merged) these clear every failure currently blocking #3959.

1. Docker image build -- pin katex to 0.18.4

Any PR that touches the docker context rebuilds the image, and the rebuild fails:

error commander@15.0.0: The engine "node" is incompatible with this module.
      Expected version ">=22.12.0". Got "20.20.2"
error Found incompatible module.

install_docs_reqs.sh installs Node 20 and then runs an unpinned yarn global add katex:

katex	published	commander
0.18.4	2026-08-10	^8.3.0
0.18.5	2026-08-31	^15.0.0

commander@15.0.0 declares engines: { node: ">=22.12.0" } and yarn enforces engines strictly. Pinned to katex@0.18.4, the last release on commander@^8.

This is the same commit as in #3959 -- it is needed here too, because fix 2 below edits requirements.txt and so triggers a rebuild. The longer-term fix is bumping the image from setup_20.x to setup_22.x; worth a separate PR so the Node bump gets reviewed on its own blast radius.

2. serving_tutorial.py -- pin fastapi below 0.139.2

File "beginner_source/serving_tutorial.py", line 116, in <module>
    class MNISTClassifier:
  ray/serve/api.py:377  pickle_dumps(app, error_msg="Failed to serialize the ASGI app.")
TypeError: Failed to serialize the ASGI app.:
  !!! FAIL serialization: cannot pickle '_thread.lock' object

fastapi 0.139.2 (2026-07-16) landed "Refactor router route building to make it thread-safe", adding to fastapi/routing.py:

_effective_routes_lock: Any = field(
    default_factory=threading.Lock, repr=False, compare=False
)

@serve.ingress(app) cloudpickles the FastAPI app, and a threading.Lock is not picklable. ray declares fastapi with no upper bound (fastapi; extra == "serve"), and requirements.txt left it unpinned, so any image rebuild picks it up. It does not reproduce on main today only because that image was last built 2026-07-08, before the release.

Bisected in a venv with ray[serve]==2.55.0, reproducing the tutorial's @serve.deployment / @serve.ingress / @serve.batch structure:

fastapi	starlette	result
0.139.0	0.50.0	OK
0.139.1	0.50.0	OK
0.139.2	0.50.0	FAIL
0.140.0	0.50.0	FAIL
0.141.1	1.6.0	FAIL
0.139.1	1.6.0	OK

The last row matters: starlette 1.6.0 is fine with fastapi 0.139.1, so despite the concurrent starlette 0.x -> 1.x major bump, starlette is not implicated and needs no pin.

A stopgap -- the real fix is upstream in ray, either excluding the lock from the pickled state or not pickling the app. Revisit when ray supports fastapi >= 0.139.2.

3. parametrizations.py -- keep the Cayley initialization on SO(3)

File "intermediate_source/parametrizations.py", line 325, in <module>
    layer_orthogonal.weight = nn.init.orthogonal_(layer_orthogonal.weight)
  parametrizations.py:310  return torch.linalg.solve(A + self.Id, self.Id - A)
torch._C._LinAlgError: torch.linalg.solve: The solver failed because the input matrix is singular.

nn.init.orthogonal_ samples from O(3), not SO(3). For an odd dimension, det(A) = -1 forces an eigenvalue at -1, so A + I is exactly singular -- and that is the matrix CayleyMap.right_inverse inverts. The block a few lines above already corrects the determinant; the "more succinctly" rewrite dropped it. This applies the same correction there, and says why inline.

200 trials with distinct seeds on torch 2.14.0+cpu, reproducing the tutorial's Skew and CayleyMap verbatim:

	succeeded
current	185 / 200
with the determinant correction	200 / 200

No seed is set anywhere in the file, which is why this surfaces as a flaky failure rather than a consistent one.

AI assistance (Claude) was used for this change.

[pytorch-bot]

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[huydhn]

The dep changes look good to me! I don't have the context on intermediate_source/parametrizations.py though, so maybe we need another approval.