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

.ci/docker/common/install_docs_reqs.sh

@@ -13,7 +13,9 @@ echo "deb https://dl.yarnpkg.com/debian/ stable main" | sudo tee /etc/apt/source
 
 apt-get update
 apt-get install -y --no-install-recommends yarn
-yarn global add katex --prefix /usr/local
+# Pin katex: 0.18.5 switched to commander@^15, which requires Node >= 22.12
+# while this image installs Node 20, and yarn enforces engines strictly.
+yarn global add katex@0.18.4 --prefix /usr/local
 
 sudo apt-get -y install doxygen
 

.ci/docker/requirements.txt

@@ -22,7 +22,10 @@ pytorch_sphinx_theme2==0.4.9
 tqdm==4.66.1
 numpy==1.24.4
 pydantic>=2.10
-fastapi
+# Pin fastapi: 0.139.2 made router route building thread-safe by adding an
+# _effective_routes_lock (threading.Lock) to APIRouter, which ray[serve]'s
+# @serve.ingress cannot cloudpickle. ray declares fastapi unbounded.
+fastapi<0.139.2
 matplotlib
 librosa
 torch==2.13

intermediate_source/parametrizations.py

@@ -321,8 +321,15 @@ def right_inverse(self, A):
 print(torch.dist(layer_orthogonal.weight, X))  # layer_orthogonal.weight == X
 
 ###############################################################################
-# This initialization step can be written more succinctly as
-layer_orthogonal.weight = nn.init.orthogonal_(layer_orthogonal.weight)
+# This initialization step can be written more succinctly by sampling straight
+# into ``layer_orthogonal.weight``. The determinant correction is still needed:
+# ``nn.init.orthogonal_`` samples from ``O(3)``, and when ``det(A) = -1`` the
+# matrix has an eigenvalue at ``-1``, which makes the ``A + I`` that
+# ``CayleyMap.right_inverse`` inverts singular.
+X = nn.init.orthogonal_(layer_orthogonal.weight)
+if X.det() < 0.:
+    X[0].neg_()
+layer_orthogonal.weight = X
 
 ###############################################################################
 # The name of this method comes from the fact that we would often expect