Part 0 — Foundations - Research Notebook

The conceptual bedrock for the whole Gaussianization curriculum. Before fitting any flow, these seven notebooks build — from scratch in JAX, then confirmed against the mature rbig and gauss_flows packages — the small set of ideas every later method reuses: the change-of-variables formula and its log-determinant, how those compose, the forward/inverse trade-off, why $\mathcal{N}(0, I)$ is the target, what a density destructor is, the numerics that keep one stable, and how to certify it converged.

Each notebook follows the same pattern: derive the idea by hand, then show the exact same quantity coming out of the library. That way the packages stop being black boxes — you have seen what every call computes.

Notebooks¶

#	notebook	master list	what you take away
00	Change of variables	0.1	$p_X(x)=p_Z(T(x))\lvert\det J_T\rvert$ ; the library’s `log_det` is this Jacobian
01	Composition & log-det	0.2	stacking maps ⇒ log-dets add; rotations are free
02	Forward vs. inverse	0.3	density vs. sampling cost; differentiating a root-find by the adjoint (`optimistix`)
03	Why $\mathcal{N}(0,I)$ ?	0.4	max-entropy, separability (TC $\to0$ ), trivial score $-z$
04	Density destructors	0.5–0.6	Gaussianization = iterated whitening + nonlinearity (RBIG)
05	Numerical mechanics	0.7–0.9	jitter/clamp, float64 log-dets, the round-trip CI test
06	Gaussianity diagnostics	0.10–0.12	QQ/moments, negentropy, energy-distance normality test

The numbering and scope follow the Part 0 rows of the project TUTORIAL_MASTER_LIST.md.

Packages¶

These notebooks use two of the author’s libraries as the source of truth:

rbig — mature NumPy/SciPy Rotation-Based Iterative Gaussianization with a full information-theory suite (AnnealedRBIG, negentropy, total_correlation, marginal/rotation bijectors).
gauss_flows — the modern JAX / flowjax successor: trainable Gaussianization flows, bijectors with transform_and_log_det, and optimistix-based inverses.

Running¶

The foundations notebooks need rbig + gauss_flows + a Jupyter stack, which live outside the conda-forge pixi envs. Create a dedicated uv virtual environment (paths assume the sibling checkouts of rbig and gauss_flows):

cd projects/gaussianization
uv venv .venv-tutorials --python 3.13
uv pip install --python .venv-tutorials/bin/python \
  -e ../../../rbig -e ../../../ml4eo/gauss_flows \
  ipykernel jupyter nbconvert jupytext matplotlib seaborn

# Re-execute the whole section end-to-end:
.venv-tutorials/bin/jupyter nbconvert --to notebook --execute --inplace \
  notebooks/00_foundations/0*.ipynb --ExecutePreprocessor.timeout=600

Notebooks are paired (jupytext, py:percent): edit the .py, then jupytext --sync to update the .ipynb. All notebooks set jax_enable_x64 so log-determinant accumulation stays exact.