GaugeFlow

Equivariance, not invariance, is the right prior for continuous physical gauges in self-supervised medical imaging.

A self-supervised objective that helps on one medical-imaging task often collapses on the next. GaugeFlow gives a mechanistic account of when it transfers, organized around one distinction: whether a task's nuisance axis is a continuous physical gauge with coincident free supervision, and whether the downstream utility is invariant or covariant under that gauge.

This repository contains the portable trainer, dataset adapters, pre-registered analyzer, and the complete per-seed evidence behind the preprint.

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The result in one table

Projection-angle gauge (CardioSYNTAX coronary angiography), same-study/same-artery retrieval@1, 5 seeds:

Objective	Retrieval Δ vs. baseline	Gauge used? (true vs. shuffled Δangle)	Angle-leakage R²
Adversarial invariance (GRL, single embedding)	−0.044, p≈0	—	0.31
Adversarial invariance (GRL, dual content/style path)	−0.014	—	0.09
Equivariance, auxiliary (SO(2) Δangle head)	−0.018, p=0.11 (n.s.)	0.079 vs. 0.028 — used	0.30
Equivariance, primary (canonical eval)	−0.080, p≈0	0.0089 vs. 0.0105 — none	0.70
Equivariance, primary (pairwise-transport eval)	−0.050, p≈0	0.0093 vs. 0.0089 — none	0.73

Leakage cap is 0.035 (raw-feature reference). Per-run baselines drift ~0.014 (MPS nondeterminism); the valid statistic is the within-run paired delta.

Reading: adversarial invariance is a no-free-lunch wall — no adversary weight holds retrieval non-inferior and meets the leakage cap. Gauge-equivariance dominates it as an auxiliary (removes the significant harm, demonstrably uses the gauge) but fails as a primary objective, because same-study-across-angles retrieval is itself an invariance metric and the projection-angle gauge is not a recoverable group action on the encoder — confirmed protocol-independent by the pairwise-transport evaluation.

The decision rule

Gauge-equivariant self-supervision is the right prior iff:

1. the nuisance is a continuous physical gauge with an observed parameter (e.g. positioner angle, contrast phase — not a discrete style/vendor bucket), and
2. the downstream utility is covariant under the gauge (depends on it), and
3. the gauge acts as a recoverable transformation of the representation.

When the utility is invariance-shaped, no gauge machinery — adversarial or equivariant — beats simply not fighting the gauge. All three conditions are checkable before a full training run: (1) from metadata, (2) from the task definition, (3) with a transport-vs-shuffle control.

DIAS contrast-front prediction satisfies all three (the future frame is gauge-covariant free supervision) and the gauge-consistent objective helps there. Projection-angle retrieval satisfies (1) but not (2)–(3), and it does not.

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Layout

paper/                       preprint (LaTeX source + compiled PDF + bib)
experiments_v2/
  trainer/gaugeflow_lite.py  portable trainer: baseline · GRL adversary (single + dual-path)
                             · SO(2) equivariance head (auxiliary) · gauge-aligned contrastive (primary)
  common/analyze.py          pre-registered analyzer: cluster-bootstrap CI, permutation null, shuffled-gauge control
  cardiosyntax_angle_adv/    projection-angle gauge: dataset adapter, configs, run scripts, per-seed verdicts
  brats_seq_gauge/           pulse-sequence gauge (MSD Task01/BraTS)
  RESULTS_v2.md              full verdicts

Every objective is a config flag on one trainer; the no-op config reproduces the baseline exactly.

Reproduce

The trainer needs only PyTorch + NumPy.

cd experiments_v2/cardiosyntax_angle_adv

./run.sh            # baseline vs. GRL adversary vs. shuffled-gauge control
./run_equiv.sh      # baseline vs. SO(2) equivariance auxiliary vs. control
./run_equiv_ptr.sh  # equivariance as primary objective, pairwise-transport eval

Each script writes per-seed per_study_metrics.jsonl and a verdict_*.json from the analyzer. The four verdict_*.json in cardiosyntax_angle_adv/ are the numbers in the table above.

To exercise the BraTS wiring without licensed data, use the synthetic smoke runner:

experiments_v2/brats_seq_gauge/smoke.sh

It checks for NumPy, Pillow, and PyTorch, creates data/cases.jsonl plus its PNG fixture, then runs the baseline, GaugeFlow, and shuffled-gauge arms with one seed. Set PY to choose another Python 3 environment or SEEDS to exercise additional seeds.

The key flags on gaugeflow_lite.py (config JSON):

flag	objective
angle_adv_loss_weight	gradient-reversal adversary (invariance)
gauge_equiv_loss_weight	SO(2) equivariance head, auxiliary
gauge_equiv_contrastive	gauge-aligned contrastive, equivariance as primary
pairwise_transport_retrieval	rigorous transport-frame retrieval at eval
gauge_shuffle	shuffled-gauge negative control

Data

The CardioSYNTAX, DIAS, and MSD Task01/BraTS imaging data are licensed by their respective providers and are not redistributed here. The dataset adapters read local shards; point them at your licensed copy. The complete per-seed evidence (metrics + verdicts) is included so every reported number is independently checkable without rerunning, and is also mirrored as a dataset on the Hugging Face Hub.

Citation

@misc{son2026gaugeflow,
  title  = {GaugeFlow: Equivariance, Not Invariance, Is the Right Prior for
            Continuous Physical Gauges in Self-Supervised Medical Imaging},
  author = {Son, Colin},
  year   = {2026},
  note   = {Seldinger, Inc.}
}

License

MIT — see LICENSE.