What a Gravitational-Wave Detector Knows Without Being Told

A CNN was trained to answer one question — is there a signal in this noise? It was never shown the mass of anything. Afterwards, a straight line through its internal state recovers it.

🔭 Live page: askretik.github.io/Gravitational-Waves

The project page, GW Probe, has an interactive Kerr shadow explorer, and every number on it is read from the pipeline's own JSON output. An offline single-file copy is at site/standalone.html: download it and open it by double-click.

UM301 flagship project. Four experiments on real LIGO/Virgo data plus a from-scratch general relativity implementation, built spec-first with pre-registered predictions and a full audit trail.

---

The headline

Chirp mass recovered from the frozen embedding	R² = 0.502 [+0.364, +0.646], p < 1e-4
Same probe on an untrained network of identical architecture	R² = 0.056
Difference, paired bootstrap	+0.424 [+0.286, +0.637], Holm p = 0.0005
Events	180 real detected black-hole mergers
Detector on real data (trained only on simulations)	AUC 0.973

The network never saw a mass label. The probe reading it is deliberately weak — a linear ridge regression, one hyperparameter — because the question is what is linearly accessible, not how well mass can be predicted.

---

The five parts

Part A — Kerr shadow generator

Implements Bardeen's closed-form photon-orbit boundary for a spinning black hole, verified symbolically against two limits where the answer is known exactly: at zero spin the shadow must be a circle of radius 3√3 M; at maximum spin the prograde photon orbit must merge with the horizon. Then uses the validated code to predict shadow diameters for M87* (EHT measured 42 ± 3 µas) and Sgr A* (48.7 ± 7 µas) from independently-measured masses, and compares against the published deviation parameters. No machine learning — this is the SDD half of the project and the interactive anchor of the page: web/shadow.js redraws the exact boundary live, with a schematic Novikov–Thorne disk, and on every load re-checks itself against the 30 Python reference cases (worst disagreement 3.55e-15).

Part B — the detector

A ~4.34 M-parameter ResNet-style CNN trained on the G2Net dataset: 2-second three-detector strain segments, whitened, bandpassed 20–500 Hz, Q-transformed (Q = 12) into 3 × 64 × 128 spectrograms, classified signal-vs-noise.

• Test AUC 0.8503 ± 0.0054, average precision 0.8875, scored once on 20 000 held-out samples
• 12-trial Optuna study at proxy scale, then one 200 000-sample confirmation run
• Learning curve flattened as predicted in writing before the run: 0.8428 → 0.8480 → 0.8525 across 30k / 100k / 200k. The model is representation-limited, not data-limited.
• Context: the competition winner scored 0.8854 with full data and large ensembles; the spectrogram-image approach caps near 0.88.

Part C — the probe

Freezes that CNN, pushes 180 real GWTC events through the identical hashed preprocessing, extracts 128-dimensional pre-classification embeddings, and fits a ridge regression under nested leave-one-out cross-validation to predict chirp mass.

Three feature sources, one probe:

Input	R²	95 % CI	MAE (M☉)
Trained CNN embedding (128-d)	+0.502	[+0.364, +0.646]	6.33
Raw pixels (24 576-d, no network)	+0.340	[+0.261, +0.422]	8.36
Untrained CNN (128-d, best of 5 seeds)	+0.056	[−0.049, +0.126]	10.49

Sim-to-real transfer: the network, trained purely on simulated injections, was shown real detections for the first time and scored AUC 0.9732 ± 0.017 against real off-source noise from the same segments (mean logit +3.34 vs +0.06, p = 2.5e-86) — higher on reality than on the simulations it learned from.

Registered null: effective spin was probed alongside mass and returned ≈ 0 from all three sources (p ≈ 0.5–0.8), exactly as predicted in advance. A method that returns "yes" to every label is not measuring anything; this one does not.

Attrition: 192 events passed selection (SNR ≥ 10, BBH only), 180 produced embeddings, 12 lack published strain. Across 576 detector-fetches: 458 ok, 99 no-file, 19 all-NaN.

Part D — the supervised comparison

XGBoost trained on GWTC catalogue features — distance, SNR, redshift, spin, false-alarm rate, p_astro — predicting the same chirp mass, with every mass-bearing column removed, with SHAP attribution.

On the same 180 events: XGBoost R² 0.595 [0.472, 0.720], MAE 6.02 M☉, against 0.502 for the label-free probe. Supervision adds +0.093 [−0.021, +0.203], Holm p = 0.105 — not significant. The decomposition: training moves R² by +0.446, supervision adds +0.093, nonlinearity adds −0.002.

Part F — settling the confound

After Part C ran, a problem surfaced by inspection rather than by any gate: ridge on raw pixels is a linear model of the image, while ridge on the embedding is a nonlinear one, because the embedding is itself a nonlinear function of the pixels. So part of the gap might be nothing more interesting than "nonlinear beats linear."

Part F gives every source the same nonlinearity budget — identical RBF kernel ridge throughout:

Source	Linear	Nonlinear	Gain from nonlinearity
trained	+0.502	+0.464	−0.038
raw pixels	+0.340	+0.338	−0.002
untrained	+0.056	+0.069	+0.013

The answer is a negative result: giving raw pixels a full nonlinear read-out moved them by −0.002. Nonlinearity buys nothing on this problem, so it cannot explain the gap.

Paired comparisons (both members refit on the same bootstrap resample):

Comparison	ΔR²	95 % CI	Holm p
trained vs untrained, both nonlinear	+0.424	[+0.286, +0.637]	0.0005
trained vs raw pixels, both linear	+0.182	[+0.106, +0.318]	0.026
trained vs raw pixels, both nonlinear	+0.155	[+0.016, +0.325]	0.261 — not significant

That last row must always be reported as non-significant. The bootstrap interval excludes zero while the permutation p-value does not reach significance; when the two disagree at this sample size, the p-value is the conservative read.

Part F recomputed Part C's linear column from scratch and reproduced it to |diff| = 0.00e+00, which is what makes the two parts comparable at all.

---

What this shows — and what it does not

Shows: training transforms the representation so that chirp mass becomes linearly readable, far beyond an untrained network of identical architecture, and not because of model class.

Does not show, and the page must never claim:

1. That the CNN "discovered" mass. The embedding is a deterministic function of the image and therefore cannot contain more information than the image does. What changed is linear accessibility, not information content.
2. That this is a good way to measure mass. It was never compared against the real alternative — matched-filter parameter estimation, which produced these labels and is far more precise. The probe is an instrument, not a product.
3. That detection training specifically is responsible. What is established is that training matters. The control that would isolate it — the same CNN trained on shuffled labels — was never run. This gap is stated openly rather than omitted.

---

Why the methodology is the real differentiator

• Pre-registration. Analysis choices and interpretation branches fixed in writing before fitting, with timestamps asserted to precede the first fit.
• Test-once discipline. A 20 000-sample held-out split the hyperparameter search never saw.
• Five controls, each killing a specific alternative explanation: untrained network (best of 5 seeds, not the average), raw pixels, SNR-only, detection-logit-only, label permutation.
• Paired bootstraps rather than overlapping marginal intervals.
• Predictions that failed, reported as failures. The learning-curve prediction landed; a prediction about Part D did not, and stays on the record.
• An amendment log. Specs that never change are specs nobody consulted:

Changed	Because
n_subset 200k recommendation reversed	the learning curve flattened — more data was not the constraint
Bundle discovery rewritten	the first Part C died in 17 s at discover_bundle()
Shadow explorer forced to a single self-contained file	it silently rendered a Schwarzschild circle at spin 0.63
Randomised window alignment reverted	Part B trained at fixed alignment; randomising degraded mass R² from 0.353 → 0.148 on identical events
"Recovery closed — strain not published" overturned	an HTTP Range-read fix lifted n from 73 → 180; the diagnosis had been a resolver bug
Part F commissioned	the model-class confound was found after Part C ran, and by inspection rather than by a gate

• Failed gates kept visible. schedule_completed (a labelling coincidence in Part B) and spin_calibration_row_present (Part F). A green table proves nothing.

---

Page structure — the order is the argument

The page follows GWprobedelta.md, one argument read top to bottom:

1. Hero — the claim, five figures read live from JSON, and a rotating Did You Know bar
2. Shadow — spin and inclination sliders over the exact Kerr boundary with a schematic disk, the EHT comparison, the ray-traced renders, and the geometry diagnostics behind click to view
3. Detector — the CNN, its single test-set score, and the learning curve beside its pre-registered prediction
4. Real data — the 0.973 sim-to-real transfer result
5. Probe — the three sources as bars, the scatter, the permutation null, the registered spin null and the attrition
6. Confound — the objection in the reader's voice, then the linear-vs-nonlinear table and the paired tests, with every non-significant row labelled n.s.
7. Supervised — what a model that does see labels gets, and the decomposition
8. Scope — what this shows, and the three things it does not
9. Method — pre-registration, test-once, five controls, the amendment log and the contract hashes
10. Conclusion — the finding, then the scope: n = 180 is the confirmed-detection catalogue after an SNR and BBH cut. A statement about the universe, not about the work.

---

Design direction

Dark blue and space, precise and typographic. The project's distinguishing feature is rigour, and the design amplifies it rather than fighting it.

• Ground #05070c fading to #0a1a3a, translucent panels, text #e8ecf4 / mid #c3cada / dim #8b93a7
• One accent, blue #5b9dff, the single knob the page is tuned on: nav, eyebrows, key figures, links, bars, glows and the focus ring all follow it
• Green #7ee59a / red #ff8a8a reserved for pass/fail badges, verdicts and error banners
• A generated, royalty-free space background (site/tools/space.py), two tiled starfields and two soft accent glows, kept dark enough that every text token holds 4.5:1
• The accretion disk is warm (ember → orange → yellow → white) and deliberately not tied to the accent, so the redshift asymmetry stays visible
• Serif display type, sans body, monospace with tabular numerals for every figure
• Motion only where it carries information or is paused on request: the shadow redrawing under a slider, and the Did You Know bar's 30-second slide (paused on hover and focus, a cross-fade under reduced motion)

The Did You Know bar carries 17 short physics notes (closed timelike curves inside rotating black holes, chronology protection, the Penrose process, ER = EPR, black hole impostors and the Buchdahl bound, gravitational-wave memory). Sources stay in facts.json for anyone checking a claim.

Every number on the page is read from JSON: cnn.json, probe.json, nonlinear.json, tabular.json, shadow.json, facts.json. Nothing is hardcoded, so a pipeline re-run updates the page by replacing one file.

---

Repository layout

Path	What it is
site/	the published page: index.html, style.css, app.js, shadow.js, synced data/ and img/, build.py, standalone.html
GWprobedelta.md	the page spec this build implements
partA.py, src/shadow/, web/	the Kerr geometry, its Python ground truth and the JS port
PartB/	the detection CNN (partB.py), its cnn.json, the trained weights and the hashed preprocessing bundle
partC.py, probe.json	the linear probe on 180 real events
partD.py, results/tabular.json	the supervised XGBoost comparison
partF.py, nonlinear.json, Part F/	the nonlinearity control
results/	pipeline figures and JSON
plan.md, specs_webpage.md	the build plan and the original page spec

Run the page locally

cd site
python3 build.py --sync          # copy the pipeline's JSON, figures and shadow.js in
python3 -m http.server 8000      # then open http://localhost:8000
python3 build.py                 # optional: rebuild the offline standalone.html

The site deploys to GitHub Pages from site/ on every push to main (.github/workflows/pages.yml).

---

Status

Part	State
A — Kerr shadow + EHT	complete; live explorer on the page
B — detection CNN	complete, AUC 0.8503
C — the probe	complete, n = 180, R² 0.502
D — XGBoost comparison	complete on the same 180 events
F — nonlinearity control	complete
E — this page	live: askretik.github.io/Gravitational-Waves