Linear mixing
THE CASE FILE
One claim.
Seven ways to test it.
Read the evidence in order. Each chapter removes one convenient assumption and asks whether learning finally earns a robust advantage.
An interactive observatory for testing what HyperMix actually demonstrates: in this benchmark, a well-calibrated spatial matched filter leads or ties the learned detector.
NLL 0.05766 vs 0.06792
within 0.005 of the full mean
THE CASE FILE
Read the evidence in order. Each chapter removes one convenient assumption and asks whether learning finally earns a robust advantage.
CHAPTER 01 · SIGNAL
Target SNR measures the target contribution against noise, not the energy of the entire scene. Move the control to inspect the low-signal regime.
20 log₁₀(target RMS / noise RMS)SPECTRAL MISMATCH
The implanted target does not change. Only the signature supplied to the detector is shifted along the spectral index.
Now remove the convenient assumption that the lab signature reaches the sensor unchanged.
↓CHAPTER 02 · PHYSICS
Measured spectra, spectral response, atmosphere, and bilinear mixing are opt-in controls. The oracle target already knows the transformation; the lab target does not.
Linear mixing
USGS + bioHSI
Gaussian response
Mismatch appears
Full forward model
Give learning measured target variation and a classical subspace a fair chance.
↓CHAPTER 03 · VARIATION
The detector is trained over measured variation, but its features still come from the nominal target. The classical subspace receives the library of plausible signatures.
SELECTED TRACK
Bacteriochlorophyll a or SmURFP/biliverdin
Correct reading: the “any reporter” track combines chemical classes. It is not intra-molecule variability. Spatial subspace beats the MLP by 0.020 AUC.
FINAL CAUSAL TESTStill no robust learned advantage.Let a model consume the raw scene and learn its background statistics without labels.
↓CHAPTER 04 · BACKGROUND
A shallow autoencoder learns only from unlabeled spectra in the test scene. It never receives labels, a target mask, or the target signature during training.
If real clutter is non-Gaussian, can scene-level background learning beat the spatial matched filter?
Both 95% confidence intervals are below zero.
This pre-specified shallow autoencoder is significantly worse on both metrics. It closes this simple instantiation, not every possible background-density model.
Global RX
0.539AUC · Pd 0.001Raw background AE
0.869AUC · Pd 0.108Ariel rewards calibrated uncertainty, not AUC alone. Ask whether learning can win on probability quality.
↓CHAPTER 05 · CALIBRATION
MF scores receive Platt scaling. The learned detector receives temperature scaling with bias correction, alone and as a three-member ensemble. Calibration and evaluation use disjoint target implants.
Can the learned ensemble beat the spatial matched filter on calibrated uncertainty while detection remains tied?
Both 95% intervals are above zero. The learned probabilities are significantly worse.
The pre-specified criterion required favorable NLL and ECE intervals. Neither was favorable, even after a fair calibration split.
NLL CI 0.00448–0.01778If detection is nearly saturated, inspect how many spectral channels actually carry the matched-filter result.
↓CHAPTER 06 · BANDS
Bands are ranked without implanted labels by the absolute full-scene matched-filter coefficient |C⁻¹(t−μ)|. The spatial MF is then recomputed using only the top-k bands.
Smallest k within 0.005 of the full-model mean. This is descriptive, not equivalence proof.
Top-3 carry only 9.8%–16.1% of absolute coefficient weight across the three scenes.
The crop-classification result does not transfer directly: fewer than three bands were not enough for this target-detection benchmark.
A detector need not be superior to make the toolkit useful. Move from ranking pixels to estimating abundance.
↓CHAPTER 07 · QUANTITY
Target MAE uses only pixels with abundance above 0.02. In Salinas, correlation concealed a relevant scale bias.
Bring a score map, inspect its threshold, then finish with the boundaries of every claim.
↓LOCAL RESULT VIEWER
Drop a detector score map and inspect candidate pixels at different thresholds. Processing stays entirely in your browser.
PNG, JPEG, or WebP · up to 12 MB
Visualization only. Pixel brightness is treated as detector score. This does not run HyperMix inference on an RGB image.
The last chapter states exactly what this benchmark can and cannot support.
↓READ BEFORE CLAIMING
There is no naturally occurring remote biological target. Backgrounds can be real or measured, but targets are implanted.
Pellets are not remote surfaces. Beer-Lambert converts absorbance into a reflectance-like target.
The MLP does not see the raw cube. It recombines MF, ACE, and smoothed versions built from the nominal target.
Three scenes are not a population. The hierarchical intervals describe this benchmark, not every sensor or ecosystem.
One background model is not the whole model class. T7a closes the pre-specified shallow autoencoder, not every density estimator.
A calibrated score is still benchmark-specific. The split uses independent implants in the same three real backgrounds, not a new sensor population.
Band sparsity is target-aware here. The ranking knows the target signature and does not establish a universal three-band sensor.