Seeing Why: Exact Evidence Maps for Quantum and Optical Image Classifiers
Abstract
When an image classifier decides, we can usually only estimate why. For quantum and all-optical classifiers that act linearly on amplitude-encoded pictures up to the measurement, with no trained classical network before or after them, each class's Born probability above its no-information share, Pg − bg, splits exactly into contributions of the encoded amplitudes, shown as Born evidence maps (BEM) over the picture. The split itself follows from known results on quadratic forms: with the transmitted light held fixed, it is what Integrated Gradients from a zero baseline and the Shapley value give. What we add is a way to measure it on the hardware that classifies, from class probabilities on a quantum chip or from camera frames on a lens bench, with no gradient circuit and no light sent backwards; a g× g map takes 1 + 2g2 runs. Deleting the 5% of pixels with the highest evidence drops accuracy from 73% to 9%, as occlusion does with 1,024 extra runs per picture, whereas gradient saliency removes much less. The classifiers share one architecture, a Fourier-plane mask followed by a brickwall circuit on qubits or by phase plates on a lens bench, read by a fixed Born headroom readout with no trained parameter; centring each picture on its own mean lets dark features count as much as bright ones. In simulation, four phase plates at a single wavelength reach 72.3% on Caltech-10 colour photographs. On IBM's ibm_kingston, with the mask applied before approximate loading, 300 test pictures were classified at 37.7% against 10% by chance (56.3% in exact simulation), and 2×2 maps of ten correctly classified pictures, one per class chosen by a stated rule, measured on the chip, agreed with the exact ones (r = 0.77). The maps also revealed a shortcut in the data; as the trim that removed it was chosen on test pictures, the Caltech-10 results are exploratory.
Related
- A comparative study of variational quantum classifiers and classical machine learning for tW−tt̅ discrimination at the LHC
- Conditional validity of quantum event classifiers under collider systematics and quantum estimation uncertainty
- Quantum Anomaly Detection in network traffic using Variational Quantum Classifiers
- Representation Geometry and Inductive Biases in Quantum Classifiers across Classical Visual Benchmarks
- Fourier Analysis of Parametrized Interactive Quantum Classifiers
BibTeX
@misc{tongloy2026seeing,
title = {{Seeing Why: Exact Evidence Maps for Quantum and Optical Image Classifiers}},
author = {Teerawat Tongloy and Rangsan Jomtarak},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01993},
eprint = {2611.01993},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01993},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Seeing Why: Exact Evidence Maps for Quantum and Optical Image Classifiers
AU - Teerawat Tongloy
AU - Rangsan Jomtarak
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01993
UR - https://arxiv.org/abs/2611.01993
AB - When an image classifier decides, we can usually only estimate why. For quantum and all-optical classifiers that act linearly on amplitude-encoded pictures up to the measurement, with no trained classical network before or after them, each class's Born probability above its no-information share, P_g − b_g, splits exactly into contributions of the encoded amplitudes, shown as Born evidence maps (BEM) over the picture. The split itself follows from known results on quadratic forms: with the transmitted light held fixed, it is what Integrated Gradients from a zero baseline and the Shapley value give. What we add is a way to measure it on the hardware that classifies, from class probabilities on a quantum chip or from camera frames on a lens bench, with no gradient circuit and no light sent backwards; a g× g map takes 1 + 2g^2 runs. Deleting the 5% of pixels with the highest evidence drops accuracy from 73% to 9%, as occlusion does with 1,024 extra runs per picture, whereas gradient saliency removes much less. The classifiers share one architecture, a Fourier-plane mask followed by a brickwall circuit on qubits or by phase plates on a lens bench, read by a fixed Born headroom readout with no trained parameter; centring each picture on its own mean lets dark features count as much as bright ones. In simulation, four phase plates at a single wavelength reach 72.3% on Caltech-10 colour photographs. On IBM's ibm_kingston, with the mask applied before approximate loading, 300 test pictures were classified at 37.7% against 10% by chance (56.3% in exact simulation), and 2×2 maps of ten correctly classified pictures, one per class chosen by a stated rule, measured on the chip, agreed with the exact ones (r = 0.77). The maps also revealed a shortcut in the data; as the trim that removed it was chosen on test pictures, the Caltech-10 results are exploratory.
ER -