  We introduce photonic kernel machines, a scheme for ultrafast spectral
analysis of noisy radio-frequency signals from single-shot optical intensity
measurements. The approach combines the versatility of machine learning and the
speed of photonic hardware to reach unprecedented throughput rates. We
theoretically describe some of the key underlying principles, and then
numerically illustrate the reached performances on a photonic lattice-based
implementation. We apply the technique both to picosecond pulsed
radio-frequency signals, on energy-spectral-density estimation and a shape
classification task, and to continuous signals, on a frequency tracking task.
The presented optical computing scheme is resilient to noise while requiring
minimal control on the photonic-lattice parameters, making it readily
implementable in realistic state-of-the-art photonic platforms.
