  The speckle pattern produced when a laser is scattered by a disordered medium
has recently been shown to give a surprisingly accurate or broadband
measurement of wavelength. Here it is shown that deep learning is an ideal
approach to analyse wavelength variations using a speckle wavemeter due to its
ability to identify trends and overcome low signal to noise ratio in complex
datasets. This combination enables wavelength measurement at high precision
over a broad operating range in a single step, with a remarkable capability to
reject instrumental and environmental noise, which has not been possible with
previous approaches. It is demonstrated that the noise rejection capabilities
of deep learning provide attometre-scale wavelength precision over an operating
range from 488 nm to 976 nm. This dynamic range is six orders of magnitude
beyond the state of the art.
