  Earthquake occurrence is notoriously difficult to predict. While some aspects
of their spatiotemporal statistics can be relatively well captured by
point-process models, very little is known regarding the magnitude of future
events, and it is deeply debated whether it is possible to predict the
magnitude of an earthquake before it starts. This is due both to the lack of
information about fault conditions and to the inherent complexity of rupture
dynamics. Consequently, even state of the art forecasting models typically
assume no knowledge about the magnitude of future events besides the
time-independent Gutenberg Richter (GR) distribution, which describes the
marginal distribution over large regions and long times. This approach
implicitly assumes that earthquake magnitudes are independent of previous
seismicity and are identically distributed. In this work we challenge this view
by showing that information about the magnitude of an upcoming earthquake can
be directly extracted from the seismic history. We present MAGNET - MAGnitude
Neural EsTimation model, an open-source, geophysically-inspired neural-network
model for probabilistic forecasting of future magnitudes from cataloged
properties: hypocenter locations, occurrence times and magnitudes of past
earthquakes. Our history-dependent model outperforms stationary and
quasi-stationary state of the art GR-based benchmarks, in real catalogs in
Southern California, Japan and New-Zealand. This demonstrates that earthquake
catalogs contain information about the magnitude of future earthquakes, prior
to their occurrence. We conclude by proposing methods to apply the model in
characterization of the preparatory phase of earthquakes, and in operational
hazard alert and earthquake forecasting systems.
