  Reconstructing samples from the training set of trained neural networks is a
major privacy concern. Haim et al. (2022) recently showed that it is possible
to reconstruct training samples from neural network binary classifiers, based
on theoretical results about the implicit bias of gradient methods. In this
work, we present several improvements and new insights over this previous work.
As our main improvement, we show that training-data reconstruction is possible
in the multi-class setting and that the reconstruction quality is even higher
than in the case of binary classification. Moreover, we show that using
weight-decay during training increases the vulnerability to sample
reconstruction. Finally, while in the previous work the training set was of
size at most $1000$ from $10$ classes, we show preliminary evidence of the
ability to reconstruct from a model trained on $5000$ samples from $100$
classes.
