  Deep neural networks are characterized by multiple symmetrical, equi-loss
solutions that are redundant. Thus, the order of neurons in a layer and feature
maps can be given arbitrary permutations, without affecting (or minimally
affecting) their output. If we shuffle these neurons, or if we apply to them
some perturbations (like fine-tuning) can we put them back in the original
order i.e. re-synchronize? Is there a possible corruption threat? Answering
these questions is important for applications like neural network white-box
watermarking for ownership tracking and integrity verification. We advance a
method to re-synchronize the order of permuted neurons. Our method is also
effective if neurons are further altered by parameter pruning, quantization,
and fine-tuning, showing robustness to integrity attacks. Additionally, we
provide theoretical and practical evidence for the usual means to corrupt the
integrity of the model, resulting in a solution to counter it. We test our
approach on popular computer vision datasets and models, and we illustrate the
threat and our countermeasure on a popular white-box watermarking method.
