On genuine invariance learning without weight-tying
Artem Moskalev Anna Sepliarskaia Erik J. Bekkers Arnold Smeulders
In this paper, we investigate properties and limitations of invariance
learned by neural networks from the data compared to the genuine invariance
achieved through invariant weight-tying. To do so, we adopt a group theoretical
perspective and analyze invariance learning in neural networks without
weight-tying constraints. We demonstrate that even when a network learns to
correctly classify samples on a group orbit, the underlying decision-making in
such a model does not attain genuine invariance. Instead, learned invariance is
strongly conditioned on the input data, rendering it unreliable if the input
distribution shifts. We next demonstrate how to guide invariance learning
toward genuine invariance by regularizing the invariance of a model at the
training. To this end, we propose several metrics to quantify learned
invariance: (i) predictive distribution invariance, (ii) logit invariance, and
(iii) saliency invariance similarity. We show that the invariance learned with
the invariance error regularization closely reassembles the genuine invariance
of weight-tying models and reliably holds even under a severe input
distribution shift. Closer analysis of the learned invariance also reveals the
spectral decay phenomenon, when a network chooses to achieve the invariance to
a specific transformation group by reducing the sensitivity to any input
perturbation.