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Paper · 2205.14258 · 2022

On the Symmetries of Deep Learning Models and their Internal Representations

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 5 functions out of this paper's own repositories and ran 2 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
pnnl/modelsym canonical 2 of 5
FunctionStatusWhere it lives
sinkhorn Ran pnnl/modelsym/model_symmetries/stitching/stitching.py
pointer only (licence: NOASSERTION) · get_code("57f3995b8ea26d10")
softsort Ran pnnl/modelsym/model_symmetries/stitching/stitching.py
pointer only (licence: NOASSERTION) · get_code("fe2339f3b4161fc7")
get_stitch_model Not yet run pnnl/modelsym/model_symmetries/stitching/stitching.py
pointer only (licence: NOASSERTION) · get_code("4592fbb994b52a15")
wreath_cka Not yet run pnnl/modelsym/model_symmetries/alignment/alignment.py
pointer only (licence: NOASSERTION) · get_code("cfa2e7f47dbee374")
wreath_procrustes Not yet run pnnl/modelsym/model_symmetries/alignment/alignment.py
pointer only (licence: NOASSERTION) · get_code("7302057fbb1a0c89")

Repositories linked to this paper

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Abstract

Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of a family of models with the symmetries of that family's internal representation of data. We do this by calculating a set of fundamental symmetry groups, which we call the intertwiner groups of the model. We connect intertwiner groups to a model's internal representations of data through a range of experiments that probe similarities between hidden states across models with the same architecture. Our work suggests that the symmetries of a network are propagated into the symmetries in that network's representation of data, providing us with a better understanding of how architecture affects the learning and prediction process. Finally, we speculate that for ReLU networks, the intertwiner groups may provide a justification for the common practice of concentrating model interpretability exploration on the activation basis in hidden layers rather than arbitrary linear combinations thereof.

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