  We introduce equi-tuning, a novel fine-tuning method that transforms
(potentially non-equivariant) pretrained models into group equivariant models
while incurring minimum $L_2$ loss between the feature representations of the
pretrained and the equivariant models. Large pretrained models can be
equi-tuned for different groups to satisfy the needs of various downstream
tasks. Equi-tuned models benefit from both group equivariance as an inductive
bias and semantic priors from pretrained models. We provide applications of
equi-tuning on three different tasks: image classification, compositional
generalization in language, and fairness in natural language generation (NLG).
We also provide a novel group-theoretic definition for fairness in NLG. The
effectiveness of this definition is shown by testing it against a standard
empirical method of fairness in NLG. We provide experimental results for
equi-tuning using a variety of pretrained models: Alexnet, Resnet, VGG, and
Densenet for image classification; RNNs, GRUs, and LSTMs for compositional
generalization; and GPT2 for fairness in NLG. We test these models on benchmark
datasets across all considered tasks to show the generality and effectiveness
of the proposed method.
