We introduce a method to generate vectorial representations of visual classification tasks that can be used to reason about the nature of those tasks and their relations. Given a dataset with ground-truth labels and a loss function, we process images through a “probe network” and compute an embedding based on estimates of the Fisher information matrix associated with the probe network parameters. This provides a fixed-dimensional embedding of the task that is independent of details such as the number of classes and requires no understanding of the class label semantics. We demonstrate that this embedding is capable of predicting task similarities that match our intuition about semantic and taxonomic relations between different visual tasks. We demonstrate the practica lvalue of this framework for the meta-task of selecting a pre-trained feature extractor for a novel task. We present a simple meta-learning framework for learning a metric on embeddings that is capable of predicting which feature extractors will perform well on which task without actually fine-tuning the model. Selecting a feature extractor with task embedding yield sperformance close to the best available feature extractor, with substantially less computational effort than exhaustively training and evaluating all available models.
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