Estimating informativeness of samples with Smooth Unique Information

Hrayr Harutyunyan · Alessandro Achille · Giovanni Paolini · Orchid Majumder · Avinash Ravichandran · Rahul Bhotika · Stefano Soatto

Keywords: [ information theory ] [ sample information ] [ stability theory ] [ ntk ] [ dataset summarization ]


We define a notion of information that an individual sample provides to the training of a neural network, and we specialize it to measure both how much a sample informs the final weights and how much it informs the function computed by the weights. Though related, we show that these quantities have a qualitatively different behavior. We give efficient approximations of these quantities using a linearized network and demonstrate empirically that the approximation is accurate for real-world architectures, such as pre-trained ResNets. We apply these measures to several problems, such as dataset summarization, analysis of under-sampled classes, comparison of informativeness of different data sources, and detection of adversarial and corrupted examples. Our work generalizes existing frameworks, but enjoys better computational properties for heavily over-parametrized models, which makes it possible to apply it to real-world networks.

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