Understanding which concepts models can and cannot represent has been fundamental to many tasks: from effective and responsible use of models to detecting out of distribution data. We introduce Gaussian process probes (GPP), a unified and simple framework for probing and measuring uncertainty about concepts represented by models. As a Bayesian extension of linear probing methods, GPP asks what kind of distribution over classifiers (of concepts) is induced by the model. This distribution can be used to measure both what the model represents and how confident the probe is about what the model represents. GPP can be applied to any pre-trained model with vector representations of inputs (e.g., activations). It does not require access to training data, gradients, or the architecture. We validate GPP on datasets containing both synthetic and real images. Our experiments show it can (1) probe a model's representations of concepts even with a very small number of examples, (2) accurately measure both epistemic uncertainty (how confident the probe is) and aleatory uncertainty (how fuzzy the concepts are to the model), and (3) detect out of distribution data using those uncertainty measures as well as classic methods do. By using Gaussian processes to expand what probing can offer, GPP provides a data-efficient, versatile and uncertainty-aware tool for understanding and evaluating the capabilities of machine learning models.
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