This paper studies task adaptive pre-trained model selection, an underexplored problem of assessing pre-trained models for the target task and select best ones from the model zoo emph{without fine-tuning}. A few pilot works addressed the problem in transferring supervised pre-trained models to classification tasks, but they cannot handle emerging unsupervised pre-trained models or regression tasks. In pursuit of a practical assessment method, we propose to estimate the maximum value of label evidence given features extracted by pre-trained models. Unlike the maximum likelihood, the maximum evidence is emph{immune to over-fitting}, while its expensive computation can be dramatically reduced by our carefully designed algorithm. The Logarithm of Maximum Evidence (LogME) can be used to assess pre-trained models for transfer learning: a pre-trained model with a high LogME value is likely to have good transfer performance. LogME is emph{fast, accurate, and general}, characterizing itself as the first practical method for assessing pre-trained models. Compared with brute-force fine-tuning, LogME brings at most $3000times$ speedup in wall-clock time and requires only $1%$ memory footprint. It outperforms prior methods by a large margin in their setting and is applicable to new settings. It is general enough for diverse pre-trained models (supervised pre-trained and unsupervised pre-trained), downstream tasks (classification and regression), and modalities (vision and language). Code is available at this repository: href{https://github.com/thuml/LogME}{https://github.com/thuml/LogME}.
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