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Transfer learning is an effective technique for tuning a deep learning model when training data or computational resources are limited. Instead of training a new model from scratch, the parameters of an existing base model are adjusted for the new task. The accuracy of such a fine-tuned model depends on the suitability of the base model chosen. Model search automates the selection of such a base model by evaluating the suitability of candidate models for a specific task. This entails inference with each candidate model on task-specific data. With thousands of models available through model stores, the computational cost of model search is a major bottleneck for efficient transfer learning. In this work, we presentAlsatian, a novel model search system. Based on the observation that many candidate models overlap to a significant extent and following a careful bottleneck analysis, we propose optimization techniques that are applicable to many model search frameworks. These optimizations include: (i) splitting models into individual blocks that can be shared across models, (ii) caching of intermediate inference results and model blocks, and (iii) selecting a beneficial search order for models to maximize sharing of cached results. In our evaluation on state-of-the-art deep learning models from computer vision and natural language processing, we show thatAlsatianoutperforms baselines by up to 14x.