Vision Transformers (ViT) is known for its scalability. In this work, we target to scale down a ViT to fit in an environment with dynamic-changing resource constraints. We observe that smaller ViTs are intrinsically the sub-networks of a larger ViT with different widths. Thus, we propose a general framework, named Scala, to enable a single network to represent multiple smaller ViTs with flexible inference capability, which aligns with the inherent design of ViT to vary from widths. Concretely, Scala activates several subnets during training, introduces Isolated Activation to disentangle the smallest sub-network from other subnets, and leverages Scale Coordination to ensure each sub-network receives simplified, steady, and accurate learning objectives. Comprehensive empirical validations on different tasks demonstrate that with only one-shot training, Scala learns slimmable representation without modifying the original ViT structure and matches the performance of Separate Training. Compared with the prior art, Scala achieves an average improvement of 1.6% on ImageNet-1K with fewer parameters. Code is available at here.

In this paper, we study the learning problem in contextual search, which is motivated by applications such as first-price auction, personalized medicine experiments, and feature-based pricing experiments. In particular, for a sequence of arriving context vectors, with each context associated with an underlying value, the decision-maker either makes a query at a certain point or skips the context. The decision-maker will only observe the binary feedback on the relationship between the query point and the value associated with the context. We study a PAC learning setting, where the goal is to learn the underlying mean value function in context with a minimum number of queries. To address this challenge, we propose a tri-section search approach combined with a margin-based active learning method. We show that the algorithm only needs to make $O(1/\varepsilon^2)$ queries to achieve an $\epsilon$-estimation accuracy. This sample complexity significantly reduces the required sample complexity in the passive setting, at least $\Omega(1/\varepsilon^4)$.