Recent work has uncovered promising ways to extract well-calibrated confidence estimates from language models (LMs), where the model's confidence score reflects how likely it is to be correct. However, while LMs may appear well-calibrated over broad distributions, this often hides significant miscalibration within narrower slices (e.g., systemic over-confidence in math can balance out systemic under-confidence in history, yielding perfect calibration in aggregate). To attain well-calibrated confidence estimates for any slice of a distribution, we propose a new framework for few-shot slice-specific recalibration. Specifically, we train a recalibration model that takes in a few unlabeled examples from any given slice and predicts a curve that remaps confidence scores to be more accurate for that slice. Our trained model can recalibrate for arbitrary new slices, without using any labeled data from that slice. This enables us to identify domain-specific confidence thresholds above which the LM's predictions can be trusted, and below which it should abstain. Experiments show that our few-shot recalibrator consistently outperforms existing calibration methods, for instance improving calibration error for PaLM2-Large on MMLU by 16%, as compared to temperature scaling.

Hashing is a popular approximate nearest neighbor search approach for large-scale image retrieval. Supervised hashing, which incorporates similarity/dissimilarity information on entity pairs to improve the quality of hashing function learning, has recently received increasing attention. However, in the existing supervised hashing methods for images, an input image is usually encoded by a vector of hand-crafted visual features. Such hand-crafted feature vectors do not necessarily preserve the accurate semantic similarities of images pairs, which may often degrade the performance of hashing function learning. In this paper, we propose a supervised hashing method for image retrieval, in which we automatically learn a good image representation tailored to hashing as well as a set of hash functions. The proposed method has two stages. In the first stage, given the pairwise similarity matrix $S$ over training images, we propose a scalable coordinate descent method to decompose $S$ into a product of $HH^T$ where $H$ is a matrix with each of its rows being the approximate hash code associated to a training image. In the second stage, we propose to simultaneously learn a good feature representation for the input images as well as a set of hash functions, via a deep convolutional network tailored to the learned hash codes in $H$ and optionally the discrete class labels of the images. Extensive empirical evaluations on three benchmark datasets with different kinds of images show that the proposed method has superior performance gains over several state-of-the-art supervised and unsupervised hashing methods.