Modern machine learning methods have recently demonstrated remarkable capability to generalize under task shift, where latent knowledge is transferred to a different, often more difficult, task under a similar data distribution. We investigate this phenomenon in an overparameterized linear regression setting where the task shifts from classification during training to regression during evaluation. In the zero-shot case, wherein no regression data is available, we prove that task shift is impossible in both sparse signal and random signal models for any Gaussian covariate distribution. In the few-shot case, wherein limited regression data is available, we propose a simple postprocessing algorithm which asymptotically recovers the ground-truth predictor. Our analysis leverages a fine-grained characterization of individual parameters arising from minimum-norm interpolation which may be of independent interest. Our results show that while minimum-norm interpolators for classification cannot transfer to regression a priori, they experience surprisingly structured attenuation which enables successful task shift with limited additional data.

Empirical risk minimization (ERM) of neural networks is prone to over-reliance on spurious correlations and poor generalization on minority groups. The recent deep feature reweighting (DFR) technique achieves state-of-the-art group robustness via simple last-layer retraining, but it requires held-out group and class annotations to construct a group-balanced reweighting dataset. In this work, we examine this impractical requirement and find that last-layer retraining can be surprisingly effective with no group annotations (other than for model selection) and only a handful of class annotations. We first show that last-layer retraining can greatly improve worst-group accuracy even when the reweighting dataset has only a small proportion of worst-group data. This implies a "free lunch" where holding out a subset of training data to retrain the last layer can substantially outperform ERM on the entire dataset with no additional data or annotations. To further improve group robustness, we introduce a lightweight method called selective last-layer finetuning (SELF), which constructs the reweighting dataset using misclassifications or disagreements. Our empirical and theoretical results present the first evidence that model disagreement upsamples worst-group data, enabling SELF to nearly match DFR on four well-established benchmarks across vision and language tasks with no group annotations and less than 3% of the held-out class annotations. Our code is available at https://github.com/tmlabonte/last-layer-retraining.

A critical object detection task is finetuning an existing model to detect novel objects, but the standard workflow requires bounding box annotations which are time-consuming and expensive to collect. Weakly supervised object detection (WSOD) offers an appealing alternative, where object detectors can be trained using image-level labels. However, the practical application of current WSOD models is limited, as they only operate at small data scales and require multiple rounds of training and refinement. To address this, we propose the Weakly Supervised Detection Transformer, which enables efficient knowledge transfer from a large-scale pretraining dataset to WSOD finetuning on hundreds of novel objects. Additionally, we leverage pretrained knowledge to improve the multiple instance learning (MIL) framework often used in WSOD methods. Our experiments show that our approach outperforms previous state-of-the-art models on large-scale novel object detection datasets, and our scaling study reveals that class quantity is more important than image quantity for WSOD pretraining. The code is available at https://github.com/tmlabonte/weakly-supervised-DETR.