We study the problem of transfer learning via Multi-Task Representation Learning (MTRL), wherein multiple source tasks are used to learn a good common representation, and a predictor is trained on top of it for the target task. Under standard regularity assumptions on the loss function and task diversity, we provide new statistical rates on the excess risk of the target task, which demonstrate the benefit of representation learning. Importantly, our rates are optimistic, i.e., they interpolate between the standard O(m 1/2)rate and the fast O(m 1)rate, depending on the difficulty of the learning task, where m is the number of samples for the target task. Besides the main result, we make several new contributions, including giving optimistic rates for excess risk of source tasks (Multi-Task Learning (MTL)), a local Rademacher complexity theorem for MTRL and MTL, as well as a chain rule for local Rademacher complexity for composite predictor classes.

We study the problem of transfer learning via Multi-Task Representation Learning (MTRL), wherein multiple source tasks are used to learn a good common representation, and a predictor is trained on top of it for the target task. Under standard regularity assumptions on the loss function and task diversity, we provide new statistical rates on the excess risk of the target task, which demonstrate the benefit of representation learning. Importantly, our rates are optimistic, i.e., they interpolate between the standard O(m 1/2)rate and the fast O(m 1)rate, depending on the difficulty of the learning task, where m is the number of samples for the target task. Besides the main result, we make several new contributions, including giving optimistic rates for excess risk of source tasks (Multi-Task Learning (MTL)), a local Rademacher complexity theorem for MTRL and MTL, as well as a chain rule for local Rademacher complexity for composite predictor classes.

In this study, we investigate the task of data pre-selection, which aims to select instances for labeling from an unlabeled dataset through a single pass, thereby optimizing performance for undefined downstream tasks with a limited annotation budget. Previous approaches to data pre-selection relied solely on visual features extracted from foundation models, such as CLIP and BLIP-2, but largely ignored the powerfulness of text features. In this work, we argue that, with proper design, the joint feature space of both vision and text can yield a better representation for data pre-selection. To this end, we introduce UP-DP, a simple yet effective unsupervised prompt learning approach that adapts vision-language models, like BLIP-2, for data pre-selection. Specifically, with the BLIP-2 parameters frozen, we train text prompts to extract the joint features with improved representation, ensuring a diverse cluster structure that covers the entire dataset. We extensively compare our method with the state-of-the-art using seven benchmark datasets in different settings, achieving up to a performance gain of 20%. Interestingly, the prompts learned from one dataset demonstrate significant generalizability and can be applied directly to enhance the feature extraction of BLIP-2 from other datasets. To the best of our knowledge, UP-DP is the first work to incorporate unsupervised prompt learning in a vision-language model for data pre-selection.

Parametric stochastic simulators are ubiquitous in science, often featuring highdimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural simulation-based inference algorithm which simultaneously offers simulation efficiency and fast empirical posterior testability, which is unique among modern algorithms. Our approach is simulation efficient by simultaneously estimating low-dimensional marginal posteriors instead of the joint posterior and by proposing simulations targeted to an observation of interest via a prior suitably truncated by an indicator function. Furthermore, by estimating a locally amortized posterior our algorithm enables efficient empirical tests of the robustness of the inference results. Since scientists cannot access the ground truth, these tests are necessary for trusting inference in real-world applications. We perform experiments on a marginalized version of the simulation-based inference benchmark and two complex and narrow posteriors, highlighting the simulator efficiency of our algorithm as well as the quality of the estimated marginal posteriors.

Hyperbolic space has become a popular choice of manifold for representation learning of various datatypes from tree-like structures and text to graphs. Building on the success of deep learning with prototypes in Euclidean and hyperspherical spaces, a few recent works have proposed hyperbolic prototypes for classification. Such approaches enable effective learning in low-dimensional output spaces and can exploit hierarchical relations amongst classes, but require privileged information about class labels to position the hyperbolic prototypes. In this work, we propose Hyperbolic Busemann Learning. The main idea behind our approach is to position prototypes on the ideal boundary of the Poincaré ball, which does not require prior label knowledge. To be able to compute proximities to ideal prototypes, we introduce the penalised Busemann loss. We provide theory supporting the use of ideal prototypes and the proposed loss by proving its equivalence to logistic regression in the one-dimensional case. Empirically, we show that our approach provides a natural interpretation of classification confidence, while outperforming recent hyperspherical and hyperbolic prototype approaches.