While deep learning models often achieve high predictive accuracy, their predictions typically do not come with any provable guarantees on risk or reliability, which are critical for deployment in high-stakes applications. The framework of conformal risk control (CRC) provides a distribution-free, finite-sample method for controlling the expected value of any bounded monotone loss function and can be conveniently applied post-hoc to any pre-trained deep learning model. However, many realworld applications are sensitive to tail risks, as opposed to just expected loss. In this work, we develop a method for controlling the general class of Optimized CertaintyEquivalent (OCE) risks, a broad class of risk measures which includes as special cases the expected loss (generalizing the original CRC method) and common tail risks like the conditional value-at-risk (CVaR).

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Recent top-performing approaches are prompt-based methods that utilize a set of learnable parameters ( i .

Continual learning requires to overcome catastrophic forgetting when training a single model on a sequence of tasks. Recent top-performing approaches are prompt-based methods that utilize a set of learnable parameters (i.e., prompts) to encode task knowledge, from which appropriate ones are selected to guide the fixed pre-trained model in generating features tailored to a certain task. However, existing methods rely on predicting prompt identities for prompt selection, where the identity prediction process cannot be optimized with task loss. This limitation leads to sub-optimal prompt selection and inadequate adaptation of pre-trained features for a specific task. Previous efforts have tried to address this by directly generating prompts from input queries instead of selecting from a set of candidates. However, these prompts are continuous, which lack sufficient abstraction for task knowledge representation, making them less effective for continual learning. To address these challenges, we propose VQ-Prompt, a prompt-based continual learning method that incorporates Vector Quantization (VQ) into end-to-end training of a set of discrete prompts. In this way, VQ-Prompt can optimize the prompt selection process with task loss and meanwhile achieve effective abstraction of task knowledge for continual learning. Extensive experiments show that VQ-Prompt outperforms state-of-the-art continual learning methods across a variety of benchmarks under the challenging class-incremental setting.

Proper quantification of predictive uncertainty is essential for the use of machine learning in safety-critical applications. V arious uncertainty measures have been proposed for this purpose, typically claiming superiority over other measures. In this paper, we argue that there is no single best measure. Instead, uncertainty quantification should be tailored to the specific application. To this end, we use a flexible family of uncertainty measures that distinguishes between total, aleatoric, and epistemic uncertainty of second-order distributions. These measures can be instantiated with specific loss functions, so-called proper scoring rules, to control their characteristics, and we show that different characteristics are useful for different tasks. In particular, we show that, for the task of selective prediction, the scoring rule should ideally match the task loss. On the other hand, for out-of-distribution detection, our results confirm that mutual information, a widely used measure of epistemic uncertainty, performs best. Furthermore, in an active learning setting, epistemic uncertainty based on zero-one loss is shown to consistently outperform other uncertainty measures.