Machine learning models--including prominent zero-shot models--are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes--or, in the case of zero-shot prediction, to improve its performance--without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping arg max with the Fréchet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes.

In reinforcement learning (RL), it is common to apply techniques used broadly in machine learning such as neural network function approximators and momentumbased optimizers [1, 2]. However, such tools were largely developed for supervised learning rather than nonstationary RL, leading practitioners to adopt target networks [3], clipped policy updates [4], and other RL-specific implementation tricks [5, 6] to combat this mismatch, rather than directly adapting this toolchain for use in RL. In this paper, we take a different approach and instead address the effect of nonstationarity by adapting the widely used Adam optimiser [7]. We first analyse the impact of nonstationary gradient magnitude--such as that caused by a change in target network--on Adam's update size, demonstrating that such a change can lead to large updates and hence sub-optimal performance. To address this, we introduce Adam with Relative Timesteps, or Adam-Rel. Rather than using the global timestep in the Adam update, Adam-Rel uses the local timestep within an epoch, essentially resetting Adam's timestep to 0 after target changes. We demonstrate that this avoids large updates and reduces to learning rate annealing in the absence of such increases in gradient magnitude. Evaluating Adam-Rel in both on-policy and off-policy RL, we demonstrate improved performance in both Atari and Craftax. We then show that increases in gradient norm occur in RL in practice, and examine the differences between our theoretical model and the observed data.

In this part, we list the main notations in Table S1 for clear reference. Table S1: Main notations used in the work. The detailed procedure of the proposed method is summarized in Algorithm 1. Algorithm 1 Pseudocode of the Proposed Method. We compared our proposed model with the following weakly-supervised methods for cancer prognosis analysis. WSISA [1]: The candidate patterns are clustered by the K-Means algorithm based on the phenotype features of tiles, followed by several DeepConvSurv [2] models to find important clusters.

The multi-instance learning (MIL) has advanced cancer prognosis analysis with whole slide images (WSIs). However, current MIL methods for WSI analysis still confront unique challenges. Previous methods typically generate instance representations via a pre-trained model or a model trained by the instances with bag-level annotations, which, however, may not generalize well to the downstream task due to the introduction of excessive label noises and the lack of fine-grained information across multi-magnification WSIs. Additionally, existing methods generally aggregate instance representations as bag ones for prognosis prediction and have no consideration of intra-bag redundancy and inter-bag discrimination. To address these issues, we propose a dual-curriculum contrastive MIL method for cancer prognosis analysis with WSIs. The proposed method consists of two curriculums, i.e., saliency-guided weakly-supervised instance encoding with cross-scale tiles and contrastive-enhanced soft-bag prognosis inference. Extensive experiments on three public datasets demonstrate that our method outperforms state-of-the-art methods in this field.

Softmax attention is the principle backbone of foundation models for various artificial intelligence applications, yet its quadratic complexity in sequence length can limit its inference throughput in long-context settings. To address this challenge, alternative architectures such as linear attention, State Space Models (SSMs), and Recurrent Neural Networks (RNNs) have been considered as more efficient alternatives. While connections between these approaches exist, such models are commonly developed in isolation and there is a lack of theoretical understanding of the shared principles underpinning these architectures and their subtle differences, greatly influencing performance and scalability. In this paper, we introduce the Dynamical Systems Framework (DSF), which allows a principled investigation of all these architectures in a common representation.

We propose A-Crab (Actor-Critic Regularized by Average Bellman error), a new practical algorithm for offline reinforcement learning (RL) in complex environments with insufficient data coverage. Our algorithm combines the marginalized importance sampling framework with the actor-critic paradigm, where the critic returns evaluations of the actor (policy) that are pessimistic relative to the offline data and have a small average (importance-weighted) Bellman error. Compared to existing methods, our algorithm simultaneously offers a number of advantages: (1) It achieves the optimal statistical rate of 1/ N--where N is the size of offline dataset--in converging to the best policy covered in the offline dataset, even when combined with general function approximators.

We propose A-Crab (Actor-Critic Regularized by Average Bellman error), a new practical algorithm for offline reinforcement learning (RL) in complex environments with insufficient data coverage. Our algorithm combines the marginalized importance sampling framework with the actor-critic paradigm, where the critic returns evaluations of the actor (policy) that are pessimistic relative to the offline data and have a small average (importance-weighted) Bellman error. Compared to existing methods, our algorithm simultaneously offers a number of advantages: (1) It achieves the optimal statistical rate of 1/ N--where N is the size of offline dataset--in converging to the best policy covered in the offline dataset, even when combined with general function approximators.

With the widespread application of Large Language Models (LLMs) to various domains, concerns regarding the trustworthiness of LLMs in safety-critical scenarios have been raised, due to their unpredictable tendency to hallucinate and generate misinformation. Existing LLMs do not have an inherent functionality to provide the users with an uncertainty/confidence metric for each response it generates, making it difficult to evaluate trustworthiness. Although several studies aim to develop uncertainty quantification methods for LLMs, they have fundamental limitations, such as being restricted to classification tasks, requiring additional training and data, considering only lexical instead of semantic information, and being prompt-wise but not response-wise. A new framework is proposed in this paper to address these issues.