A common way to extend the memory of large language models (LLMs) is by retrieval augmented generation (RAG), which inserts text retrieved from a larger memory into an LLM's context window. However, the context window is typically limited to several thousand tokens, which limits the number of retrieved passages that can inform a model's response. For this reason, it's important to avoid occupying context window space with redundant information by ensuring a degree of diversity among retrieved passages. At the same time, the information should also be relevant to the current task. Most prior methods that encourage diversity among retrieved results, such as Maximal Marginal Relevance (MMR), do so by incorporating an objective that explicitly trades off diversity and relevance. We propose a novel simple optimization metric based on relevant information gain, a probabilistic measure of the total information relevant to a query for a set of retrieved results. By optimizing this metric, diversity organically emerges from our system. When used as a drop-in replacement for the retrieval component of a RAG system, this method yields state-of-the-art performance on question answering tasks from the Retrieval Augmented Generation Benchmark (RGB), outperforming existing metrics that directly optimize for relevance and diversity.

Existing multi-camera solutions for automatic scorekeeping in steel-tip darts are very expensive and thus inaccessible to most players. Motivated to develop a more accessible low-cost solution, we present a new approach to keypoint detection and apply it to predict dart scores from a single image taken from any camera angle. This problem involves detecting multiple keypoints that may be of the same class and positioned in close proximity to one another. The widely adopted framework for regressing keypoints using heatmaps is not well-suited for this task. To address this issue, we instead propose to model keypoints as objects. We develop a deep convolutional neural network around this idea and use it to predict dart locations and dartboard calibration points within an overall pipeline for automatic dart scoring, which we call DeepDarts. Additionally, we propose several task-specific data augmentation strategies to improve the generalization of our method. As a proof of concept, two datasets comprising 16k images originating from two different dartboard setups were manually collected and annotated to evaluate the system. In the primary dataset containing 15k images captured from a face-on view of the dartboard using a smartphone, DeepDarts predicted the total score correctly in 94.7% of the test images. In a second more challenging dataset containing limited training data (830 images) and various camera angles, we utilize transfer learning and extensive data augmentation to achieve a test accuracy of 84.0%. Because DeepDarts relies only on single images, it has the potential to be deployed on edge devices, giving anyone with a smartphone access to an automatic dart scoring system for steel-tip darts. The code and datasets are available.