Large Language Models still encounter substantial challenges in reasoning tasks, especially for smaller models, which many users may be restricted to due to resource constraints (e.g. GPU memory restrictions). Inference-time methods to boost LLM performance, such as prompting methods to invoke certain reasoning pathways in responses, have been shown effective in past works, though they largely rely on sequential queries. The ensemble method, which consists of multiple constituent models running in parallel, is a promising approach to achieving better inference-time performance, especially given recent developments that enabled significant speed-ups in LLM batch inference. In this work, we propose a novel, training-free LLM ensemble framework where a single LLM model is fed an optimized, diverse set of prompts in parallel, effectively producing an ensemble at inference time to achieve performance improvement in reasoning tasks. We empirically demonstrate that our method leads to significant gains on math reasoning tasks, e.g., on MATH, where our ensemble consisting of a few small models (e.g., three Qwen2-MATH-1.5B-it models) can outperform a larger model (e.g., Qwen2-MATH-7B-it).

Despite recent advancements in Large Language Models (LLMs), their performance on tasks involving long contexts remains sub-optimal. In-Context Learning (ICL) with few-shot examples may be an appealing solution to enhance LLM performance in this scenario; However, naively adding ICL examples with long context introduces challenges, including substantial token overhead added for each few-shot example and context mismatch between the demonstrations and the target query. In this work, we propose to automatically generate few-shot examples for long context QA tasks by recycling contexts. Specifically, given a long input context (1-3k tokens) and a query, we generate additional query-output pairs from the given context as few-shot examples, while introducing the context only once. This ensures that the demonstrations are leveraging the same context as the target query while only adding a small number of tokens to the prompt. We further enhance each demonstration by instructing the model to explicitly identify the relevant paragraphs before the answer, which improves performance while providing fine-grained attribution to the answer source. We apply our method on multiple LLMs and obtain substantial improvements (+23\% on average across models) on various QA datasets with long context, especially when the answer lies within the middle of the context. Surprisingly, despite introducing only single-hop ICL examples, LLMs also successfully generalize to multi-hop long-context QA using our approach.

Conventional rule learning algorithms aim at finding a set of simple rules, where each rule covers as many examples as possible. In this paper, we argue that the rules found in this way may not be the optimal explanations for each of the examples they cover. Instead, we propose an efficient algorithm that aims at finding the best rule covering each training example in a greedy optimization consisting of one specialization and one generalization loop. These locally optimal rules are collected and then filtered for a final rule set, which is much larger than the sets learned by conventional rule learning algorithms. A new example is classified by selecting the best among the rules that cover this example. In our experiments on small to very large datasets, the approach's average classification accuracy is higher than that of state-of-the-art rule learning algorithms. Moreover, the algorithm is highly efficient and can inherently be processed in parallel without affecting the learned rule set and so the classification accuracy. We thus believe that it closes an important gap for large-scale classification rule induction.