How to interact with LLMs through \emph{instructions} has been widely studied by researchers. However, previous studies have treated the emergence of instructions and the training of LLMs on task data as separate processes, overlooking the inherent unity between the two. This paper proposes a neural network framework, VaiBot, that integrates VAE and VIB, designed to uniformly model, learn, and infer both deduction and induction tasks under LLMs. Through experiments, we demonstrate that VaiBot performs on par with existing baseline methods in terms of deductive capabilities while significantly surpassing them in inductive capabilities. We also find that VaiBot can scale up using general instruction-following data and exhibits excellent one-shot induction abilities. We finally synergistically integrate the deductive and inductive processes of VaiBot. Through T-SNE dimensionality reduction, we observe that its inductive-deductive process significantly improves the distribution of training parameters, enabling it to outperform baseline methods in inductive reasoning tasks. The code and data for this paper can be found at https://anonymous.4open.science/r/VaiBot-021F.

Although Large Language Models (LLMs) are showing impressive performance on a wide range of Natural Language Processing tasks, researchers have found that they still have limited ability to conduct induction. Recent works mainly adopt ``post processes'' paradigms to improve the performance of LLMs on induction (e.g., the hypothesis search & refinement methods), but their performance is still constrained by the inherent inductive capability of the LLMs. In this paper, we propose a novel framework, Induction through Deduction (ItD), to enable the LLMs to teach themselves induction through deduction. The ItD framework is composed of two main components: a Deductive Data Generation module to generate induction data and a Naive Bayesian Induction module to optimize the fine-tuning and decoding of LLMs. Our empirical results showcase the effectiveness of ItD on two induction benchmarks, achieving relative performance improvement of 36% and 10% compared with previous state-of-the-art, respectively. Our ablation study verifies the effectiveness of two key modules of ItD. We also verify the effectiveness of ItD across different LLMs and deductors. The data and code of this paper can be found at https://anonymous.4open.science/r/ItD-E844.

Black-box Large Language Models (LLMs) have shown great power in solving various tasks and are considered general problem solvers. However, LLMs still fail in many specific tasks although understand the task instruction. In this paper, we focus on the problem of boosting the ability of black-box LLMs to solve downstream tasks. We propose ExpNote, an automated framework to help LLMs better adapt to unfamiliar tasks through reflecting and noting experiences from training data and retrieving them from external memory during testing. We evaluate ExpNote on multiple tasks and the experimental results demonstrate that the proposed method significantly improves the performance of black-box LLMs. The data and code are available at https://github.com/forangel2014/ExpNote