Dense retrieval systems are commonly used for information retrieval (IR). They rely on learning text representations through an encoder and usually require supervised modeling via labelled data which can be costly to obtain or simply unavailable. In this study, we introduce a novel unsupervised text representation learning technique via instruction-tuning the pre-trained encoder-decoder large language models (LLM) under the dual-encoder retrieval framework. We demonstrate the corpus representation can be augmented by the representations of relevant synthetic queries generated by the instruct-tuned LLM founded on the Rao-Blackwell theorem. Furthermore, we effectively align the query and corpus text representation with self-instructed-tuning. Specifically, we first prompt an open-box pre-trained LLM to follow defined instructions (i.e. question generation and keyword summarization) to generate synthetic queries. Next, we fine-tune the pre-trained LLM with defined instructions and the generated queries that passed quality check. Finally, we generate synthetic queries with the instruction-tuned LLM for each corpora and represent each corpora by weighted averaging the synthetic queries and original corpora embeddings. We evaluate our proposed method under low-resource settings on three English and one German retrieval datasets measuring NDCG@10, MRR@100, Recall@100. We significantly improve the average zero-shot retrieval performance on all metrics, increasing open-box FLAN-T5 model variations by [3.34%, 3.50%] in absolute and exceeding three competitive dense retrievers (i.e. mDPR, T-Systems, mBART-Large), with model of size at least 38% smaller, by 1.96%, 4.62%, 9.52% absolute on NDCG@10.

The alignments of reasoning abilities between smaller and larger Language Models are largely conducted via Supervised Fine-Tuning (SFT) using demonstrations generated from robust Large Language Models (LLMs). Although these approaches deliver more performant models, they do not show sufficiently strong generalization ability as the training only relies on the provided demonstrations. In this paper, we propose the Self-refine Instruction-tuning method that elicits Smaller Language Models to self-refine their abilities. Our approach is based on a two-stage process, where reasoning abilities are first transferred between LLMs and Small Language Models (SLMs) via Instruction-tuning on demonstrations provided by LLMs, and then the instructed models Self-refine their abilities through preference optimization strategies. In particular, the second phase operates refinement heuristics based on the Direct Preference Optimization algorithm, where the SLMs are elicited to deliver a series of reasoning paths by automatically sampling the generated responses and providing rewards using ground truths from the LLMs. Results obtained on commonsense and math reasoning tasks show that this approach significantly outperforms Instruction-tuning in both in-domain and out-domain scenarios, aligning the reasoning abilities of Smaller and Larger Language Models.