Prompt Engineering

Chain-of-Thought (CoT) Reasoning is a prompting technique introduced by Wei et al. (2022) in which a large language model is induced to generate a series of intermediate natural-language reasoning steps as part of its output, prior to producing a final answer. The technique was shown to significantly improve LLM performance on arithmetic, commonsense, and symbolic reasoning benchmarks where standard few-shot prompting yields flat or poor results. In the original formulation (few-shot CoT), a small number of exemplar question-answer pairs are included in the prompt, where each answer consists of a chain of thought followed by the final answer. The model learns from these demonstrations to produce its own reasoning chains. A subsequent zero-shot variant (Kojima et al., 2022) showed that appending the phrase 'Let's think step by step' to a question is sufficient to elicit reasoning chains from large models without any exemplars. CoT is an emergent property: empirical results in the originating paper show that reasoning ability via CoT prompting appears only in models above a certain parameter threshold (approximately 100B parameters for the models tested in 2022), with smaller models not benefiting or performing worse. This relationship has been revisited by subsequent work as smaller models have been fine-tuned on CoT data. Key extensions include Self-Consistency CoT (Wang et al., 2022), which samples multiple reasoning paths and selects the most frequent final answer; Tree of Thoughts (Yao et al., 2023), which frames reasoning as search over a tree of intermediate thoughts; and native reasoning models such as OpenAI o1 (2024) and DeepSeek-R1 (2025), which internalize extended reasoning through reinforcement learning on process reward signals rather than relying on prompting.

Retrieval-Augmented Generation (RAG) was introduced by Lewis et al. (2020) as a general-purpose fine-tuning recipe combining pre-trained parametric memory (a seq2seq language model, specifically BART in the original paper) with non-parametric memory (a dense vector index of Wikipedia, accessed via Dense Passage Retrieval, DPR). In the original formulation, both the retriever and the generator are fine-tuned end-to-end: given an input query x, the retriever retrieves top-k documents z from the corpus, and the generator produces an output y conditioned on x and z. Two formulations were proposed: RAG-Sequence (the same retrieved documents condition the full output sequence) and RAG-Token (different documents may be used per generated token, marginalized during generation). In widespread contemporary usage (post-2022, with the growth of LLM applications), 'RAG' has expanded to describe a broader class of retrieve-then-generate pipelines, typically with a frozen LLM, a vector store containing pre-computed dense embeddings of document chunks, and a retrieval step that fetches top-k relevant chunks based on embedding similarity to the query. The retrieved chunks are appended to the prompt as context before the LLM generates a response. This non-trainable pipeline variant is technically distinct from the original Lewis et al. formulation but is the dominant practical interpretation of RAG as of 2023–2025. The canonical modern RAG pipeline consists of an offline indexing phase (document chunking, embedding computation, storage in a vector database) and an online query phase (query embedding, approximate nearest neighbor search, context-augmented generation). Key design decisions include: chunk size and overlap, embedding model choice, retrieval strategy (dense, sparse/BM25, or hybrid), number of retrieved documents k, and context integration method (prepend to prompt, cross-attention injection, or fusion-in-decoder). RAG addresses two fundamental limitations of parametric-only LLMs: the knowledge cutoff problem (inability to access post-training information) and hallucination (generation of factually incorrect content). However, RAG introduces its own failure modes, including retrieval of irrelevant or misleading context and the LLM's susceptibility to being distracted by retrieved content that contradicts its parametric knowledge.