1 Understanding reasoning models

This chapter introduces reasoning as it is used in large language models: making intermediate steps explicit before giving an answer, often called chain-of-thought. It clarifies that, unlike deterministic symbolic systems, LLM “reasoning” is probabilistic next-token prediction that can look convincing without guaranteeing logical soundness. Framing the book’s goal, the author emphasizes a hands-on, code-first approach that starts from a pre-trained LLM and adds reasoning capabilities from scratch so practitioners can understand how these methods work in practice and where they help or fall short.

To ground the discussion, the chapter reviews the conventional LLM pipeline: massive pre-training for next-token prediction, followed by post-training via supervised instruction tuning and preference tuning (e.g., RLHF), with chat behavior layered on top. It then outlines three major routes to stronger reasoning: inference-time compute scaling (e.g., step-by-step prompting and sampling strategies that spend more compute at inference), reinforcement learning that updates weights using verifiable rewards for task success, and distillation that transfers reasoning behaviors from stronger models into smaller ones through high-quality supervision. These techniques are positioned as extensions to the standard pipeline that specifically target complex, multi-step tasks in coding, math, and logic.

The chapter contrasts pattern matching with logical reasoning using examples: LLMs often answer correctly by drawing on statistical associations (e.g., “Berlin” for a capital, or common corrections of “penguins can’t fly”) rather than explicit rule application, which works well in familiar contexts but can fail on novel or intricate problems. It argues for building reasoning systems from scratch to understand trade-offs, especially since reasoning models can be more verbose, costlier, and sometimes prone to overthinking—so they should be applied selectively where complexity warrants it. The roadmap ahead loads a capable base model, establishes evaluation to track gains, and then incrementally adds reasoning via inference techniques and targeted training, culminating in practical, testable improvements.

A simplified illustration of how a conventional, non-reasoning LLM might respond to a question with a short answer.

A simplified illustration of how a reasoning LLM might tackle a multi-step reasoning task using a chain-of-thought. Rather than just recalling a fact, the model combines several intermediate reasoning steps to arrive at the correct conclusion. The intermediate reasoning steps may or may not be shown to the user, depending on the implementation.

Overview of a typical LLM training pipeline. The process begins with an initial model initialized with random weights, followed by pre-training on large-scale text data to learn language patterns by predicting the next token. Post-training then refines the model through instruction fine-tuning and preference fine-tuning, which enables the LLM to follow human instructions better and align with human preferences.

Example responses from a language model at different training stages. The prompt asks for a summary of the relationship between sleep and health. The pre-trained LLM produces a relevant but unfocused answer without directly following the instructions. The instruction-tuned LLM generates a concise and accurate summary aligned with the prompt. The preference-tuned LLM further improves the response by using a friendly tone and engaging language, which makes the answer more relatable and user-centered.

Three approaches commonly used to improve reasoning capabilities in LLMs. These methods (inference-compute scaling, reinforcement learning, and distillation) are typically applied after the conventional training stages (initial model training, pre-training, and post-training with instruction and preference tuning), but reasoning techniques can also be applied to the pre-trained base model.

Illustration of how contradictory premises lead to a logical inconsistency. From "All birds can fly" and "A penguin is a bird," we infer "Penguin can fly." This conclusion conflicts with the established fact "Penguin cannot fly," which results in a contradiction.

An illustrative example of how a language model (GPT-4o in ChatGPT) appears to "reason" about a contradictory premise.

Token-by-token generation in an LLM. At each step, the LLM takes the full sequence generated so far and predicts the next token, which may represent a word, subword, or punctuation mark depending on the tokenizer. The newly generated token is appended to the sequence and used as input for the next step. This iterative decoding process is used in both standard language models and reasoning-focused models.

A mental model of the main reasoning model development stages covered in this book. We start with a conventional LLM as base model (stage 1). In stage 2, we cover evaluation strategies to track the reasoning improvements introduced via the reasoning methods in stages 3 and 4.

• Conventional LLM training occurs in several stages:
• Pre-training, where the model learns language patterns from vast amounts of text.
• Instruction fine-tuning, which improves the model's responses to user prompts.
• Preference tuning, which aligns model outputs with human preferences.
• Reasoning methods are applied on top of a conventional LLM.
• Reasoning in LLMs refers to improving a model so that it explicitly generates intermediate steps (chain-of-thought) before producing a final answer, which often increases accuracy on multi-step tasks.
• Reasoning in LLMs is different from rule-based reasoning and it also likely works differently than human reasoning; currently, the common consensus is that reasoning in LLMs relies on statistical pattern matching.
• Pattern matching in LLMs relies purely on statistical associations learned from data, which enables fluent text generation but lacks explicit logical inference.
• Improving reasoning in LLMs can be achieved through:
• Inference-time compute scaling, enhancing reasoning without retraining (e.g., chain-of-thought prompting).
• Reinforcement learning, training models explicitly with reward signals.
• Supervised fine-tuning and distillation, using examples from stronger reasoning models.
• Building reasoning models from scratch provides practical insights into LLM capabilities, limitations, and computational trade-offs.

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