Parallel Test-Time Compute

A reasoning model (also: large reasoning model, LRM, reasoning language model, RLM) is a type of large language model that has been specifically post-trained to solve complex multi-step problems by explicitly generating intermediate reasoning steps before committing to a final response. Unlike standard LLMs that generate a direct response in a single forward pass, reasoning models allocate additional computation at inference time — a property known as test-time compute scaling — by producing a long internal chain of thought (CoT). The reasoning trace typically includes steps such as problem decomposition, hypothesis generation, self-verification, reflection, and correction of errors. The defining characteristics of reasoning models are: (1) post-training via large-scale reinforcement learning (RL) using reward signals based on final answer correctness (and sometimes intermediate step quality via process reward models); (2) the emergence of extended, often hidden, reasoning traces that precede the final answer; (3) a consistent empirical relationship between the length or computational budget allocated to the reasoning trace and final answer quality (test-time scaling law); (4) superior performance on verifiable tasks requiring multi-step logic, such as mathematics, competitive programming, and scientific reasoning. The term 'reasoning model' was introduced as a product category by OpenAI in September 2024 with the release of the o1-preview model. OpenAI described o1 as trained via a large-scale RL algorithm teaching the model to use chain of thought productively. The approach does not rely on explicit tree search algorithms; instead, implicit search emerges via RL-trained CoT generation. In January 2025, DeepSeek published the first detailed open technical description of this class of models in the DeepSeek-R1 paper (arXiv:2501.12948), demonstrating that reasoning capabilities can be incentivized via pure RL without supervised fine-tuning, using Group Relative Policy Optimization (GRPO) as the RL framework. Reasoning models typically employ the same base Transformer decoder architecture as standard LLMs, with the key difference residing entirely in the post-training pipeline: RL replaces or augments standard RLHF/SFT, and reward signals are grounded in verifiable outcomes. The resulting models generate substantially longer token sequences during inference (reasoning tokens), which are often hidden from end users but incur real compute costs. Performance consistently improves with both more training-time RL compute and more inference-time thinking budget.

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.

Reinforcement Learning from Human Feedback (RLHF) is a multi-stage training pipeline used to align language models and other AI systems with human preferences and intent. The approach was formally introduced for deep RL in Christiano et al. (2017), and scaled to large language models in Ouyang et al. (2022) (InstructGPT), where it became the primary alignment technique for systems such as ChatGPT, Claude, and Gemini. The standard RLHF pipeline for LLMs consists of three sequential stages: 1. Supervised Fine-Tuning (SFT): A pretrained language model is fine-tuned on a curated dataset of high-quality (prompt, response) pairs produced by human annotators, yielding a base aligned policy π_SFT. 2. Reward Model Training: Human annotators compare pairs of model responses to the same prompt and express preferences (which response is better). These pairwise comparisons are used to train a scalar reward model r_φ(x, y), typically using a Bradley-Terry model as the preference objective: loss = -E[log σ(r(x, y_w) - r(x, y_l))], where y_w is the preferred and y_l the rejected response. 3. RL Fine-Tuning via PPO: The SFT-initialized policy π_θ is optimized with Proximal Policy Optimization (PPO) to maximize the reward from r_φ, subject to a KL divergence penalty that prevents the policy from drifting too far from π_SFT: Objective(x, y) = r_φ(x, y) − β · KL(π_θ(y|x) || π_SFT(y|x)). The KL penalty with coefficient β is critical to prevent reward hacking. During PPO training, four models are needed simultaneously: the active policy, a frozen reference policy (π_SFT), the reward model, and a value/critic network. This makes RLHF computationally expensive, requiring substantial GPU memory. A key limitation is reward hacking: since the reward model is a proxy for human preferences trained on finite data, the policy can find ways to exploit its imperfections — generating outputs that score highly on the reward model but are degenerate or low-quality. The KL penalty is the primary mitigation mechanism. Direct Preference Optimization (DPO, Rafailov et al., 2023) was proposed as a mathematically equivalent simplification of RLHF that eliminates the explicit reward model and RL training loop, replacing them with a single supervised loss directly on preference pairs.