Glossary/Reasoning Models (o1, o3, R1)

Definition

Reasoning models are large language models trained to spend extra computation 'thinking' before producing a final answer, by generating a long internal chain of reasoning. OpenAI's o1 (late 2024) and o3 made this mainstream; DeepSeek R1 (January 2025) matched o1 as an open model and published its training recipe. The approach trades latency and cost for far higher accuracy on problems with verifiable answers — competition math, scientific reasoning, and complex coding. By mid-2026 this capability is built into the flagship models themselves (GPT-5.5, Claude with adaptive thinking, Gemini Deep Think) rather than living in a separate product.

What makes a reasoning model different: test-time compute

A standard model produces its answer in essentially one pass — it is fast but commits early. A reasoning model first writes out a long hidden chain of thought, exploring steps, checking intermediate results, and backtracking, before composing the answer you see. This is called scaling test-time (or inference-time) compute: rather than only making the model bigger, you let it think longer on hard problems. The result is a different cost profile — more tokens and more latency per query, in exchange for markedly better accuracy where careful, multi-step logic matters.

  • Standard model — one fast pass; great for chat, drafting, summarization, and routine code
  • Reasoning model — long internal chain of thought; great for math proofs, hard debugging, and analysis
  • The tradeoff is concrete: reasoning answers cost more tokens and take longer to return

How reasoning models are trained: RL on verifiable rewards

The breakthrough was reinforcement learning on problems where the answer can be checked automatically — a math result is right or wrong, code passes tests or it does not. The model is rewarded for reaching correct final answers, and it learns on its own to produce longer, more careful reasoning because that reasoning leads to higher reward. DeepSeek's R1 made one method, GRPO (Group Relative Policy Optimization), widely known by training the model on groups of sampled answers and reinforcing the better ones relative to the group average.

  • Outcome rewards — score only the final answer's correctness; simple and scalable
  • Process rewards — score individual reasoning steps; more guidance but harder to build
  • Verifiable domains (math, code) are ideal because correctness is automatic and cheap to check
  • A striking finding: with enough RL, models develop self-correction and 'wait, let me reconsider' behavior on their own

The lineage: o1 to unified reasoning

ModelReleasedNotable for
OpenAI o1-previewSept 12, 2024The founding release: 83% on IMO-qualifier math vs GPT-4o's 13%; published the test-time-compute scaling curves
OpenAI o1 (full) + o1-proDec 5, 2024GPQA Diamond 78.3%, Codeforces 89th percentile; launched alongside ChatGPT Pro
OpenAI o3 (announced)Dec 20, 2024ARC-AGI 87.5% (high compute) vs o1's ~29%; FrontierMath 25.2% when prior SOTA was ~2%; Codeforces Elo 2727
DeepSeek R1Jan 20, 2025Open MIT-licensed model matching o1 (AIME 79.8%, MATH-500 97.3%); published the GRPO training recipe
o3 (full) + o4-miniApr 16, 2025SWE-bench Verified 69.1%; multimodal reasoning ("thinking with images")
GPT-5Aug 7, 2025Reasoning folded into the base model with an automatic router; o-series retired from ChatGPT
GPT-5.2Dec 11, 2025First model past 90% on ARC-AGI-1; ARC-AGI-2 54.2%; AIME 2025 saturated at 100%
GPT-5.5 / 5.6Apr / Jul 2026Current line: adaptive reasoning effort from "none" to "max", natively multimodal

Where the line is now (mid-2026)

The separate 'reasoning model' is fading as a product category. GPT-5.x routes between instant and thinking modes automatically; Claude uses adaptive thinking that scales depth to the task; Gemini offers Deep Think; DeepSeek's V4 builds thinking directly into tool use. You increasingly get reasoning on demand from one model rather than choosing a distinct o-series model — the o-series brand itself is scheduled to fully retire from ChatGPT in August 2026.

Milestones that defined the reasoning era

  • Sept 2024 — the scaling law of thinking: OpenAI's o1 announcement showed accuracy climbing smoothly with both more RL training and more test-time thinking — the founding result of the whole category.
  • Dec 2024 — ARC-AGI falls: o3 hit 87.5% on ARC-AGI-1 (human threshold ~85%), a benchmark expressly designed to resist memorization; a year later GPT-5.2 crossed 90% and reached ~54% on the much harder ARC-AGI-2.
  • Jan 2025 — the recipe goes public: DeepSeek R1's paper showed pure RL on verifiable rewards (R1-Zero) spontaneously producing self-checking, backtracking, and 'wait, let me reconsider' behavior — and its $294K RL-stage cost (disclosed in its peer-reviewed Nature paper, Sept 2025) demonstrated reasoning training is cheap relative to pre-training.
  • Jul 19, 2025 — IMO gold: an experimental OpenAI reasoning model and Google DeepMind's Gemini Deep Think each solved 5 of 6 International Mathematical Olympiad problems under contest conditions — no tools, no internet, graded by former IMO medalists. DeepSeek's open V3.2-Speciale reached the same gold-medal level by December 2025.
  • 2026 — saturation and dials: with AIME at 100% and FrontierMath the new yardstick, the frontier shifted from raw scores to efficiency: API reasoning-effort settings now run from 'none' to 'max', letting developers buy exactly as much thinking as a task needs.

What reasoning models still get wrong

More thinking is not free accuracy. Reasoning models can overthink simple questions (spending thousands of tokens to answer a lookup), their visible reasoning can rationalize an answer reached for other reasons — so a plausible-looking chain of thought is not proof of a sound process — and on tasks without verifiable answers (strategy, taste, open-ended writing) the RL-on-correctness recipe has far less grip. Match the tool to the task.

When to use a reasoning model vs a standard model

  • Use reasoning for: competition-level math, multi-step logic, hard debugging, scientific analysis, and planning that must be correct
  • Use a standard pass for: chat, drafting, summarization, classification, and routine code, where speed and cost matter more
  • Watch the budget — reasoning can use many times more tokens per answer, so reserve it for problems that actually need it
  • On modern flagships you often do not choose explicitly; you ask for harder reasoning and the model allocates more thinking itself

Benchmarks: how reasoning models score

ModelAIME 2024GPQA DiamondMATH-500 / ARC-AGI
OpenAI o1~78%~76%~96% MATH-500
OpenAI o3~96.7%~87.7%~87.5% ARC-AGI (low-compute)
DeepSeek R179.8%71.5%97.3% MATH-500

Why these benchmarks

AIME (competition math), GPQA Diamond (PhD-level science), MATH-500, and ARC-AGI (novel visual reasoning) reward careful multi-step thinking, which is exactly what reasoning models are built for — and where they pull far ahead of standard models. Scores are reported figures and vary by configuration and compute budget.

Frequently asked questions

Are reasoning models worth the extra cost? For genuinely hard, verifiable problems — competition math, complex debugging, scientific analysis — yes; the accuracy gain is large. For chat, drafting, and routine code, a standard pass is faster and far cheaper.

Is DeepSeek R1 as good as o1? On math and reasoning benchmarks it is close — R1 matched o1 on AIME 2024 and MATH-500 — and it is open-source under MIT at a fraction of the cost. OpenAI's o3 then pushed the frontier higher again.

Do I still need a separate reasoning model? Increasingly no. Flagship models now build reasoning in: GPT-5.5 routes between instant and thinking modes automatically, Claude uses adaptive thinking, and Gemini offers Deep Think.

What is test-time compute? Letting a model spend more computation thinking at inference time — generating a long internal chain of reasoning before answering — rather than only making the model larger. It is the core idea behind reasoning models.

On LumiChats

LumiChats lets you switch between fast standard models and deeper reasoning models in one place, so you can match the thinking budget to the difficulty of each task.

Try it free

✦ Under $1 / day

Practice what you just learned

Quiz Hub + Study Mode lock in every concept. 40+ AI models, Agent Mode, page-locked answers — all for less than a dollar a day.

Start Free — Under $1/day

Related Terms

5 terms