Reasoning Models Explained: From Chain-of-Thought to o3 — How do openai o3 thinking llms work

The Evolution of AI Reasoning

The journey from basic language model outputs to genuine multi-step reasoning represents one of the most significant advances in AI. Understanding this evolution — from simple chain-of-thought prompting to dedicated reasoning models like o3 and DeepSeek R1 — is essential for any developer working with LLMs.

Level 1: Chain-of-Thought Prompting (2022)

The story begins with Google's chain-of-thought (CoT) paper in January 2022. The insight was deceptively simple: if you ask a model to "think step by step," it performs dramatically better on reasoning tasks.

# Without CoT
Q: If a store has 42 apples and sells 3/7 of them, how many remain?
A: 18  ← WRONG

# With CoT
Q: If a store has 42 apples and sells 3/7 of them, how many remain?
A: Let me think step by step.
   3/7 of 42 = 42 × 3/7 = 126/7 = 18 apples sold
   42 - 18 = 24 apples remain
A: 24  ← CORRECT

Why it works: By generating intermediate steps, the model creates a "scratchpad" that keeps partial results in context. Without CoT, the model must compute multi-step answers in a single forward pass through its weights — effectively doing mental arithmetic without paper.

Limitation: The model does not actually reason differently. It generates text that looks like reasoning, and this text happens to improve accuracy by keeping intermediate results in the context window.

Level 2: Self-Consistency and Verification (2023)

Researchers improved on basic CoT with techniques that generate multiple reasoning chains and select the best:

• Self-Consistency: Generate N different reasoning chains for the same problem, then take the majority vote on the final answer
• Tree of Thought: Explore multiple reasoning paths as a tree, evaluating and pruning branches
• Self-Verification: After generating an answer, ask the model to verify its own reasoning and correct errors

These techniques improved accuracy but multiplied inference costs linearly with the number of generated chains.

Level 3: Trained Reasoning — o1 and o3 (2024-2025)

OpenAI's o1 (September 2024) and o3 (December 2025) represented a paradigm shift: instead of prompting a general model to reason, these are models trained specifically to reason.

flowchart TD
    HUB(("The Evolution of AI<br/>Reasoning"))
    HUB --> L0["Level 1: Chain-of-Thought<br/>Prompting (2022)"]
    style L0 fill:#e0e7ff,stroke:#6366f1,color:#1e293b
    HUB --> L1["Level 2: Self-Consistency<br/>and Verification (2023)"]
    style L1 fill:#e0e7ff,stroke:#6366f1,color:#1e293b
    HUB --> L2["Level 3: Trained Reasoning —<br/>o1 and o3 (2024-2025)"]
    style L2 fill:#e0e7ff,stroke:#6366f1,color:#1e293b
    HUB --> L3["Level 4: Open Reasoning<br/>Models — DeepSeek R1 (2025)"]
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    HUB --> L4["How Reasoning Models Differ<br/>Technically"]
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    HUB --> L5["When to Use Reasoning Models"]
    style L5 fill:#e0e7ff,stroke:#6366f1,color:#1e293b
    HUB --> L6["The Inference-Time Compute<br/>Revolution"]
    style L6 fill:#e0e7ff,stroke:#6366f1,color:#1e293b
    style HUB fill:#4f46e5,stroke:#4338ca,color:#fff

Key differences from prompted CoT:

Internal chain of thought: o1/o3 generate hidden reasoning tokens that are not shown to the user. The model "thinks" in an internal monologue before producing a response.

Reinforcement learning from reasoning: These models are trained using reinforcement learning (RL) where the reward signal is based on reaching correct answers through valid reasoning chains. The model learns which reasoning strategies work and which fail.

Compute allocation: The model dynamically allocates more "thinking" tokens to harder problems. A simple factual question might use 50 internal tokens; a complex math proof might use 10,000+.

Deliberative alignment: The model actively reasons about safety policies and constraints within its chain of thought, rather than relying solely on RLHF-trained instincts.

Level 4: Open Reasoning Models — DeepSeek R1 (2025)

DeepSeek R1, released in January 2025, demonstrated that reasoning capabilities could be achieved through a surprisingly elegant training process:

1. Cold start: Basic supervised fine-tuning on a small set of reasoning examples
2. Pure RL training: Large-scale reinforcement learning where the model is rewarded only for correct final answers — no human-written reasoning chains required
3. Emergent behaviors: The model spontaneously developed reasoning strategies including self-verification, backtracking, and multi-approach problem-solving

The remarkable finding: reasoning capability emerged from RL training alone, without requiring explicit reasoning demonstrations.

# DeepSeek R1's emergent reasoning pattern
<think>
Let me approach this problem step by step.
First, I will try direct calculation...
Wait, that gives 17, which seems wrong because...
Let me try a different approach using modular arithmetic...
Yes, this confirms the answer is 23.
</think>

The answer is 23.

How Reasoning Models Differ Technically

Aspect	Standard LLM	CoT Prompting	o3 / R1
Reasoning method	Implicit (single pass)	Explicit (prompted)	Trained (RL-optimized)
Token overhead	None	2-5x	5-100x
Training cost	Standard	None (prompt-only)	Significant RL training
Reasoning quality	Low on hard problems	Medium	High
Consistency	Variable	Improved with SC	Strong
Self-correction	Rare	Occasional	Systematic

When to Use Reasoning Models

Use reasoning models (o3, R1) for:

• Mathematical proofs and competition-level problems
• Complex code generation requiring architectural planning
• Multi-step logical reasoning with constraints
• Scientific analysis requiring hypothesis evaluation
• Tasks where accuracy matters more than speed or cost

Use standard models with CoT for:

• Most production applications where reasoning complexity is moderate
• Latency-sensitive applications
• High-volume workloads where reasoning model costs are prohibitive
• Tasks where approximate reasoning is sufficient

The Inference-Time Compute Revolution

The core insight behind reasoning models is a new scaling axis: inference-time compute. Traditional scaling focused on training — more data, more parameters, more GPU-hours during training. Reasoning models scale at inference time — more thinking per query, dynamically allocated based on problem difficulty.

This has profound implications for AI system design. Rather than deploying the largest model for every query, systems can route simple questions to fast, cheap models and reserve reasoning models for genuinely hard problems. The cost per token matters less when the model uses 10x more tokens but gets the answer right the first time instead of requiring multiple retries.

---

Sources: OpenAI — Learning to Reason with LLMs, DeepSeek — DeepSeek R1 Technical Report, Google Research — Chain-of-Thought Prompting

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        EMB["Embed"]
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        ATTN["Self attention layers"]
        MLP["Feed forward layers"]
    end
    subgraph POST["Post processing"]
        SAMP["Sampling"]
        DETOK["Detokenize"]
    end
    OUT(["Generated text"])
    IN --> TOK --> EMB --> ATTN --> MLP --> SAMP --> DETOK --> OUT
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    style CORE fill:#ede9fe,stroke:#7c3aed,color:#1e1b4b
    style OUT fill:#059669,stroke:#047857,color:#fff

flowchart TD
    HUB(("The Evolution of AI<br/>Reasoning"))
    HUB --> L0["Level 1: Chain-of-Thought<br/>Prompting (2022)"]
    style L0 fill:#e0e7ff,stroke:#6366f1,color:#1e293b
    HUB --> L1["Level 2: Self-Consistency<br/>and Verification (2023)"]
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    HUB --> L2["Level 3: Trained Reasoning —<br/>o1 and o3 (2024-2025)"]
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    HUB --> L3["Level 4: Open Reasoning<br/>Models — DeepSeek R1 (2025)"]
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    HUB --> L4["How Reasoning Models Differ<br/>Technically"]
    style L4 fill:#e0e7ff,stroke:#6366f1,color:#1e293b
    HUB --> L5["When to Use Reasoning Models"]
    style L5 fill:#e0e7ff,stroke:#6366f1,color:#1e293b
    HUB --> L6["The Inference-Time Compute<br/>Revolution"]
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    style HUB fill:#4f46e5,stroke:#4338ca,color:#fff

Background and Key Concepts: How do openai o3 thinking llms work

This guide is written for engineers and operators evaluating how do openai o3 thinking llms work in real production systems. How do openai o3 thinking llms work sits alongside additional post, math problem, model openai, o3 model in the daily work of teams shipping production AI. The notes below give a plain-language reference for terms used throughout the article.

• additional post — referenced in this guide when discussing how do openai o3 thinking llms work.
• math problem — referenced in this guide when discussing how do openai o3 thinking llms work.
• model openai — referenced in this guide when discussing how do openai o3 thinking llms work.
• o3 model — referenced in this guide when discussing how do openai o3 thinking llms work.

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