Reasoning Models

Fast Thinking vs Slow Thinking

Nobel laureate Daniel Kahneman introduced the famous dual-system theory in Thinking, Fast and Slow: human cognition operates through System 1 (fast, intuitive) and System 2 (slow, deliberate). This analogy perfectly explains the difference between standard LLMs and reasoning models.

System 1 (Standard LLM): Sees a question and immediately outputs an answer. It relies on pattern matching -- having seen countless similar problems during training, it can "blurt out" a response. Ask "What's 2+2?" and it instantly says "4".

System 2 (Reasoning Model): "Thinks" before answering. It generates a chain of thinking tokens, breaking complex problems into small steps and reasoning through each one. Faced with "Prove the Pythagorean theorem," it writes out the proof step by step.

Chain-of-Thought — The Magic of Showing Your Work

In 2022, Google researchers discovered something remarkable: simply adding "Let's think step by step" to a prompt dramatically improved LLM accuracy on math and logic tasks. This technique is called Chain-of-Thought (CoT) prompting.

Without CoT, the model jumps straight to an answer -- and often gets it wrong:

Q: 17 x 24 = ?  A: __(often incorrect)

With CoT, the model "shows its work," and accuracy improves significantly:

Q: 17 x 24 = ? Let me think: 17x20=340, 17x4=68, 340+68=408 ✓

Taking this further, models like o1, R1, and QwQ are trained to automatically generate chain-of-thought. They produce hundreds or even thousands of thinking tokens before giving a final answer -- this is known as Extended Thinking.

o1, R1, QwQ — The Reasoning Model Race

Starting in 2024, major AI labs began releasing dedicated reasoning models, sparking an entirely new competition:

OpenAI o1/o3: Pioneered "test-time compute scaling" -- the model invests more computation during inference, and the longer it thinks, the better its answers. o1 achieved stunning results on math competitions and coding tasks.

DeepSeek R1: An open-source reasoning model distilled from a 671B Mixture-of-Experts (MoE) model down to sizes ranging from 1.5B to 70B. It proved that small models can possess powerful reasoning abilities.

Qwen QwQ: Alibaba's reasoning model, demonstrating strong reasoning performance across multilingual benchmarks.

The core insight shared by all these models: learn to allocate more compute to harder problems.

Test-Time Compute — More Thinking, Better Answers

The traditional path to smarter AI is training-time compute: more data, bigger models, longer training. OpenAI's Scaling Laws formalize this approach.

But reasoning models open a second path: test-time compute. The same model, when faced with harder problems, thinks longer -- generating more thinking tokens -- and achieves higher accuracy.

This introduces an important trade-off: reasoning models are slower and consume more tokens (thinking tokens cost money too). But for complex tasks, the accuracy improvement far outweighs the extra cost. The key caveat: diminishing returns -- thinking too long yields progressively smaller gains.

Summary