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Basic Theory

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🌱 Level 1 β€” Beginner

Reasoning

AI reasoning capabilities - chain of thought, thinking models, and logical inference.

Reasoning is one of the most important and rapidly evolving capabilities of modern AI. While early LLMs could generate fluent text, they often struggled with multi-step logic, math, and complex problem-solving. The introduction of chain-of-thought prompting and dedicated reasoning models has dramatically improved these capabilities.

Models like OpenAI o1/o3, DeepSeek-R1, and QwQ use "thinking tokens" β€” they reason step-by-step internally before producing a final answer. This mirrors the human distinction between fast intuitive thinking (System 1) and slow deliberate reasoning (System 2). Understanding these capabilities and their limits is crucial for knowing when to trust AI outputs.

Key Topics Covered
Chain-of-Thought (CoT) Prompting
Asking models to "think step by step" dramatically improves accuracy on complex problems. Instead of jumping to answers, the model shows its work β€” breaking problems into manageable steps.
Reasoning Models
OpenAI o1/o3, DeepSeek-R1, QwQ (Alibaba) are specifically trained for multi-step reasoning. They use extra inference-time compute to "think longer" before answering.
Thinking Tokens
Internal reasoning traces generated before the final answer. These tokens are the model's "scratch pad" β€” working through logic, checking steps, considering alternatives.
Extended Thinking
Allocating more compute at inference time for harder problems. The model can "think longer" on complex questions, trading speed for accuracy. Test-time compute scaling.
Math Reasoning
Solving competition-level math (AIME, AMC), formal proofs, symbolic manipulation. Reasoning models have made dramatic progress here β€” approaching human expert level.
Code Reasoning
Debugging complex codebases, analyzing architecture, implementing sophisticated algorithms. Code reasoning is one of the most practically valuable AI capabilities.
Logical Inference
Syllogisms, deduction, constraint satisfaction, planning. Models can follow logical rules but still struggle with certain types of novel reasoning and common-sense physics.
System 1 vs System 2 Thinking
Kahneman's framework applied to AI: System 1 = fast intuitive responses (standard LLM), System 2 = slow deliberate reasoning (reasoning models with thinking tokens).
Current Limitations
Reasoning models still fail on truly novel problems, can produce convincing but wrong chains of reasoning, and may overthink simple questions. Verification remains essential.
Reasoning Benchmarks
MATH (competition math), GSM8K (grade school), ARC-AGI (general reasoning), SWE-bench (real software engineering), Codeforces (competitive programming).
Key Terms
Chain-of-ThoughtTechnique where models explain their reasoning step-by-step before giving an answer.
Thinking TokensInternal reasoning traces generated by reasoning models before the final output.
System 1/System 2Kahneman's framework: fast intuitive vs slow deliberate thinking, applied to AI.
Test-Time ComputeAllocating more processing at inference time to improve reasoning on harder problems.
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