In 2025, Reinforcement Learning from Verifiable Rewards (RLVR) emerged as the de facto new major stage to add to this mix. By training LLMs against automatically verifiable rewards across a number of environments (e.g. think math/code puzzles), the LLMs spontaneously develop strategies that look like "reasoning" to humans - they learn to break down problem solving into intermediate calculations and they learn a number of problem solving strategies for going back and forth to figure things out (see DeepSeek R1 paper for examples).

— Andrej Karpathy, 2025 LLM Year in Review

Tags: andrej-karpathy, llm, generative-ai, llm-reasoning, definitions, ai, llms, deepseek