A thinking budget bounds test-time compute with a number: the model may spend at most N tokens on its chain of thought before answering. Gemini 2.5 exposed this as thinkingBudget, Anthropic as budget_tokens, and Qwen3 as a thinking-budget setting; implementations treat it as a target or a hard stop depending on the provider.
Budgets were the second generation of reasoning controls, after binary thinking toggles and before behavioural effort levels. Both Anthropic and Google have since migrated their APIs from token budgets to categorical effort or thinking levels, keeping budget-style hard stops mainly as a backstop for runaway traces.