Conditional Probability & Why Temperature Exists
~15 min read
The conditional-probability foundation of next-token prediction, and why sampling (not always picking the highest-probability token) is necessary for useful, non-repetitive LLM output.
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Key points
- •Conditional probability P(A|B) is 'the probability of A given B has occurred' — e.g., P(rain | cloudy)
- •Next-token prediction is exactly this: P(next_token | previous_tokens)
- •Always picking the single highest-probability token (greedy) leads to repetitive, low-creativity output
- •Temperature reshapes the softmax distribution before sampling: low temperature → nearly greedy; high temperature → more uniform/random
- •This conditional-probability framing is the conceptual foundation for the full sampling pipeline (temperature, top-k, top-p, min-p) covered elsewhere in this topic