Log Probabilities

What Log Probabilities Represent in Model Output

Log probabilities express a model’s token or output probabilities on a logarithmic scale, which preserves ordering while compressing tiny values into a range that is easier to compare, aggregate, and inspect during generation.

Because raw probabilities for longer sequences quickly become extremely small, log space avoids numerical underflow and lets practitioners reason about preference strength without losing precision. That is why log probabilities are a core part of decoding and ranking pipelines rather than a cosmetic transformation.

Why Log Probabilities Matter for Decoding and Ranking

During decoding, the model often evaluates multiple candidate tokens, phrases, or completions. Log probabilities make it practical to compare those candidates and choose the most likely continuation, especially when beam search, reranking, or sampling strategies need to accumulate many steps of uncertainty.

They are also useful because probability multiplication becomes addition in log space. This makes sequence scoring more stable and more computationally tractable when a system must combine many token-level estimates into a single score for an entire output.

How Log Probabilities Support Confidence Analysis

Log probabilities help reveal how strongly a model prefers one option over another. A small difference can indicate close competition between outputs, while a larger gap can show a clearer preference. That makes them useful for comparing alternatives, spotting ambiguous generations, and building downstream confidence heuristics.

They should still be treated as model scores, not as calibrated truth. A high log probability means the model found a candidate likely under its internal distribution, but that does not guarantee factual correctness, task success, or safe behavior.

Limits, Interpretation, and Practical Use

Log probabilities are best interpreted relative to the decoding setup, model architecture, and tokenization scheme in use. Different tokenizations can change how scores distribute across outputs, so comparisons are most reliable when candidates are evaluated under the same conditions.

In practice, they are most valuable when paired with other signals such as task constraints, external verification, or human review. Used that way, log probabilities become a diagnostic and ranking tool, not a standalone measure of answer quality.

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