Investigating a Production Scoring Bug: Softmax Normalization vs. Autoregressive Sequence Log-Probability
You are reviewing a production LLM feature that ranks two candidate continuations for the same user prompt x by computing a score for each full continuation y and choosing the higher-scoring one. The intended scoring rule is to choose , using the autoregressive decomposition . The model produces next-token logits at each step, which should be converted to probabilities with softmax over the full vocabulary.
A teammate implemented the scorer as follows: at each step i, they take the logit for the candidate’s next token and subtract , where is a small, request-specific shortlist of 50 tokens (not the full vocabulary). They then sum these per-token values across the continuation to get the sequence score.
In an A/B test, the system starts preferring verbose, low-quality continuations that repeat common tokens, even when the model’s raw logits for the “good” continuation look higher at several positions.
As the on-call ML engineer, analyze whether the teammate’s scoring method is mathematically consistent with maximizing under an autoregressive language model. In your answer, explain (1) how softmax normalization affects the conditional next-token probability , (2) why using a changing shortlist can distort the summed log-likelihood comparison between two full sequences, and (3) what concrete change you would make to the scoring computation to correctly rank candidates by .
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Ch.2 Generative Models - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
Ch.1 Pre-training - Foundations of Large Language Models
Ch.5 Inference - Foundations of Large Language Models
Data Science
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