Conditional Probability in Sequence-to-Sequence Generation

Next-Token Probability Calculation in Autoregressive Decoders

Example of Autoregressive Generation and Log-Probability Calculation

An auto-regressive language model is generating text following the input 'The cat sat on the'. The model's objective is to find the output sequence with the highest total log-probability. It is considering two possible two-word continuations:

Path A: 'warm mat'

• log Pr('warm' | 'The cat sat on the') = -0.9
• log Pr('mat' | 'The cat sat on the warm') = -1.5

Path B: 'plush rug'

• log Pr('plush' | 'The cat sat on the') = -1.2
• log Pr('rug' | 'The cat sat on the plush') = -1.1

Based on the provided conditional log-probabilities, which path will the model choose and why?

Debugging a Generation Model's Choice

Greedy Decoding vs. Optimal Sequence Probability

Reconciling Training Log-Likelihood with Inference-Time Sequence Selection

Diagnosing a “High-Confidence Wrong Token” Bug in Autoregressive Scoring

Explaining a Counterintuitive Decoding Outcome Using Softmax, Next-Token Conditionals, and Sequence Log-Probability

Auditing a Candidate Completion Using Softmax Next-Token Probabilities and Autoregressive Log-Probability

Investigating a Production Scoring Bug: Softmax Normalization vs. Autoregressive Sequence Log-Probability

Root-Cause Analysis: Why a “More Likely” Token-by-Token Completion Loses on Total Sequence Score

Design a Correct Sequence-Scoring Function for Autoregressive LLM Outputs

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Direct Computation of Output Sequence Log-Probability in LLMs

Incremental Calculation of Sequence Log-Probability

Example of Autoregressive Generation and Log-Probability Calculation

A language model is generating a continuation for the input 'The best way to learn a new skill is'. It has produced two candidate sequences and calculated their total log-probabilities as follows:

• Sequence A: '...by practicing consistently.' (Total log-probability = -1.15)
• Sequence B: '...through osmotic absorption.' (Total log-probability = -7.82)

Based on these values, which sequence is considered more plausible by the model, and why?

When a language model evaluates different possible output sequences, why is it standard practice to sum their log-probabilities instead of multiplying their raw probabilities?

A language model has generated the sequence 'The sun is' with a cumulative log-probability of -2.5. The model is now considering the next token. Given the following conditional log-probabilities for the next token, which choice would result in the most probable three-word sequence?