Explaining a Counterintuitive Decoding Outcome Using Softmax, Next-Token Conditionals, and Sequence Log-Probability
You are reviewing an internal demo of an autoregressive LLM used to draft short customer-support replies. For a given prompt x, the model must generate exactly two tokens y1 y2 (then stop). The engineer shows you the model’s final-layer logits (before Softmax) for the next token at step 1, and then (depending on the chosen y1) the logits for step 2:
Step 1 logits over the vocabulary {A, B}: u(A)=0, u(B)=0.
If y1=A, then Step 2 logits over {C, D}: u(C)=10, u(D)=0. If y1=B, then Step 2 logits over {C, D}: u(C)=1, u(D)=1.
The engineer claims: “Because A and B are equally likely at step 1, greedy decoding is fine; it will pick either A or B, and then we’ll get the best overall two-token completion anyway.”
Write an analysis that (1) computes the relevant next-token probabilities using Softmax at each step, (2) uses the autoregressive decomposition to compute and compare the total conditional log-probability log Pr(y1,y2|x) for the best completion under y1=A versus under y1=B, and (3) explains—using the log-likelihood/sequence-scoring perspective—whether the engineer’s claim is correct and why. Your answer should make clear how per-step conditional probabilities interact to determine the best overall sequence under the argmax objective.
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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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