Design a Correct Sequence-Scoring Function for Autoregressive LLM Outputs
You are building an internal evaluation service that ranks multiple candidate completions produced by an autoregressive LLM for the same prompt. The model returns, for each generation step i, a vector of logits u_i over the vocabulary V (one logit per token) computed from the context (prompt x plus previously generated tokens y_<i). Your service must (1) compute the conditional probability of each chosen token y_i from u_i, (2) compute the total conditional log-probability log Pr(y|x) for the full candidate sequence y = (y_1,...,y_n) using the autoregressive decomposition, and (3) return the best candidate y_hat = argmax_y log Pr(y|x).
Create a precise, implementation-ready specification (math + clear pseudocode) for a function score_and_select(prompt_tokens x, candidates Y, logits_by_candidate U) that returns (best_candidate, scores). Your spec must explicitly show: how Softmax converts logits to next-token probabilities; how you extract Pr(y_i|x,y_<i) for the actually generated token at each step; how you aggregate across steps into a single sequence score consistent with the inference objective; and how this relates to the log-likelihood objective used in training (i.e., what quantity training maximizes that your scorer is computing at inference). Assume
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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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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?
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Design a Correct Sequence-Scoring Function for Autoregressive LLM Outputs
Your team is building an internal tool that ranks ...
You’re reviewing an internal evaluation script tha...
You’re reviewing an internal LLM evaluation pipeli...
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You’re reviewing an internal evaluation script tha...
Your team is building an internal tool that ranks ...
You’re reviewing an internal LLM evaluation pipeli...
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An autoregressive language model is given the sequence of tokens: 'The', 'cat', 'sat', 'on', 'the'. It is now tasked with predicting the very next token. Which of the following expressions correctly represents the primary calculation the model performs to determine the likelihood of the word 'mat' appearing next?
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Your team is building an internal tool that ranks ...
You’re reviewing an internal LLM evaluation pipeli...
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A language model is being trained on the sentence '
The cat sat'. The model calculates the following conditional log-probabilities at each step, where ' ' is a fixed start-of-sequence token: log P('The' | '<BOS>') = -1.5log P('cat' | '<BOS>', 'The') = -0.9log P('sat' | '<BOS>', 'The', 'cat') = -1.2
Based on the standard training objective for this single sequence, what is the total log-likelihood value that the model aims to maximize?
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z = [z_1, z_2, ..., z_K]into a probability distribution. This function operates by first applying the standard exponential function to each score and then normalizing these new values by dividing each by their sum. If a constant valueCis added to every score in the input vectorz, resulting in a new vectorz' = [z_1+C, z_2+C, ..., z_K+C], how will the resulting output probability distribution be affected?Consider two input vectors of raw scores (logits) for a 3-class classification problem: Vector A =
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