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Notation for Concatenated Token Sequences
In language modeling, an input sequence and an output sequence are often processed together as a single, combined sequence. This concatenation is formally denoted as , representing the sequence of tokens from followed by the tokens from : . An alternative notation for this combined sequence is .
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Ch.5 Inference - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
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Mathematical Formulation of LLM Inference
Single-Round Prediction Problem
Token-Level Representation of Input and Output Sequences for a Forward Pass
Multi-Round Prediction Problem
Notation for Concatenated Token Sequences
A language model is given an input sequence of tokens representing the phrase 'The best way to learn a new skill is'. The model then calculates the likelihood for several possible completing sequences. Based on the formal objective of the text generation process, which of the following sequences should the model select to output?
Analyzing Model Output Selection
A language model is given an input context
x. It then evaluates two potential output sequences,y_1andy_2. The model's internal calculations determine thaty_1has a higher probability of occurring afterxthany_2. However, a human evaluator findsy_2to be more creative and detailed. According to the formal objective of the text generation process, what should the model do?
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Probability of a Concatenated Token Sequence
An input sequence of tokens is defined as
x = (The, cat, sat)and a subsequent output sequence is defined asy = (on, the, mat). Which of the following correctly represents the single, combined sequence denoted by[x, y]?Using [SEP] Tokens for Sequence Concatenation
Deconstructing a Concatenated Token Sequence
Given two token sequences,
x = (start, process)andy = (end, result), the concatenated sequence denoted by[x, y]is identical to the sequence denoted by[y, x].Input Formatting with Separator Tokens