Omission of Parameter Superscripts in Language Model Probability Notation
In mathematical expressions involving parameterized models, it is a common convention to simplify the notation by omitting explicit parameters. For instance, superscripts like (representing Softmax weights) and (representing encoder parameters) may be dropped from probability distributions for brevity, even though the dependency on these parameters is still implied.
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Ch.1 Pre-training - Foundations of Large Language Models
Foundations of Large Language Models
Computing Sciences
Foundations of Large Language Models Course
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Comparison of Output Probability Meaning: Language Modeling vs. Encoder Pre-training
A language model computes probability distributions for a sequence of tokens
xusing a two-stage process: an encoder with parametersθgenerates representations, which are then passed to a Softmax layer with a weight matrixW. This model is consistently outputting a nearly uniform probability distribution for every token position, meaning every word in the vocabulary is considered almost equally likely, regardless of the input. Which of the following is the most direct and plausible explanation for this behavior?Evaluating Component Independence in a Language Model
A language model calculates the probability distribution for each token in an input sequence,
x, by first generating a sequence of numerical representations and then applying a final transformation. Arrange the following steps in the correct computational order to produce the probability vector,p_i, for the token at a specific positioni.Omission of Parameter Superscripts in Language Model Probability Notation
Learn After
A research paper on language models presents the probability of an output token
ygiven an input contextxin two different ways:Expression 1:
p(y | x; W, θ)Expression 2:p(y | x)Assuming both expressions refer to the same underlying model where
Wandθare the model's parameters, what is the most accurate interpretation of the relationship between them?Interpreting Model Notation in a Research Context
In the context of parameterized machine learning models, the mathematical expression
p(y|x)indicates that the probability of outputygiven inputxis calculated without relying on any learned model parameters.