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An instruction-fine-tuned Large Language Model can be formally represented as a conditional probability distribution, denoted as $$\Pr(\mathbf{y}|\mathbf{c},\mathbf{z})$$. In this mathematical expression, $$\mathbf{c}$$ stands for the instruction provided, $$\mathbf{z}$$ represents the user's input, and $$\mathbf{y}$$ is the corresponding generated model output or response.

Formal Representation of an Instruction-Tuned LLM

An instruction-tuned model's behavior can be formally represented as a conditional probability distribution `Pr(y|c, z)`. Match each variable from this representation to its corresponding description.

A developer is testing a translation model. The model is given the instruction, 'Translate the following English sentence to French,' and the input, 'The cat is on the mat.' The model considers two possible outputs: (y1) 'Le chat est sur le tapis' and (y2) 'Le tapis est sur le chat.' Using the formal representation `Pr(y|c, z)`, explain how the model computationally distinguishes between these two outputs and determines the more appropriate translation.

Analyzing Model Output Probability

A user interacts with a language model by providing an instruction and an input. The instruction is 'Summarize the key point of the following text.' The input text is 'Jupiter is the fifth planet from the Sun and the largest in the Solar System.' The model generates the output 'Jupiter is the largest planet in our solar system.' How is the conditional probability of the model generating this specific output formally represented?

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