1Cademy - Conditional Log-Probability of a Response in Multi-Round Dialogue

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Multi-Round Prediction Problem

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Conditional Log-Probability of a Response in Multi-Round Dialogue

In a multi-round dialogue with $K$ turns, the generation of a response $\mathbf{y}^k$ at any given round $k$ is conditioned on the entire preceding conversational history. This history includes all prior user requests and model responses up to the current request. For a conversation with sequence $\mathbf{x}^1, \mathbf{y}^1, \dots, \mathbf{x}^K, \mathbf{y}^K$ , the conditional log-probability of generating the $k$ -th response is expressed as: $\log \mathrm{Pr}_{\theta}(\mathbf{y}^k|\mathbf{x}^1, \mathbf{y}^1, \dots, \mathbf{x}^k)$ . This value is a key component in defining the overall training objective for dialogue models.

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Updated 2026-05-02

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