Formula

Training Objective as Joint Log-Likelihood Maximization of Concatenated Sequences

A training objective for a model can be formulated as maximizing the joint log-likelihood of concatenated input-output sequences. For a dataset D of input-output pairs (x, y), the optimal parameters ˜θ are found by maximizing the sum of the log-probabilities of the combined sequence seq_{x,y}. The formula is: ˜θ=argmaxθ(x,y)DlogPrθ(seqx,y)˜θ = \arg \max_{\theta} \sum_{(x,y)∈D} \log \text{Pr}_{\theta}(\text{seq}_{x,y}) This approach is equivalent to maximizing the conditional log-likelihood log Pr(y|x) when the input distribution Pr(x) is not dependent on the model parameters θ.

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Updated 2025-10-08

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Ch.4 Alignment - Foundations of Large Language Models

Foundations of Large Language Models

Foundations of Large Language Models Course

Computing Sciences