Formula

Fine-Tuning Objective Function

The fine-tuning process is a standard optimization procedure aimed at finding the best model parameters, (ω~,θ~)(\tilde{\omega}, \tilde{\theta}), by minimizing a loss function over a dataset of tuning samples. Each sample, (x,ygold)(\mathbf{x}, \mathbf{y}_{\text{gold}}), consists of an input and its correct output. The optimization begins with parameters initialized from a pre-trained model, θ^\hat{\theta}. The formal objective is: (ω~,θ~)=argminω,θ^+(x,ygold)DLoss(yω,θ^+,ygold)(\tilde{\omega}, \tilde{\theta}) = \arg \min_{\omega, \hat{\theta}^{+}} \sum_{(\mathbf{x}, \mathbf{y}_{\text{gold}}) \in \mathcal{D}} \text{Loss}(\mathbf{y}_{\omega, \hat{\theta}^{+}}, \mathbf{y}_{\text{gold}}) In this equation, θ^+\hat{\theta}^{+} indicates that the parameters start from the pre-trained values. The term yω,θ^+\mathbf{y}_{\omega, \hat{\theta}^{+}} is the model's output for a given input, computed using the parameters being tuned.

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Updated 2026-05-02

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