Definition. Fine-tuning run [ftip-006Q]

Given the base artifact \(M_0=(\tau ,\delta ,\mathsf {cfg},\theta _K,\mathsf {num})\) from Definition [ftip-001K], a fine-tuning run declares training records, a finite update count \(J\geq 0\), a loss \(L_{\rm ft}\), gradient estimators \(g_j^{\rm ft}\), optimizer states \(s_j^{\rm ft}\), and update specifications \((U_j,\eta _j^{\rm ft})\). It starts from \(\theta ^{\rm ft}_0=\theta _K\).

For each \(j=0,\ldots ,J-1\), the update is

\[ (\theta ^{\rm ft}_{j+1},s^{\rm ft}_{j+1}) =U_j\left (\theta ^{\rm ft}_j,s^{\rm ft}_j, g_j^{\rm ft},\eta _j^{\rm ft}\right ). \]

Its output artifact replaces \(\theta _K\) by the final \(\theta ^{\rm ft}_J\). Any change to the tokenizer, architecture configuration, numerical convention, or other artifact field must be stated separately. Fine-tuning is not identified with one loss or data type.