
|
**Loss 1: reconstruction.** A normalized MSE against the receiver's own prefill cache $`C^{\mathcal R}_d`$,
where $`\sigma`$ is the RMS of $`C^{\mathcal R}_d`$ per layer and head, for keys and values separately. Keys are compared
before RoPE.
$`\displaystyle \mathcal L_{\mathrm{recon}} = \mathrm{MSE}\left(\frac{\underline M_{i\to j}(C^{\mathcal S}_d,\mathcal T_{\mathcal R})}{\sigma},\ \frac{C^{\mathcal R}_d}{\sigma}\right)`$
|
**Loss 2: Negative log-likelihood.** The receiver's next-token loss on a target continuation $`y`$ (an answer or a
reasoning trace) after a task prompt $`q`$, with the transferred cache in place of the text. Gradients pass through the
frozen receiver into SwaT only.
$`\displaystyle \mathcal L_{\mathrm{NLL}} = -\frac{1}{|y|}\sum_{t=1}^{|y|}\log p_{\mathcal R}\left(y_t \mid \underline M_{i\to j}(C^{\mathcal S}_d,\mathcal T_{\mathcal R}),\, q,\, y_{\lt t}\right)`$
|

