Example. Response-only supervision on one instruction record [ftip-002H]
Example. Response-only supervision on one instruction record [ftip-002H]
Two instruction positions provide conditioning context but lie outside the response-loss index set. The loss is taken on the two generated tokens.
Declare \(\pi (r_1\mid u_1,u_2)=1/2\) and \(\pi (r_2\mid u_1,u_2,r_1)=1/4\). The instruction tokens are not indexed by the response mask. With mask one on each displayed response token, the sum and mean are \[ L_{\rm sum}=-\log \tfrac 12-\log \tfrac 14=\log 8, \qquad L_{\rm mean}=\tfrac 12\log 8\approx 1.040. \]
The supervised objective in Definition [ftip-002F] and the causal factorization in Definition [ftip-000I] specialize to the displayed token strip. Its mask is a local choice on response positions; other instruction-tuning implementations may supervise a different subset of response tokens or declare a larger loss domain explicitly.