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name: combined_kd_objective description: Combine supervised, output distillation, and RAIL intermediate losses with validated RAIL-KD lambda weights.

Combined KD Objective

Use this skill when constructing a RAIL-KD training or proxy recovery objective. It preserves the paper's equation (4): the student minimizes a weighted sum of supervised task loss, output-logit knowledge distillation loss, and the randomized intermediate representation loss. Do not use this skill as a replacement for computing the RAIL representation loss itself.

Inputs

• ce_loss: finite scalar for supervised cross-entropy/task loss.
• kd_loss: finite scalar for output prediction distillation.
• rail_loss: finite scalar from RAIL-KDl or RAIL-KDc.
• lambdas: three non-negative weights (lambda1, lambda2, lambda3) that sum to one.

Outputs

• Total scalar objective.
• Weighted contribution dictionary for audit logs.
• Validation status or an exception for invalid inputs.

Workflow

1. Validate that all loss components are finite numeric scalars.
2. Validate that all lambda weights are non-negative and sum to one within tolerance.
3. Compute the total weighted objective.
4. Return component contributions so recovery can report what the optimizer minimized.

Validation

Run:

python scripts/kd_objective.py --ce 0.4 --kd 0.3 --rail 0.2 --lambdas 0.2 0.3 0.5
python -m pytest tests

Limitations

This skill computes scalar composition only. Production training code still needs a differentiable implementation for framework tensors, but the same validation and contribution reporting should be preserved.