---

name: soft_regularization description: Compute soft movement-pruning sigmoid sparsity penalties and gradients for threshold-mask recovery checks.

Soft Movement Sparsity Regularization

Use this skill when implementing or auditing soft movement pruning. It computes the paper penalty lambda_mvp * sum(sigmoid(S)) and the corresponding score-gradient contribution.

Inputs

• scores: flat or nested numeric scores.
• lambda_mvp: nonnegative regularization strength.
• Optional threshold and lr for before/after keep-ratio diagnostics.

Outputs

Penalty value, gradient contribution with the same shape as scores, sigmoid mass, and optional threshold keep-ratio diagnostics.

Workflow

1. Compute stable sigmoid values.
2. Sum sigmoid scores and multiply by lambda_mvp.
3. Compute lambda_mvp * sigmoid(S) * (1 - sigmoid(S)).
4. Optionally simulate a regularization-only gradient step to show scores are pushed downward.

Validation

Run python tests/test_soft_regularization.py. Tests check zero-lambda behavior, sigmoid-at-zero values, and non-increasing scores under the penalty update.

Limitations

This skill supplies only the regularizer component; task loss and score masks must be handled by other skills.