---

name: influence_weight_update description: Compute influence-style hypergradients and projected unlabeled weight updates from validation gradients, per-example unsupervised gradients, and a damped Hessian approximation.

Influence Weight Update

Use this skill when implementing the outer loop of per-example SSL weighting. It turns validation gradients and per-example unsupervised gradients into influence-style hypergradients for unlabeled weights.

Do not use this skill for ordinary supervised optimization or for a single global unlabeled scalar unless the experiment explicitly ablates the paper mechanism.

Inputs

• Validation gradient with respect to the last-layer parameter vector.
• Per-example unsupervised gradients for selected unlabeled examples.
• A positive Hessian diagonal or damped curvature approximation.
• Current non-negative weights and a learning rate.

Outputs

• Influence hypergradients, one per selected unlabeled example.
• Projected non-negative updated weights.
• Diagnostics showing which examples were upweighted or downweighted.

Workflow

1. Invert the damped last-layer Hessian approximation elementwise.
2. Compute - validation_gradient^T H^{-1} unsupervised_gradient for each selected example.
3. Apply a gradient step to each selected weight and project to zero or above.
4. Return explicit diagnostics rather than hiding sign conventions in the caller.

Validation

Run python tests/test_influence.py or validate through validate_skill_tree.py --run-tests.

Limitations

The script implements a deterministic last-layer/diagonal proxy. Full deep-network recovery should replace the curvature input with an exact last-layer Hessian or a validated Hessian-vector solver.