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name: rectified_velocity_regression description: Fit and audit a small rectified-flow velocity model with least-squares regression and optimizer evidence.

Rectified Velocity Regression

Use this skill when rectified-flow records must be converted into a trained velocity field or when recovery must prove that an optimizer step happened. Do not use it to construct interpolation records.

Inputs

• Records with xt, t, and target_velocity.
• Affine parameters w_x, w_t, and b per dimension.
• A learning rate and optional step count.

Outputs

• Loss before and after training.
• Parameter values before and after training.
• Optimizer-change evidence and gradients.

Workflow

1. Evaluate v(x,t) = w_x * x + w_t * t + b per dimension.
2. Compute mean squared error against target_velocity.
3. Compute analytic gradients and update parameters with SGD.
4. Report loss reduction and parameter changes.

Validation

Run python tests/test_velocity.py or validate with --run-tests.

Limitations

This deterministic affine model is intended for bounded recovery and unit tests; it is not a replacement for the paper's full neural image model.