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name: stochastic_interpolant_objectives description: Compute stochastic-interpolant velocity, denoiser, and score objective diagnostics from sampled tuples without evaluating densities.

Stochastic Interpolant Objectives

Use this skill when a recovery needs the paper's quadratic learning signals for velocity, denoiser, or score fields. Do not use it to define endpoint interpolation or to integrate a sampler.

Inputs

• Velocity targets dot_x_t from the interpolant protocol.
• Latent noise z and positive interior gamma values.
• Predictions for velocity b_hat and denoiser eta_hat.

Outputs

• Mean velocity objective from Eq. (2.13).
• Mean denoiser objective from Eq. (2.19).
• Denoiser-derived score values -eta/gamma for safe interior times.
• Loss-comparison diagnostics for recovery traces.

Workflow

1. Compute per-sample velocity terms 0.5*b_hat^2 - dot_x_t*b_hat.
2. Compute per-sample denoiser terms 0.5*eta_hat^2 - z*eta_hat.
3. Convert denoiser to score only when gamma >= min_gamma.
4. In reduced recovery, compare before/after losses and log parameter updates.

Validation

Run:

python scripts/objectives.py --demo
python tests/test_objectives.py

Limitations

The included implementation is scalar/list based for deterministic recovery checks. Neural parameterizations can reuse the same objective formulas with tensor libraries in an isolated environment.