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name: atomic_loss_training description: Build and optimize the finite-atom APT contrastive loss with proposal posterior correction.

Atomic Loss Training

Use this skill to implement the APT finite-atom objective from Section 3.2. It is appropriate for reduced recovery, ablations, and deterministic tests where the posterior estimator is represented by a simple differentiable score function.

Inputs

• Atom parameter values and the index of the positive simulated parameter.
• Observation value and affine score parameters.
• Prior and proposal log-density values for the atoms.
• Learning rate for one optimizer step.

Outputs

• Cross-entropy loss before and after update.
• Probability assigned to the positive atom.
• Parameter values before and after the optimizer step.

Workflow

1. Score each atom with an observation-conditioned affine model.
2. Apply the proposal-posterior transform before computing probabilities.
3. Compute cross-entropy against the positive atom.
4. Compute analytic gradients and update trainable parameters.
5. Record a trace compatible with recovery validation.

Validation

Run python scripts/atomic_loss.py --self-test. The deterministic test verifies that the optimizer changes parameters and reduces loss.

Limitations

The provided script is a compact recovery implementation. Full APT normally uses neural density estimators such as mixtures or flows.