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name: schrodinger_bridge_coupling description: Build small entropy-regularized coupling checks and bridge variance schedules for SB conditional flow matching.

Schrödinger Bridge Coupling

Use this skill when a recovery or implementation needs a compact SB-CFM mechanism check: entropy-regularized pair weights and bridge variance behavior. Do not treat the simple row-normalized Gibbs helper as a full Sinkhorn solver for production transport.

Inputs

• Source and target minibatches.
• Positive entropy coefficient epsilon.
• Time t and bandwidth sigma for the bridge variance schedule.

Outputs

• Stabilized Gibbs weights derived from squared costs.
• Row-normalized coupling proxy for small tests.
• Bridge standard deviation sigma * sqrt(t * (1 - t)).

Workflow

1. Compute squared costs between source and target points.
2. Convert costs to stabilized exp(-cost / epsilon) weights.
3. Normalize rows for a lightweight concentration diagnostic.
4. Compute bridge variance and verify endpoint behavior.

Validation

Run python tests/test_sb_coupling.py or the Distiller skill-tree validator with tests enabled.

Limitations

This skill supports reduced recovery checks. A full SB-CFM implementation should use Sinkhorn/IPF normalization and stochastic bridge sampling.