Proofs

This module collects the maintained proof API: tensor facts, selected autograd correctness theorems, runtime-approximation theorems, model proofs, and verification soundness results.

These are the proof modules included in the supported library, separate from tests, examples, and executable workflows.

Proof landmarks:

• real-analysis and numerics helper theorems: NN.Proofs.Analysis,
• analytic autograd correctness fragments: NN.Proofs.Autograd.FDeriv.*,
• tape/DAG reverse-mode correctness fragments: NN.Proofs.Autograd.Tape.*,
• model-level invariants: NN.Proofs.Models,
• probability-kernel facts: NN.Proofs.Probability,
• runtime-approximation bounds: NN.Proofs.RuntimeApprox.*,
• verification envelopes: NN.Proofs.Verification.

Backend contract data lives under NN.Backend. It is not re-exported here until the proof layer has semantic/refinement theorems rather than planner metadata.

References:

• PyTorch autograd background: https://pytorch.org/docs/stable/autograd.html
• The theorem bundles re-exported here document the math/model references they rely on locally.