The discipline that bounds neurosymbolic AI’s correctness claims.
What it is
Fidelity is the standard metric in NSAI for comparing a symbolic description — a set of rules, a logic program, a decision tree — against the trained neural network from which it was extracted. High fidelity means the description reproduces the network’s input-output behaviour closely; low fidelity means the description has lost or distorted information.
Fidelity is computed empirically. Both the network and the symbolic system are run on a held-out set of inputs and their outputs compared for agreement. The metric is independent of whether either system is correct against ground truth — it asks only whether the two agree with each other.
Why it matters
Without fidelity, extraction is unmoored. A symbolic description that diverges from its source network gives reasoning guarantees about something the network does not actually do — formally rigorous, but about the wrong system. Fidelity is the discipline that prevents this: a description is only usable if it stays within a stated fidelity error of the network it represents.
The metric also bounds NSAI’s correctness claims. When NSAI promises provable correctness, it means correctness within the fidelity error of the extracted description. Improving fidelity is therefore one of the levers for tightening downstream guarantees, alongside improving extraction techniques themselves.