Establish semantic soundness of bounded-error normalization constraints

Establish whether every witness satisfying the finite-field approximation range permitted by the implemented LayerNorm and RMSNorm constraints yields the same output tokens as the intended canonical model.

Background

The SLP verifier uses finite-field relations for normalization operations that permit bounded approximation errors. Although these relations can be proved sound with respect to their encoded constraints, the paper distinguishes that property from establishing that all admissible witnesses preserve the model’s token-level behavior. The unresolved issue is therefore a composition or semantic-soundness result connecting local normalization tolerances to the final output tokens of the transformer.

This question matters because full chunk coverage would verify the implemented approximate relations without necessarily proving equivalence to the intended model computation. A positive result would characterize when the normalization error bounds are sufficiently restrictive to preserve outputs; alternatively, a negative result would require bounding the resulting network-wide behavioral deviation.

References

The resulting finite-field relation admits an approximation range, and we have not proved that every witness inside that range yields the same output tokens.

— Seal, Then Sample: Sampled Layerwise Proofs for Verifiable LLM Inference from GPT-2 to 70B  (2609.27367 - Lim et al., 23 Sep 2026) in Section 2.1, “The object being verified”; discussed further in Section 8.2, “Approximate relations and model authenticity”