Fine-tuning is now the primary method for adapting large neural networks, but it also introduces new integrity risks. An untrusted party can insert backdoors, change safety behavior, or overwrite large parts of a model while claiming only small updates. Existing verification tools focus on inference correctness or full-model provenance and do not address this problem. We introduce Fine-Tuning Integrity (FTI) as a security goal for controlled model evolution. An FTI system certifies that a fine-tuned model differs from a trusted base only within a policy-defined drift class. We propose Succinct Model Difference Proofs (SMDPs) as a new cryptographic primitive for enforcing these drift constraints. SMDPs provide zero-knowledge proofs that the update to a model is norm-bounded, low-rank, or sparse. The verifier cost depends only on the structure of the drift, not on the size of the model. We give concrete SMDP constructions based on random projections, polynomial commitments, and streaming linear checks. We also prove an information-theoretic lower bound showing that some form of structure is necessary for succinct proofs. Finally, we present architecture-aware instantiations for transformers, CNNs, and MLPs, together with an end-to-end system that aggregates block-level proofs into a global certificate.

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