On the Fundamental Limits of Formally Proving Robustness in Proof-of-Learning

Proof-of-learning (PoL) proposes a model owner use machine learning training checkpoints to establish a proof of having expended the necessary compute for training. The authors of PoL forego cryptographic approaches and trade rigorous security guarantees for scalability to deep learning by being applicable to stochastic gradient descent and adaptive variants. This lack of formal analysis leaves the possibility that an attacker may be able to spoof a proof for a model they did not train. We contribute a formal analysis of why the PoL protocol cannot be formally (dis)proven to be robust against spoofing adversaries. To do so, we disentangle the two roles of proof verification in PoL: (a) efficiently determining if a proof is a valid gradient descent trajectory, and (b) establishing precedence by making it more expensive to craft a proof after training completes (i.e., spoofing). We show that efficient verification results in a tradeoff between accepting legitimate proofs and rejecting invalid proofs because deep learning necessarily involves noise. Without a precise analytical model for how this noise affects training, we cannot formally guarantee if a PoL verification algorithm is robust. Then, we demonstrate that establishing precedence robustly also reduces to an open problem in learning theory: spoofing a PoL post hoc training is akin to finding different trajectories with the same endpoint in non-convex learning. Yet, we do not rigorously know if priori knowledge of the final model weights helps discover such trajectories. We conclude that, until the aforementioned open problems are addressed, relying more heavily on cryptography is likely needed to formulate a new class of PoL protocols with formal robustness guarantees. In particular, this will help with establishing precedence. As a by-product of insights from our analysis, we also demonstrate two novel attacks against PoL.