Physics-Aligned Decoding (PAD) for Discrete Protein Structure Representations

Discrete representations learned by deep autoencoders are increasingly reused as intermediate state spaces in generative, conditional, and autoregressive models. In this work, we empirically identify an objective-level failure mode in discrete protein structure tokenizers trained with reconstruction-aligned losses: despite low global reconstruction error, learned tokens encode locally unphysical geometry, including covalent distortions and steric clashes. We show that these violations are deterministic and persistent under reuse. We test the hypothesis that this behavior arises from objective misspecification rather than architectural limitations, and introduce Physics-Aligned Decoding (PAD), a minimal intervention that augments reconstruction objectives with differentiable physical priors. Without changing architecture or regenerating the codebook, PAD reshapes token semantics and restores physical validity while preserving reconstruction accuracy. Our results highlight how loss geometry determines representation semantics, and demonstrate the importance of objective alignment when discrete representations are reused beyond static reconstruction.