  The equivalent nature of 3D coordinates has posed long term challenges in
protein structure representation learning, alignment, and generation. Can we
create a compact and invariant language that equivalently represents protein
structures? Towards this goal, we propose FoldToken2 to transfer equivariant
structures into discrete tokens, while maintaining the recoverability of the
original structures. From FoldToken1 to FoldToken2, we improve three key
components: (1) invariant structure encoder, (2) vector-quantized compressor,
and (3) equivalent structure decoder. We evaluate FoldToken2 on the protein
structure reconstruction task and show that it outperforms previous FoldToken1
by 20\% in TMScore and 81\% in RMSD. FoldToken2 probably be the first method
that works well on both single-chain and multi-chain protein structures
quantization. We believe that FoldToken2 will inspire further improvement in
protein structure representation learning, structure alignment, and structure
generation tasks.
