The performance of generative models is assessed by sampling molecules from the latent space for the decoder to convert into a readable representation; random sampling is commonly used for this. Once sampled, it must be determined whether the sampled molecule is reasonable. For Cage-VAE, we represent cages in a deconstructed form and Figure shows The quality of generated molecules from corresponding latent variables is evaluated by several metrics, including common benchmarks such as validity, novelty and uniqueness and specific metrics designed for cages, such as precursor validity and symmetry (see Supplementary Information Section 5.1 for full definitions of these metrics). First, the validity of the generated molecules should be the top priority. Recall that in this model, Cage-VAE is designed to focus on the generation of BB2 skeletons as a component of disassembled cage representations and generate other components from finite sets. Therefore, the validity of POCs can be simplified as the validity of generated BB2 skeletons. In practice, this is achieved by determining whether the generated SMILES representation is syntactically and semantically valid enough to construct a molecular graph. To quantify validity, we sampled 1000 latent variables randomly; the validity of the decoded molecules reaches 0.917, as shown in Table . This indicates that our model effectively captures basic chemical rules without prior knowledge. It also indicates that the latent space is even and smooth to be decoded to valid SMILES strings. The proportion of randomly generated molecules whose precursors are symmetrical is 0.917. This suggests that the model successfully recognises symmetry as a higher-level feature for the generation of BB2 precursors. The perception of symmetry is difficult as this feature is a completely recessive constraint. No information regarding molecular symmetry is explicitly input to the model during the training. In addition, the SMILES representation is lightweight to be used in generative modelling, but inherently weak in the depiction of molecular symmetry due to the depth-first tree traversal pattern. Thus, our model's capability to implicitly recognise and prioritise the concept of symmetry, despite the limitations of the SMILES representation, underscores its learning and generalisation capabilities.