GRAFT: Hyperdimensional Computing-based Graph Reconstruction via Algebraic Fixed Transformations

Many scientific domains, chemistry foremost among them, represent their primary objects as attributed graphs, and learning on these objects typically requires mapping them to and from a fixed-dimensional continuous space. One important capability such representations support is graph reconstruction - encoding an attributed graph into a single vector and recovering it exactly - which underpins retrieval and structure generation. Existing solutions are learned encoder-decoder models, with graph autoencoders as the canonical example: training takes hundreds of GPU-hours and yields codecs that are confined to the distribution they were trained on. We introduce GRAFT (Graph Reconstruction via Algebraic Fixed Transformations), a graph encoder-decoder architecture that maps graphs to fixed-dimensional hypervectors and back through deterministic binding, bundling, and message-passing operations over a fixed set of random reference vectors: the encoder and decoder contain no trainable parameters. On a standard molecular-graph reconstruction benchmark, GRAFT recovers 93% of molecular graphs with up to 32 heavy atoms exactly and 91% of graphs with up to 64 heavy atoms, substantially improving on state-of-the-art learned autoencoders without any encoder or decoder training. Paired with standard task-specific learned heads, GRAFT is suitable for MoleculeNet property prediction, supports molecular generation on ZINC250K, and substantially outperforms baselines on the Fingerprint2Graph translation task.