An Empirical Study of Neurosymbolic Depth Generalisation

Neural networks trained on structured, compositional inputs often fail to generalise beyond the structural complexity seen during training. This thesis investigates whether a neurosymbolic architecture, combining a tree-structured encoder with semantic supervision and hand-written fuzzy rules, improves compositional depth generalisation relative to purely neural alternatives. The task is predicting the sign of arithmetic expressions built from addition, subtraction, and multiplication. Models train only on depth one to three and are evaluated on depth four and five, with no out-of-distribution examples during training. The architecture combines a Tree-LSTM encoder, a perception module projecting the root representation onto a latent symbolic space aligned with nineteen arithmetic properties (thirteen supervised), a fuzzy rule pathway applying five hand-written rules over this space, and a parallel neural classifier. Predictions are combined via a mixing coefficient, studied in heuristic and learned variants. Six configurations, including a bidirectional LSTM baseline, are compared across three seeds in a fully ablated design. The tree-structured encoder drives depth generalisation, accounting for roughly 87% of the accuracy gain over the sequence baseline. Semantic supervision produces an interpretable latent representation, with near-perfect alignment between learned symbols and supervised properties, but adds negligible accuracy gain. The fuzzy rules do not improve generalisation: precision falls sharply under depth shift, and the learned mixing coefficient confirms this is a failure of the rules, not the fusion mechanism. Contributions: a controlled ablation study with a strict no-OOD-during-training protocol; a demonstration that structural bias dominates neurosymbolic supervision here; a dissociation between interpretability and generalisation; and an analysis of mixing-coefficient behaviour under distribution shift.