Holographic Memory for Zero-Shot Compositional Reasoning in Knowledge Graphs: A Mechanistic Study of Where and Why It Fails

A new study on holographic memory for zero-shot compositional reasoning in knowledge graphs found that while Holographic Reduced Representations (HRR) and Fourier HRR (FHRR) perform competitively on single-hop queries, they fail on zero-shot compositional queries. The failure is not due to the bind-unbind algebra or cleanup, but because facts in compositional chains are intrinsically harder for superposed memory to retrieve, a capacity and interference effect present even at a single hop.

arXiv:2606.24948v1 Announce Type: new Abstract: Knowledge graph embedding KGE models predict single-hop links well but have no mechanism for zero-shot compositional queries: multi-hop questions whose relation chains never appeared during training. Holographic Reduced Representations HRR , which bind and unbind symbols via circular convolution, are a theoretically attractive candidate, since binding is approximately invertible and associative. We test whether this promise holds. We study two holographic memory variants, real-valued HRR and phase-only Fourier HRR FHRR , each with a modern Hopfield cleanup, on FB15k-237 over five seeds. Four findings follow. First, both are competitive single-hop retrievers filtered MRR 0.358 +/- 0.002 for HRR, 0.350 +/- 0.021 for FHRR . Second, neither composes zero-shot: accuracy stays at chance across all cleanup temperatures. Third, the main contribution, we localise the failure mechanistically. A hop-1 probe shows the memory recovers the correct intermediate entity with high fidelity MRR 0.896 +/- 0.002 for HRR , yet composition still fails even with a verified-correct intermediate. A second probe shows why: posing the ground-truth second-hop fact as a standalone atomic query, bypassing composition entirely, already recovers it at only 0.26 to 0.48x average atomic accuracy, uniformly across relation fan-out. The bottleneck is not the bind-unbind algebra or the cleanup; it is that facts compositional chains pass through are intrinsically harder for the superposed memory to retrieve, a capacity and interference effect present already at a single hop. Fourth, we prove Lemma 4.1 that FHRR's softmax cleanup is not phase-equivariant, compounding the primary failure on the minority of chains where hop-1 itself errs. Fixing zero-shot composition requires improving retrieval capacity under superposition, not just redesigning the cleanup.