[2606.24948] Holographic Memory for Zero-Shot Compositional Reasoning in Knowledge Graphs: A Mechanistic Study of Where and Why It Fails
[Submitted on 23 Jun 2026]
Title:Holographic Memory for Zero-Shot Compositional Reasoning in Knowledge Graphs: A Mechanistic Study of Where and Why It Fails
View a PDF of the paper titled Holographic Memory for Zero-Shot Compositional Reasoning in Knowledge Graphs: A Mechanistic Study of Where and Why It Fails, by Randhir Kumar
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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.
Comments: 15 pages, 5 figures, 5 tables. Code available at this https URL
Subjects:
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
Cite as: arXiv:2606.24948 [cs.LG]
(or arXiv:2606.24948v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.24948
arXiv-issued DOI via DataCite
Submission history
From: Randhir Kumar [view email] [v1] Tue, 23 Jun 2026 07:33:27 UTC (20 KB)
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