Hidden Unit Interpretability in RBM Quantum States:Encoding Antiferromagnetic Order in Heisenberg Spin Rings

• URL: http://arxiv.org/abs/2603.24223v1
• Date: Wed, 25 Mar 2026 11:51:59 GMT
• Title: Hidden Unit Interpretability in RBM Quantum States:Encoding Antiferromagnetic Order in Heisenberg Spin Rings
• Abstract summary: We show that individual hidden units spontaneously specialize to capture staggered magnetization patterns characteristic of antiferromagnetic ground states.<n>No individual hidden unit reproduces the full antiferromagnetic correlations, indicating that quantum order emerges through collective encoding.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate how Restricted Boltzmann Machines (RBMs) encode antiferromagnetic order when trained as variational ansätze for one-dimensional Heisenberg spin rings with periodic boundary conditions. Through systematic hidden unit analysis and ablation studies on $N=4$ and $N=8$ spin systems, we show that individual hidden units spontaneously specialize to capture staggered magnetization patterns characteristic of antiferromagnetic ground states. Hidden units naturally segregate into two classes: those essential for ground-state energy and correlation structure, and supplementary units providing smaller corrections. Removing important units induces clear energy penalties and disrupts the staggered correlation pattern in $C_{zz}(r)$, whereas removing supplementary units has modest effects. Single-unit analysis confirms that no individual hidden unit reproduces the full antiferromagnetic correlations, indicating that quantum order emerges through collective encoding across the hidden layer. Extending this analysis to $N=8$ through $20$ with hidden unit densities $α= 2$ to $5$ and ten independent seeds per configuration, we find that the fraction of important hidden units decreases with system size, consistent with sublinear growth $m' \sim N^k$ ($k \approx 0.4$). The energy-correlation impact relationship persists for small to moderate system sizes, though it weakens for the largest systems studied. These results provide a quantitative framework for RBM interpretability in quantum many-body systems.

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