Hidden Unit Interpretability in RBM Quantum States:Encoding Antiferromagnetic Order in Heisenberg Spin Rings
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arXiv
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| Format: | Preprint |
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2026
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| author | Mummaneni, Bharadwaj Chowdary Sajjan, Manas |
| author_facet | Mummaneni, Bharadwaj Chowdary Sajjan, Manas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24223 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hidden Unit Interpretability in RBM Quantum States:Encoding Antiferromagnetic Order in Heisenberg Spin Rings Mummaneni, Bharadwaj Chowdary Sajjan, Manas Strongly Correlated Electrons Quantum Physics 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. |
| title | Hidden Unit Interpretability in RBM Quantum States:Encoding Antiferromagnetic Order in Heisenberg Spin Rings |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2603.24223 |