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

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.