A Hamiltonian-Inspired Local-Operator Ansatz for Slimming Large Language Models

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arXiv:2605.25344v2 Announce Type: replace Abstract: Dense linear maps carry much of the parameter and computational burden of modern neural networks, yet their dense form leaves the organization of learned couplings implicit. Quantum many-body physics organizes exponentially large operators by writing a global Hamiltonian as a sum of local terms, \(\hat H=\sum_k\hat h_k\). Whether the same structural principle can carry learned neural maps is unknown. We introduce Tensor Mixture (MixT), which represents a dense map as a natively executable sum of overlapping local tensor operators without imposing an explicit matrix-rank constraint. The local-term count \(N_T\) sets the effective nonlocality and operator complexity, while the number of replaced Transformer blocks \(N_B\) extends this structural coordinate across network depth. Tests on Qwen3-8B and LLaMA2-7B reveal a broad recoverable regime followed by an abrupt, model-specific boundary that is remarkably stable against changes in \(N_T\). Accuracy and output-distribution statistics reorganize together across the boundary; in LLaMA2-7B, the same depth separates two scaling regimes of inter-layer geometry drift. The directly executed structure also reduces parameters, arithmetic, storage, and memory. These results establish the local-sum structure as a viable organizing principle for learned linear maps at billion-parameter scale and expose a sharp boundary in their tolerance to structural simplification.

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