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

arXiv:2605.25344v2 Announce Type: replace-cross 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.

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.

Computation and Language (cs.CL); Artificial Intelligence (cs.AI); Machine Learning (cs.LG); Quantum Physics (quant-ph)

arXiv:2605.25344 [cs.CL]

(or arXiv:2605.25344v2 [cs.CL] for this version)

https://doi.org/10.48550/arXiv.2605.25344 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

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

Related coverage