Title: Joint Structure Search for Tensor Network Operators Inspired by Symmetry Breaking
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)
Keywords: tensor decomposition, tensor networks.

Abstract: Tensor networks (TNs) offer a compact representation for high-dimensional operators in physics and machine learning. While TN structure search (TN-SS) has advanced model selection, prior work is limited to a single operator. Yet real systems, such as transformers and quantum circuits, would contain multiple coupled operators, where treating them independently or enforcing a single shared structure is fundamentally limiting. We introduce joint TN-SS, the first framework for multi-operator structure search. Our physics-inspired algorithm runs in two phases: a symmetry phase, where standard TN-SS finds a shared structure capturing common inductive bias; and a symmetry-breaking phase, where operator-specific diversity emerges through greedy core masking, guided by task-explainable loss tolerances. Across tensor decomposition, parameter-efficient fine-tuning of LLMs, and quantum circuit optimization, joint TN-SS delivers more compact representations with equal or better accuracy than state-of-the-arts, with affordable search cost. These results demonstrate that symmetry-driven diversification offers a simple, general, and scalable solution to TN structure selection in multi-operator systems.