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arXiv2026

DeSyR: A Decoupled Symbolic Recovery Framework with PINN-Guided Structure Search and Physics-Informed Coefficient Refinement

Recovering compact explicit solutions from neural approximations is challenging when imperfect teacher data guide symbolic topology search and coefficient estimation. We present DeSyR, a decoupled symbolic recovery framework for differential equations. A physics-informed neural network guides repeated searches to construct candidate topologies with provisional constants. Once a topology is fixed, its coefficients are refined solely from the governing equation and prescribed constraints, followed by gated selection and verification. For linear fixed-topology parameterizations, we characterize teacher-error inheritance and show that finite-weight mixed data--physics fitting retains an $O(β^{-1})$ teacher-dependent contribution when the teacher error projects onto the model space. Under well-posedness, representability, zero-residual attainment, and discrete determinacy, physics-only refinement conditionally recovers exact coefficients; for nonlinear parameterizations, the corresponding guarantees are local. DeSyR is evaluated on 15 differential-equation problems across 18 configurations covering high-order, space--time, multidimensional, nonlinear, and coupled systems. A candidate-level audit yields a 99.23% convergence rate among free-parameter refits, while every selected refinement involving free coefficients converges. Configuration-level median refined relative $L_2$ errors are $2.31\times10^{-14}$ or lower. In same-topology comparisons, refinement reduces error by eight to fourteen orders of magnitude. These results show that an approximate neural teacher can guide topology discovery without imposing its error scale on final recovered coefficients, provided a target-capable topology is retained and physics-only refinement converges.

cs.LG↗

arXiv2026

LiST: Local-Simplex Test-Time LoRA Fusion

Task-specific LoRA adapters offer a modular way to specialize large language and vision-language models. However, existing adapter composition methods are mostly static and cannot adapt to individual test inputs. To address these issues, we propose \textbf{LiST}, a label-free test-time LoRA fusion framework that converts an existing LoRA bank into a target-conditioned local simplex and searches sample-specific fusion weights at inference time. LiST builds joint task representations from LoRA parameter anchors and prompt-level behavior vectors, retrieves neighboring adapters as a local search space, and performs branch-preserving fusion without updating the backbone or adapters. Candidate weights are selected by a prompt-level energy with prior, geometric, and stochastic-consistency constraints, and are deployed only when they pass a safe acceptance rule. Otherwise, LiST falls back to a target-conditioned prior. Experiments on multimodal and language benchmarks show that LiST outperforms static LoRA merging and conventional test-time adaptation baselines, while preserving task-specific adapter utility and improving robustness on unseen tasks.

cs.CV↗