The paper introduces a structured transfer learning framework for learning solution operators of differential equations when target data are scarce. It leverages abundant observations from related source systems by accounting for unknown sparse differences in governing equations, using a resolvent identity and whitened instrumental variables to build unbiased source estimating equations. A three‑stage estimator—target‑only ridge pilot, source‑wise sparse calibration, and projected refit—along with an iterative recalibration scheme, achieves non‑asymptotic prediction bounds and demonstrates clear performance gains over target‑only learning, naive pooling, and existing transfer methods.
arXiv:2607. 03005v1 Announce Type: new Abstract: In high-dimensional Ising model estimation, target sample sizes are often limited, and effectively using auxiliary binary datasets of unknown relevance remains challenging.
arXiv:2412. 18081v3 Announce Type: replace-cross Abstract: We study Heterogeneous Transfer Learning (HTL) for high-dimensional regression with differing feature sets.
The paper introduces a transfer learning framework for structured matrix estimation when both the ambient dimension and the intrinsic representation grow over time. It models the target parameter as an embedded source component plus low‑rank innovations and sparse edits, and proposes an anchored alternating projection estimator that preserves the transferred subspace while estimating only the new components. Deterministic error bounds are derived that separate target noise, representation growth, and source estimation error, showing improved rates when rank and sparsity increments are small, and the framework is applied to Markov transition matrix estimation and structured covariance estimation with theoretical guarantees and empirical validation.
arXiv:2609.37083v1 Announce Type: cross Abstract: We study the problem of recovering the governing ODE of a dynamical system from unstructured, high-dimensional observations such as images. Existing...
arXiv:2507.02248v2 Announce Type: replace-cross Abstract: In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank t...
The paper demonstrates that a neural solver trained on a single condition can generate a reusable response space via its output Jacobian, enabling efficient cross‑condition solution transfer. By introducing Linearized Subspace Transfer (LST) and Active Transfer Modeling (ATM), the authors recover target solutions through residual minimization and selectively acquire additional response spaces based on coverage indicators. Experiments on six PDE systems show that this approach reduces error and offline construction cost compared to physics‑informed baselines, achieving significant accuracy gains and rapid target adaptation.
arXiv:2607. 06287v1 Announce Type: cross Abstract: We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from predicted observations.
arXiv:2608. 13504v1 Announce Type: new Abstract: We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data.
The paper addresses the mismatch between learner and client data distributions in federated learning, noting that traditional client selection methods often ignore this misalignment. It introduces a dynamic, influence-aware client selection framework that uses a small proxy dataset to estimate each client's utility for the learner’s objective, prioritizing informative sources while mitigating noise and heterogeneity. Experiments on CIFAR-10 with heterogeneous partitions show the proposed method outperforms static and dynamic baselines, achieving faster convergence and higher accuracy.
We study kernel-based operator learning in a two-stage sampling framework, where an offline kernel regression operator learns a discretized representation of the target operator from input-output pairs and an online kernel reconstruction operator recovers the output function from predicted observations. Our main theoretical contribution is an explicit budget allocation condition relating the number $N$ of training pairs, the number $n$ of input observations, and the output resolution $m$.
arXiv:2610. 23337v1 Announce Type: new Abstract: Pretrained models are often reused across downstream tasks, motivating the question of whether this transfer learning procedure can provide a substantial performance improvement, namely, in terms of the scaling law.
arXiv:2501. 10870v2 Announce Type: replace-cross Abstract: The principal objective of this work is twofold within nonparametric regression settings: (1) to establish the minimax optimal convergence rates for fixed-bandwidth Gaussian kernel spectral algorithms when the true regression function resides in a Sobolev space, and (2) to apply Gaussian spectral algorithms for achieving robust and adaptive transfer learning under concept shift.