Linear Models
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Related Articles from SNS
A Conformation-Centric Generative Foundation Model for Linear Polymer Modeling and Design
arXiv:2510.16023v2 Announce Type: replace Abstract: Linear polymers, macromolecules formed from monomers covalently bonded into continuous chains, underpin countless technologies and are indispensable to modern life. While deep learning is advancing polymer science, existing methods typically represent the whole linear polymer solely through monomer-level descriptors, overlooking the global structural information inherent in polymer conformations, which ultimately limits their practical...
When Both Layers Learn: Training Dynamics of Representing Linear Models via ReLU Networks
arXiv:2606.04476v1 Announce Type: new Abstract: In this paper, we study the gradient descent dynamics for jointly training both layers of a one-hidden-layer ReLU network to fit a linear target function. Concretely, we consider a realizable setting where inputs are drawn i.i.d. from a Gaussian distribution and labels follow a planted linear model.
FreqLite: A Lightweight Frequency-Decomposed Linear Model with Adaptive Reversible Normalization for Robust Long-Term Time-Series Forecasting
arXiv:2606.01339v1 Announce Type: new Abstract: Long-term time-series forecasting needs models that are accurate yet efficient enough for commodity hardware. Lightweight linear forecasters are remarkably strong in this regime, yet they leave two openings: reversible instance normalization (RevIN) de-normalizes the entire horizon with a single lookback statistic, which is inaccurate under non-stationarity, and time-domain trend/seasonal decomposition relies on a fixed, non-adaptive filter. We...
Sequential Least-Squares Estimators with Fast Randomized Sketching for Linear Statistical Models
arXiv:2509.06856v2 Announce Type: replace-cross Abstract: We propose a novel randomized framework for the estimation problem of large-scale linear statistical models, namely Sequential Least-Squares Estimators with Fast Randomized Sketching (SLSE-FRS), which integrates Sketch-and-Solve and Iterative-Sketching methods for the first time. By iteratively constructing and solving sketched least-squares (LS) subproblems with increasing sketch sizes to achieve better precisions, SLSE-FRS gradually...
Fine-Tuning Without Forgetting In-Context Learning: A Theoretical Analysis of Linear Attention Models
Announce Type: replace Abstract: Transformer-based large language models exhibit in-context learning, enabling adaptation to downstream tasks via few-shot prompting with demonstrations. In practice, such models are often fine-tuned to improve zero-shot performance on downstream tasks, allowing them to solve tasks without examples and thereby reducing inference costs. However, fine-tuning can degrade in-context learning, limiting the performance of fine-tuned models on tasks not seen during...
Dynamic sliding and rolling friction models for linear viscoelastic contact pairs
arXiv:2606.09128v1 Announce Type: new Abstract: This paper considers the sliding and rolling contact between viscoelastic bodies. Combining linear viscoelastic rheologies for bristle-like elements with nonlinear dynamic friction models, it derives a class of viscoelasto-kinematic equations, formulated as a system of partial differential equations (PDEs) governing the evolution of the frictional force, bristle deformations, and internal state variables at the interface between the contacting...
Quilting the Brain: Whole-Brain iEEG Reconstruction via Incomplete Observation Linear Mixed Models
Mapping human brain function at high spatiotemporal resolution is constrained by the physical limitations of non-invasive imaging and the sparse sampling of invasive electrophysiology. While intracranial electroencephalography (iEEG) captures local field potentials with millimeter precision, clinical implantation strategies result in a ``coverage paradox'': observations are restricted to disjoint, patient-specific patches, leaving most of the cortex unobserved. This study introduces the...
$H_2$ optimal model reduction of linear systems with multiple quadratic outputs
Announce Type: replace Abstract: In this work, we consider the $H_2$ optimal model reduction of dynamical systems that are linear in the state equation and up to quadratic nonlinearity in the output equation. As our primary theoretical contributions, we derive gradients of the squared $H_2$ system error with respect to the reduced model quantities and, from the stationary points of these gradients, introduce Gramian-based first-order necessary conditions for the $H_2$ optimal approximation...
$\mathcal{H}_2$-optimal model reduction of linear quadratic-output systems by multivariate rational interpolation
Announce Type: replace Abstract: This paper addresses the $\mathcal{H}_2$-optimal approximation of linear dynamical systems with quadratic-output functions, also known as linear quadratic-output systems. Our major contributions are threefold. First, we derive interpolatory first-order optimality conditions for the linear quadratic-output $\mathcal{H}_2$ minimization problem.
Generalized Forcing Method: Generation of Diverse Data for Training Linear Transport PDE Closure Models
arXiv:2606.05141v1 Announce Type: new Abstract: Data-driven closure modeling for transport partial differential equations requires training data that are accurate, affordable, diverse, and directly tailored to the target closure fields. We develop the Generalized Forcing Method (GFM), a data-generation framework for training linear transport closure models. GFM generates such data by running simulations with a zero initial condition and an extra body force that is constructed compatibly with...