LAIR-Net: Leaky Alignment-Impulse Residual Networks for Tabular Regression
Abstract
Deep randomized models fix hidden-layer parameters through random initialization and learn only closed-form readouts, typically adding depth by stacking random trans formations without target-aware control of hidden-state evolution. We propose LAIR Net, the Leaky Alignment-Impulse Residual Network, which mixes a shallow learned anchor into each hidden state through a leaky residual transition. We derive a depth uniform bound on input-perturbation sensitivity and use controlled simulations to attribute gains over a randomized baseline to the anchor rather than recursion or added capacity. Benefits emerge when a nonlinear target structure is learnable at the available noise level and diminish for nearly linear targets or dominant noise. Across 23 benchmark datasets, LAIR-Net achieves the best average rank among eight randomized networks and twelve conventional models, with relative performance associated with the same nonlinear-structure and noise quantities identified in simulation.
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BibTeX
@misc{goswami2026lairnet,
title = {{LAIR-Net: Leaky Alignment-Impulse Residual Networks for Tabular Regression}},
author = {Rahul Goswami and Aryan Bhambu and Bittu Karmakar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.11538},
eprint = {2610.11538},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.11538},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - LAIR-Net: Leaky Alignment-Impulse Residual Networks for Tabular Regression
AU - Rahul Goswami
AU - Aryan Bhambu
AU - Bittu Karmakar
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.11538
UR - https://arxiv.org/abs/2610.11538
AB - Deep randomized models fix hidden-layer parameters through random initialization and learn only closed-form readouts, typically adding depth by stacking random trans formations without target-aware control of hidden-state evolution. We propose LAIR Net, the Leaky Alignment-Impulse Residual Network, which mixes a shallow learned anchor into each hidden state through a leaky residual transition. We derive a depth uniform bound on input-perturbation sensitivity and use controlled simulations to attribute gains over a randomized baseline to the anchor rather than recursion or added capacity. Benefits emerge when a nonlinear target structure is learnable at the available noise level and diminish for nearly linear targets or dominant noise. Across 23 benchmark datasets, LAIR-Net achieves the best average rank among eight randomized networks and twelve conventional models, with relative performance associated with the same nonlinear-structure and noise quantities identified in simulation.
ER -