aiqbench analysis
This paper introduces a probabilistic extension of manifold meta-learning, utilizing amortized Variational Inference to address overfitting in low-data regimes for nonlinear system identification. By combining Maximum A Posteriori estimation with Laplace approximation, the method provides calibrated uncertainty bounds while maintaining predictive accuracy comparable to deterministic baselines on dynamical systems like Bouc–Wen.
Variational meta-learning inference for low dimensional neural system identification
arXiv:2607.18965v1 Announce Type: cross Abstract: Deep learning has proven highly effective for nonlinear system identification, but heavily parameterized neural networks are prone to overfitting in low-data regimes and lack reliable uncertainty quantification. The recently developed manifold meta-learning framework addresses the data efficiency problem by restricting the model parameters to a meta-learned low-dimensional manifold. However, that method is purely deterministic. We propose a fully probabilistic extension of the manifold meta-learning framework, based on amortized Variational Inference, where a generative prior over the low-dimensional parameter manifold is learned. During task-specific adaptation, we combine Maximum A Posteriori estimation with the Laplace approximation to yield a mathematically grounded posterior approximation. Evaluated on a static regression task and the Bouc--Wen dynamical system benchmark, the proposed approach achieves predictive accuracy comparable to its deterministic counterpart while successfully providing calibrated uncertainty bounds in severely low-data regimes.
Abstract:Deep learning has proven highly effective for nonlinear system identification, but heavily parameterized neural networks are prone to overfitting in low-data regimes and lack reliable uncertainty quantification. The recently developed manifold meta-learning framework addresses the data efficiency problem by restricting the model parameters to a meta-learned low-dimensional manifold. However, that method is purely deterministic. We propose a fully probabilistic extension of the manifold meta-learning framework, based on amortized Variational Inference, where a generative prior over the low-dimensional parameter manifold is learned. During task-specific adaptation, we combine Maximum A Posteriori estimation with the Laplace approximation to yield a mathematically grounded posterior approximation. Evaluated on a static regression task and the Bouc--Wen dynamical system benchmark, the proposed approach achieves predictive accuracy comparable to its deterministic counterpart while successfully providing calibrated uncertainty bounds in severely low-data regimes.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Systems and Control (eess.SY)
arXiv:2607.18965 [cs.LG]
(or arXiv:2607.18965v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.18965 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 235 words
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