Variational meta-learning inference for low dimensional neural system identification

• URL: http://arxiv.org/abs/2607.18965v1
• Date: Tue, 21 Jul 2026 10:55:48 GMT
• Title: Variational meta-learning inference for low dimensional neural system identification
• Abstract summary: Recently developed manifold meta-learning framework addresses the data efficiency problem by restricting the model parameters to a meta-learned low-dimensional manifold.<n>We propose a fully probabilistic extension of the manifold meta-learning framework, based on amortized Variational Inference.<n>During task-specific adaptation, we combine A Posteriori estimation with the Laplace approximation to yield a mathematically grounded posterior approximation.
• Score: 0.5505634045241289
• License: http://creativecommons.org/publicdomain/zero/1.0/
• 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.

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