Neural networks have emerged as powerful and versatile tools in the field of deep learning. As the complexity of the task increases, so do size and architectural complexity of the causing compression techniques to become a focus of current research. Parameter truncation can provide a significant reduction in memory and computational complexity. Originating from a model order reduction framework, the Discrete Empirical Interpolation Method is applied to the gradient descent training of neural networks and analyze for important parameters. The approach for various state-of-the-art neural networks is compared to established truncation methods. Further metrics like L₂ and Cross-Entropy Loss, as well as accuracy and compression rate are reported.

We discuss discrete-time dynamical systems depending on a parameter μ. Assuming that the system matrix A(μ) is given, but the parameter μ is unknown, we infer the most-likely parameter μ_m≈μ from an observed trajectory x of the dynamical system. We use parametric eigenpairs (v_i(μ),lambda_i(μ) of the system matrix A(μ) computed with Newton's method based on a Chebyshev expansion. We then represent x in the eigenvector basis defined by the v_i(μ) and compare the decay of the components with predictions based on the lambda_i(μ). The resulting estimates for μ are combined using a kernel density estimator to find the most likely value for μ_m and a corresponding uncertainty quantification.