conference paper published yes Leonardo Iurada author Simone Bombari author ca726dda-de17-11ea-bc14-f9da834f63aa Tatiana Tommasi author Marco Mondelli author 27EB676C-8706-11E9-9510-7717E66974250000-0002-3242-7020 GradSch department MaMo department ICLR: International Conference on Learning Representations Inference in High Dimensions: Light-speed Algorithms and Information Limits project Trustworthy Deep Learning Theory: Private Over-Parameterized Models and Robust LLMs project Large-scale deep learning models are known to memorize parts of the training set. In machine learning theory, memorization is often framed as interpolation or label fitting, and classical results show that this can be achieved when the number of parameters p in the model is larger than the number of training samples n. In this work, we consider memorization from the perspective of data reconstruction, demonstrating that this can be achieved when p is larger than dn, where d is the dimensionality of the data. More specifically, we show that, in the random features model, when p ≫ dn, the subspace spanned by the training samples in feature space gives sufficient information to identify the individual samples in input space. Our analysis suggests an optimization method to reconstruct the dataset from the model parameters, and we demonstrate that this method performs well on various architectures (random features, two-layer fully-connected and deep residual networks). Our results reveal a law of data reconstruction, according to which the entire training dataset can be recovered as p exceeds the threshold dn. https://research-explorer.ista.ac.at/download/22894/22907/2026_ICLR_Iurada.pdf application/pdfno OpenReview2026Rio de Janeiro, Brazil eng 9798331339678 2509.22214 2026145275-145314 https://research-explorer.ista.ac.at/record/22857 Iurada, L., Bombari, S., Tommasi, T., &#38; Mondelli, M. (2026). A law of data reconstruction for random features (and beyond). In <i>14th International Conference on Learning Representations</i> (Vol. 2026, pp. 145275–145314). Rio de Janeiro, Brazil: OpenReview. L. Iurada, S. Bombari, T. Tommasi, and M. Mondelli, “A law of data reconstruction for random features (and beyond),” in <i>14th International Conference on Learning Representations</i>, Rio de Janeiro, Brazil, 2026, vol. 2026, pp. 145275–145314. Iurada, Leonardo, et al. “A Law of Data Reconstruction for Random Features (and Beyond).” <i>14th International Conference on Learning Representations</i>, vol. 2026, OpenReview, 2026, pp. 145275–314. Iurada L, Bombari S, Tommasi T, Mondelli M. A law of data reconstruction for random features (and beyond). In: <i>14th International Conference on Learning Representations</i>. Vol 2026. OpenReview; 2026:145275-145314. Iurada, Leonardo, Simone Bombari, Tatiana Tommasi, and Marco Mondelli. “A Law of Data Reconstruction for Random Features (and Beyond).” In <i>14th International Conference on Learning Representations</i>, 2026:145275–314. OpenReview, 2026. Iurada L, Bombari S, Tommasi T, Mondelli M. 2026. A law of data reconstruction for random features (and beyond). 14th International Conference on Learning Representations. ICLR: International Conference on Learning Representations vol. 2026, 145275–145314. L. Iurada, S. Bombari, T. Tommasi, M. Mondelli, in:, 14th International Conference on Learning Representations, OpenReview, 2026, pp. 145275–145314. 228942026-09-09T13:31:46Z2026-09-11T12:26:43Z