arXiv:2605. 06938v2 Announce Type: replace-cross Abstract: Recently Brown et al.
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arXiv:2310.16295v2 Announce Type: replace-cross Abstract: Neural network have achieved remarkable successes in many scientific fields. However, the interpretability of the neural network model is sti...
arXiv:2602.06042v2 Announce Type: replace-cross Abstract: The Moore-Penrose Pseudo-inverse (PInv) serves as the fundamental solution for linear systems. In this paper, we propose a natural generaliza...
arXiv:2607. 08843v1 Announce Type: new Abstract: In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space.
The paper presents a theoretical analysis of symmetric autoencoders, a class of deep learning architectures frequently used in machine learning tasks. It distinguishes between different symmetric designs and shows that the reconstruction error of orthonormal symmetric autoencoders can be interpreted via the Eckart‑Young‑Schmidt theorem. Building on this insight, the authors propose an EYS‑based initialization strategy using repeated SVD, and validate its effectiveness through numerical experiments comparing it to conventional deep autoencoders.
The paper introduces Linearized Subspace Refinement (LSR), a post‑training framework that uses the local linearized model of a trained neural network to compute a low‑dimensional correction via a reduced least‑squares problem. LSR is architecture‑agnostic and improves accuracy across tasks such as function approximation, operator learning, physics‑informed fine‑tuning, and noisy inverse problems, often achieving order‑of‑magnitude error reductions. The method reveals that standard training can leave significant accuracy plateaus due to numerical ill‑conditioning, and it offers a subspace rank that balances correction strength, stability, and noise sensitivity.
arXiv:2507. 05164v2 Announce Type: replace-cross Abstract: In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms.