arXiv:2607. 23454v1 Announce Type: new Abstract: Data-driven remaining useful life (RUL) prediction requires complete degradation trajectories for training, yet such run-to-failure data are scarce and expensive.
arXiv:2602.06797v3 Announce Type: replace-cross Abstract: We study optimal learning rate (LR) schedules under the functional scaling law (FSL) framework (Li et al., 2025), which decomposes training d...
The paper investigates whether a looped estimator—one that repeatedly applies a single fitted operator with shared parameters—can enhance statistical accuracy while staying within a fixed parameter budget. It establishes upper and lower bounds on squared Hellinger risk for looped sieve maximum likelihood and compares them to the untied counterpart, revealing a tradeoff between parameter sharing, iteration count, and accuracy. For models with known H"older smoothness, looped residual feedforward networks and a post‑layer‑normalized Transformer achieve minimax polynomial rates with a fixed number of bounded real parameters, and under certain conditions the looped estimator’s worst‑case risk vanishes as sample size grows, outperforming the untied approach.
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.
arXiv:2303. 08777v3 Announce Type: replace-cross Abstract: Cross-validation is one of the most widely used tools for risk estimation and model selection in statistics and machine learning, yet its theoretical properties when embedded in a learning procedure remain insufficiently understood.
arXiv:2607. 22268v1 Announce Type: cross Abstract: Remaining useful life (RUL) prediction and failure-mode classification are central tasks in predictive maintenance.
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
arXiv:2602. 05657v2 Announce Type: replace Abstract: The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm.
arXiv:2606. 01894v1 Announce Type: new Abstract: Accurate Remaining Useful Life prediction is critical for industrial predictive maintenance.
arXiv:2606. 27711v1 Announce Type: cross Abstract: We introduce a neural network-based framework for learning time series estimators through a process we term decision-theoretic pretraining.
arXiv:2507. 01598v5 Announce Type: replace Abstract: Muon, a recently proposed optimizer that leverages the inherent matrix structure of neural network parameters, has demonstrated strong empirical performance, indicating its potential as a successor to standard optimizers such as AdamW.
arXiv:2608. 20183v1 Announce Type: new Abstract: Classical information criteria such as the Bayesian Information Criterion (BIC) rely on regularity assumptions that break down for singular models, leading to incorrect model selection in settings such as deep learning.
arXiv:2604. 07328v3 Announce Type: replace Abstract: How does the choice of training data influence an AI model?