The paper introduces Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training that turns hierarchical feature learning into an explicit iterative spectral procedure. In this framework, each layer independently selects directions with maximal low-degree correlation to the label, providing a tractable surrogate for deep learning and a kernel-space interpretation. Experiments on fully connected and convolutional networks show that Neural LoFi outperforms lazy random-feature baselines, recovers meaningful structured filters, and aligns with early gradient-descent feature discovery on real datasets.
arXiv:2311. 02960v5 Announce Type: replace Abstract: Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data.
Over the past decade, deep neural networks (DNNs) have achieved remarkable success on complex machine-learning tasks, yet the theoretical foundations of their performance remain incomplete. From a statistical viewpoint, a natural question is: can DNNs attain feature-learning and prediction consistency comparable to that of classical models?
arXiv:2510. 24616v4 Announce Type: replace-cross Abstract: For four decades statistical physics has been providing a framework to analyse neural networks.
arXiv:2605. 31244v2 Announce Type: replace Abstract: Neural scaling laws describe predictable power-law relationships between model size, dataset size, compute, and performance.
arXiv:2506. 13139v3 Announce Type: replace-cross Abstract: Modern Machine Learning (ML) and Deep Neural Networks (DNNs) often operate on high-dimensional data and rely on overparameterized models, where classical low-dimensional intuitions break down.
arXiv:2602. 06065v3 Announce Type: replace-cross Abstract: Understanding how the structure of language can be learned from sentences alone is a central question in both cognitive science and machine learning.
arXiv:2602. 20062v2 Announce Type: replace Abstract: Pretraining and fine-tuning are central stages in modern machine learning systems.
Muon has recently emerged as a strong optimizer for large-scale deep learning, where it reshapes gradient updates through approximate orthogonalization and has been reported to outperform Adam and AdamW in large language model training. Its empirical success has motivated a growing body of theoretical work that interprets Muon as steepest descent under the spectral norm.
arXiv:2607. 13246v1 Announce Type: cross Abstract: Muon has recently emerged as a strong optimizer for large-scale deep learning, where it reshapes gradient updates through approximate orthogonalization and has been reported to outperform Adam and AdamW in large language model training.
arXiv:2604. 11613v4 Announce Type: replace-cross Abstract: Transformers can perform in-context classification from a few labeled examples, yet the inference-time algorithm remains opaque.
arXiv:2606. 30813v1 Announce Type: cross Abstract: Deep neural networks with repeated architectural blocks, such as transformers, often exhibit structured relationships across layers that emerge during training.
arXiv:2606. 05863v1 Announce Type: new Abstract: Grokking suggests that fitting the training data and learning a simple underlying rule may occur on different time scales.