arXiv:2607. 04535v4 Announce Type: replace Abstract: Orthogonal and Stiefel constraints are widely used in neural network optimization to control weight geometry, improve conditioning, and stabilize signal propagation.
arXiv:2607. 04535v1 Announce Type: new Abstract: Orthogonal and Stiefel layers give neural weights exact spectral control, but they also impose a strong modeling constraint: all represented singular values are fixed at one.
The paper introduces Spectral‑Sphere‑Constrained Hyper‑Connections (s²HC), a new method for controlling the residual matrices used in Hyper‑Connections (HC). Unlike previous doubly stochastic constraints that caused identity degeneration, expressivity bottlenecks, and parameterization inefficiencies, s²HC confines these matrices to a spectral norm sphere, restoring flexibility over subdominant spectra and eliminating unstable Sinkhorn‑Knopp iterations. This approach preserves training stability while allowing expressive, non‑degenerate residual matrices.
arXiv:2602. 00722v2 Announce Type: replace Abstract: Parameter-efficient continual learning aims to adapt pre-trained models to sequential tasks without forgetting previously acquired knowledge.
arXiv:2606. 19411v1 Announce Type: new Abstract: Selecting a small, diverse, high-quality subset from a massive pool of candidates is a recurring primitive in modern machine learning -- data curation and coreset selection for training and fine-tuning large models, active-learning batch acquisition, prompt and exemplar selection for in-context learning, retrieval diversification, and experimental design.
arXiv:2607. 25299v1 Announce Type: cross Abstract: Optimization over the Stiefel manifold plays a significant role in various machine learning tasks.
arXiv:2601. 21487v2 Announce Type: replace-cross Abstract: We study minimization of smooth functions over feasible sets that have smooth embedded-manifold structure throughout or only on selected regions, using linear minimization oracles (LMOs) to determine search directions under user-chosen norms.
arXiv:2609.21039v1 Announce Type: new Abstract: A pervasive structural pattern in modern deep learning is the linear factorization block: a submodule of the form $W = BA$ in which two parameter matri...
arXiv:2605. 17109v3 Announce Type: replace-cross Abstract: In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly.
arXiv:2604.22494v2 Announce Type: replace-cross Abstract: We introduce two federated learning frameworks for the classical SPDnet model operating on symmetric positive definite (SPD) matrices with St...
arXiv:2602. 22895v2 Announce Type: replace-cross Abstract: Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages.
SPARCL introduces a spectral partitioned analytic continual learning method that addresses forgetting in analytic class‑incremental learning. By decomposing the running autocorrelation into a high‑energy core and a residual complement, SPARCL freezes core components for old classes and updates only the residual block, ensuring closed‑form updates with an invariance guarantee. Experiments on CIFAR‑100, CUB‑200, ImageNet‑R, and ImageNet‑A with a frozen ViT‑B/16 protocol show that SPARCL narrows the performance gap between classical analytic learners and strong representation matchers while complementing sparse feature‑decorrelation approaches.
arXiv:2607. 19771v1 Announce Type: cross Abstract: Muon and related matrix-sign optimizers are increasingly used to pre-train large language models, but their effect on the internal geometry of individual weight matrices is not well understood.