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This paper classifies when the represented mobility map of parameter gradient flow is fully determined by the representation, proving an initialization classification for wide two-factor matrix representations and relating ordinary closure to invariant-level metric factorization in analytic and smooth regimes.
GEM-KMeans introduces a spectrally normalized, memory-efficient NLR formulation for K-means clustering that fuses updates into a single matrix-multiplication epilogue, reducing GPU HBM storage to one factor while maintaining clustering accuracy at massive scale.
A PyTorch-enabled, GPU-accelerated clustering pipeline optimizes financial portfolio grouping at scale, delivering hard labels, soft factor loadings, and structural-break signals efficiently for instruments up to a million.
This paper evaluates the Muon optimizer on low-rank matrix factorization, finding it does not consistently outperform AdamW, challenging earlier claims about its advantages in large-scale deep learning.
This paper proposes a robust subspace-constrained quadratic model for learning low-dimensional structures from high-dimensional data, accommodating heavy-tailed noise. A gradient-based algorithm with backtracking line search is developed, and experiments show improved robustness and reconstruction accuracy.