Xfredhd May 2026

¹ Department of Computer Science, University of Valencia, Spain ² Department of Electrical Engineering, Indian Institute of Technology Delhi, India ³ Data Science Lab, Stanford University, USA

[ \mathcalL = \sum_k=1^3\lambda_k,\mathcalL \textrec^(k) + \lambda_g ,\mathcalL \textGPR ]

| Domain | Typical Dimensionality | Example | |----------------------------|------------------------|-----------------------------------------| | Genomics & Transcriptomics | 10⁶ – 10⁸ | Single‑cell RNA‑seq expression matrices | | Remote Sensing | 10⁴ – 10⁶ | Hyperspectral cubes (hundreds of bands) | | Recommender Systems | 10⁶ – 10⁹ | User–item interaction tensors | | Natural Language Processing| 10⁵ – 10⁷ | Contextualized token embeddings | xfredhd

Resulting sketch (\tildeX) ∈ ℝ^N × S is , can be computed on‑the‑fly, and fits comfortably in GPU memory for S ≈ 10³–10⁴.

[ \textsim_X (x_i, x_j) \approx \textsim_Z (f(x_i), f(x_j)) ] ¹ Department of Computer Science, University of Valencia,

The total loss:

XFREDHD: A Novel Framework for Extreme‑Scale Feature‑Rich Embedding and Dimensionality Reduction in High‑Dimensional Data Authors: Dr. A. M. Sanchez¹, Prof. L. K. Rao², Dr. J. H. Miller³ H. Miller³ [ \big|\langle \tildex_i

[ \big|\langle \tildex_i, \tildex_j\rangle - \langle x_i, x_j\rangle\big| \le \epsilon |x_i|,|x_j| ]