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Matricized low-rank approximation via SVD is a standard surrogate for tensor decompositions, but entry-wise reconstruction error fails to capture multiway geometric degradation. Under an orthogonal Tucker model, we characterize this degradation using two metrics: cross-mode Direction Loss, measuring geometric subspace deviation from rank truncation and noise rotation, and Interaction Loss, quantifying multilinear interaction distortion in the core tensor.
arXiv:2609.28029v1 Announce Type: cross Abstract: The key-value (KV) cache of autoregressive transformers can be viewed as a fourth-order tensor spanning attention heads, tokens, features, and groupe...
The key-value (KV) cache of autoregressive transformers can be viewed as a fourth-order tensor spanning attention heads, tokens, features, and grouped layers. We measure the singular-value spectra of...
arXiv:2608. 05136v1 Announce Type: new Abstract: Gradient descent on a factored model $W = UV^\top$ is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not.
The paper introduces MultiHU‑TD, an interpretable framework for multifeature hyperspectral unmixing that employs tensor decomposition and incorporates the abundance sum‑to‑one constraint via an ADMM algorithm. It extends previous models by adding mathematical morphology and neighborhood patch analysis, and provides detailed mathematical, physical, and graphical interpretations linked to the extended linear mixing model. Experiments on real hyperspectral images demonstrate the model’s interpretability and effectiveness, with code released on GitHub.
arXiv:2609.14307v1 Announce Type: new Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, u...