arXiv Statistics ML
Structure and Exact Certification of Nonnegative Tensor Decompositions
Read the original on arXiv Statistics ML →The Flow has not summarised this story yet — read it at arXiv Statistics ML.
Related stories
arXiv Machine Learning
Sep 11
Identifiability of Nonnegative Tensor Decompositions via Positive Scattering
arXiv:2609. 11606v1 Announce Type: cross Abstract: Identifiability of tensor decompositions is often established through linear-algebraic conditions on the factor families.
Hugging Face Trending Papers
Sep 10
Identifiability of Nonnegative Tensor Decompositions via Positive Scattering
The paper introduces a new concept called positive scattering to enhance identifiability of nonnegative tensor decompositions. By combining this scattering term with existing dimension-based conditions, the authors derive two sufficient criteria that guarantee minimality, nonnegative rank, and uniqueness for subsets of components. The key result is a positive splitting inequality that links dimension constraints with support-induced geometric rigidity, and the authors show that the scattering term’s mode costs are discrete, enabling an exact activation characterization via graph connectivity. This criterion can certify sparse nonnegative tensor decompositions that elude traditional Kruskal and Lovitz–Petrov conditions, even after reshaping, and reduces to familiar matrix results in the two-dimensional case.
arXiv Machine Learning
Sep 23
Intrinsic Interaction Geometry Controls the Low-Rank Complexity of Softmax Attention
arXiv:2608.28150v2 Announce Type: replace Abstract: How much matrix rank is required to preserve every bounded value output of normalized softmax attention? We study the unrestricted maximum-row-\(\e...
arXiv AI
Jul 16
ExTernD: Expanded-Rank Ternary Decomposition Ternary LLM PTQ with Accuracy Approaching Any Quantization Level
arXiv:2607. 13511v1 Announce Type: cross Abstract: We introduce ExTernD (Expanded-rank Ternary Decomposition), a post-training factorization of each LLM weight matrix $A \in \mathbb{R}^{m \times n}$ into $A \approx B \mathrm{diag}(D) C$ with ternary factors $B \in \{-1,0,+1\}^{m \times k}$, $C \in \{-1,0,+1\}^{k \times n}$ and a real scale vector $D \in \mathbb{R}^k$.
arXiv Machine Learning
Aug 20
Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems
The paper proposes a new dimension‑reduction strategy for transfer‑operator models of dynamical systems that focuses on scoring the σ‑algebra generated by coordinates rather than the operator’s spectral span. By using a χ²‑divergence criterion between embedded present and future states, the method guarantees that twice the intrinsic system dimension suffices to capture the full operator spectrum, even for systems with weakly interacting components that would otherwise require exponentially many modes. Experiments on benchmark systems show that this algebraic approach recovers masked components missed by rank‑based methods and enables accurate prediction of those components from few labels.
arXiv Machine Learning
Aug 5
Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications
arXiv:2605. 25303v3 Announce Type: replace-cross Abstract: The $2 \rightarrow q$ norm of a matrix $X \in \mathbb{R}^{n \times d}$ is defined as $\lVert X \rVert_{2 \rightarrow q} = \sup_{\lVert v \rVert_2 = 1} \lVert Xv \rVert_q$.