Kronecker
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Related Articles from SNS
Rethinking Bregman Divergences in Kronecker-Factored Optimizers
arXiv:2606.00542v2 Announce Type: replace Abstract: Shampoo-style optimizers approximate gradient covariance matrices using Kronecker-factored structures. Recent work~\cite{lin2026understanding} showed that such approximations can be viewed as projections under Bregman matrix divergences, leading to different Kronecker-factored preconditioners. However, it remains unclear what role the choice of divergence plays when the covariance is not exactly Kronecker-factored.
Diving into Kronecker Adapters: Component Design Matters
arXiv:2602.01267v2 Announce Type: replace Abstract: Kronecker adapters have emerged as a promising approach for fine-tuning large-scale models, enabling high-rank updates through tunable component structures. However, existing work largely treats the component structure as a fixed or heuristic design choice, leaving the dimensions and number of Kronecker components underexplored. In this paper, we identify component structure as a key factor governing the capacity of Kronecker adapters.
Kronecker products and iterated matrix multiplication
arXiv:2606.08363v1 Announce Type: new Abstract: We observe that the Kronecker product of tensors is the operation that converts the determinant polynomial into Cayley's first hyperdeterminant. We apply the Kronecker product to iterated matrix multiplication, which results in the hypercomputant, a VNP-complete and VW[1]-complete polynomial whose hardness we prove via the equivariance of the Kronecker product. The construction works over arbitrary commutative semirings and also for the tensor...
A Kronecker algorithm for locally closed sets over a perfect field
arXiv:2512.14888v2 Announce Type: replace-cross Abstract: We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety $V$ defined over a perfect field $k$. The variety $V$ is the Zariski closure of the set of common zeros $\{F_1=0,\ldots,F_r=0,G\not=0\}$ of multivariate polynomials $F_1,\ldots,F_r\in k[X_1,\ldots,X_n]$ outside a prescribed hypersurface $\{G=0\}$. We assume that $F_1,\ldots,F_r$...
Structure-Informed Bounds on the Kronecker Rank of Block-Structured Matrices
arXiv:2605.30908v1 Announce Type: new Abstract: We derive theoretical bounds on the Kronecker rank of block-structured matrices that possess both inner and outer structure. Building on the matrix-to-tensor and tensor-to-matrix framework of Kilmer and Saibaba ($\textit{SIAM J. Matrix Anal.
KromHC: Manifold-Constrained Hyper-Connections with Kronecker-Product Residual Matrices
Announce Type: replace Abstract: The success of Hyper-Connections (HC) in neural networks (NN) has also highlighted issues related to training instability and restricted scalability. The Manifold-Constrained Hyper-Connections (mHC) mitigate these challenges by projecting the residual connection space onto a Birkhoff polytope, however, it faces two issues: 1) its iterative Sinkhorn-Knopp (SK) algorithm does not always yield exactly doubly stochastic residual matrices; 2) mHC incurs a...
Spectral Asymptotics of Neural Network Loss Landscapes: An Exact Decomposition of the Curvature Exponent
arXiv:2606.02596v1 Announce Type: new Abstract: The curvature exponent $\alpha$ in $h_k \propto \sigma_k^\alpha$ -- governing how Hessian eigenvalues scale with gradient singular values -- varies systematically across layer types ($\alpha \approx 2$ for convolutions, $\approx 1$ for transformer attention, $< 1$ for MLP up-projections). We prove the Spectral Alignment Decomposition: $\alpha = 2 + d\log\Phi_k / d\log\sigma_k$, where $\Phi_k$ measures alignment between Kronecker factor...
Deep learning four decades of human migration
Abstract Human migration is a fundamental driver of global demographic change, shaping population structure, labour markets and social policy across countries1,2,3. Although long-term migration patterns are often linked to economic development4, they can shift rapidly in response to shocks such as conflict, environmental crises and political change5. Despite its importance, migration remains difficult to measure consistently: existing data are sparse, concentrated in high-income settings and...
Model-Preserving Adaptive Rounding
Announce Type: replace Abstract: The goal of quantization is to produce a compressed model whose output distribution is as close to the original model's as possible. To do this tractably, most quantization algorithms minimize the immediate activation error of each layer as a proxy for the end-to-end error. However, this ignores the effect of future layers, making it a poor proxy.
Deconstructing the Composite Channel for Beyond Diagonal RIS: Channel Estimation and Beamforming Design
arXiv:2606.01564v1 Announce Type: cross Abstract: As beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) gain increasing attention in high-frequency wireless communications, accurate and scalable channel-estimation methods become essential. This paper develops a parametric channel-estimation and beamforming framework that deconstructs the composite BD-RIS channel into its generating directional factors, revealing the tensor structure induced jointly by propagation geometry and...