Tootfinder

Efficient randomized algorithms for the fixed Tucker-rank problem of Tucker decomposition with adaptive shifts
Maolin Che, Yimin Wei, Chong Wu, Hong Yan
https://arxiv.org/abs/2506.04840

Efficient randomized algorithms for the fixed Tucker-rank problem of Tucker decomposition with adaptive shifts
Randomized numerical linear algebra is proved to bridge theoretical advancements to offer scalable solutions for approximating tensor decomposition. This paper introduces fast randomized algorithms for solving the fixed Tucker-rank problem of Tucker decomposition, through the integration of adaptive shifted power iterations. The proposed algorithms enhance randomized variants of truncated high-order singular value decomposition (T-HOSVD) and sequentially T-HOSVD (ST-HOSVD) by incorporating dyna…

CORA: Coalitional Rational Advantage Decomposition for Multi-Agent Policy Gradients
Mengda Ji, Genjiu Xu, Liying Wang
https://arxiv.org/abs/2506.04265 http…

CORA: Coalitional Rational Advantage Decomposition for Multi-Agent Policy Gradients
This work focuses on the credit assignment problem in cooperative multi-agent reinforcement learning (MARL). Sharing the global advantage among agents often leads to suboptimal policy updates as it fails to account for the distinct contributions of agents. Although numerous methods consider global or individual contributions for credit assignment, a detailed analysis at the coalition level remains lacking in many approaches. This work analyzes the over-updating problem during multi-agent policy…

Diffusion Tensor MRI and Spherical-Deconvolution-Based Tractography on an Ultra-Low Field Portable MRI System
James Gholam, Phil Schmid, Joshua Ametepe, Alix Plumley, Leandro Beltrachini, Francesco Padormo, Rui Teixeira, Rafael OHalloran, Kaloian Petkov, Klaus Engel, Steven CR Williams, Sean Deoni, Mara Cercignani, Derek K Jones
https://

Diffusion Tensor MRI and Spherical-Deconvolution-Based Tractography on an Ultra-Low Field Portable MRI System
Ultra-low-field (ULF) MRI is emerging as an alternative modality to high-field (HF) MRI due to its lower cost, minimal siting requirements, portability, and enhanced accessibility factors that enable large-scale deployment. Although ULF-MRI exhibits lower signal-to-noise ratio (SNR), advanced imaging and data-driven denoising methods enabled by high-performance computing have made contrasts like diffusion-weighted imaging (DWI) feasible at ULF. This study investigates the potential and limitati…

Beyond Monoliths: Expert Orchestration for More Capable, Democratic, and Safe Large Language Models
Philip Quirke, Narmeen Oozeer, Chaithanya Bandi, Amir Abdullah, Jason Hoelscher-Obermaier, Jeff M. Phillips, Joshua Greaves, Clement Neo, Fazl Barez, Shriyash Upadhyay
https://arxiv.org/abs/2506.00051

Beyond Monoliths: Expert Orchestration for More Capable, Democratic, and Safe Large Language Models
This position paper argues that the prevailing trajectory toward ever larger, more expensive generalist foundation models controlled by a handful of big companies limits innovation and constrains progress. We challenge this approach by advocating for an "Expert Orchestration" framework as a superior alternative that democratizes LLM advancement. Our proposed framework intelligently selects from thousands of existing models based on query requirements and decomposition, focusing on identifying w…

Burnside rings for racks and quandles
Nadia Mazza, Markus Szymik
https://arxiv.org/abs/2507.01425 https://arxiv.org/pdf/2507.01425

Burnside rings for racks and quandles
We restructure and advance the classification theory of finite racks and quandles by employing powerful methods from transformation groups and representation theory, especially Burnside rings. These rings serve as universal receptacles for those invariants of racks and quandles that are additive with respect to decompositions. We present several fundamental results regarding their structure, including additive bases and multiplicative generators. We also develop a theory of marks, which is anal…

Causal Decompositions of 1D Quantum Cellular Automata
Augustin Vanrietvelde, Octave Mestoudjian, Pablo Arrighi
https://arxiv.org/abs/2506.22219 https://

Causal Decompositions of 1D Quantum Cellular Automata
Understanding quantum theory's causal structure stands out as a major matter, since it radically departs from classical notions of causality. We present advances in the research program of causal decompositions, which investigates the existence of an equivalence between the causal and the compositional structures of unitary channels. Our results concern one-dimensional Quantum Cellular Automata (1D QCAs), i.e. unitary channels over a line of $N$ quantum systems (with or without periodic boundar…

Maximum volume coordinates for Grassmann interpolation: Lagrange, Hermite, and errors
Rasmus Jensen, Ralf Zimmermann
https://arxiv.org/abs/2506.01574 https…

Maximum volume coordinates for Grassmann interpolation: Lagrange, Hermite, and errors
We present a novel approach to Riemannian interpolation on the Grassmann manifold. Instead of relying on the Riemannian normal coordinates, i.e. the Riemannian exponential and logarithm maps, we approach the interpolation problem with an alternative set of local coordinates and corresponding parameterizations. A special property of these coordinates is that their calculation does not require any matrix decompositions. This is a numerical advantage over Riemann normal coordinates and many other …

Advanced linear algebra
Teo Banica
https://arxiv.org/abs/2506.18666 https://arxiv.org/pdf/2506.18666…

Advanced linear algebra
This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the theory of the resultant and discriminant. Then we discuss the Jordan form and its basic applications to physics, and other advanced decomposition results for the matrices. We then go into positivity topics, involving matrices and bilinear forms, and with a look in…

Noise-tolerant tomography of multimode linear optical interferometers with single photons
Yu. A. Biriukov, R. D. Morozov, I. V. Dyakonov, M. V. Rakhlin, A. I. Galimov, G. V. Klimko, S. V. Sorokin, I. V. Sedova, M. M. Kulagina, Yu. M. Zadiranov, A. A. Toropov, A. A. Korneev, S. P. Kulik, S. S. Straupe
https://arxiv.org/abs/2506.2…

Noise-tolerant tomography of multimode linear optical interferometers with single photons
Linear optical networks are fundamental to the advancement of quantum technologies, including quantum computing, communication, and sensing. The accurate characterization of these networks, described by unitary matrices, is crucial to their effective utilization and scalability. In this work, we present the method for reconstructing the transfer matrix of a linear optical interferometer based on the analysis of cross-correlation functions of photon counts between pairs of output modes. Our appr…

Scalable inference of large-scale random kronecker graphs via tensor decomposition and Einstein summation
Sanaa Khobizy
https://arxiv.org/abs/2506.22292 ht…

Scalable inference of large-scale random kronecker graphs via tensor decomposition and Einstein summation
In this paper, we extend the analysis of random Kronecker graphs to multi-dimensional networks represented as tensors, enabling a more detailed and nuanced understanding of complex network structures. We decompose the adjacency tensor of such networks into two components: a low-rank signal tensor that captures the essential network structure and a zero-mean noise tensor that accounts for random variations. Building on recent advancements in tensor decomposition and random tensor theory, we intr…