Search arXivSearch

arXiv · 2602.05490

Report on the second Toulouse Tensor Workshop

Abstract

This report documents the program of the second Toulouse Tensor Workshop which took place at the University of Toulouse on September 17-19, 2025, and summarizes the main points of discussion. This workshop follows the first Workshop (CECAM workshop on Tensor Contraction Library Standardization), which took place in Toulouse one year earlier, on May 24-25, 2024 and led to the formation of a tensor standardization working group, which has since specified a low-level standard interface for tensor operations available freely on GitHub. The 2025 workshop brought together developers of applications which rely extensively on tensor computations such as quantum many-body simulations in chemistry and physics (material science and electronic structure calculations), as well as developers and experts of tensor software who have the know-how to provide the technical support for such applications. The workshop enabled the community to provide feedback on the specified low-level interface and how it can be further refined. It also initiated a discussion on how the standardization efforts should be oriented in the near feature, in particular on what should be higher-level interfaces and how to tackle other requirements of the community such as tensor decompositions, symmetric tensors and structured sparsity support.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jan Brandejs, Trond Saue, Andre Severo Pereira Gomes, Lucas Visscher, Paolo Bientinesi. 2026-02-05. Report on the second Toulouse Tensor Workshop. https://arxiv.org/abs/2602.05490

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

The Pauli Lightcone: Information-Theoretic Error Mitigation Beyond the Autocorrelation

We introduce the wavemap: a spatial portrait of noise effects that assigns each site a per-noise-level arrival delay l_γ(v) and cross-entropy loss L_γ(v). These observables are exact at the lightcone frontier, where bond dimension χis small and the simulation is most faithful. Eigenvalue analysis of the composed gate-plus-noise Pauli transfer matrices confirms that the studied noise is pure amplitude damping: the spatial propagation pattern is entirely determined by the gate, making the wavemap a model-free noise diagnostic. We apply the multi-product formula (MPF) to recover the noiseless Pauli weight field from the noisy samples, subject to the Lieb-Robinson causal constraint nMPF <= nnl . Fitting time-adaptive coefficients α(t) over the frontier recovers up to 55% of the information loss relative to the best noisy sample, exploiting the fact that the frontier is where truncation error is smallest. On an IBM heavy-hex lattice with heterogeneous hardware noise the method identifies an information-starved regime, pointing to calibrated synthetic noise as the next required experiment.

cs.MS

Ozaki Scheme II: A GEMM-oriented emulation of floating-point matrix multiplication using an integer modular technique

This paper addresses emulation algorithms for matrix multiplication. General Matrix-Matrix Multiplication (GEMM), a fundamental operation in the Basic Linear Algebra Subprograms (BLAS), is typically optimized for specific hardware architectures. The Ozaki scheme is a well-established GEMM-based emulation method for matrix multiplication, wherein input matrices are decomposed into several low-precision components to ensure that the resulting matrix product is computed exactly through numerical operations. This study proposes a novel GEMM-based emulation method for matrix multiplication that leverages the Chinese Remainder Theorem. The proposed method inherits the computational efficiency of highly optimized GEMM routines and further enables control over the number of matrix multiplications, which can enhance computational accuracy. We present numerical experiments featuring INT8 Tensor Core operations on GPUs and FP64 arithmetic on CPUs as case studies. The results demonstrate that FP64 emulation using the proposed method achieves performance levels of up to 7.4 to 9.8 TFLOPS on the NVIDIA RTX 4090 and 56.6 to 80.2 TFLOPS on the NVIDIA GH200, exceeding the measured performance of native FP64 arithmetic. Furthermore, for FP64 computations on CPUs, the proposed method achieved up to a 2.3x speedup in emulating quadruple-precision arithmetic compared to the conventional Ozaki scheme.

cs.MS

Eigensolvers for polynomial roots and tensor decomposition

Computing eigenvalues and eigenvectors is at the heart of the solution of many non-linear problems. For instance, finding the roots of polynomial systems reduces to computing joint eigenvectors of operators of multiplication. Similarly, tensor decomposition can be performed via the joint diagonalization of submatrices of the Catalecticant of the tensor. We describe and illustrate symbolic-numeric methods for computing the solutions of these algebraic problems from the computation of joint eigenvectors of commuting operators, and for analysing their multiplicity structure, as well as their implementation in the package AlgebraicSolvers.jl.

cs.MS