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Tensor renormalization group approach to entanglement entropy
Takahiro Hayazaki, Daisuke Kadoh, Shinji Takeda, Gota Tanaka
https://arxiv.org/abs/2509.02185 https://

Tensor renormalization group approach to entanglement entropy
We propose a method to compute the entanglement entropy (EE) using the tensor renormalization group (TRG) method. The reduced density matrix of a $d$-dimensional quantum system is represented as a $(d+1)$-dimensional tensor network. We develop an explicit algorithm for $d=1$ that enables the calculation of EE for single-interval subsystems of arbitrary size. We test our method in two-dimensional tensor network of the Ising model. The central charge is obtained as $c=0.49997(8)$ for $D=96$, whic…

Noise-reduced stochastic resolution of identity to CC2 for large-scale calculations via tensor hypercontraction
Chongxiao Zhao, Wenjie Dou
https://arxiv.org/abs/2509.21885 https…

Noise-reduced stochastic resolution of identity to CC2 for large-scale calculations via tensor hypercontraction
The stochastic resolution of identity (sRI) approximation significantly reduces the computational scaling of CC2 from O(N^5) to O(N^3), where N is a measure of system size. However, the inherent stochastic noise, while controllable, can introduce substantial errors in energy derivatives, limiting its reliability for molecular dynamics simulations. To mitigate this limitation, we introduce a noise-reduced approach, termed THC-sRI-CC2, which synergistically combines the sRI framework with tensor …

Succinct Oblivious Tensor Evaluation and Applications: Adaptively-Secure Laconic Function Evaluation and Trapdoor Hashing for All Circuits
Damiano Abram, Giulio Malavolta, Lawrence Roy
https://arxiv.org/abs/2508.09673

Succinct Oblivious Tensor Evaluation and Applications: Adaptively-Secure Laconic Function Evaluation and Trapdoor Hashing for All Circuits
We propose the notion of succinct oblivious tensor evaluation (OTE), where two parties compute an additive secret sharing of a tensor product of two vectors $\mathbf{x} \otimes \mathbf{y}$, exchanging two simultaneous messages. Crucially, the size of both messages and of the CRS is independent of the dimension of $\mathbf{x}$. We present a construction of OTE with optimal complexity from the standard learning with errors (LWE) problem. Then we show how this new technical tool enables a host o…

veScale: Consistent and Efficient Tensor Programming with Eager-Mode SPMD
Youjie Li, Cheng Wan, Zhiqi Lin, Hongyu Zhu, Jiacheng Yang, Ziang Song, Xinyi Di, Jiawei Wu, Huiyao Shu, Wenlei Bao, Yanghua Peng, Haibin Lin, Li-Wen Chang
https://arxiv.org/abs/2509.07003

veScale: Consistent and Efficient Tensor Programming with Eager-Mode SPMD
Large Language Models (LLMs) have scaled rapidly in size and complexity, requiring increasingly intricate parallelism for distributed training, such as 3D parallelism. This sophistication motivates a shift toward simpler, more debuggable programming paradigm like Single Program Multiple Data (SPMD). However, SPMD in eager execution introduces two key challenges: ensuring consistency with single-device execution and achieving high performance at scale. In this paper, we introduce veScale, an eag…

KVCompose: Efficient Structured KV Cache Compression with Composite Tokens
Dmitry Akulov, Mohamed Sana, Antonio De Domenico, Tareq Si Salem, Nicola Piovesan, Fadhel Ayed
https://arxiv.org/abs/2509.05165

KVCompose: Efficient Structured KV Cache Compression with Composite Tokens
Large language models (LLMs) rely on key-value (KV) caches for efficient autoregressive decoding; however, cache size grows linearly with context length and model depth, becoming a major bottleneck in long-context inference. Prior KV cache compression methods either enforce rigid heuristics, disrupt tensor layouts with per-attention-head variability, or require specialized compute kernels. We propose a simple, yet effective, KV cache compression framework based on attention-guided, layer-adap…

Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model
Yintati Zhang, Aritra Sinha, Marek M. Rams, Jacek Dziarmaga
https://arxiv.org/abs/2510.04756

Finite temperature dopant-induced spin reorganization explored via tensor networks in the two-dimensional $t$-$J$ model
Doped Mott insulators host intertwined spin-charge phenomena that evolve with temperature and can culminate in stripe order or superconductivity at low temperatures. The two-dimensional $t$-$J$ model captures this interplay yet finite-temperature, infinite-size calculations remain difficult. Using purification represented by a tensor network - an infinite projected entangled-pair state (iPEPS) ansatz - we simulate the $t$-$J$ model at finite temperature directly in the thermodynamic limit, reac…

A Note on Lower Bounds in Szemer\'edi's Theorem with Random Differences
Jason Zheng
https://arxiv.org/abs/2508.01187 https://arxiv.org/pdf/2508.011…

A Note on Lower Bounds in Szemerédi's Theorem with Random Differences
In this note, we consider Szemerédi's theorem on $k$-term arithmetic progressions over finite fields $\mathbb{F}_p^n$, where the allowed set $S$ of common differences in these progressions is chosen randomly of fixed size. Combining a generalization of an argument of Altman with Moshkovitz--Zhu's bounds for the partition rank of a tensor in terms of its analytic rank, we (slightly) improve the best known lower bounds (due to Briët) on the size $|S|$ required for Szemerédi's theorem…

Congestion bounds via Laplacian eigenvalues and their application to tensor networks with arbitrary geometry
Sayan Mukherjee, Shinichiro Akiyama
https://arxiv.org/abs/2510.02725

Congestion bounds via Laplacian eigenvalues and their application to tensor networks with arbitrary geometry
Embedding the vertices of arbitrary graphs into trees while minimizing some measure of overlap is an important problem with applications in computer science and physics. In this work, we consider the problem of bijectively embedding the vertices of an $n$-vertex graph $G$ into the leaves of an $n$-leaf rooted binary tree $\mathcal{B}$. The congestion of such an embedding is given by the largest size of the cut induced by the two components obtained by deleting any vertex of $\mathcal{B}$. The c…

Low-rank matrix and tensor approximations: advancing efficiency of machine-learning interatomic potentials
Igor Vorotnikov, Fedor Romashov, Nikita Rybin, Maxim Rakhuba, Ivan S. Novikov
https://arxiv.org/abs/2509.04440

Low-rank matrix and tensor approximations: advancing efficiency of machine-learning interatomic potentials
Machine-learning interatomic potentials (MLIPs) have become a mainstay in computationally-guided materials science, surpassing traditional force fields due to their flexible functional form and superior accuracy in reproducing physical properties of materials. This flexibility is achieved through mathematically-rigorous basis sets that describe interatomic interactions within a local atomic environment. The number of parameters in these basis sets influences both the size of the training datase…