Tootfinder

MaXIFE: Multilingual and Cross-lingual Instruction Following Evaluation
Yile Liu, Ziwei Ma, Xiu Jiang, Jinglu Hu, Jing Chang, Liang Li
https://arxiv.org/abs/2506.01776

MaXIFE: Multilingual and Cross-lingual Instruction Following Evaluation
With the rapid adoption of large language models (LLMs) in natural language processing, the ability to follow instructions has emerged as a key metric for evaluating their practical utility. However, existing evaluation methods often focus on single-language scenarios, overlooking the challenges and differences present in multilingual and cross-lingual contexts. To address this gap, we introduce MaXIFE: a comprehensive evaluation benchmark designed to assess instruction-following capabilities a…

On the rank of a random symmetric matrix in the large deviation regime
Yi Han
https://arxiv.org/abs/2506.01155 https://arxiv.org/pdf/…

On the rank of a random symmetric matrix in the large deviation regime
Let $A$ be an $n\times n$ random symmetric matrix with independent identically distributed subgaussian entries of unit variance. We prove the following large deviation inequality for the rank of $A$: for all $1\leq k\leq c\sqrt{n}$, $$\mathbb{P}(\operatorname{Rank}(A)\geq n-k)\geq 1-\exp(-c'kn),$$ for some fixed constants $c,c'>0$. A similar large deviation inequality is proven for the rank of the adjacency matrix of dense Erdos-Renyi graphs. This corank estimate enhances the recent breakthroug…

Rescaled topological entropy
E. Rego, C. Rojas, X. Wen
https://arxiv.org/abs/2506.02383 https://arxiv.org/pdf/2506.02383

Rescaled topological entropy
We prove that to any smooth vector field of a closed manifold it can be assigned a nonnegative number called {\em rescaled topological entropy} satisfying the following properties: it is an upper bound for both the topological entropy and the rescaled metric entropy \cite{ww}; coincides with the topological entropy for nonsingular vector fields; is positive for certain surface vector fields (in contrast to the topological entropy); is invariant under rescaled topological conjugacy; and serves a…

Associative triple trisystems and standard embeddings
Ra\'ul Felipe, Guillermo Vera de Salas
https://arxiv.org/abs/2506.04191 https://

Associative triple trisystems and standard embeddings
Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the classical relationships between associative, Jordan, and Lie triple systems within the context of trisystems. We present a significant example by equipping the space of matrices with a non-trivial associative dialgebra structure. We conclude defining the concept of d…

Violation of Luttinger's theorem in one-dimensional interacting fermions
Meng Gao, Yin Zhong
https://arxiv.org/abs/2506.04064 https://

Violation of Luttinger's theorem in one-dimensional interacting fermions
Using the density matrix renormalization group method, we systematically investigate the evolution of the Luttinger integral in the one-dimensional generalized t-V model as a function of filling and interaction strength, identifying three representative phases. In the weak-coupling regime, the zero-frequency Green's function shows a branch-cut structure at the Fermi momentum, and the Luttinger integral accurately reflects the particle density. As the interaction increases, the spectral weight n…

On the genericity of irreducible subfactors
Yoonkyeong Lee, Brent Nelson
https://arxiv.org/abs/2506.01838 https://arxiv.org/pdf/2506.…

On the genericity of irreducible subfactors
We show that finitely generated irreducible $\mathrm{II}_1$ subfactors are generic in the following sense. Given a separable $\mathrm{II}_1$ factor $M$ and an integer $n\geq 2$, equip the set of $n$-tuples of self-adjoint operators in $M$ with norm at most $1$ with the metric $d(x,y) = \max_{1\leq i \leq n} \|x_i - y_i\|_2$. Then the set of $n$-tuples that generate an irreducible subfactor of $M$ forms a dense $G_δ$ set in this metric space. On the way to proving this result, we show…

Join Andrew Musselman and Trevor Grant as they present the latest developments in Mahout's new quantum compute layer, Qumat. They will provide an overview of the project, explain why Qumat was developed, and demonstrate its current capabilities. They will also present a demo of Qumat in action and conclude with calls to action for researchers and engineers who are interested in using and contributing to the project.
Learn more:

Qumat: Apache Mahout Quantum Compute
Following Mahout's core values of interoperability and providing tools for matrix arithmetic at scale, we have added a new layer (qumat) alongside our existing distributed matrix math framework (Samsara), that allows quantum researchers and developers to write code once and run it on any back-end available. As with distributed compute systems like Spark and Flink, moving from one platform to another typically requires a complete code rewrite. This is prohibitive in most cases, but Samsara allow…

MATLAB developer bringing systems back online following ransomware attack https://therecord.media/matlab-developer-bringing-systems-online-ransomware