Tootfinder

Personalized Exercise Recommendation with Semantically-Grounded Knowledge Tracing
Yilmazcan Ozyurt, Tunaberk Almaci, Stefan Feuerriegel, Mrinmaya Sachan
https://arxiv.org/abs/2507.11060

Personalized Exercise Recommendation with Semantically-Grounded Knowledge Tracing
We introduce ExRec, a general framework for personalized exercise recommendation with semantically-grounded knowledge tracing. Our method builds on the observation that existing exercise recommendation approaches simulate student performance via knowledge tracing (KT) but they often overlook two key aspects: (a) the semantic content of questions and (b) the sequential, structured progression of student learning. To address this, our ExRec presents an end-to-end pipeline, from annotating the KCs…

F-isocrystals of Higher Direct Images of $p$-Divisible Groups
Zhenghui Li, Yanshuai Qin
https://arxiv.org/abs/2506.11736 https://arxi…

F-isocrystals of Higher Direct Images of $p$-Divisible Groups
For a $p$-divisible group $G$ over a smooth projective variety $X$ over $k$, where $k$ is a field finitely generated over a perfect field of characteristic $p$, we show that the formal group $R^i f_{\fppf*} G$ is isogenous to a $p$-divisible group. The Dieudonné crystal of its divisible part is canonically isomorphic to the slope-$[0,1]$ part of $R^i f_{\crys*} \cM^{cr}(G)$ in the category of $F$-isocrystals over $k$. This provides an answer to the rational form of a question of Artin--Mazur r…

Can Mixture-of-Experts Surpass Dense LLMs Under Strictly Equal Resources?
Houyi Li, Ka Man Lo, Ziqi Wang, Zili Wang, Wenzhen Zheng, Shuigeng Zhou, Xiangyu Zhang, Daxin Jiang
https://arxiv.org/abs/2506.12119

Can Mixture-of-Experts Surpass Dense LLMs Under Strictly Equal Resources?
Mixture-of-Experts (MoE) language models dramatically expand model capacity and achieve remarkable performance without increasing per-token compute. However, can MoEs surpass dense architectures under strictly equal resource constraints - that is, when the total parameter count, training compute, and data budget are identical? This question remains under-explored despite its significant practical value and potential. In this paper, we propose a novel perspective and methodological framework to …

No-dimensional Tverberg-type problems
Alexander Polyanskii
https://arxiv.org/abs/2506.13451 https://arxiv.org/pdf/2506.13451

No-dimensional Tverberg-type problems
Recently, Adiprasito et al. have initiated the study of the so-called no-dimensional Tverberg problem. This problem can be informally stated as follows: Given $n\geq k$, partition an $n$-point set in Euclidean space into $k$ parts such that their convex hulls intersect a ball of relatively small radius. In this survey, we aim to present the recent progress towards solving the no-dimensional Tverberg problem and new open questions arising in its context. Also, we discuss the colorful variation…

Approximating fixed size quantum correlations in polynomial time
Julius A. Zeiss, Gereon Ko{\ss}mann, Omar Fawzi, Mario Berta
https://arxiv.org/abs/2507.12302

Approximating fixed size quantum correlations in polynomial time
We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to previous analytic approaches, which focused on scaling with the number of questions and answers, but yielded only strict $\mathrm{exp}(1/\varepsilon)$ guarantees. Our main result is based on novel Bose-symmetric quantum de Finetti theorems tailored for constrai…

Restoring Gaussian Blurred Face Images for Deanonymization Attacks
Haoyu Zhai, Shuo Wang, Pirouz Naghavi, Qingying Hao, Gang Wang
https://arxiv.org/abs/2506.12344

Restoring Gaussian Blurred Face Images for Deanonymization Attacks
Gaussian blur is widely used to blur human faces in sensitive photos before the photos are posted on the Internet. However, it is unclear to what extent the blurred faces can be restored and used to re-identify the person, especially under a high-blurring setting. In this paper, we explore this question by developing a deblurring method called Revelio. The key intuition is to leverage a generative model's memorization effect and approximate the inverse function of Gaussian blur for face restora…

Lifting residual Galois representations with the same semi-simplification
Stefan Nikoloski
https://arxiv.org/abs/2506.12644 https://a…

Lifting residual Galois representations with the same semi-simplification
If a $p$-adic Galois representation $ρ_{f,ν}:Γ_{\mathbb Q} \to \GL_2(E_{f,ν})$ attached to some eigenform $f$ is residually reducible it will have 2 non-isomorphic reductions, which have the same semi-simplification. In this paper, we answer a version of the inverse question, first brought up by Toby Gee and Alice Pozzi. Starting with two modulo $p$ non-semi-simple representations $\overline{ρ_1},\overline{ρ_2}:Γ_{\mathbb Q} \to \GL_2(k)$, which have the same semi-simplification we show …

NFC North 2025 preview, plus the Colts QB competition https://www.nytimes.com/athletic/6430697/2025/06/16/nfc-north-preview-nfl-2025-bears-vikings-packers-lions-scoop-city/

Constructing targeted minimum loss/maximum likelihood estimators: a simple illustration to build intuition
Rachael K. Ross, Lina M. Montoya, Dana E. Goin, Ivan Diaz, Audrey Renson
https://arxiv.org/abs/2507.11680

Constructing targeted minimum loss/maximum likelihood estimators: a simple illustration to build intuition
Use of machine learning to estimate nuisance functions (e.g. outcomes models, propensity score models) in estimators used in causal inference is increasingly common, as it can mitigate bias due to model misspecification. However, it can be challenging to achieve valid inference (e.g., estimate valid confidence intervals). The efficient influence function (EIF) provides a recipe to go from a statistical estimand relevant to our causal question, to an estimator that can validly incorporate machin…

A note on the second-largest number of dissociation sets in connected graphs
Pingshan Li, Ke Yang, Wei Jin
https://arxiv.org/abs/2506.12740 https://…

A note on the second-largest number of dissociation sets in connected graphs
A subset of vertices is called a dissociation set if it induces a subgraph with vertex degree at most one. Recently, Yuan et al. established the upper bound of the maximum number of dissociation sets among all connected graphs of order n and characterized the corresponding extremal graphs.They also proposed a question regarding the second-largest number of dissociation sets among all connected graphs of order n and the corresponding extremal graphs. In this paper, we give a positive answer to t…