Tootfinder

This https://arxiv.org/abs/2505.17282 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Attention with Trained Embeddings Provably Selects Important Tokens
Token embeddings play a crucial role in language modeling but, despite this practical relevance, their theoretical understanding remains limited. Our paper addresses the gap by characterizing the structure of embeddings obtained via gradient descent. Specifically, we consider a one-layer softmax attention model with a linear head for binary classification, i.e., $\texttt{Softmax}( p^\top E_X^\top ) E_X v = \frac{ \sum_{i=1}^T \exp(p^\top E_{x_i}) E_{x_i}^\top v}{\sum_{j=1}^T \exp(p^\top E_{x_{j…

This https://arxiv.org/abs/2503.03933 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Arithmetic properties of Cantor sets involving non-diagonal forms
We show conditions on $k$ such that any number $x$ in the interval $[0, k/2]$ can be represented in the form $x_1^{a_1} x_2^{a_2} + x_3^{a_3} x_4^{a_4} + \cdots + x_{k-1}^{a_{k-1}} x_k^{a_k}$, where the exponents $a_{2i-1}$ and $a_{2i}$ are positive integers satisfying $a_{2i-1} + a_{2i} = s$ for $i = 1, 2, \dots, k/2$, and each $x_i$ belongs to the generalized Cantor set. Moreover, we discuss different types of non-diagonal polynomials and clarify the optimal results in low-dimensional cases.

This https://arxiv.org/abs/2503.21940 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Normalized vector solutions of nonlinear Schrödinger systems
Given $μ>0$ we look for solutions $ λ\in\mathbb{R}$ and $v_1,\dots,v_k\in H^1(\mathbb{R}^N)$ of the system \[ \begin{cases} \displaystyle -Δv_i+ λv_i+V_i(x)v_i = \sum_{\substack{j=1}}^kβ_{ij} v_iv_j^2 &\text{ in } \mathbb{R}^N, \text{ } i=1,\dots,k,\newline \displaystyle \int_{\mathbb{R}^N} \left(v_1^2+\dots+v_k^2 \right)\mathrm{d} x = μ, \end{cases}\] where $N=1,2,3$, $V_i:\mathbb R^N\to \mathbb R$ and $β_{ij}\in\mathbb{R}$ satisfy $β_{ij}=β_{ji}$ and $β_{ii}>0$. Under …

Constructing strong starters of orders $3p$: triplication with SAT solver
Oleg Ogandzhanyants, Sergey Sadov, Margo Kondratieva
https://arxiv.org/abs/2506.06461

Constructing strong starters of orders $3p$: triplication with SAT solver
A novel approach to building strong starters in cyclic groups of orders $n$ divisible by 3 from starters of smaller orders is presented. A strong starter in $Z_n$ ($n$ odd) is a partition of the set $\{1,2,\dots,n-1\}$ into pairs $\{a_i,b_i\}$ such that all pair sums $a_i+b_i$ are distinct and nonzero modulo $n$ and all differences $\pm(a_i-b_i)$ are distinct and nonzero modulo $n$. A special interest to strong starters of odd orders divisible by 3 is motivated by Horton's conjecture which clai…

This https://arxiv.org/abs/2411.13425 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCR_…

Watermark under Fire: A Robustness Evaluation of LLM Watermarking
Various watermarking methods (``watermarkers'') have been proposed to identify LLM-generated texts; yet, due to the lack of unified evaluation platforms, many critical questions remain under-explored: i) What are the strengths/limitations of various watermarkers, especially their attack robustness? ii) How do various design choices impact their robustness? iii) How to optimally operate watermarkers in adversarial environments? To fill this gap, we systematize existing LLM watermarkers and water…

This https://arxiv.org/abs/2506.04560 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Universality of convergence rate of rightmost eigenvalue of complex IID random matrices
Let $X$ be an $n\times n$ matrix with independent and identically distributed (i.i.d.) entries $x_{ij} \stackrel{\text { d }}{=} n^{-1 / 2} ξ$ with $ξ$ being a complex random variable of mean zero and variance one. Let $\{σ_i\}_{1\le i\le n}$ be the eigenvalues of $X,$ and $R_n:=\max_i \Re σ_i$ and $Z_n$ be some scaled version of $R_n.$ It was proved that $Z_n$ converges weakly to the Gumbel distribution $Λ$ under certain moment conditions on $ξ.$ We further prove that for a complex rando…

This https://arxiv.org/abs/2506.00120 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Type II RR string fields and exotic diffeomorphisms
We study the theory of massless fields of type II strings arising from the string field theory that uses two string fields, a physical one and an extra one that allows the writing of an action, but whose degrees of freedom ultimately decouple. The mechanism allowing the description of the self-dual five-form of type IIB, anticipated by Sen, is used by the SFT to describe all Ramond-Ramond forms in type IIB and IIA in a manifestly duality-invariant way. We find explicit expressions for the leadi…

This https://arxiv.org/abs/2506.01323 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCG_…

Computing Diverse and Nice Triangulations
We initiate the study of computing diverse triangulations to a given polygon. Given a simple $n$-gon $P$, an integer $ k \geq 2 $, a quality measure $σ$ on the set of triangulations of $P$ and a factor $ α\geq 1 $, we formulate the Diverse and Nice Triangulations (DNT) problem that asks to compute $k$ \emph{distinct} triangulations $T_1,\dots,T_k$ of $P$ such that a) their diversity, $\sum_{i < j} d(T_i,T_j) $, is as large as possible \emph{and} b) they are nice, i.e., $σ(T_i) \leq ασ^* $ …

This https://arxiv.org/abs/2506.05831 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Heartcare Suite: Multi-dimensional Understanding of ECG with Raw Multi-lead Signal Modeling
We present Heartcare Suite, a multimodal comprehensive framework for finegrained electrocardiogram (ECG) understanding. It comprises three key components: (i) Heartcare-220K, a high-quality, structured, and comprehensive multimodal ECG dataset covering essential tasks such as disease diagnosis, waveform morphology analysis, and rhythm interpretation. (ii) Heartcare-Bench, a systematic and multi-dimensional benchmark designed to evaluate diagnostic intelligence and guide the optimization of Medi…

This https://arxiv.org/abs/2504.11666 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A note on the second supplementary law of rational power residue symbols
As a natural generalization of the Legendre symbol, the $q$-th power residue symbol $(a/p)_q$ is defined for primes $p$ and $q$ with $p\equiv 1 \bmod q$. In this paper, we generalize the second supplementary law by providing an explicit condition for $(q/p)_q = 1$, when $p$ has a special form $p = \sum_{i=0}^{q-1} m^i n^{q-1-i}$. This condition is expressed in terms of the polylogarithm $\mathrm{Li}_{1-q}(x)$ of negative index. Our proof relies on an argument similar to Lemmermeyer's proof of E…