arXiv subjects

Vasiliki Velona

Publications and source records attributed to Vasiliki Velona.

7 recordsLinked to original sources

arXiv2026

QEDBENCH: Quantifying the Alignment Gap in Automated Evaluation of University-Level Mathematical Proofs

As Large Language Models (LLMs) saturate elementary benchmarks, the research frontier has shifted from generation to the reliability of automated evaluation. We demonstrate that standard "LLM-as-a-Judge" protocols suffer from a systematic Alignment Gap when applied to upper-undergraduate to early graduate level mathematics. To quantify this, we introduce QEDBench, the first large-scale dual-rubric alignment benchmark to systematically measure alignment with human experts on university-level math proofs by contrasting course-specific rubrics against expert common knowledge criteria. By deploying a dual-evaluation matrix (7 judges x 5 solvers) against 1,000+ hours of human evaluation, we reveal that certain frontier evaluators like Claude Opus 4.5, DeepSeek-V3, Qwen 2.5 Max, and Llama 4 Maverick exhibit significant positive bias (up to +0.18, +0.20, +0.30, +0.36 mean score inflation, respectively). Furthermore, we uncover a critical reasoning gap in the discrete domain: while Gemini 3.0 Pro achieves state-of-the-art performance (0.91 average human evaluation score), other reasoning models like GPT-5 Pro and Claude Sonnet 4.5 see their performance significantly degrade in discrete domains. Specifically, their average human evaluation scores drop to 0.72 and 0.63 in Discrete Math, and to 0.74 and 0.50 in Graph Theory. In addition to these research results, we also release QEDBench as a public benchmark for evaluating and improving AI judges. Our benchmark is publicly published at https://github.com/qqliu/Yale-QEDBench.

cs.LG↗

arXiv2024

Inference in balanced community modulated recursive trees

We introduce a random recursive tree model with two communities, called balanced community modulated random recursive tree, or BCMRT in short. In this setting, pairs of nodes of different type appear sequentially. Each node of the pair decides independently to attach to their own type with probability 1-q, or to the other type with probability q, and then chooses its parent uniformly within the set of existing nodes with the selected type. We find that the limiting degree distributions coincide for different q. Therefore, as far as inference is concerned, other statistics have to be studied. We first consider the setting where the time-labels of the nodes, i.e., their time of arrival, are observed but their type is not. In this setting, we design a consistent estimator for q and provide bounds for the feasibility of testing between two different values of q. Moreover, we show that if q is small enough, then it is possible to cluster the nodes in a way correlated with the true partition, even though the algorithm is exponential in time (in passing, we show that our clustering procedure is intimately connected to the NP-hard problem of minimum fair bisection). In the unlabelled setting, i.e., when only the tree structure is observed, we show that it is possible to test between different values of q in a strictly better way than by random guessing. This follows from a delicate analysis of the sum-of-distances statistic.

math.ST↗

arXiv2021

Learning partial correlation graphs and graphical models by covariance queries

We study the problem of recovering the structure underlying large Gaussian graphical models or, more generally, partial correlation graphs. In high-dimensional problems it is often too costly to store the entire sample covariance matrix. We propose a new input model in which one can query single entries of the covariance matrix. We prove that it is possible to recover the support of the inverse covariance matrix with low query and computational complexity. Our algorithms work in a regime when this support is represented by tree-like graphs and, more generally, for graphs of small treewidth. Our results demonstrate that for large classes of graphs, the structure of the corresponding partial correlation graphs can be determined much faster than even computing the empirical covariance matrix.

math.ST↗

arXiv2021

Broadcasting on random recursive trees

We study the broadcasting problem when the underlying tree is a random recursive tree. The root of the tree has a random bit value assigned. Every other vertex has the same bit value as its parent with probability $1-q$ and the opposite value with probability $q$, where $q \in [0,1]$. The broadcasting problem consists in estimating the value of the root bit upon observing the unlabeled tree, together with the bit value associated with every vertex. In a more difficult version of the problem, the unlabeled tree is observed but only the bit values of the leaves are observed. When the underlying tree is a uniform random recursive tree, in both variants of the problem we characterize the values of $q$ for which the optimal reconstruction method has a probability of error bounded away from $1/2$. We also show that the probability of error is bounded by a constant times $q$. Two simple reconstruction rules are analyzed in detail. One of them is the simple majority vote, the other is the bit value of the centroid of the tree. Most results are extended to linear preferential attachment trees as well.

math.PR↗

arXiv2020

Structure and enumeration of K4-minor-free links and link-diagrams

We study the class L of link-types that admit a K4-minor-free diagram, i.e., they can be projected on the plane so that the resulting graph does not contain any subdivision of K4. We prove that L is the closure of a subclass of torus links under the operation of connected sum. Using this structural result, we enumerate L and subclasses of it, with respect to the minimum number of crossings or edges in a projection of L' in L. Further, we obtain counting formulas and asymptotic estimates for the connected K4-minor-free link-diagrams, minimal K4-minor-free link-diagrams, and K4-minor-free diagrams of the unknot.

math.CO↗

arXiv2019

Minor-Obstructions for Apex Sub-unicyclic Graphs

A graph is sub-unicyclic if it contains at most one cycle. We also say that a graph $G$ is $k$-apex sub-unicyclic if it can become sub-unicyclic by removing $k$ of its vertices. We identify 29 graphs that are the minor-obstructions of the class of $1$-apex sub-unicyclic graphs, i.e., the set of all minor minimal graphs that do not belong in this class. For bigger values of $k$, we give an exact structural characterization of all the cactus graphs that are minor-obstructions of $k$-apex sub-unicyclic graphs and we enumerate them. This implies that, for every $k$, the class of $k$-apex sub-unicyclic graphs has at least $0.34\cdot k^{-2.5}(6.278)^{k}$ minor-obstructions.

math.CO↗

arXiv2018

Encoding and avoiding 2-connected patterns in polygon dissections and outerplanar graphs

Let $Δ=\{ δ_1,δ_2,...,δ_m \} $ be a finite set of 2-connected patterns, i.e. graphs up to vertex relabelling. We study the generating function $D_{Δ}(z,u_1,u_2,...,u_m),$ which counts polygon dissections and marks subgraph copies of $δ_i$ with the variable $u_i$. We prove that this is always algebraic, through an explicit combinatorial decomposition depending on $Δ$. The decomposition also gives a defining system for $D_{Δ}(z,\mathbf{0})$, which encodes polygon dissections that restrict these patterns as subgraphs. In this way, we are able to extract normal limit laws for the patterns when they are encoded, and perform asymptotic enumeration of the resulting classes when they are avoided. The results can be directly transferred in the case of labelled outerplanar graphs. We give examples and compute the relevant constants when the patterns are small cycles or dissections.

math.CO↗