arXiv subjects

Ioannis Tzachristas

Publications and source records attributed to Ioannis Tzachristas.

7 recordsLinked to original sources

arXiv2026

A solution to the Erdős Problem #1040

For a compact set $K\subset\mathbb{C}$, let $\vartheta(K)$ be the infimum of the planar areas of the unit lemniscates of all monic polynomials with zeros in $K$, allowing arbitrary degree and repeated zeros. We prove that $\vartheta(K)=0$ whenever $\operatorname{cap}(K)=1$, with no regularity assumption on $K$. The proof uses a centered harmonic polynomial that is positive on all but a set of arbitrarily small area in the polynomial hull of $K$. A Fourier average of exterior harmonic measures realizes this polynomial as the logarithmic potential of a signed measure having bounded density with respect to the equilibrium measure. A positive perturbation and an $L^1$ approximation by empirical measures then produce the required polynomials. This extends the smooth-boundary result of Krishnapur, Lundberg, and Ramachandran to arbitrary compact sets of capacity one. Together with the capacity-greater-than-one theorem of Ghosh and Ramachandran and an elementary argument for unbounded sets, it follows that $\vartheta(F)=0$ for every closed infinite set $F\subset\mathbb{C}$ of transfinite diameter at least one, answering the vanishing question in Erdős Problem 1040.

math.CA↗

arXiv2026

Aristotelian Virtue Profiling of LLMs through Ethical Dilemmas

Large Language Models (LLMs) often face ethical tradeoffs in which several responses may be defensible but express different priorities, such as fairness, honesty, courage, or restraint. We introduce VirtueMap, a framework for describing these patterns through an Aristotelian virtue-ethics lens. Instead of asking for a single correct answer, VirtueMap asks humans or LLMs to rank all five responses to each of seven general, non-lethal, non-political, and non-religious ethical dilemmas. To define the reference orderings used for scoring, we first proposed, for each dilemma and virtue, an ordering of the five responses from most to least expressive of that virtue. We then collected more than 100 respondent evaluations per ordering and retained it as operational ground truth only when at least 95% confirmed it. Rankings are scored against these retained orderings using normalized Borda alignment, yielding profiles over Practical Wisdom, Justice, Truthfulness, Courage, and Temperance. We apply VirtueMap to nine LLM families in a repeated-run evaluation and find high mean rank consistency (90.3%), with the largest differences appearing on Courage, Temperance, and Justice. We also release an interactive website that computes profiles locally in the browser and compares respondents with measured LLM profiles.

cs.AI↗

arXiv2026

NOEM$^{3}$A: a Neuro-symbolic Ontology-Enhanced Method for Multi-intent understanding in Mobile Agents

Mobile agents must map natural-language requests to executable intents under tight latency and privacy constraints. Scaling the language model is often an inefficient way to improve this component. We present NOEM$^{3}$A, a lightweight neuro-symbolic layer that augments compact language models with an intent ontology. For each query, NOEM$^{3}$A retrieves a small ontology neighborhood, injects candidate action labels into the prompt and applies a token-level decoding prior toward valid labels. This injects symbolic intent structure into both input and output representations while keeping inference suitable for local interaction. We also use Semantic Intent Similarity (SIS), a hierarchy-aware diagnostic based on ontology depth, to capture semantic proximity when predicted intents differ lexically. Experiments on MultiWOZ 2.3 dialogues show that ontology augmentation consistently improves TinyLlama and Llama-3.2-3B on exact match and Slot-F1. Our results suggest that symbolic alignment is an effective strategy for accurate, responsive and privacy-preserving on-device NLU.

cs.AI↗

arXiv2026

LLMs on Tabular Data with Limited Semantics: Evidence from Industrial Car Retrofit Prediction

Industrial retrofit planning depends on structured operational data rather than free text: planners must estimate whether a newly registered prototype will require a retrofit, which retrofit package it will need, and how long the work will take. We study an industrial dataset linking a prototype-registration system (284,271 vehicles) with a retrofit-management system (48,716 cleaned visits), and compare strong tabular machine learning baselines with three LLM-based strategies on row-serialized inputs: embedding features (Amazon Titan), direct prompted classification (Claude Sonnet 4), and an ML+LLM stacking approach. Across binary occurrence prediction, 15-way retrofit-type classification, per-visit duration regression, and an aggregated monthly benchmark, classical tree ensembles remain the strongest standalone models. However, the LLM results reveal a consistent pattern: embeddings remain useful on tables (binary AUC = 0.982), direct prompting collapses once semantic signal is stripped by hashing (binary AUC = 0.500; multiclass weighted F1 = 0.018), and hybrid stacking yields the best manually built multiclass model (weighted F1 = 0.626). On the monthly benchmark, lag-based machine learning outperforms time-series foundation models, though Chronos-small remains competitive in zero-shot forecasting. The results suggest that on privacy-constrained industrial tables, LLMs are more effective as complementary components than as replacements for strong tabular baselines.

cs.LG↗

arXiv2025

A Mathematical Theory of Top-$k$ Sparse Attention via Total Variation Distance

We develop a unified mathematical framework for certified Top-$k$ attention truncation that quantifies approximation error at both the distribution and output levels. For a single attention distribution $P$ and its Top-$k$ truncation $\hat P$, we show that the total-variation distance coincides with the discarded softmax tail mass and satisfies $\mathrm{TV}(P,\hat P)=1-e^{-\mathrm{KL}(\hat P\Vert P)}$, yielding sharp Top-$k$-specific bounds in place of generic inequalities. From this we derive non-asymptotic deterministic bounds -- from a single boundary gap through multi-gap and blockwise variants -- that control $\mathrm{TV}(P,\hat P)$ using only the ordered logits. Using an exact head-tail decomposition, we prove that the output error factorizes as $\|\mathrm{Attn}(q,K,V)-\mathrm{Attn}_k(q,K,V)\|_2=τ\|μ_{\mathrm{tail}}-μ_{\mathrm{head}}\|_2$ with $τ=\mathrm{TV}(P,\hat P)$, yielding a new head-tail diameter bound $\|\mathrm{Attn}(q,K,V)-\mathrm{Attn}_k(q,K,V)\|_2\leτ\,\mathrm{diam}_{H,T}$ and refinements linking the error to $\mathrm{Var}_P(V)$. Under an i.i.d. Gaussian score model $s_i\sim\mathcal N(μ,σ^2)$ we derive closed-form tail masses and an asymptotic rule for the minimal $k_\varepsilon$ ensuring $\mathrm{TV}(P,\hat P)\le\varepsilon$, namely $k_\varepsilon/n\approxΦ_c(σ+Φ^{-1}(\varepsilon))$. Experiments on bert-base-uncased and synthetic logits confirm the predicted scaling of $k_\varepsilon/n$ and show that certified Top-$k$ can reduce scored keys by 2-4$\times$ on average while meeting the prescribed total-variation budget.

cs.LG↗

arXiv2025

Guided Persona-based AI Surveys: Can we replicate personal mobility preferences at scale using LLMs?

This study explores the potential of Large Language Models (LLMs) to generate artificial surveys, with a focus on personal mobility preferences in Germany. By leveraging LLMs for synthetic data creation, we aim to address the limitations of traditional survey methods, such as high costs, inefficiency and scalability challenges. A novel approach incorporating "Personas" - combinations of demographic and behavioural attributes - is introduced and compared to five other synthetic survey methods, which vary in their use of real-world data and methodological complexity. The MiD 2017 dataset, a comprehensive mobility survey in Germany, serves as a benchmark to assess the alignment of synthetic data with real-world patterns. The results demonstrate that LLMs can effectively capture complex dependencies between demographic attributes and preferences while offering flexibility to explore hypothetical scenarios. This approach presents valuable opportunities for transportation planning and social science research, enabling scalable, cost-efficient and privacy-preserving data generation.

cs.CL↗

arXiv2024

Creating an LLM-based AI-agent: A high-level methodology towards enhancing LLMs with APIs

Large Language Models (LLMs) have revolutionized various aspects of engineering and science. Their utility is often bottlenecked by the lack of interaction with the external digital environment. To overcome this limitation and achieve integration of LLMs and Artificial Intelligence (AI) into real-world applications, customized AI agents are being constructed. Based on the technological trends and techniques, we extract a high-level approach for constructing these AI agents, focusing on their underlying architecture. This thesis serves as a comprehensive guide that elucidates a multi-faceted approach for empowering LLMs with the capability to leverage Application Programming Interfaces (APIs). We present a 7-step methodology that begins with the selection of suitable LLMs and the task decomposition that is necessary for complex problem-solving. This methodology includes techniques for generating training data for API interactions and heuristics for selecting the appropriate API among a plethora of options. These steps eventually lead to the generation of API calls that are both syntactically and semantically aligned with the LLM's understanding of a given task. Moreover, we review existing frameworks and tools that facilitate these processes and highlight the gaps in current attempts. In this direction, we propose an on-device architecture that aims to exploit the functionality of carry-on devices by using small models from the Hugging Face community. We examine the effectiveness of these approaches on real-world applications of various domains, including the generation of a piano sheet. Through an extensive analysis of the literature and available technologies, this thesis aims to set a compass for researchers and practitioners to harness the full potential of LLMs augmented with external tool capabilities, thus paving the way for more autonomous, robust, and context-aware AI agents.

cs.SE↗