arXiv subjects

Feodor Dragan

Publications and source records attributed to Feodor Dragan.

5 recordsLinked to original sources

arXiv2026

PLUME: Parameter-Efficient Personalization of Large Language Models via Low-Rank User Modulation in Shared Subspaces

Personalizing large language models (LLMs) is essential for delivering AI assistance that aligns with individual users' styles, intents, and preferences. While per-user fine-tuning can substantially enhance personalization quality, it introduces significant parameter and storage overhead, limiting scalability to large user populations. We propose PLUME (Personalized Low-Rank Adaptation through User Modulation and Shared Subspace), a lightweight framework that achieves efficient and expressive per-user adaptation by leveraging a shared task-specific subspace. Specifically, PLUME first learns a global task subspace from aggregated user data. Personalization is then achieved by training only a lightweight small square matrix within this subspace, enabling each user to obtain a tailored model while keeping shared components fixed. Cross-layer shared parameters and rank-1 residual terms are further introduced to significantly reduce redundancy while maintaining expressiveness. Experiments on multiple personalized text generation benchmarks demonstrate that PLUME achieves comparable or superior performance to strong baselines, while reducing per-user parameters by over 95%. These results establish shared-subspace modulation with minimal residuals as a scalable and semantically grounded approach to LLM personalization.

cs.AI↗

arXiv2026

Gradient-Aligned Pair Selection for Personalized Preference Optimization

Personalizing large language models (LLMs) requires aligning generation behavior with user-specific preferences rather than aggregate quality. While Direct Preference Optimization (DPO) provides a stable framework for preference learning, its effectiveness in personalized settings critically depends on how preference pairs are selected. Existing approaches typically rely on heuristic criteria, such as likelihood-based extremes, which decouple optimization from explicit user utility and can lead to degraded personalization. We formalize personalized preference learning as a geometry-aligned optimization problem by analyzing the first-order interaction between gradients of expected user utility and DPO update directions. Our analysis reveals that, under off-policy sampling, the DPO update transitions from a purely error-corrective signal to a reinforcement-like update when preference margins are directionally aligned with utility gradients. This perspective exposes pair selection as a geometric decision that governs whether preference optimization advances or hinders personalization. Motivated by this insight, we propose GAP-DPO (Geometry-Aligned Preference DPO), an iterative algorithm that performs utility-aware, geometry-aligned pair selection while controlling distribution shift via epoch-wise regeneration. Experiments on personalized text generation benchmarks show that GAP-DPO consistently improves stylistic fidelity, preference alignment, and generation quality compared to standard DPO variants. Together, our results establish gradient alignment as a unifying principle for personalized preference optimization and demonstrate that pair selection is an intrinsic component of the optimization geometry rather than a heuristic preprocessing step.

cs.AI↗

arXiv2025

On $G^p$-unimodality of radius functions in graphs: structure and algorithms

For every weight assignment $π$ to the vertices in a graph $G$, the radius function $r_π$ maps every vertex of $G$ to its largest weighted distance to the other vertices. The center problem asks to find a center, i.e., a vertex of $G$ that minimizes $r_π$. We here study some local properties of radius functions in graphs, and their algorithmic implications; our work is inspired by the nice property that in Euclidean spaces every local minimum of every radius function $r_π$ is a center. We study a discrete analogue of this property for graphs, which we name $G^p$-unimodality: specifically, every vertex that minimizes the radius function in its ball of radius $p$ must be a central vertex. While it has long been known since Dragan (1989) that graphs with $G$-unimodal radius functions $r_π$ are exactly the Helly graphs, the class of graphs with $G^2$-unimodal radius functions has not been studied insofar. We prove the latter class to be much larger than the Helly graphs, since it also comprises (weakly) bridged graphs, graphs with convex balls, and bipartite Helly graphs. Recently, using the $G$-unimodality of radius functions $r_π$, a randomized $\widetilde{\mathcal{O}}(\sqrt{n}m)$-time local search algorithm for the center problem on Helly graphs was proposed by Ducoffe (2023). Assuming the Hitting Set Conjecture (Abboud et al., 2016), we prove that a similar result for the class of graphs with $G^2$-unimodal radius functions is unlikely. However, we design local search algorithms (randomized or deterministic) for the center problem on many of its important subclasses.

cs.DS↗

arXiv2019

Pruned Landmark Labeling Meets Vertex Centric Computation: A Surprisingly Happy Marriage!

In this paper, we study how the Pruned Landmark Labeling (PPL) algorithm can be parallelized in a scalable fashion, producing the same results as the sequential algorithm. More specifically, we parallelize using a Vertex-Centric (VC) computational model on a modern SIMD powered multicore architecture. We design a new VC-PLL algorithm that resolves the apparent mismatch between the inherent sequential dependence of the PLL algorithm and the Vertex- Centric (VC) computing model. Furthermore, we introduce a novel batch execution model for VC computation and the BVC-PLL algorithm to reduce the computational inefficiency in VC-PLL. Quite surprisingly, the theoretical analysis reveals that under a reasonable assumption, BVC-PLL has lower computational and memory access costs than PLL and indicates it may run faster than PLL as a sequential algorithm. We also demonstrate how BVC-PLL algorithm can be extended to handle directed graphs and weighted graphs and how it can utilize the hierarchical parallelism on a modern parallel computing architecture. Extensive experiments on real-world graphs not only show the sequential BVC-PLL can run more than two times faster than the original PLL, but also demonstrates its parallel efficiency and scalability.

cs.DB↗

arXiv2010

Constant approximation algorithms for embedding graph metrics into trees and outerplanar graphs

In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algorithms of Bǎdoiu, Indyk, and Sidiropoulos (2007) and Bǎdoiu, Demaine, Hajiaghayi, Sidiropoulos, and Zadimoghaddam (2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding a graph metric into an outerplanar metric. For this, we introduce a general notion of metric relaxed minor and show that if G contains an alpha-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is at meast alpha. Then, for H=K_{2,3}, we present an algorithm which either finds an alpha-relaxed minor, or produces an O(alpha)-embedding into an outerplanar metric.

math.MG↗