arXiv subjects

Ivan Sergeev

Publications and source records attributed to Ivan Sergeev.

9 recordsLinked to original sources

arXiv2026

Beyond Isolated Clients: Integrating Graph-Based Embeddings into Event Sequence Models

Large-scale digital platforms generate billions of timestamped user-item interactions (events) that are crucial for predicting user attributes in, e.g., fraud prevention and recommendations. While self-supervised learning (SSL) effectively models the temporal order of events, it typically overlooks the global structure of the user-item interaction graph. To bridge this gap, we propose three model-agnostic strategies for integrating this structural information into contrastive SSL: enriching event embeddings, aligning client representations with graph embeddings, and adding a structural pretext task. Experiments on four financial and e-commerce datasets demonstrate that our approach consistently improves the accuracy (up to a 2.3% AUC) and reveals that graph density is a key factor in selecting the optimal integration strategy.

cs.LG↗

arXiv2026

Embedding-Aware Feature Discovery: Bridging Latent Representations and Interpretable Features in Event Sequences

Industrial financial systems operate on temporal event sequences such as transactions, user actions, and system logs. While recent research emphasizes representation learning and large language models, production systems continue to rely heavily on handcrafted statistical features due to their interpretability, robustness under limited supervision, and strict latency constraints. This creates a persistent disconnect between learned embeddings and feature-based pipelines. We introduce Embedding-Aware Feature Discovery (EAFD), a unified framework that bridges this gap by coupling pretrained event-sequence embeddings with a self-reflective LLM-driven feature generation agent. EAFD iteratively discovers, evaluates, and refines features directly from raw event sequences using two complementary criteria: \emph{alignment}, which explains information already encoded in embeddings, and \emph{complementarity}, which identifies predictive signals missing from them. Across both open-source and industrial transaction benchmarks, EAFD consistently outperforms embedding-only and feature-based baselines, achieving relative gains of up to $+5.8\%$ over state-of-the-art pretrained embeddings, resulting in new state-of-the-art performance across event-sequence datasets.

cs.LG↗

arXiv2026

A Blueprint for the Formalization of Seymour's Matroid Decomposition Theorem

This document is a blueprint for the formalization in Lean of the structural theory of regular matroids underlying Seymour's decomposition theorem. We present a modular account of regularity via totally unimodular representations, show that regularity is preserved under $1$-, $2$-, and $3$-sums, and establish regularity for several special classes of matroids, including graphic, cographic, and the matroid $R_{10}$. The blueprint records the logical structure of the proof, the precise dependencies between results, and their correspondence with Lean declarations. It is intended both as a guide for the ongoing formalization effort and as a human-readable reference for the organization of the proof.

math.CO↗

arXiv2025

Composition Direction of Seymour's Theorem for Regular Matroids -- Formally Verified

Seymour's decomposition theorem is a hallmark result in matroid theory presenting a structural characterization of the class of regular matroids. Formalization of matroid theory faces many challenges, most importantly that only a limited number of notions and results have been implemented so far. In this work, we formalize the proof of the forward (composition) direction of Seymour's theorem for regular matroids. To this end, we develop a library in Lean 4 that implements definitions and results about totally unimodular matrices, vector matroids, their standard representations, regular matroids, and 1-, 2-, and 3-sums of matrices and binary matroids given by their standard representations. Using this framework, we formally state Seymour's decomposition theorem and implement a formally verified proof of the composition direction in the setting where the matroids have finite rank and may have infinite ground sets.

math.CO↗

arXiv2024

On contention resolution for the hypergraph matching, knapsack, and $k$-column sparse packing problems

The contention resolution framework is a versatile rounding technique used as a part of the relaxation and rounding approach for solving constrained submodular function maximization problems. We apply this framework to the hypergraph matching, knapsack, and $k$-column sparse packing problems. In the hypergraph matching setting, we adapt the technique of Guruganesh, Lee (2018) to non-constructively prove that the correlation gap is at least $\frac{1-e^{-k}}{k}$ and provide a monotone $\left(b,\frac{1-e^{-bk}}{bk}\right)$-balanced contention resolution scheme, generalizing the results of Bruggmann, Zenklusen (2019). For the knapsack problem, we prove that the correlation gap of instances where exactly $k$ copies of each item fit into the knapsack is at least $\frac{1-e^{-2}}{2}$ and provide several monotone contention resolution schemes: a $\frac{1-e^{-2}}{2}$-balanced scheme for instances where all item sizes are strictly bigger than $\frac{1}{2}$, a $\frac{4}{9}$-balanced scheme for instances where all item sizes are at most $\frac{1}{2}$, and a $0.279$-balanced scheme for instances with arbitrary item sizes. For $k$-column sparse packing integer programs, we slightly modify the $\left(2k+o\left(k\right)\right)$-approximation algorithm for $k$-CS-PIP based on the strengthened LP relaxation presented in Brubach et al. (2019) to obtain a $\frac{1}{4k+o\left(k\right)}$-balanced contention resolution scheme and hence a $\left(4k+o\left(k\right)\right)$-approximation algorithm for $k$-CS-PIP based on the natural LP relaxation.

cs.DS↗

arXiv2023

Constant-Competitiveness for Random Assignment Matroid Secretary Without Knowing the Matroid

The Matroid Secretary Conjecture is a notorious open problem in online optimization. It claims the existence of an $O(1)$-competitive algorithm for the Matroid Secretary Problem (MSP). Here, the elements of a weighted matroid appear one-by-one, revealing their weight at appearance, and the task is to select elements online with the goal to get an independent set of largest possible weight. $O(1)$-competitive MSP algorithms have so far only been obtained for restricted matroid classes and for MSP variations, including Random-Assignment MSP (RA-MSP), where an adversary fixes a number of weights equal to the ground set size of the matroid, which then get assigned randomly to the elements of the ground set. Unfortunately, these approaches heavily rely on knowing the full matroid upfront. This is an arguably undesirable requirement, and there are good reasons to believe that an approach towards resolving the MSP Conjecture should not rely on it. Thus, both Soto [SIAM Journal on Computing 2013] and Oveis Gharan & Vondrak [Algorithmica 2013] raised as an open question whether RA-MSP admits an $O(1)$-competitive algorithm even without knowing the matroid upfront. In this work, we answer this question affirmatively. Our result makes RA-MSP the first well-known MSP variant with an $O(1)$-competitive algorithm that does not need to know the underlying matroid upfront and without any restriction on the underlying matroid. Our approach is based on first approximately learning the rank-density curve of the matroid, which we then exploit algorithmically.

cs.DS↗

arXiv2022

Simple Random Order Contention Resolution for Graphic Matroids with Almost no Prior Information

Random order online contention resolution schemes (ROCRS) are structured online rounding algorithms with numerous applications and links to other well-known online selection problems, like the matroid secretary conjecture. We are interested in ROCRS subject to a matroid constraint, which is among the most studied constraint families. Previous ROCRS required to know upfront the full fractional point to be rounded as well as the matroid. It is unclear to what extent this is necessary. Fu, Lu, Tang, Turkieltaub, Wu, Wu, and Zhang (SOSA 2022) shed some light on this question by proving that no strong (constant-selectable) online or even offline contention resolution scheme exists if the fractional point is unknown, not even for graphic matroids. In contrast, we show, in a setting with slightly more knowledge and where the fractional point reveals one by one, that there is hope to obtain strong ROCRS by providing a simple constant-selectable ROCRS for graphic matroids that only requires to know the size of the ground set in advance. Moreover, our procedure holds in the more general adversarial order with a sample setting, where, after sampling a random constant fraction of the elements, all remaining (non-sampled) elements may come in adversarial order.

math.OC↗

arXiv2021

Improved approximation algorithms for two Euclidean k-Center variants

The $k$-Center problem is one of the most popular clustering problems. After decades of work, the complexity of most of its variants on general metrics is now well understood. Surprisingly, this is not the case for a natural setting that often arises in practice, namely the Euclidean setting, in which the input points are points in $\mathbb{R}^d$, and the distance between them is the standard $\ell_2$ Euclidean distance. In this work, we study two Euclidean $k$-Center variants, the Matroid Center problem on the real line and the Robust Euclidean $k$-Supplier problem, and provide algorithms that improve upon the best approximation guarantees known for these problems. In particular, we present a simple $2.5$-approximation algorithm for the Matroid Center problem on the real line, thus improving upon the $3$-approximation factor algorithm of Chen, Li, Liang, and Wang (2016) that works for general metrics. Moreover, we present a $(1 + \sqrt{3})$-approximation algorithm for the Robust Euclidean $k$-Supplier problem, thus improving upon the state-of-the-art $3$-approximation algorithm for Robust $k$-Supplier on general metrics and matching the best approximation factor known for the non-robust setting by Nagarajan, Schieber and Shachnai (2020).

cs.DS↗

arXiv2019

Generalizations of $2$-dimensional diagonal quantum channels with constant Frobenius norm

We introduce the set of quantum channels with constant Frobenius norm, the set of diagonal channels and the notion of equivalence of one-parameter families of channels. First, we show that all diagonal $2$-dimensional channels with constant Frobenius norm are equivalent. Next, we generalize four one-parameter families of $2$-dimensional diagonal channels with constant Frobenius norm to an arbitrary dimension $n$. Finally, we prove that the generalizations are not equivalent in any dimension $n \ge 3$.

quant-ph↗