arXiv subjects

Ioannis Koutis

Publications and source records attributed to Ioannis Koutis.

At least 19 recordsLinked to original sources

arXiv2026

Improved large-scale graph learning through ridge spectral sparsification

Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We consider the problem of learning over this Laplacian in a distributed streaming setting, where new edges of the graph are observed in real time by a network of workers. In this setting, it is hard to learn quickly or approximately while keeping a distributed representation of L. To address this challenge, we present a novel algorithm, GSQUEAK, which efficiently sparsifies the Laplacian by maintaining a small subset of effective resistances. We show that our algorithm produces sparsifiers with strong spectral approximation guarantees, all while processing edges in a single pass and in a distributed fashion.

cs.LG↗

arXiv2025

Minimum Weighted Feedback Arc Sets for Ranking from Pairwise Comparisons

The Minimum Weighted Feedback Arc Set (MWFAS) problem is closely related to the task of deriving a global ranking from pairwise comparisons. Recent work by He et al. (ICML 2022) advanced the state of the art on ranking benchmarks using learning based methods, but did not examine the underlying connection to MWFAS. In this paper, we investigate this relationship and introduce efficient combinatorial algorithms for solving MWFAS as a means of addressing the ranking problem. Our experimental results show that these simple, learning free methods achieve substantially faster runtimes than recent learning based approaches, while also delivering competitive, and in many cases superior, ranking accuracy. These findings suggest that lightweight combinatorial techniques offer a scalable and effective alternative to deep learning for large scale ranking tasks.

cs.IR↗

arXiv2025

Hierarchical Mamba Meets Hyperbolic Geometry: A New Paradigm for Structured Language Embeddings

Selective state-space models excel at long-sequence modeling, but their capacity for language representation -- in complex hierarchical reasoning -- remains underexplored. Most large language models rely on \textit{flat} Euclidean embeddings, limiting their ability to capture latent hierarchies. To address this, we propose {\it Hierarchical Mamba (HiM)}, integrating efficient Mamba2 with hyperbolic geometry to learn hierarchy-aware language embeddings for deeper linguistic understanding. Mamba2-processed sequences are projected to the Poincaré ball or Lorentzian manifold with ``learnable'' curvature, optimized with a hyperbolic loss. Our HiM model facilitates the capture of relational distances across varying hierarchical levels, enabling effective long-range reasoning for tasks like mixed-hop prediction and multi-hop inference in hierarchical classification. Experimental results show both HiM variants effectively capture hierarchical relationships across four linguistic and medical datasets, surpassing Euclidean baselines, with HiM-Poincaré providing fine-grained distinctions with higher h-norms, while HiM-Lorentz offers more stable, compact, and hierarchy-preserving embeddings-favoring robustness. The source code is publicly available at https://github.com/BerryByte/HiM.

cs.CL↗

arXiv2025

HiPerMotif: Novel Parallel Subgraph Isomorphism in Large-Scale Property Graphs

Subgraph isomorphism, essential for pattern detection in large-scale graphs, faces scalability challenges in attribute-rich property graphs used in neuroscience, systems biology, and social network analysis. Traditional algorithms explore search spaces vertex-by-vertex from empty mappings, leading to extensive early-stage exploration with limited pruning opportunities. We introduce HiPerMotif, a novel hybrid parallel algorithm that fundamentally shifts the search initialization strategy. After structurally reordering the pattern graph to prioritize high-degree vertices, HiPerMotif systematically identifies all possible mappings for the first edge (vertices 0,1) in the target graph, validates these edge candidates using efficient vertex and edge validators, and injects the validated partial mappings as states at depth 2. The algorithm then continues with traditional vertex-by-vertex exploration from these pre-validated starting points, effectively pruning the expensive early search tree branches while enabling natural parallelization over edge candidates. Our contributions include the edge-centric initialization paradigm with state injection, a structural reordering strategy achieving up to 5x speedup, rapid edge and vertex validators for attribute-rich graphs, and efficient parallel enumeration over target graph edges. Implemented in the open-source Arachne framework, HiPerMotif achieves up to 66x speedup over state-of-the-art baselines (VF2-PS, VF3P, Glasgow) on diverse datasets where baselines successfully complete execution. Additionally, HiPerMotif successfully processes massive datasets such as the H01 connectome with 147 million edges, which existing methods cannot handle due to memory constraints. Comprehensive evaluation across synthetic and real-world graphs demonstrates HiPerMotif's scalability, enabling advanced analysis in computational neuroscience and beyond.

cs.DS↗

arXiv2024

TGB 2.0: A Benchmark for Learning on Temporal Knowledge Graphs and Heterogeneous Graphs

Multi-relational temporal graphs are powerful tools for modeling real-world data, capturing the evolving and interconnected nature of entities over time. Recently, many novel models are proposed for ML on such graphs intensifying the need for robust evaluation and standardized benchmark datasets. However, the availability of such resources remains scarce and evaluation faces added complexity due to reproducibility issues in experimental protocols. To address these challenges, we introduce Temporal Graph Benchmark 2.0 (TGB 2.0), a novel benchmarking framework tailored for evaluating methods for predicting future links on Temporal Knowledge Graphs and Temporal Heterogeneous Graphs with a focus on large-scale datasets, extending the Temporal Graph Benchmark. TGB 2.0 facilitates comprehensive evaluations by presenting eight novel datasets spanning five domains with up to 53 million edges. TGB 2.0 datasets are significantly larger than existing datasets in terms of number of nodes, edges, or timestamps. In addition, TGB 2.0 provides a reproducible and realistic evaluation pipeline for multi-relational temporal graphs. Through extensive experimentation, we observe that 1) leveraging edge-type information is crucial to obtain high performance, 2) simple heuristic baselines are often competitive with more complex methods, 3) most methods fail to run on our largest datasets, highlighting the need for research on more scalable methods.

cs.LG↗

arXiv2023

Resource-constrained knowledge diffusion processes inspired by human peer learning

We consider a setting where a population of artificial learners is given, and the objective is to optimize aggregate measures of performance, under constraints on training resources. The problem is motivated by the study of peer learning in human educational systems. In this context, we study natural knowledge diffusion processes in networks of interacting artificial learners. By `natural', we mean processes that reflect human peer learning where the students' internal state and learning process is mostly opaque, and the main degree of freedom lies in the formation of peer learning groups by a coordinator who can potentially evaluate the learners before assigning them to peer groups. Among else, we empirically show that such processes indeed make effective use of the training resources, and enable the design of modular neural models that have the capacity to generalize without being prone to overfitting noisy labels.

cs.LG↗

arXiv2023

Towards Foundational Models for Molecular Learning on Large-Scale Multi-Task Datasets

Recently, pre-trained foundation models have enabled significant advancements in multiple fields. In molecular machine learning, however, where datasets are often hand-curated, and hence typically small, the lack of datasets with labeled features, and codebases to manage those datasets, has hindered the development of foundation models. In this work, we present seven novel datasets categorized by size into three distinct categories: ToyMix, LargeMix and UltraLarge. These datasets push the boundaries in both the scale and the diversity of supervised labels for molecular learning. They cover nearly 100 million molecules and over 3000 sparsely defined tasks, totaling more than 13 billion individual labels of both quantum and biological nature. In comparison, our datasets contain 300 times more data points than the widely used OGB-LSC PCQM4Mv2 dataset, and 13 times more than the quantum-only QM1B dataset. In addition, to support the development of foundational models based on our proposed datasets, we present the Graphium graph machine learning library which simplifies the process of building and training molecular machine learning models for multi-task and multi-level molecular datasets. Finally, we present a range of baseline results as a starting point of multi-task and multi-level training on these datasets. Empirically, we observe that performance on low-resource biological datasets show improvement by also training on large amounts of quantum data. This indicates that there may be potential in multi-task and multi-level training of a foundation model and fine-tuning it to resource-constrained downstream tasks.

cs.LG↗

arXiv2023

Sidestepping Barriers for Dominating Set in Parameterized Complexity

We study the classic {\sc Dominating Set} problem with respect to several prominent parameters. Specifically, we present algorithmic results that sidestep time complexity barriers by the incorporation of either approximation or larger parameterization. Our results span several parameterization regimes, including: (i,ii,iii) time/ratio-tradeoff for the parameters {\em treewidth}, {\em vertex modulator to constant treewidth} and {\em solution size}; (iv,v) FPT-algorithms for the parameters {\em vertex cover number} and {\em feedback edge set number}; and (vi) compression for the parameter {\em feedback edge set number}.

cs.DS↗

arXiv2023

Neural Network Pruning as Spectrum Preserving Process

Neural networks have achieved remarkable performance in various application domains. Nevertheless, a large number of weights in pre-trained deep neural networks prohibit them from being deployed on smartphones and embedded systems. It is highly desirable to obtain lightweight versions of neural networks for inference in edge devices. Many cost-effective approaches were proposed to prune dense and convolutional layers that are common in deep neural networks and dominant in the parameter space. However, a unified theoretical foundation for the problem mostly is missing. In this paper, we identify the close connection between matrix spectrum learning and neural network training for dense and convolutional layers and argue that weight pruning is essentially a matrix sparsification process to preserve the spectrum. Based on the analysis, we also propose a matrix sparsification algorithm tailored for neural network pruning that yields better pruning result. We carefully design and conduct experiments to support our arguments. Hence we provide a consolidated viewpoint for neural network pruning and enhance the interpretability of deep neural networks by identifying and preserving the critical neural weights.

cs.LG↗

arXiv2023

K-SpecPart: Supervised embedding algorithms and cut overlay for improved hypergraph partitioning

State-of-the-art hypergraph partitioners follow the multilevel paradigm that constructs multiple levels of progressively coarser hypergraphs that are used to drive cut refinement on each level of the hierarchy. Multilevel partitioners are subject to two limitations: (i) hypergraph coarsening processes rely on local neighborhood structure without fully considering the global structure of the hypergraph; and (ii) refinement heuristics risk entrapment in local minima. In this paper, we describe K-SpecPart, a supervised spectral framework for multi-way partitioning that directly tackles these two limitations. K-SpecPart relies on the computation of generalized eigenvectors and supervised dimensionality reduction techniques to generate vertex embeddings. These are computational primitives that are fast and capture global structural properties of the hypergraph that are not explicitly considered by existing partitioners. K-SpecPart then converts the vertex embeddings into multiple partitioning solutions. K-SpecPart introduces the idea of ''ensembling'' multiple solutions via a cut-overlay clustering technique that often enables the use of computationally demanding partitioning methods such as ILP (integer linear programming). Using the output of a standard partitioner as a supervision hint, K-SpecPart effectively combines the strengths of established multilevel partitioning techniques with the benefits of spectral graph theory and other combinatorial algorithms. K-SpecPart significantly extends ideas and algorithms that first appeared in our previous work on the bipartitioner SpecPart. Our experiments demonstrate the effectiveness of K-SpecPart. For bipartitioning, K-SpecPart produces solutions with up to 15% cutsize improvement over SpecPart. For multi-way partitioning, K-SpecPart produces solutions with up to 20% cutsize improvement over leading partitioners hMETIS and KaHyPar.

cs.LG↗

arXiv2022

SGC: A semi-supervised pipeline for gene clustering using self-training approach in gene co-expression networks

A widely used approach for extracting information from gene expression data employ the construction of a gene co-expression network and the subsequent application of algorithms that discover network structure. In particular, a common goal is the computational discovery of gene clusters, commonly called modules. When applied on a novel gene expression dataset, the quality of the computed modules can be evaluated automatically, using Gene Ontology enrichment, a method that measures the frequencies of Gene Ontology terms in the computed modules and evaluates their statistical likelihood. In this work we propose SGC a novel pipeline for gene clustering based on relatively recent seminal work in the mathematics of spectral network theory. SGC consists of multiple novel steps that enable the computation of highly enriched modules in an unsupervised manner. But unlike all existing frameworks, it further incorporates a novel step that leverages Gene Ontology information in a semi-supervised clustering method that further improves the quality of the computed modules. Comparing with already well-known existing frameworks, we show that SGC results in higher enrichment in real data. In particular, in 12 real gene expression datasets, SGC outperforms in all except one.

q-bio.GN↗

arXiv2018

Spectrally Robust Graph Isomorphism

We initiate the study of spectral generalizations of the graph isomorphism problem. (a)The Spectral Graph Dominance (SGD) problem: On input of two graphs $G$ and $H$ does there exist a permutation $π$ such that $G\preceq π(H)$? (b) The Spectrally Robust Graph Isomorphism (SRGI) problem: On input of two graphs $G$ and $H$, find the smallest number $κ$ over all permutations $π$ such that $ π(H) \preceq G\preceq κc π(H)$ for some $c$. SRGI is a natural formulation of the network alignment problem that has various applications, most notably in computational biology. Here $G\preceq c H$ means that for all vectors $x$ we have $x^T L_G x \leq c x^T L_H x$, where $L_G$ is the Laplacian $G$. We prove NP-hardness for SGD. We also present a $κ$-approximation algorithm for SRGI for the case when both $G$ and $H$ are bounded-degree trees. The algorithm runs in polynomial time when $κ$ is a constant.

cs.DS↗

arXiv2017

Directed Hamiltonicity and Out-Branchings via Generalized Laplacians

We are motivated by a tantalizing open question in exact algorithms: can we detect whether an $n$-vertex directed graph $G$ has a Hamiltonian cycle in time significantly less than $2^n$? We present new randomized algorithms that improve upon several previous works: 1. We show that for any constant $0<λ<1$ and prime $p$ we can count the Hamiltonian cycles modulo $p^{\lfloor (1-λ)\frac{n}{3p}\rfloor}$ in expected time less than $c^n$ for a constant $c<2$ that depends only on $p$ and $λ$. Such an algorithm was previously known only for the case of counting modulo two [Björklund and Husfeldt, FOCS 2013]. 2. We show that we can detect a Hamiltonian cycle in $O^*(3^{n-α(G)})$ time and polynomial space, where $α(G)$ is the size of the maximum independent set in $G$. In particular, this yields an $O^*(3^{n/2})$ time algorithm for bipartite directed graphs, which is faster than the exponential-space algorithm in [Cygan et al., STOC 2013]. Our algorithms are based on the algebraic combinatorics of "incidence assignments" that we can capture through evaluation of determinants of Laplacian-like matrices, inspired by the Matrix--Tree Theorem for directed graphs. In addition to the novel algorithms for directed Hamiltonicity, we use the Matrix--Tree Theorem to derive simple algebraic algorithms for detecting out-branchings. Specifically, we give an $O^*(2^k)$-time randomized algorithm for detecting out-branchings with at least $k$ internal vertices, improving upon the algorithms of [Zehavi, ESA 2015] and [Björklund et al., ICALP 2015]. We also present an algebraic algorithm for the directed $k$-Leaf problem, based on a non-standard monomial detection problem.

cs.DS↗

arXiv2016

On Fully Dynamic Graph Sparsifiers

We initiate the study of dynamic algorithms for graph sparsification problems and obtain fully dynamic algorithms, allowing both edge insertions and edge deletions, that take polylogarithmic time after each update in the graph. Our three main results are as follows. First, we give a fully dynamic algorithm for maintaining a $ (1 \pm ε) $-spectral sparsifier with amortized update time $poly(\log{n}, ε^{-1})$. Second, we give a fully dynamic algorithm for maintaining a $ (1 \pm ε) $-cut sparsifier with \emph{worst-case} update time $poly(\log{n}, ε^{-1})$. Both sparsifiers have size $ n \cdot poly(\log{n}, ε^{-1})$. Third, we apply our dynamic sparsifier algorithm to obtain a fully dynamic algorithm for maintaining a $(1 + ε)$-approximation to the value of the maximum flow in an unweighted, undirected, bipartite graph with amortized update time $poly(\log{n}, ε^{-1})$.

cs.DS↗

arXiv2016

Incremental Spectral Sparsification for Large-Scale Graph-Based Semi-Supervised Learning

While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on efficiently approximating the whole spectrum of the graph Laplacian constructed from the data. This is in contrast to various subsampling and quantization methods proposed in the past, which may fail in preserving the graph spectra. However, the impact of the approximation of the spectrum on the final generalization error is either unknown, or requires strong assumptions on the data. In this paper, we introduce Sparse-HFS, an efficient edge-sparsification algorithm for SSL. By constructing an edge-sparse and spectrally similar graph, we are able to leverage the approximation guarantees of spectral sparsification methods to bound the generalization error of Sparse-HFS. As a result, we obtain a theoretically-grounded approximation scheme for graph-based SSL that also empirically matches the performance of known large-scale methods.

stat.ML↗

arXiv2016

Scalable Constrained Clustering: A Generalized Spectral Method

We present a principled spectral approach to the well-studied constrained clustering problem. It reduces clustering to a generalized eigenvalue problem on Laplacians. The method works in nearly-linear time and provides concrete guarantees for the quality of the clusters, at least for the case of 2-way partitioning. In practice this translates to a very fast implementation that consistently outperforms existing spectral approaches. We support this claim with experiments on various data sets: our approach recovers correct clusters in examples where previous methods fail, and handles data sets with millions of data points - two orders of magnitude larger than before.

cs.SI↗

arXiv2016

Scalable Constrained Clustering: A Generalized Spectral Method

We present a simple spectral approach to the well-studied constrained clustering problem. It captures constrained clustering as a generalized eigenvalue problem with graph Laplacians. The algorithm works in nearly-linear time and provides concrete guarantees for the quality of the clusters, at least for the case of 2-way partitioning. In practice this translates to a very fast implementation that consistently outperforms existing spectral approaches both in speed and quality.

cs.SI↗

arXiv2014

A Generalized Cheeger Inequality

The generalized conductance $ϕ(G,H)$ between two graphs $G$ and $H$ on the same vertex set $V$ is defined as the ratio $$ ϕ(G,H) = \min_{S\subseteq V} \frac{cap_G(S,\bar{S})}{ cap_H(S,\bar{S})}, $$ where $cap_G(S,\bar{S})$ is the total weight of the edges crossing from $S$ to $\bar{S}=V-S$. We show that the minimum generalized eigenvalue $λ(L_G,L_H)$ of the pair of Laplacians $L_G$ and $L_H$ satisfies $$ λ(L_G,L_H) \geq ϕ(G,H) ϕ(G)/8, $$ where $ϕ(G)$ is the usual conductance of $G$. A generalized cut that meets this bound can be obtained from the generalized eigenvector corresponding to $λ(L_G,L_H)$. The inequality complements a recent proof that $ϕ(G)$ cannot be replaced by $Θ(ϕ(G,H))$ in the above inequality, unless the Unique Games Conjecture is false.

cs.DM↗