arXiv subjects

Saku Peltonen

Publications and source records attributed to Saku Peltonen.

5 recordsLinked to original sources

arXiv2026

GraphARC: A Comprehensive Benchmark for Graph-Based Abstract Reasoning

Relational reasoning lies at the heart of intelligence, but existing benchmarks are typically confined to formats such as grids or text. We introduce GraphARC, a benchmark for abstract reasoning on graph-structured data. GraphARC generalizes the few-shot transformation learning paradigm of the Abstraction and Reasoning Corpus (ARC). Each task requires inferring a transformation rule from a few input-output pairs and applying it to a new test graph, covering local, global, and hierarchical graph transformations. Unlike grid-based ARC, GraphARC instances can be generated at scale across diverse graph families and sizes, enabling systematic evaluation of generalization abilities. We evaluate state-of-the-art language models on GraphARC and observe clear limitations. Models can answer questions about graph properties but often fail to solve the full graph transformation task, revealing a comprehension-execution gap. Performance further degrades on larger instances, exposing scaling barriers. More broadly, by combining aspects of node classification, link prediction, and graph generation within a single framework, GraphARC provides a promising testbed for future graph foundation models.

cs.AI↗

arXiv2026

From Message-Passing to Linearized Graph Sequence Models

Message-passing based approaches form the default backbone of most learning architectures on graph-structured data. However, the rapid progress of modern deep learning architectures in other domains, particularly sequence modeling, raises the question of how graph learning can benefit from these advances. We introduce Linearized Graph Sequence Models, a framework that recasts message-passing graph computation from the perspective of sequence modeling to simplify architectural choices. Our approach systematically separates the computational processing depth from the information propagation depth, allowing core graph architectural decisions to be treated as sequence modeling choices. Specifically, we analyze, both empirically and theoretically, what sequence properties make methods effective for learning and preserving the graph inductive bias. In particular, we validate our findings, demonstrating improved performance on long-range information tasks in graphs. Our findings provide a principled way to integrate modern sequence modeling advances into message-passing based graph learning. Beyond this, our work demonstrates how the separation of processing and information depth can recast central architectural questions as input modeling choices.

cs.LG↗

arXiv2026

On the Expressive Power of GNNs for Boolean Satisfiability

Machine learning approaches to solving Boolean Satisfiability (SAT) aim to replace handcrafted heuristics with learning-based models. Graph Neural Networks have emerged as the main architecture for SAT solving, due to the natural graph representation of Boolean formulas. We analyze the expressive power of GNNs for SAT solving through the lens of the Weisfeiler-Leman (WL) test. As our main result, we prove that the full WL hierarchy cannot, in general, distinguish between satisfiable and unsatisfiable instances. We show that indistinguishability under higher-order WL carries over to practical limitations for WL-bounded solvers that set variables sequentially. We further study the expressivity required for several important families of SAT instances, including regular, random and planar instances. To quantify expressivity needs in practice, we conduct experiments on random instances from the G4SAT benchmark and industrial instances from the International SAT Competition. Our results suggest that while random instances are largely distinguishable, industrial instances often require more expressivity to predict a satisfying assignment.

cs.LG↗

arXiv2024

Distributed Lovász Local Lemma under Bandwidth Limitations

The constructive Lovász Local Lemma has become a central tool for designing efficient distributed algorithms. While it has been extensively studied in the classic LOCAL model that uses unlimited bandwidth, much less is known in the bandwidth-restricted CONGEST model. In this paper, we present bandwidth- and time-efficient algorithms for various subclasses of LLL problems, including a large class of subgraph sampling problems that are naturally formulated as LLLs. Lastly, we use our LLLs to design efficient CONGEST algorithms for coloring sparse and triangle-free graphs with few colors. These coloring algorithms are exponentially faster than previous LOCAL model algorithms.

cs.DS↗

arXiv2023

Distributed Symmetry Breaking on Power Graphs via Sparsification

In this paper, we present efficient distributed algorithms for classical symmetry breaking problems, maximal independent sets (MIS) and ruling sets, in power graphs. We work in the standard CONGEST model of distributed message passing, where the communication network is abstracted as a graph $G$. Typically, the problem instance in CONGEST is identical to the communication network $G$, that is, we perform the symmetry breaking in $G$. In this work, we consider a setting where the problem instance corresponds to a power graph $G^k$, where each node of the communication network $G$ is connected to all of its $k$-hop neighbors. Our main contribution is a deterministic polylogarithmic time algorithm for computing $k$-ruling sets of $G^k$, which (for $k>1$) improves exponentially on the current state-of-the-art runtimes. The main technical ingredient for this result is a deterministic sparsification procedure which may be of independent interest. On top of being a natural family of problems, ruling sets (in power graphs) are well-motivated through their applications in the powerful shattering framework [BEPS JACM'16, Ghaffari SODA'19] (and others). We present randomized algorithms for computing maximal independent sets and ruling sets of $G^k$ in essentially the same time as they can be computed in $G$. We also revisit the shattering algorithm for MIS [BEPS JACM'16] and present different approaches for the post-shattering phase. Our solutions are algorithmically and analytically simpler (also in the LOCAL model) than existing solutions and obtain the same runtime as [Ghaffari SODA'16].

cs.DS↗