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ARXIV:2602.13106 · GRAPH NEURAL NETWORKS · SUBMITTED 02 APR · 02:30 UTC · FRESHNESS STALE
ARXIV:2602.13106GRAPH NEURAL NETWORKSSUBMITTED 02 APR · 02:30 UTCFRESHNESS STALEarXiv
A theoretical framework to ensure generalization of Graph Neural Networks to larger inputs in neural algorithmic reasoning.
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Pain A theoretical framework to ensure generalization of Graph Neural Networks to larger inputs in neural algorithmic reasoning.
Evidence 0 refs | 0 sources | 17% coverage
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A theoretical framework to ensure generalization of Graph Neural Networks to larger inputs in neural algorithmic reasoning. The goal is to integrate algorithmic reasoning capabilities into larger neural pipelines.
In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a line of work often referred to as neural algorithmic reasoning. The goal is to…
ScienceToStartup currently rates this 3.0/10 on the public viability pass. In addition, we establish impossibility results for a wide range of algorithmic tasks, showing that standard MPNNs cannot learn them, and we derive more…
Graph Neural Networks moved forward this cycle; last verified April 2026. Public score 3.0/10.
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A theoretical framework to ensure generalization of Graph Neural Networks to larger inputs in neural algorithmic reasoning.
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10.48550/arXiv.2602.13106A theoretical framework to ensure generalization of Graph Neural Networks to larger inputs in neural algorithmic reasoning.
Abstract
In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a line of work often referred to as neural algorithmic reasoning. The goal is to integrate algorithmic reasoning capabilities into larger neural pipelines. Many such architectures are based on (message-passing) graph neural networks (MPNNs), owing to their permutation equivariance and ability to deal with sparsity and variable-sized inputs. However, existing work is either largely empirical and lacks formal guarantees or it focuses solely on expressivity, leaving open the question of when and how such architectures generalize beyond a finite training set. In this work, we propose a general theoretical framework that characterizes the sufficient conditions under which MPNNs can learn an algorithm from a training set of small instances and provably approximate its behavior on inputs of arbitrary size. Our framework applies to a broad class of algorithms, including single-source shortest paths, minimum spanning trees, and general dynamic programming problems, such as the $0$-$1$ knapsack problem. In addition, we establish impossibility results for a wide range of algorithmic tasks, showing that standard MPNNs cannot learn them, and we derive more expressive MPNN-like architectures that overcome these limitations. Finally, we refine our analysis for the Bellman-Ford algorithm, yielding a substantially smaller required training set and significantly extending the recent work of Nerem et al. [2025] by allowing for a differentiable regularization loss. Empirical results largely support our theoretical findings.
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PROBLEM
A theoretical framework to ensure generalization of Graph Neural Networks to larger inputs in neural algorithmic reasoning. The goal is to integrate algorithmic reasoning capabilities into larger neural pipelines.
METHOD
In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a line of work often referred to as neural algorithmic reasoning. The goal is to integrate algorithmic reasoning capabilities into larger neur...
RESULT
ScienceToStartup currently rates this 3.0/10 on the public viability pass. In addition, we establish impossibility results for a wide range of algorithmic tasks, showing that standard MPNNs cannot learn them, and we derive more expressive MPNN-like architectures that overcome th...
WHY NOW
Graph Neural Networks moved forward this cycle; last verified April 2026. Public score 3.0/10.
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A theoretical framework to ensure generalization of Graph Neural Networks to larger inputs in neural algorithmic reasoning. The goal is to integrate algorithmic reasoning capabilities into larger neural pipelines.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a line of work often referred to as neural algorithmic reasoning. The goal is to integrate algorithmic reasoning capabilities into larger neural pipelines.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
ScienceToStartup currently rates this 3.0/10 on the public viability pass. In addition, we establish impossibility results for a wide range of algorithmic tasks, showing that standard MPNNs cannot learn them, and we derive more expressive MPNN-like architectures that overcome these limitations.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
Graph Neural Networks moved forward this cycle; last verified April 2026. Public score 3.0/10.
Abstract-backed fallback claim; anchored extraction has not materialized a public claim row yet.
partial
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A theoretical framework to ensure generalization of Graph Neural Networks to larger inputs in neural algorithmic reasoning.
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Graph Neural Networks
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