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ARXIV:2603.26140 · GRAPH NEURAL NETWORKS · SUBMITTED 30 MAR · 22:00 UTC · FRESHNESS STALE
ARXIV:2603.26140GRAPH NEURAL NETWORKSSUBMITTED 30 MAR · 22:00 UTCFRESHNESS STALEMostafa Haghir Chehreghani · arXiv
This paper theoretically investigates the computational complexity of optimizing graph structures to improve Graph Neural Network performance, proving NP-hardness for exact solutions.
Opportunity summary
Pain This paper theoretically investigates the computational complexity of optimizing graph structures to improve Graph Neural Network performance, proving NP-hardness for exact solutions.
Evidence 25 refs | 3 sources | 50% coverage
Blocker Evidence unverified
This paper theoretically investigates the computational complexity of optimizing graph structures to improve Graph Neural Network performance, proving NP-hardness for exact solutions. Both phenomena are intimately tied to the underlying graph structure, raising a…
Graph Neural Networks (GNNs) face two fundamental challenges when scaled to deep architectures: oversmoothing, where node representations converge to indistinguishable vectors, and oversquashing, where information from distant nodes fails to propagate through bottlenecks. Both…
ScienceToStartup currently rates this 2.0/10 on the public viability pass. Our results provide theoretical foundations for understanding the fundamental limits of graph rewiring for GNN optimization and justify the use of approximation algorithms and…
Graph Neural Networks moved forward this cycle; last verified April 2026. Public score 2.0/10.
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This paper theoretically investigates the computational complexity of optimizing graph structures to improve Graph Neural Network performance, proving NP-hardness for exact solutions.
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10.48550/arXiv.2603.26140This paper theoretically investigates the computational complexity of optimizing graph structures to improve Graph Neural Network performance, proving NP-hardness for exact solutions.
Abstract
Graph Neural Networks (GNNs) face two fundamental challenges when scaled to deep architectures: oversmoothing, where node representations converge to indistinguishable vectors, and oversquashing, where information from distant nodes fails to propagate through bottlenecks. Both phenomena are intimately tied to the underlying graph structure, raising a natural question: can we optimize the graph topology to mitigate these issues? This paper provides a theoretical investigation of the computational complexity of such graph structure optimization. We formulate oversmoothing and oversquashing mitigation as graph optimization problems based on spectral gap and conductance, respectively. We prove that exact optimization for either problem is NP-hard through reductions from Minimum Bisection, establishing NP-completeness of the decision versions. Our results provide theoretical foundations for understanding the fundamental limits of graph rewiring for GNN optimization and justify the use of approximation algorithms and heuristic methods in practice.
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Extraction status
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Proof status
unverified25 refs; 3 sources; 50% coverage.
What was readable
Derived fallback: Estimated from adjacent evidence; not verified from source.
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Dimensions overall score 2.0
PROBLEM
This paper theoretically investigates the computational complexity of optimizing graph structures to improve Graph Neural Network performance, proving NP-hardness for exact solutions. Both phenomena are intimately tied to the underlying graph structure, raising a natural questio...
METHOD
Graph Neural Networks (GNNs) face two fundamental challenges when scaled to deep architectures: oversmoothing, where node representations converge to indistinguishable vectors, and oversquashing, where information from distant nodes fails to propagate through bottlenecks. Both p...
RESULT
ScienceToStartup currently rates this 2.0/10 on the public viability pass. Our results provide theoretical foundations for understanding the fundamental limits of graph rewiring for GNN optimization and justify the use of approximation algorithms and heuristic methods in practic...
WHY NOW
Graph Neural Networks moved forward this cycle; last verified April 2026. Public score 2.0/10.
We prove that exact optimization for either problem is NP-hard through reductions from Minimum Bisection, establishing NP-completeness of the decision versions.
The abstract explicitly states this and the analysis mentions reductions from Minimum Bisection to prove NP-hardness for oversmoothing mitigation.
partial
We prove that exact optimization for either problem is NP-hard through reductions from Minimum Bisection, establishing NP-completeness of the decision versions.
The abstract explicitly states this and the analysis mentions reductions from Minimum Bisection to prove NP-hardness for oversquashing mitigation.
partial
GROC is NP-hard, and with membership in NP it is NP-complete.
The paper explicitly defines GROS and states its NP-hardness, supported by reductions from Minimum Bisection.
partial
However, the fundamental computational complexity of such graph optimization problems has remained unexplored.
The abstract and introduction highlight this as a gap that the paper addresses, stating 'the fundamental computational complexity of such graph optimization problems has remained unexplored.'
partial
Our results provide theoretical foundations for understanding the fundamental limits of graph rewiring for GNN optimization and justify the use of approximation algorithms and heuristic methods in practice.
The abstract and analysis explicitly state that the NP-hardness results justify the use of these methods.
partial
For a regular graph, the symmetric normalized propagation matrixP = D−1/2AD−1/2 has eigenvalues 1 = µ1(P ) ≥µ 2(P ) ≥ · · · ≥µ n(P ) ≥ −1. The Dirichlet energy after L layers decays as E(X (L)) ≤ (µ2(P ))2LE(X (0)). Thus, to prevent over-smoothing, we wish to minimize µ2(P ).
The paper formulates oversmoothing mitigation based on spectral gap and explains the relationship between the spectral gap and Dirichlet energy decay.
partial
We formulate oversmoothing and oversquashing mitigation as graph optimization problems based on spectral gap and conductance, respectively.
The paper formulates oversquashing mitigation as a problem based on conductance.
partial
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This paper theoretically investigates the computational complexity of optimizing graph structures to improve Graph Neural Network performance, proving NP-hardness for exact solutions.
Segment
Graph Neural Networks
Adoption evidence
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Commercial read
2.0/10 public viability
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proof status
unverified
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Evidence coverage
OpportunityKernel evidence_receipt
25 refs / 3 sources / 50% coverage
stale
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Build readiness
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passport absent
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Technical feasibility
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Current read
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Evidence
25 references, 3 sources, 50% evidence coverage.
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ARTIFACTS
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DEFENSIBILITY
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