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FLOYDNET: A LEARNING PARADIGM FOR GLOBAL RELATIONAL REASONING

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
GraphReasoningGNNTransformer
Abstract:

Developing models capable of complex, multi-step reasoning is a central goal in artificial intelligence. While representing problems as graphs is a powerful approach, Graph Neural Networks (GNNs) are fundamentally constrained by their message-passing mechanism, which imposes a local bottleneck that limits global, holistic reasoning. We argue that dynamic programming (DP), which solves problems by iteratively refining a global state, offers a more powerful and suitable learning paradigm. We introduce FloydNet, a new architecture that embodies this principle. In contrast to local message passing, FloydNet maintains a global, all-pairs relationship tensor and learns a generalized DP operator to progressively refine it. This enables the model to develop a task-specific relational calculus, providing a principled framework for capturing long-range dependencies. Theoretically, we prove that FloydNet achieves 3-WL (2-FWL) expressive power, and its generalized form aligns with the k-FWL hierarchy. FloydNet demonstrates state-of-the-art performance across challenging domains: it achieves near-perfect scores (often >99%) on the CLRS-30 algorithmic benchmark, finds exact optimal solutions for the general Traveling Salesman Problem (TSP) at rates significantly exceeding strong heuristics, and empirically matches the 3-WL test on the BREC benchmark. Our results establish this learned, DP-style refinement as a powerful and practical alternative to message passing for high-level graph reasoning.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

FloydNet introduces a dynamic programming paradigm for global relational reasoning, maintaining an all-pairs relationship tensor refined by a learned DP operator. The paper resides in the 'Expressive Power and Theoretical Foundations' leaf, which contains only four papers total, indicating a relatively sparse research direction focused on theoretical expressiveness rather than empirical architecture design. This leaf sits within the broader 'Graph Neural Network Architectures for Relational Reasoning' branch, distinguishing itself from attention-based mechanisms, global aggregation methods, and multi-granularity frameworks that populate sibling leaves.

The taxonomy reveals neighboring leaves addressing attention-based relational mechanisms, global aggregation and interaction modeling, and multi-granularity representations—all exploring alternatives to standard message passing. FloydNet's DP-inspired approach diverges from these by framing reasoning as iterative global state refinement rather than attention-weighted aggregation or coordinate-space interactions. The broader branch excludes temporal dynamics and domain applications, positioning FloydNet as a foundational contribution to architectural expressiveness. Related branches on knowledge graph reasoning and domain-specific applications suggest the field balances theoretical foundations with practical deployment, though FloydNet's leaf emphasizes the former.

Among twenty-six candidates examined, the dynamic programming paradigm and FloydNet architecture contributions show no clear refutation across ten and six candidates respectively. However, the theoretical characterization of k-FloydNet expressive power examined ten candidates and found three potentially refutable prior works, suggesting this contribution overlaps more substantially with existing theoretical analyses. The limited search scope—top-K semantic matches plus citation expansion—means these statistics reflect a focused sample rather than exhaustive coverage. The architecture and paradigm contributions appear more distinctive within this bounded search, while the expressiveness claims encounter more prior theoretical work.

Based on the limited literature search, FloydNet occupies a sparse theoretical niche with few direct siblings, though its expressive power claims intersect with existing theoretical frameworks. The analysis covers top-26 semantic matches and does not guarantee exhaustive identification of all relevant prior work. The architecture's novelty appears stronger than its theoretical characterization within the examined scope, though the sparse leaf population suggests room for foundational contributions in this direction.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
26
Contribution Candidate Papers Compared
3
Refutable Paper

Research Landscape Overview

Core task: learning global relational reasoning on graphs. The field encompasses diverse approaches to capturing and exploiting relational structure in graph-structured data. At the highest level, the taxonomy distinguishes between foundational Graph Neural Network Architectures for Relational Reasoning—which explore expressive power, theoretical limits, and novel message-passing schemes—and more application-driven branches such as Knowledge Graph Reasoning and Completion, Integration of Knowledge Graphs with Language Models, and Domain-Specific Relational Reasoning Applications. Additional branches address Self-Supervised and Contrastive Learning on Graphs, Dynamic and Evolving Graph Reasoning for temporal settings, and broad Knowledge Graph Construction and Representation Surveys. Representative works like Graph Global Reasoning[1] and Global Relational Models[14] illustrate early efforts to move beyond local neighborhood aggregation, while recent studies such as Relational Inductive Biases[2] and Epistemic Graph Networks[13] delve into the theoretical underpinnings of how networks encode and propagate relational information. Within the architecture-focused branch, a particularly active line of inquiry examines the expressive power and theoretical foundations of graph models, asking how well different designs can capture complex global dependencies and higher-order interactions. FloydNet[0] sits squarely in this cluster, emphasizing principled mechanisms for global relational reasoning alongside neighbors like Relational Inductive Biases[2] and Epistemic Graph Networks[13]. While Relational Inductive Biases[2] investigates the structural priors that enable generalization, and Epistemic Graph Networks[13] explores epistemic constraints on reasoning, FloydNet[0] contributes a distinct algorithmic perspective inspired by classical graph algorithms. This contrasts with application-oriented works such as Social Relation Reasoning[3] or domain-specific modules like Relational Reasoning Module[5], which prioritize task performance over foundational expressiveness. The central tension across these lines remains balancing theoretical guarantees with scalability and practical utility, a theme that continues to drive innovation in global relational reasoning on graphs.

Claimed Contributions

Dynamic programming paradigm for global relational reasoning

The authors propose shifting from local message passing to a global, DP-inspired refinement paradigm that maintains and iteratively refines an all-pairs relationship tensor, enabling the model to develop task-specific relational calculus and capture long-range dependencies.

10 retrieved papers
FloydNet architecture with Pivotal Attention mechanism

The authors introduce FloydNet, a novel architecture that implements the DP paradigm through a learned generalized DP operator called Pivotal Attention, which updates pairwise relationships by aggregating information from all two-hop relational paths mediated by pivot nodes.

6 retrieved papers
Theoretical characterization of k-FloydNet expressive power

The authors formally prove that FloydNet is equivalent to the 2-FWL (3-WL) test and that its generalized k-FloydNet form aligns with the k-FWL hierarchy, establishing a precise theoretical characterization of the architecture's distinguishing power.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Dynamic programming paradigm for global relational reasoning

The authors propose shifting from local message passing to a global, DP-inspired refinement paradigm that maintains and iteratively refines an all-pairs relationship tensor, enabling the model to develop task-specific relational calculus and capture long-range dependencies.

Contribution

FloydNet architecture with Pivotal Attention mechanism

The authors introduce FloydNet, a novel architecture that implements the DP paradigm through a learned generalized DP operator called Pivotal Attention, which updates pairwise relationships by aggregating information from all two-hop relational paths mediated by pivot nodes.

Contribution

Theoretical characterization of k-FloydNet expressive power

The authors formally prove that FloydNet is equivalent to the 2-FWL (3-WL) test and that its generalized k-FloydNet form aligns with the k-FWL hierarchy, establishing a precise theoretical characterization of the architecture's distinguishing power.

Table of Contents

FLOYDNET: A LEARNING PARADIGM FOR GLOBAL RELATIONAL REASONING | Novelty Validation