Title: FLOYDNET: A LEARNING PARADIGM FOR GLOBAL RELATIONAL REASONING
Primary area: foundation or frontier models, including LLMs
Keywords: Graph, Reasoning, GNN, Transformer

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 and complex graph
structures. 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 on the BREC
benchmark, its expressive power is empirically equivalent to the 3-WL test, while
its general form aligns with the k-FWL test. Our results establish this learned,
DP-style refinement as a powerful and practical alternative to message passing for
high-level graph reasoning.

TL;DR: Moving Beyond Transformers to a new Paradigm of Relational Reasoning.