A Model-Agnostic Graph Neural Network for Integrating Local and Global Information

TL;DR

A novel Model-agnostic Graph Neural Network (MaGNet) framework is proposed, able to effectively integrate information of various orders, extract knowledge from high-order neighbors, and provide meaningful and interpretable results by identifying influential compact graph structures.

Abstract

Graph Neural Networks (GNNs) have achieved promising performance in a variety of graph-focused tasks. Despite their success, however, existing GNNs suffer from two significant limitations: a lack of interpretability in their results due to their black-box nature, and an inability to learn representations of varying orders. To tackle these issues, we propose a novel Model-agnostic Graph Neural Network (MaGNet) framework, which is able to effectively integrate information of various orders, extract knowledge from high-order neighbors, and provide meaningful and interpretable results by identifying influential compact graph structures. In particular, MaGNet consists of two components: an estimation model for the latent representation of complex relationships under graph topology, and an interpretation model that identifies influential nodes, edges, and node features. Theoretically, we establish the generalization error bound for MaGNet via empirical Rademacher complexity, and demonstrate its power to represent layer-wise neighborhood mixing. We conduct comprehensive numerical studies using simulated data to demonstrate the superior performance of MaGNet in comparison to several state-of-the-art alternatives. Furthermore, we apply MaGNet to a real-world case study aimed at extracting task-critical information from brain activity data, thereby highlighting its effectiveness in advancing scientific research.

Figures (5)

• Figure 1: An illustrative example of $3$-layers neural architecture of the actor-critic graph neural network.
• Figure 2: The feature-interpretation performance over $50$ repeated experiments
• Figure 3: (a.) The task involves repeated presentations of sequences of odors and requires rats to determine whether each odor was presented “in sequence” (InSeq; e.g., ABC…) or “out of sequence” (OutSeq; e.g., ABD…). Using an automated delivery system (left), all odors were presented in the same odor port (median interval between odors $\sim$5 s). Recordings were performed from electrodes organized into two bundles (right), which spanned much of the proximo-distal axis of dorsal CA1. (b.) In each session, the same sequence was presented multiple times, with approximately half the presentations including all InSeq trials (left) and the other half including one OutSeq trial (right). Each odor presentation was initiated by a nosepoke and rats were required to correctly identify each odor as either InSeq (by holding their nosepoke response until a tone signaled the end of the odor at 1.2 s) or OutSeq (by withdrawing their nose before the signal; <1.2 s) to receive a water reward. Incorrect responses resulted in the termination of the sequence. (c.) Location of three electrode tips (red circles). The leftmost and rightmost electrodes approximate the extent of the CA1 transverse axis recorded in each animal.
• Figure 4: Barplot of estimation accuracy for the MaGNet estimation model and alternative competing approaches on decoding the two main trial types.
• Figure 5: (a.) Significant decoding of InSeq and OutSeq trials based on LFP activity during the first 500ms of odor trials. Scores peak during the 185-320 ms period, prior to the behavioral response. Grey traces indicate individual subject decodings, the black line indicates the mean across subjects. (b.) Informative electrode nodes in the distal region of CA1. Schematic showing side view of electrode bundles implanted across the CA1 proximal-distal axis (Top). Schematic showing a top view of the anatomical distribution of electrodes across subjects based on electrode tract reconstruction (bottom). Yellow indicates significant nodes (electrodes). (c.) The clustering of informative nodes in distal CA1 is consistent with known anatomical differences in input connections. Odor information enters the hippocampus primarily through the LEC, which more strongly projects to the distal segment of CA1. In contrast, the MEC more strongly projects to proximal CA1. Approximate location of the implanted electrode bundles is shown.

Theorems & Definitions (5)

• Definition 3.1
• Theorem 5.1
• Definition 5.1
• Theorem 5.2
• Theorem 5.3