# Visualization and Analysis of the Loss Landscape in Graph Neural Networks

arXiv: https://arxiv.org/abs/2509.11792 · HTML: https://mlsanity.com/paper/2509.11792/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 15 Sep 2025.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Identifying and attacking the saddle point problem in high-dimensional non-convex optimization](https://mlsanity.com/paper/1406.2572/) (2014)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Combining Label Propagation and Simple Models Out-performs Graph Neural Networks](https://mlsanity.com/paper/2010.13993/) (2020)
- [Qualitatively characterizing neural network optimization problems](https://mlsanity.com/paper/1412.6544/) (2014)
- [Convergence Analysis of Two-layer Neural Networks with ReLU Activation](https://mlsanity.com/paper/1705.09886/) (2017)
- [Theoretical insights into the optimization landscape of over-parameterized shallow neural networks](https://mlsanity.com/paper/1707.04926/) (2017)
- [Weisfeiler and Leman go Machine Learning: The Story so far](https://mlsanity.com/paper/2112.09992/) (2021)
- [Graph Attention Multi-Layer Perceptron](https://mlsanity.com/paper/2206.04355/) (2022)
- [The loss surface of deep and wide neural networks](https://mlsanity.com/paper/1704.08045/) (2017)
- [Optimization of Graph Neural Networks with Natural Gradient Descent](https://mlsanity.com/paper/2008.09624/) (2020)
- [An empirical analysis of the optimization of deep network loss surfaces](https://mlsanity.com/paper/1612.04010/) (2016)
- [Exploring loss function topology with cyclical learning rates](https://mlsanity.com/paper/1702.04283/) (2017)
- [Efficient Mixed Precision Quantization in Graph Neural Networks](https://mlsanity.com/paper/2505.09361/) (2025)

## Abstract (arXiv)

Graph Neural Networks (GNNs) are powerful models for graph-structured data, with broad applications. However, the interplay between GNN parameter optimization, expressivity, and generalization remains poorly understood. We address this by introducing an efficient learnable dimensionality reduction method for visualizing GNN loss landscapes, and by analyzing the effects of over-smoothing, jumping knowledge, quantization, sparsification, and preconditioner on GNN optimization. Our learnable projection method surpasses the state-of-the-art PCA-based approach, enabling accurate reconstruction of high-dimensional parameters with lower memory usage. We further show that architecture, sparsification, and optimizer's preconditioning significantly impact the GNN optimization landscape and their training process and final prediction performance. These insights contribute to developing more efficient designs of GNN architectures and training strategies.