GLL：为神经网络设计的可微图学习层

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Abstract:Standard deep learning architectures used for classification generate label predictions with a projection head and softmax activation function. Although successful, these methods fail to leverage the relational information between samples for generating label predictions. In recent works, graph-based learning techniques, namely Laplace learning, have been heuristically combined with neural networks for both supervised and semi-supervised learning (SSL) tasks. However, prior works approximate the gradient of the loss function with respect to the graph learning algorithm or decouple the processes; end-to-end integration with neural networks is not achieved. In this work, we derive backpropagation equations, via the adjoint method, for inclusion of a general family of graph learning layers into a neural network. The resulting method, distinct from graph neural networks, allows us to precisely integrate similarity graph construction and graph Laplacian-based label propagation into a neural network layer, replacing a projection head and softmax activation function for general classification task. Our experimental results demonstrate smooth label transitions across data, improved generalization and robustness to adversarial attacks, and improved training dynamics compared to a standard softmax-based approach.

Comments:	58 pages, 12 figures. Preprint. Submitted to the Journal of Machine Learning Research. v2: several new experiments, improved exposition
Subjects:	Machine Learning (cs.LG); Machine Learning (stat.ML)
MSC classes:	68T05, 68T07, 35R02
ACM classes:	I.2.6; I.2.10; I.4.0
Cite as:	arXiv:2412.08016 [cs.LG]
	(or arXiv:2412.08016v3 [cs.LG] for this version)
	https://doi.org/10.48550/arXiv.2412.08016 arXiv-issued DOI via DataCite

Submission history

From: Harris Hardiman-Mostow [view email]
[v1] Wed, 11 Dec 2024 01:54:29 UTC (4,656 KB)
[v2] Mon, 8 Dec 2025 21:01:09 UTC (2,452 KB)
[v3] Wed, 14 Oct 2026 02:24:55 UTC (2,452 KB)