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Graph convolutional neural networks (GCNs) embed nodes in a graph into Euclidean space, which has been shown to incur a large distortion when embedding real-world graphs with scale-free or hierarchical structure. Hyperbolic geometry offers an exciting alternative, as it enables embeddings with much smaller distortion. However, extending GCNs to hyperbolic geometry presents several unique challenges because it is not clear how to define neural network operations, such as feature transformation and aggregation, in hyperbolic space. Furthermore, since input features are often Euclidean, it is unclear how to transform the features into hyperbolic embeddings with the right amount of curvature. Here we propose Hyperbolic Graph Convolutional Neural Network (HGCN), the first inductive hyperbolic GCN that leverages both the expressiveness of GCNs and hyperbolic geometry to learn inductive node representations for hierarchical and scale-free graphs. We derive GCNs operations in the hyperboloid model of hyperbolic space and map Euclidean input features to embeddings in hyperbolic spaces with different trainable curvature at each layer. Experiments demonstrate that HGCN learns embeddings that preserve hierarchical structure, and leads to improved performance when compared to Euclidean analogs, even with very low dimensional embeddings: compared to state-of-the-art GCNs, HGCN achieves an error reduction of up to 63.1% in ROC AUC for link prediction and of up to 47.5% in F1 score for node classification, also improving state-of-the art on the PubMed dataset.
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PME: pruning-based multi-size embedding for recommender systems
Embedding is widely used in recommendation models to learn feature representations. However, the traditional embedding technique that assigns a fixed size to all categorical features may be suboptimal due to the following reasons. In recommendation domain, the majority of categorical features' embeddings can be trained with less capacity without impacting model performance, thereby storing embeddings with equal length may incur unnecessary memory usage. Existing work that tries to allocate customized sizes for each feature usually either simply scales the embedding size with feature's popularity or formulates this size allocation problem as an architecture selection problem. Unfortunately, most of these methods either have large performance drop or incur significant extra time cost for searching proper embedding sizes. In this article, instead of formulating the size allocation problem as an architecture selection problem, we approach the problem from a pruning perspective and proposePruning-basedMulti-sizeEmbedding (PME) framework. During the search phase, we prune the dimensions that have the least impact on model performance in the embedding to reduce its capacity. Then, we show that the customized size of each token can be obtained by transferring the capacity of its pruned embedding with significant less search cost. Experimental results validate that PME can efficiently find proper sizes and hence achieve strong performance while significantly reducing the number of parameters in the embedding layer.
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- Award ID(s):
- 1849085
- PAR ID:
- 10499082
- Publisher / Repository:
- Frontiers
- Date Published:
- Journal Name:
- Frontiers in Big Data
- Volume:
- 6
- ISSN:
- 2624-909X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3389/fdata.2023.1195742
