MetricEmbedding: Accelerate Metric Nearness by Tropical Inner Product
Authors: Muyang Cao, Jiajun Yu, Xin Du, Gang Pan, Wei Wang
ICML 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results demonstrate that our method achieves up to 60 speed improvements over state-of-the-art approaches, and efficiently scales from 1e4 1e4 to 1e5 1e5 matrices with significantly lower memory usage. [...] Table 1. Comparison of Methods: Ours, TRF, HLWB, and PAF for Different Matrix Sizes. The table compares computation time, NMSE, and triangle inequality violations for four methods: Ours, TRF, HLWB, and PAF. Figure 2. Performance comparison of the model under different missing rates and noise levels. |
| Researcher Affiliation | Academia | 1College of Computer Science and Technology, Zhejiang University 2Shanghai Innovation Institute 3Shool of Software Technology, Zhejiang University 4 The Hong Kong University of Science and Technology (Guangzhou) 5 The Hong Kong University of Science and Technology. Correspondence to: Xin Du <EMAIL>, Wei Wang <EMAIL>. |
| Pseudocode | Yes | Algorithm 1 Training Procedure for Metric Embedding Input: Target matrix D, Adam W optimizer,threshold Output: Optimized weight matrices W0, W1, . . . , Wd Optimized bias vectors b1, . . . , bd Final output matrix O [...] Algorithm 2 Minibatch Training Procedure for Metric Embedding Input: Target matrix D, batch size B, Adam W optimizer, threshold Output: Optimized weight matrices W0, W1, . . . , Wd Optimized bias vectors b1, . . . , bd Final output matrix approximation from minibatches |
| Open Source Code | No | The recently open-sourced Python C implementation of HLWB may offer improved runtime performance. |
| Open Datasets | Yes | We used the Cora dataset, which contains 2708 nodes, and followed the standard data split used in GCN (Kipf & Welling, 2017). |
| Dataset Splits | Yes | We used the Cora dataset, which contains 2708 nodes, and followed the standard data split used in GCN (Kipf & Welling, 2017). |
| Hardware Specification | Yes | The experiments are conducted on a machine with an RTX 4090D GPU (24GB) and 32 v CPUs (Intel Xeon Platinum 8474C), running on a Linux-based operating system. |
| Software Dependencies | No | For Metric Embedding, the learning rate is set to 0.001 using the Adam W optimizer. The model is initialized as described earlier. We use Python implementations of TRF and HLWB, and the Julia implementation of PAF.1 All methods are evaluated based on their convergence time. |
| Experiment Setup | Yes | For Metric Embedding, the learning rate is set to 0.001 using the Adam W optimizer. The model is initialized as described earlier. [...] We utilized the dropout adj function in Py G to randomly perturb edges with a perturbation ratio of 0.1 to generate augmented views. The configuration used a learning rate of 0.01, 1000 epochs, with hidden and projection dimensions set to 64. |