Papers › No Routing Needed Between Capsules

No Routing Needed Between Capsules

24 Jan 2020arXiv:2001.09136archive 2025-07-28

Adam Byerly, Tatiana Kalganova, Ian Dear

Most capsule network designs rely on traditional matrix multiplication between capsule layers and computationally expensive routing mechanisms to deal with the capsule dimensional entanglement that the matrix multiplication introduces. By using Homogeneous Vector Capsules (HVCs), which use element-wise multiplication rather than matrix multiplication, the dimensions of the capsules remain unentangled. In this work, we study HVCs as applied to the highly structured MNIST dataset in order to produce a direct comparison to the capsule research direction of Geoffrey Hinton, et al. In our study, we show that a simple convolutional neural network using HVCs performs as well as the prior best performing capsule network on MNIST using 5.5x fewer parameters, 4x fewer training epochs, no reconstruction sub-network, and requiring no routing mechanism. The addition of multiple classification branches to the network establishes a new state of the art for the MNIST dataset with an accuracy of 99.87% for an ensemble of these models, as well as establishing a new state of the art for a single model (99.83% accurate).

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Code

AdamByerly/BMCNNwHFCs officialmentioned in papermentioned on GitHubtf report

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Tasks

Image Classification

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Image Classification MNIST Branching/Merging CNN + Homogeneous Vector Capsules Accuracy 99.87 #1 of 81 Archive leaderboard report
Image Classification MNIST Branching/Merging CNN + Homogeneous Vector Capsules Percentage error 0.13 #1 of 81 Archive leaderboard report
Image Classification MNIST Branching/Merging CNN + Homogeneous Vector Capsules Trainable Parameters 1514187 #1 of 81 Archive leaderboard report

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Methods

AdamCapsule Network

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