Densely Connected G-invariant Deep Neural Networks with Signed Permutation Representations
Authors: Devanshu Agrawal, James Ostrowski
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Finally, we apply G-DNNs to two example problems (1) multiplication in { 1, 1} (with theoretical guarantees) and (2) 3D object classification finding that the inclusion of signed perm-reps significantly boosts predictive performance compared to baselines with only ordinary (i.e., unsigned) perm-reps. |
| Researcher Affiliation | Academia | Devanshu Agrawal EMAIL Department of Industrial and Systems Engineering University of Tennessee Knoxville, TN 37996, USA James Ostrowski EMAIL Department of Industrial and Systems Engineering University of Tennessee Knoxville, TN 37996, USA |
| Pseudocode | Yes | Algorithm 1 Implementation of Thm. 6 (b) for the forward pass of a G-DNN f. Here g(i)(x) and h(i)(x) should be regarded as variable names. Algorithm 2 Implementation of the function θ that exploits existing functions in GAP. |
| Open Source Code | Yes | Code for our implementation and for reproducing all results in this paper is available at: https:// github.com/dagrawa2/gdnn_code. |
| Open Datasets | Yes | Our second example application demonstrates that G-DNNs with type 2 signed perm-reps carry inductive bias that can be useful in the wild . We consider the Model Net40 dataset(Wu et al., 2015), which contains 9843 training and 2468 validation samples of 3D CAD mesh representations of 40 different objects ranging from airplanes to toilets. |
| Dataset Splits | Yes | We investigate Ex. 2 empirically by generating the complete dataset {(x, f(x)) : x X} for m = 16. Since f(x) = 1, then we regard the estimation of f as a binary classification problem. We use a random 20% of the dataset (with class stratification) for training and the rest for validation. Our second example application demonstrates that G-DNNs with type 2 signed perm-reps carry inductive bias that can be useful in the wild . We consider the Model Net40 dataset(Wu et al., 2015), which contains 9843 training and 2468 validation samples of 3D CAD mesh representations of 40 different objects ranging from airplanes to toilets. |
| Hardware Specification | No | No specific hardware details are provided for running the experiments. The text mentions that the current G-DNN implementation does not scale well to high resolution but does not specify the hardware used for the existing implementation or experiments. |
| Software Dependencies | No | The paper mentions the Adam optimizer, Re LU activation, batch normalization, and the GAP language but does not provide specific version numbers for any of these software components. |
| Experiment Setup | Yes | We trained all architectures for 5 epochs with the Adam optimizer with minibatch size 64, learning rate 0.01, and learning rate decay 0.99 per step. We trained all architectures for 500 epochs with the Adam optimizer with minibatch size 64, learning rate 0.01, and learning rate decay 0.99 per step. We included batchnorm as described in Sec. 3.4 after each Re LU layer. In each run, we performed retroactive early stopping by recording the highest validation accuracy achieved over all epochs. |