Image Classification on MNIST rotated (test)
0.59Test Error (%)Sim(2) Separable G-CNN
Evaluation Results
| Method | Links | |
|---|---|---|
| Sim(2) Separable G-CNNSeparable configuration=along dilation and rotations dimensions, Train-time augmentation=continuous rotations2021.10 | 0.59 | |
| SE(2) Separable G-CNNTrain-time augmentation=continuous rotations2021.10 | 0.66 | |
| Sim(2) Separable G-CNNSeparable configuration=along dilation and rotations dimensions2021.10 | 0.66 | |
| E(2)-NNTrain-time augmentation=continuous rotations2021.10 | 0.68 | |
| E(2)-equivariant steerable CNNsgroup=D16 -> C16, representation=regular2019.11 | 0.682 | |
| E(2)-equivariant steerable CNNsgroup=C16, representation=quotient2019.11 | 0.705 | |
| PDO-eConvData Augmentation=Continuous rotations, Parameters=0.65M, Layers=72020.07 | 0.709 | |
| SFCNNData Augmentation=Continuous rotations2020.07 | 0.714 | |
| [7]group=C16, representation=regular2019.11 | 0.714 | |
| SFCNNTrain-time augmentation=continuous rotations2021.10 | 0.714 | |
| E2CNNData Augmentation=Continuous rotations2020.07 | 0.716 | |
| E(2)-equivariant steerable CNNsgroup=C16, representation=regular2019.11 | 0.716 | |
| SFCNN2021.10 | 0.88 | |
| PTN-CNNData Augmentation=Continuous rotations2020.07 | 0.89 | |
| SE(2) Separable G-CNN2021.10 | 0.89 | |
| RotEqNettest-time augmentation=true2016.12 | 1.01 | |
| RotEqNet2016.12 | 1.09 | |
| RotEqNetData Augmentation=Continuous rotations2020.07 | 1.09 | |
| [13]group=C17, representation=regular/vector2019.11 | 1.09 | |
| ORN-8(ORAlign)time(s)=17.8, params(%)=31.412017.01 | 1.12 | |
| TI-pooling2016.12 | 1.2 | |
| [40]2019.11 | 1.2 | |
| ORN-8(ORPooling)time(s)=17.9, params(%)=12.872017.01 | 1.21 | |
| LieConv2021.10 | 1.24 | |
| TIPooling(x8)time(s)=126.7, params(%)=100.002017.01 | 1.26 | |
| ORN-4(ORPooling)time(s)=8, params(%)=7.952017.01 | 1.33 | |
| ORN-8(None)time(s)=17.5, params(%)=31.412017.01 | 1.33 | |
| ORN-4(ORAlign)time(s)=8.1, params(%)=15.912017.01 | 1.34 | |
| ORN-8(ORPooling)time(s)=17.9, params(%)=12.872017.01 | 1.37 | |
| RED-NN2021.10 | 1.39 | |
| ORN-8(ORAlign)time(s)=17.8, params(%)=31.412017.01 | 1.42 | |
| ORN2016.12 | 1.54 | |
| OR-TIPooling(with augmentation)Augmentation=true2017.01 | 1.54 | |
| OR-TIPoolingData Augmentation=Continuous rotations2020.07 | 1.54 | |
| ORN-4(None)time(s)=7.9, params(%)=15.912017.01 | 1.55 | |
| ORN-8(None)time(s)=17.5, params(%)=31.412017.01 | 1.57 | |
| H-Net2016.12 | 1.69 | |
| ORN-4(ORAlign)time(s)=8.1, params(%)=15.912017.01 | 1.69 | |
| H-NetData Augmentation=Continuous rotations2020.07 | 1.69 | |
| [12]group=SO(2), representation=irreducible2019.11 | 1.69 | |
| H-Net2021.10 | 1.69 | |
| STN(affine)time(s)=18.5, params(%)=100.402017.01 | 1.82 | |
| ORN-4(ORPooling)time(s)=8, params(%)=7.952017.01 | 1.84 | |
| PDO-eConvparams=26k, Data Augmentation=None2020.07 | 1.87 | |
| ORN-4(None)time(s)=7.9, params(%)=15.912017.01 | 1.88 | |
| TIPooling(with augmentation)Augmentation=true2017.01 | 1.93 | |
| STN(rotation)time(s)=18.7, params(%)=100.392017.01 | 1.93 | |
| RotEqNetmodel_variant=only scalar field2016.12 | 2.01 | |
| Baseline CNNtime(s)=16.4, params(%)=100.002017.01 | 2.19 | |
| TI-Poolingparams=13.3M, Data Augmentation=None2020.07 | 2.2 | |
| ORN-8(ORAlign)Number of orientations=8, Alignment=ORAlign2017.01 | 2.25 | |
| ORN-8 (ORNAlign)params=0.53M, Data Augmentation=None2020.07 | 2.25 | |
| P4CNNgroup=p4, pooling=no pooling over rotations in intermediate layers2016.02 | 2.28 | |
| G-CNNparams=25k, Data Augmentation=None2020.07 | 2.28 | |
| [6]group=C4, representation=regular2019.11 | 2.28 | |
| G-CNN2021.10 | 2.28 | |
| STN(affine)time(s)=18.5, params(%)=100.402017.01 | 2.52 | |
| Baseline CNNtime(s)=16.4, params(%)=100.002017.01 | 2.82 | |
| STN(rotation)time(s)=18.7, params(%)=100.392017.01 | 2.88 | |
| P4CNNRotationPoolinggroup=p4, pooling=coset max-pooling over rotations2016.02 | 3.21 | |
| [6]group=C4, representation=regular/scalar2019.11 | 3.21 | |
| Schmidt & Roth (2012)2016.02 | 3.98 | |
| Sohn & Lee (2012)2016.02 | 4.2 | |
| TIRBM2016.12 | 4.2 | |
| TIRBM2014.04 | 4.2 | |
| TIRBM2017.01 | 4.2 | |
| TIRBMData Augmentation=None2020.07 | 4.2 | |
| CNN2017.01 | 4.34 | |
| Z2CNNlayers=7 layers of 3x3 convolutions, channels=20 per layer, group=Z22016.02 | 5.03 | |
| CNNparams=22k, Data Augmentation=None2020.07 | 5.03 | |
| PCANet-2Number of stages=22014.04 | 7.37 | |
| PCANet-22017.01 | 7.37 | |
| PCANet-2Data Augmentation=None2020.07 | 7.37 | |
| ScatNet-22014.04 | 7.48 | |
| ScatNet-22017.01 | 7.48 | |
| ScatNet-2Data Augmentation=None2020.07 | 7.48 | |
| LDANet-2Number of stages=22014.04 | 7.52 | |
| PCANet-1Number of stages=1, k1=132014.04 | 8.3 | |
| RandNet-2Number of stages=22014.04 | 8.47 | |
| CAE-22014.04 | 9.66 | |
| Larochelle et al. (2007)2016.02 | 10.38 | |
| PCANet-1Number of stages=12014.04 | 10.55 | |
| LDANet-1Number of stages=12014.04 | 11.4 | |
| RandNet-1Number of stages=12014.04 | 14.25 | |
| ORN-8(ORAlign)time(s)=17.8, params(%)=31.412017.01 | 16.21 | |
| ORN-8(ORPooling)time(s)=17.9, params(%)=12.872017.01 | 16.67 | |
| ORN-4(ORPooling)time(s)=8, params(%)=7.952017.01 | 27.74 | |
| ORN-4(ORAlign)time(s)=8.1, params(%)=15.912017.01 | 27.92 | |
| STN(rotation)time(s)=18.7, params(%)=100.392017.01 | 55.59 | |
| Baseline CNNtime(s)=16.4, params(%)=100.002017.01 | 56.28 | |
| STN(affine)time(s)=18.5, params(%)=100.402017.01 | 56.44 | |
| ORN-8(None)time(s)=17.5, params(%)=31.412017.01 | 58.98 | |
| ORN-4(None)time(s)=7.9, params(%)=15.912017.01 | 59.67 | |
| SFCNNsInitialization=CoeffInit, Data Augmentation=train time augmentation2017.11 | 71.4 | |
| SFCNNsInitialization=CoeffInit2017.11 | 88 | |
| SFCNNsInitialization=HeInit2017.11 | 95.7 | |
| Marcos et al.Data Augmentation=test time augmentation2017.11 | 101 | |
| Marcos et al.2017.11 | 109 | |
| Laptev et al.2017.11 | 120 | |
| Worrall et al.2017.11 | 169 |