| Output Size | Layer Name | Focal-Tiny | Focal-Small | Focal-Base | ||||
| stage 1 | 56×56 | Patch Embedding | p1= 4;c1 = 96 | p1=4;c1= 96 | p1 = 4;c1 = 128 | |||
| 56×56 | Transformer Block | {1,13} 三 s={7,7 | ×2 | 二 {1,13} ={7,7} | ×2 | {1,13} ={7,7} | ×2 | |
| stage 2 | 28×28 | Patch Embedding | P2=2;c=192 | P2=2;C=192 | P2=2;C= 256 | |||
| 28×28 | Transformer Block | {1,13} 三 swr={7,5} 1 | ×2 | ={1,13} sw,r={7,5} 1 | ×2 | {1,13} 二 su,r={7,5} | ×2 | |
| stage 3 | 14 × 14 | Patch Embedding | p3=2;c3=384 | p3=2; c3= 384 | p3=2; c3= 512 | |||
| 14 × 14 | Transformer Block | ={1,13} s={7,3} | ×6 | ={1,13} ={7,3} | ×18 | ={1,13} ={7,3} | ×18 | |
| stage 4 | 7×7 | Patch Embedding | P4=2;C4=768 | P4=2;C4=768 | P4= 2;C4=1024 | |||
| 7×7 | Transformer Block | 二 {1,7} | ×2 | {1,7} s 三 ={7,1} | ×2 | 二 {1,7} su,r {7,1} 二 | ×2 |
| Model | #Params. FLOPs | Top-1 (%) |
| ResNet-50 [33] | 25.0 4.1 | 76.2 |
| DeiT-Small/16 [55] | 22.1 4.6 | 79.9 |
| PVT-Small [60] | 24.5 3.8 | 79.8 |
| ViL-Small [76] | 24.6 5.1 | 82.0 |
| CvT-13 [64] | 20.0 4.5 | 81.6 |
| Swin-Tiny [43] | 28.3 4.5 | 81.2 |
| Focal-Tiny (Ours) | 28.9 4.9 | 82.2 |
| ResNet-101[33] | 45.0 7.9 | 77.4 |
| PVT-Medium [60] | 44.2 6.7 | 81.2 |
| CvT-21 [64] | 32.0 7.1 | 82.5 |
| ViL-Medium [76] | 39.7 9.1 | 83.3 |
| Swin-Small [43] | 49.6 8.7 | 83.1 |
| Focal-Small (Ours) | 51.1 9.4 | 83.6 |
| ResNet-152[33] | 60.0 11.0 | 78.3 |
| ViT-Base/16 [21] | 86.6 17.6 | 77.9 |
| DeiT-Base/16 [55] | 17.5 | 81.8 |
| 86.6 | ||
| PVT-Large [60] | 61.4 9.8 | 81.7 |
| ViL-Base[76] | 55.7 13.4 | 83.2 |
| Swin-Base [43] | 87.8 15.4 | 83.4 |
| Focal-Base (Ours) | 89.8 | 16.4 84.0 |
| Backbone | RetinaNet | Mask R-CNN | |
| APb | Apb | APm | |
| ResNet-50 [33] | 36.3 | 38.0 | 34.4 |
| PVT-Small | 40.4 | 40.4 | 37.8 |
| ViL-Small [76] | 41.6 | 41.8 | 38.5 |
| Swin-Tiny [43] | 42.0 | 43.7 | 39.8 |
| Focal-Tiny (Ours) | 43.7 (+1.7) | 44.8 (+1.1) | 41.0 (+1.3) |
| ResNet-101[33] | 38.5 | 40.4 | 36.4 |
| ResNeXt101-32x4d [67] | 39.9 | 41.9 | 37.5 |
| PVT-Medium [60] | 41.9 | 42.0 | 39.0 |
| ViL-Medium [76] | 42.9 | 43.4 | 39.7 |
| Swin-Small [43] | 45.0 | 46.5 | 42.1 |
| Focal-Small (Ours) | 45.6 (+0.6) | 47.4 (+0.9) | 42.8 (+0.7) |
| ResNeXt101-64x4d[67] 41.0 | 42.8 | 38.4 | |
| PVT-Large [60] | 42.6 | 42.9 | 39.5 |
| ViL-Base[76] | 44.3 | 45.1 | 41.0 |
| Swin-Base [43] | 45.0 | 46.9 | 42.3 |
| Focal-Base (Ours) | 46.3 (+1.3) | 47.8 (+0.9) | 43.2 (+0.9) |
| Backbone | #Params (M) | FLOPs (G) | RetinaNet 3x schedule + MS | Mask R-CNN 3x schedule + MS | ||||||||||
| AP | AP5 | AP | APs | APM | APL | AP6 | AP | AP | Apm | AP | AP | |||
| ResNet50 [33] | 37.7/44.2 | 239/260 | 39.0 | 58.4 | 41.8 | 22.4 | 42.8 | 51.6 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| PVT-Small[60] | 34.2/44.1 | 226/245 | 42.2 | 62.7 | 45.0 | 26.2 | 45.2 | 57.2 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| ViL-Small [76] | 35.7/45.0 | 252/174 42.9 | 63.8 | 45.6 | 27.8 | 46.4 | 56.3 | 43.4 | 64.9 | 47.0 | 39.6 | 62.1 | 42.4 | |
| Swin-Tiny [43] | 38.5/47.8 | 245/264 45.0 | 65.9 | 48.4 | 29.7 | 48.9 | 58.1 | 46.0 | 68.1 | 50.3 | 41.6 | 65.1 | 44.9 | |
| Focal-Tiny (Ours) | 39.4/48.8 | 265/291 | 45.5 | 66.3 | 48.8 | 31.2 | 49.2 | 58.7 | 47.2 | 69.4 | 51.9 | 42.7 | 66.5 | 45.9 |
| ResNet101 [33] | 56.7/63.2 | 315/33640.9 | 60.1 | 44.0 | 23.7 | 45.0 | 53.8 | 42.8 | 63.2 | 47.1 | 38.5 | 60.1 | 41.3 | |
| ResNeXt101-32x4d [67] | 56.4/62.8 | 319/340 | 41.4 | 61.0 | 44.3 | 23.9 | 45.5 | 53.7 | 44.0 | 64.4 | 48.0 | 39.2 | 61.4 | 41.9 |
| PVT-Medium [60] | 53.9/63.9 | 283/302 | 43.2 | 63.8 | 46.1 | 27.3 | 46.3 | 58.9 | 44.2 | 66.0 | 48.2 | 40.5 | 63.1 | 43.5 |
| ViL-Medium [76] | 50.8/60.1 | 339/261 | 43.7 | 64.6 | 46.4 | 27.9 | 47.1 | 56.9 | 44.6 | 66.3 | 48.5 | 40.7 | 63.8 | 43.7 |
| Swin-Small [43] | 59.8/69.1 | 335/354 46.4 | 67.0 | 50.1 | 31.0 | 50.1 | 60.3 | 48.5 | 70.2 | 53.5 | 43.3 | 67.3 | 46.6 | |
| Focal-Small (Ours) | 61.7/71.2 | 367/401 | 47.3 | 67.8 | 51.0 | 31.6 | 50.9 | 61.1 | 48.8 | 70.5 | 53.6 | 43.8 | 67.7 | 47.2 |
| ResNeXt101-64x4d [67] | 95.5/102 | 473/493 | 41.8 | 61.5 | 44.4 | 25.2 | 45.4 | 54.6 | 44.4 | 64.9 | 48.8 | 39.7 | 61.9 | 42.6 |
| PVT-Large[60] | 71.1/81.0 | 345/364 43.4 | 63.6 | 46.1 | 26.1 | 46.0 | 59.5 | 44.5 | 66.0 | 48.3 | 40.7 | 63.4 | 43.7 | |
| ViL-Base [76] | 66.7/76.1 | 443/365 44.7 | 65.5 | 47.6 | 29.9 | 48.0 | 58.1 | 45.7 | 67.2 | 49.9 | 41.3 | 64.4 | 44.5 | |
| Swin-Base 43] | 98.4/107 | 477/496 45.8 | 66.4 | 49.1 | 29.9 | 49.4 | 60.3 | 48.5 | 69.8 | 53.2 | 43.4 | 66.8 | 46.9 | |
| Focal-Base (Ours) | 100.8/110.0 514/533 46.9 | 67.8 | 50.3 | 31.9 | 50.3 | 61.5 | 49.0 | 70.1 | 53.6 | 43.7 | 67.6 | 47.0 | ||
| Method | #Param FLOPs | mini-val | test-dev | |||
| Apb | APm | Apb | Apm | |||
| X101-64x4d [67] | 155M | 1033G 52.3 | 46.0 | |||
| EfficientNet-D7 [54] | 77M | 410G | 54.4 | - | 55.1 | = |
| GCNet*[7] | - | 1041G | 51.8 | 44.7 | 52.3 | 45.4 |
| ResNeSt-200 [75] | = | 52.5 | = | 53.3 | 47.1 | |
| Copy-paste [28] | 185M | 1440G 55.9 | 47.2 | 56.0 | 47.4 | |
| BoTNet-200 [51] | - | 49.7 | - | |||
| SpineNet-190 [22] | 164M | 1885G 52.6 | 52.8 | |||
| CenterNet2 [84] | - | = | - | - | 56.4 | = |
| Swin-L (HTC++) [43] | 284M | 1470G 57.1 | 49.5 | 57.7 | 50.2 | |
| Swin-L (DyHead)[17] | 213M | 965G | 56.2 | - | - | - |
| Swin-L† (HTC++) [43] | 284M | 58.0 | 50.4 | 58.7 | 51.1 | |
| Swin-L† (DyHead) [17] | 213M | 58.4 | - | 58.7 | ||
| Swin-L† (QueryInst) [25] | - | 56.1 | 1 | 56.1 | ||
| Focal-L (HTC++) (Ours) | 265M | 1165G | 57.0 | 49.9 | - | = |
| Focal-L (DyHead) (Ours) | 229M | 1081G | 56.4 | - | - | = |
| Focal-L† (HTC++) (Ours) | 265M | - | 58.1 | 50.9 | 58.4 | 51.3 |
| Focal-L† (DyHead) (Ours) | 229M | - | 58.7 | - | 59.0 | - |
| Backbone | Method | #Param FLOPs mIoU +MS | |||
| ResNet-101 | DANet [45] | 69M | 1119G | 45.3 | |
| ResNet-101 | ACNet [26] | = | = | 45.9 | |
| ResNet-101 | DNL [69] | 69M | 1249G | 46.0 | |
| ResNet-101 | UperNet [65] | 86M | 1029G | 44.9 | |
| HRNet-w48 [53] | OCRNet [73] | 71M | 664G | 45.7 | = |
| ResNeSt-200 [75] | DLab.v3+ [12] | 88M | 1381G | 48.4 | = |
| Swin-T[43] | UperNet [65] | 60M | 945G | 44.5 | 45.8 |
| Swin-S [43] | UperNet [65] | 81M | 1038G | 47.6 | 49.5 |
| Swin-B [43] | UperNet [65] | 121M | 1188G | 48.1 | 49.7 |
| Twins-SVT-L[15] | UperNet [65] | 133M | 48.8 | 50.2 | |
| MiT-B5 [66] | SegFormer [66] | 85M | 51.0 | 51.8 | |
| ViT-L/16+ [21] | SETR[80] | 308M | 50.3 | = | |
| Swin-L* [43] | UperNet [65] | 234M | 3230G | 52.1 | 53.5 |
| ViT-L/16 [21] | Segmenter [52] | 334M | = | 51.8 | 53.6 |
| Swin-L‡ [43] | K-Net [77] | = | = | 54.3 | |
| Swin-L‡ [43] | PatchDiverse [29] | 234M | 53.1 | 54.4 | |
| VOLO-D5 [72] | UperNet [65] | = | - | 54.3 | |
| Focal-T (Ours) | UperNet [65] | 62M | 998G | 45.8 | 47.0 |
| Focal-S (Ours) | UperNet [65] | 85M | 1130G | 48.0 | 50.0 |
| Focal-B (Ours) | UperNet [65] | 126M | 1354G | 49.0 | 50.5 |
| Focal-L‡ (Ours) | UperNet [65] | 240M | 3376G | 54.0 | 55.4 |
| Model | W-Size FLOPs Top-1(%) APb APm | ||
| Swin-Tiny | 7 | 4.5 | 81.2 43.739.8 |
| 14 | 4.9 | 82.1 44.0 40.5 | |
| Focal-Tiny | 7 | 4.9 | 82.2 44.941.1 |
| 14 | 5.2 | 82.3 45.5 41.5 |
| Model | W-Shift Top-1(%) APb APm | |||
| Swin-Tiny | √ | 80.2 81.2 | 38.8 43.7 | 36.4 39.8 |
| Focal-Tiny | 82.2 | 44.8 | 41.0 | |
| √ | 81.9 | 44.9 | 41.1 | |
| Depths Model #Params. FLOPs Top-1(%) APb Apm | |||||
| 2-2-2-2 | Swin | 21.2 | 3.1 | 78.7 | 38.2 35.7 |
| Focal | 21.7 | 3.4 | 79.9 | 40.5 37.6 | |
| 2-2-4-2 | Swin | 24.7 | 3.8 | 80.2 | 41.2 38.1 |
| Focal | 25.4 | 4.1 | 81.4 | 43.3 39.8 | |
| 2-2-6-2 | Swin | 28.3 | 4.5 | 81.2 | 43.7 39.8 |
| Focal | 29.1 | 4.9 | 82.2 | 44.8 41.0 | |
| Output Size | Layer Name | Focal-Tiny | Focal-Small | Focal-Base | ||||
| stage 1 | 56×56 | Patch Embedding | p1= 4;c1 = 96 | p1=4;c1= 96 | p1 = 4;c1 = 128 | |||
| 56×56 | Transformer Block | {1,13} 三 s={7,7 | ×2 | 二 {1,13} ={7,7} | ×2 | {1,13} ={7,7} | ×2 | |
| stage 2 | 28×28 | Patch Embedding | P2=2;c=192 | P2=2;C=192 | P2=2;C= 256 | |||
| 28×28 | Transformer Block | {1,13} 三 swr={7,5} 1 | ×2 | ={1,13} sw,r={7,5} 1 | ×2 | {1,13} 二 su,r={7,5} | ×2 | |
| stage 3 | 14 × 14 | Patch Embedding | p3=2;c3=384 | p3=2; c3= 384 | p3=2; c3= 512 | |||
| 14 × 14 | Transformer Block | ={1,13} s={7,3} | ×6 | ={1,13} ={7,3} | ×18 | ={1,13} ={7,3} | ×18 | |
| stage 4 | 7×7 | Patch Embedding | P4=2;C4=768 | P4=2;C4=768 | P4= 2;C4=1024 | |||
| 7×7 | Transformer Block | 二 {1,7} | ×2 | {1,7} s 三 ={7,1} | ×2 | 二 {1,7} su,r {7,1} 二 | ×2 |
| Model | #Params. FLOPs | Top-1 (%) |
| ResNet-50 [33] | 25.0 4.1 | 76.2 |
| DeiT-Small/16 [55] | 22.1 4.6 | 79.9 |
| PVT-Small [60] | 24.5 3.8 | 79.8 |
| ViL-Small [76] | 24.6 5.1 | 82.0 |
| CvT-13 [64] | 20.0 4.5 | 81.6 |
| Swin-Tiny [43] | 28.3 4.5 | 81.2 |
| Focal-Tiny (Ours) | 28.9 4.9 | 82.2 |
| ResNet-101[33] | 45.0 7.9 | 77.4 |
| PVT-Medium [60] | 44.2 6.7 | 81.2 |
| CvT-21 [64] | 32.0 7.1 | 82.5 |
| ViL-Medium [76] | 39.7 9.1 | 83.3 |
| Swin-Small [43] | 49.6 8.7 | 83.1 |
| Focal-Small (Ours) | 51.1 9.4 | 83.6 |
| ResNet-152[33] | 60.0 11.0 | 78.3 |
| ViT-Base/16 [21] | 86.6 17.6 | 77.9 |
| DeiT-Base/16 [55] | 17.5 | 81.8 |
| 86.6 | ||
| PVT-Large [60] | 61.4 9.8 | 81.7 |
| ViL-Base[76] | 55.7 13.4 | 83.2 |
| Swin-Base [43] | 87.8 15.4 | 83.4 |
| Focal-Base (Ours) | 89.8 | 16.4 84.0 |
| Backbone | RetinaNet | Mask R-CNN | |
| APb | Apb | APm | |
| ResNet-50 [33] | 36.3 | 38.0 | 34.4 |
| PVT-Small | 40.4 | 40.4 | 37.8 |
| ViL-Small [76] | 41.6 | 41.8 | 38.5 |
| Swin-Tiny [43] | 42.0 | 43.7 | 39.8 |
| Focal-Tiny (Ours) | 43.7 (+1.7) | 44.8 (+1.1) | 41.0 (+1.3) |
| ResNet-101[33] | 38.5 | 40.4 | 36.4 |
| ResNeXt101-32x4d [67] | 39.9 | 41.9 | 37.5 |
| PVT-Medium [60] | 41.9 | 42.0 | 39.0 |
| ViL-Medium [76] | 42.9 | 43.4 | 39.7 |
| Swin-Small [43] | 45.0 | 46.5 | 42.1 |
| Focal-Small (Ours) | 45.6 (+0.6) | 47.4 (+0.9) | 42.8 (+0.7) |
| ResNeXt101-64x4d[67] 41.0 | 42.8 | 38.4 | |
| PVT-Large [60] | 42.6 | 42.9 | 39.5 |
| ViL-Base[76] | 44.3 | 45.1 | 41.0 |
| Swin-Base [43] | 45.0 | 46.9 | 42.3 |
| Focal-Base (Ours) | 46.3 (+1.3) | 47.8 (+0.9) | 43.2 (+0.9) |
| Backbone | #Params (M) | FLOPs (G) | RetinaNet 3x schedule + MS | Mask R-CNN 3x schedule + MS | ||||||||||
| AP | AP5 | AP | APs | APM | APL | AP6 | AP | AP | Apm | AP | AP | |||
| ResNet50 [33] | 37.7/44.2 | 239/260 | 39.0 | 58.4 | 41.8 | 22.4 | 42.8 | 51.6 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| PVT-Small[60] | 34.2/44.1 | 226/245 | 42.2 | 62.7 | 45.0 | 26.2 | 45.2 | 57.2 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| ViL-Small [76] | 35.7/45.0 | 252/174 42.9 | 63.8 | 45.6 | 27.8 | 46.4 | 56.3 | 43.4 | 64.9 | 47.0 | 39.6 | 62.1 | 42.4 | |
| Swin-Tiny [43] | 38.5/47.8 | 245/264 45.0 | 65.9 | 48.4 | 29.7 | 48.9 | 58.1 | 46.0 | 68.1 | 50.3 | 41.6 | 65.1 | 44.9 | |
| Focal-Tiny (Ours) | 39.4/48.8 | 265/291 | 45.5 | 66.3 | 48.8 | 31.2 | 49.2 | 58.7 | 47.2 | 69.4 | 51.9 | 42.7 | 66.5 | 45.9 |
| ResNet101 [33] | 56.7/63.2 | 315/33640.9 | 60.1 | 44.0 | 23.7 | 45.0 | 53.8 | 42.8 | 63.2 | 47.1 | 38.5 | 60.1 | 41.3 | |
| ResNeXt101-32x4d [67] | 56.4/62.8 | 319/340 | 41.4 | 61.0 | 44.3 | 23.9 | 45.5 | 53.7 | 44.0 | 64.4 | 48.0 | 39.2 | 61.4 | 41.9 |
| PVT-Medium [60] | 53.9/63.9 | 283/302 | 43.2 | 63.8 | 46.1 | 27.3 | 46.3 | 58.9 | 44.2 | 66.0 | 48.2 | 40.5 | 63.1 | 43.5 |
| ViL-Medium [76] | 50.8/60.1 | 339/261 | 43.7 | 64.6 | 46.4 | 27.9 | 47.1 | 56.9 | 44.6 | 66.3 | 48.5 | 40.7 | 63.8 | 43.7 |
| Swin-Small [43] | 59.8/69.1 | 335/354 46.4 | 67.0 | 50.1 | 31.0 | 50.1 | 60.3 | 48.5 | 70.2 | 53.5 | 43.3 | 67.3 | 46.6 | |
| Focal-Small (Ours) | 61.7/71.2 | 367/401 | 47.3 | 67.8 | 51.0 | 31.6 | 50.9 | 61.1 | 48.8 | 70.5 | 53.6 | 43.8 | 67.7 | 47.2 |
| ResNeXt101-64x4d [67] | 95.5/102 | 473/493 | 41.8 | 61.5 | 44.4 | 25.2 | 45.4 | 54.6 | 44.4 | 64.9 | 48.8 | 39.7 | 61.9 | 42.6 |
| PVT-Large[60] | 71.1/81.0 | 345/364 43.4 | 63.6 | 46.1 | 26.1 | 46.0 | 59.5 | 44.5 | 66.0 | 48.3 | 40.7 | 63.4 | 43.7 | |
| ViL-Base [76] | 66.7/76.1 | 443/365 44.7 | 65.5 | 47.6 | 29.9 | 48.0 | 58.1 | 45.7 | 67.2 | 49.9 | 41.3 | 64.4 | 44.5 | |
| Swin-Base 43] | 98.4/107 | 477/496 45.8 | 66.4 | 49.1 | 29.9 | 49.4 | 60.3 | 48.5 | 69.8 | 53.2 | 43.4 | 66.8 | 46.9 | |
| Focal-Base (Ours) | 100.8/110.0 514/533 46.9 | 67.8 | 50.3 | 31.9 | 50.3 | 61.5 | 49.0 | 70.1 | 53.6 | 43.7 | 67.6 | 47.0 |
| Method | #Param FLOPs | mini-val | test-dev | |||
| Apb | APm | Apb | Apm | |||
| X101-64x4d [67] | 155M | 1033G 52.3 | 46.0 | |||
| EfficientNet-D7 [54] | 77M | 410G | 54.4 | - | 55.1 | = |
| GCNet*[7] | - | 1041G | 51.8 | 44.7 | 52.3 | 45.4 |
| ResNeSt-200 [75] | = | 52.5 | = | 53.3 | 47.1 | |
| Copy-paste [28] | 185M | 1440G 55.9 | 47.2 | 56.0 | 47.4 | |
| BoTNet-200 [51] | - | 49.7 | - | |||
| SpineNet-190 [22] | 164M | 1885G 52.6 | 52.8 | |||
| CenterNet2 [84] | - | = | - | - | 56.4 | = |
| Swin-L (HTC++) [43] | 284M | 1470G 57.1 | 49.5 | 57.7 | 50.2 | |
| Swin-L (DyHead)[17] | 213M | 965G | 56.2 | - | - | - |
| Swin-L† (HTC++) [43] | 284M | 58.0 | 50.4 | 58.7 | 51.1 | |
| Swin-L† (DyHead) [17] | 213M | 58.4 | - | 58.7 | ||
| Swin-L† (QueryInst) [25] | - | 56.1 | 1 | 56.1 | ||
| Focal-L (HTC++) (Ours) | 265M | 1165G | 57.0 | 49.9 | - | = |
| Focal-L (DyHead) (Ours) | 229M | 1081G | 56.4 | - | - | = |
| Focal-L† (HTC++) (Ours) | 265M | - | 58.1 | 50.9 | 58.4 | 51.3 |
| Focal-L† (DyHead) (Ours) | 229M | - | 58.7 | - | 59.0 | - |
| Backbone | Method | #Param FLOPs mIoU +MS | |||
| ResNet-101 | DANet [45] | 69M | 1119G | 45.3 | |
| ResNet-101 | ACNet [26] | = | = | 45.9 | |
| ResNet-101 | DNL [69] | 69M | 1249G | 46.0 | |
| ResNet-101 | UperNet [65] | 86M | 1029G | 44.9 | |
| HRNet-w48 [53] | OCRNet [73] | 71M | 664G | 45.7 | = |
| ResNeSt-200 [75] | DLab.v3+ [12] | 88M | 1381G | 48.4 | = |
| Swin-T[43] | UperNet [65] | 60M | 945G | 44.5 | 45.8 |
| Swin-S [43] | UperNet [65] | 81M | 1038G | 47.6 | 49.5 |
| Swin-B [43] | UperNet [65] | 121M | 1188G | 48.1 | 49.7 |
| Twins-SVT-L[15] | UperNet [65] | 133M | 48.8 | 50.2 | |
| MiT-B5 [66] | SegFormer [66] | 85M | 51.0 | 51.8 | |
| ViT-L/16+ [21] | SETR[80] | 308M | 50.3 | = | |
| Swin-L* [43] | UperNet [65] | 234M | 3230G | 52.1 | 53.5 |
| ViT-L/16 [21] | Segmenter [52] | 334M | = | 51.8 | 53.6 |
| Swin-L‡ [43] | K-Net [77] | = | = | 54.3 | |
| Swin-L‡ [43] | PatchDiverse [29] | 234M | 53.1 | 54.4 | |
| VOLO-D5 [72] | UperNet [65] | = | - | 54.3 | |
| Focal-T (Ours) | UperNet [65] | 62M | 998G | 45.8 | 47.0 |
| Focal-S (Ours) | UperNet [65] | 85M | 1130G | 48.0 | 50.0 |
| Focal-B (Ours) | UperNet [65] | 126M | 1354G | 49.0 | 50.5 |
| Focal-L‡ (Ours) | UperNet [65] | 240M | 3376G | 54.0 | 55.4 |
| Model | W-Size FLOPs Top-1(%) APb APm | ||
| Swin-Tiny | 7 | 4.5 | 81.2 43.739.8 |
| 14 | 4.9 | 82.1 44.0 40.5 | |
| Focal-Tiny | 7 | 4.9 | 82.2 44.941.1 |
| 14 | 5.2 | 82.3 45.5 41.5 |
| Model | W-Shift Top-1(%) APb APm | |||
| Swin-Tiny | √ | 80.2 81.2 | 38.8 43.7 | 36.4 39.8 |
| Focal-Tiny | 82.2 | 44.8 | 41.0 | |
| √ | 81.9 | 44.9 | 41.1 |
| Depths Model #Params. FLOPs Top-1(%) APb Apm | |||||
| 2-2-2-2 | Swin | 21.2 | 3.1 | 78.7 | 38.2 35.7 |
| Focal | 21.7 | 3.4 | 79.9 | 40.5 37.6 | |
| 2-2-4-2 | Swin | 24.7 | 3.8 | 80.2 | 41.2 38.1 |
| Focal | 25.4 | 4.1 | 81.4 | 43.3 39.8 | |
| 2-2-6-2 | Swin | 28.3 | 4.5 | 81.2 | 43.7 39.8 |
| Focal | 29.1 | 4.9 | 82.2 | 44.8 41.0 |
| Output Size | Layer Name | Focal-Tiny | Focal-Small | Focal-Base | ||||
| stage 1 | 56×56 | Patch Embedding | p1= 4;c1 = 96 | p1=4;c1= 96 | p1 = 4;c1 = 128 | |||
| 56×56 | Transformer Block | {1,13} 三 s={7,7 | ×2 | 二 {1,13} ={7,7} | ×2 | {1,13} ={7,7} | ×2 | |
| stage 2 | 28×28 | Patch Embedding | P2=2;c=192 | P2=2;C=192 | P2=2;C= 256 | |||
| 28×28 | Transformer Block | {1,13} 三 swr={7,5} 1 | ×2 | ={1,13} sw,r={7,5} 1 | ×2 | {1,13} 二 su,r={7,5} | ×2 | |
| stage 3 | 14 × 14 | Patch Embedding | p3=2;c3=384 | p3=2; c3= 384 | p3=2; c3= 512 | |||
| 14 × 14 | Transformer Block | ={1,13} s={7,3} | ×6 | ={1,13} ={7,3} | ×18 | ={1,13} ={7,3} | ×18 | |
| stage 4 | 7×7 | Patch Embedding | P4=2;C4=768 | P4=2;C4=768 | P4= 2;C4=1024 | |||
| 7×7 | Transformer Block | 二 {1,7} | ×2 | {1,7} s 三 ={7,1} | ×2 | 二 {1,7} su,r {7,1} 二 | ×2 |
| Output Size | Layer Name | Focal-Tiny | Focal-Small | Focal-Base | ||||
| stage 1 | 56×56 | Patch Embedding | p1= 4;c1 = 96 | p1=4;c1= 96 | p1 = 4;c1 = 128 | |||
| 56×56 | Transformer Block | {1,13} 三 s={7,7 | ×2 | 二 {1,13} ={7,7} | ×2 | {1,13} ={7,7} | ×2 | |
| stage 2 | 28×28 | Patch Embedding | P2=2;c=192 | P2=2;C=192 | P2=2;C= 256 | |||
| 28×28 | Transformer Block | {1,13} 三 swr={7,5} 1 | ×2 | ={1,13} sw,r={7,5} 1 | ×2 | {1,13} 二 su,r={7,5} | ×2 | |
| stage 3 | 14 × 14 | Patch Embedding | p3=2;c3=384 | p3=2; c3= 384 | p3=2; c3= 512 | |||
| 14 × 14 | Transformer Block | ={1,13} s={7,3} | ×6 | ={1,13} ={7,3} | ×18 | ={1,13} ={7,3} | ×18 | |
| stage 4 | 7×7 | Patch Embedding | P4=2;C4=768 | P4=2;C4=768 | P4= 2;C4=1024 | |||
| 7×7 | Transformer Block | 二 {1,7} | ×2 | {1,7} s 三 ={7,1} | ×2 | 二 {1,7} su,r {7,1} 二 | ×2 |
| Model | #Params. FLOPs | Top-1 (%) |
| ResNet-50 [33] | 25.0 4.1 | 76.2 |
| DeiT-Small/16 [55] | 22.1 4.6 | 79.9 |
| PVT-Small [60] | 24.5 3.8 | 79.8 |
| ViL-Small [76] | 24.6 5.1 | 82.0 |
| CvT-13 [64] | 20.0 4.5 | 81.6 |
| Swin-Tiny [43] | 28.3 4.5 | 81.2 |
| Focal-Tiny (Ours) | 28.9 4.9 | 82.2 |
| ResNet-101[33] | 45.0 7.9 | 77.4 |
| PVT-Medium [60] | 44.2 6.7 | 81.2 |
| CvT-21 [64] | 32.0 7.1 | 82.5 |
| ViL-Medium [76] | 39.7 9.1 | 83.3 |
| Swin-Small [43] | 49.6 8.7 | 83.1 |
| Focal-Small (Ours) | 51.1 9.4 | 83.6 |
| ResNet-152[33] | 60.0 11.0 | 78.3 |
| ViT-Base/16 [21] | 86.6 17.6 | 77.9 |
| DeiT-Base/16 [55] | 17.5 | 81.8 |
| 86.6 | ||
| PVT-Large [60] | 61.4 9.8 | 81.7 |
| ViL-Base[76] | 55.7 13.4 | 83.2 |
| Swin-Base [43] | 87.8 15.4 | 83.4 |
| Focal-Base (Ours) | 89.8 | 16.4 84.0 |
| Backbone | RetinaNet | Mask R-CNN | |
| APb | Apb | APm | |
| ResNet-50 [33] | 36.3 | 38.0 | 34.4 |
| PVT-Small | 40.4 | 40.4 | 37.8 |
| ViL-Small [76] | 41.6 | 41.8 | 38.5 |
| Swin-Tiny [43] | 42.0 | 43.7 | 39.8 |
| Focal-Tiny (Ours) | 43.7 (+1.7) | 44.8 (+1.1) | 41.0 (+1.3) |
| ResNet-101[33] | 38.5 | 40.4 | 36.4 |
| ResNeXt101-32x4d [67] | 39.9 | 41.9 | 37.5 |
| PVT-Medium [60] | 41.9 | 42.0 | 39.0 |
| ViL-Medium [76] | 42.9 | 43.4 | 39.7 |
| Swin-Small [43] | 45.0 | 46.5 | 42.1 |
| Focal-Small (Ours) | 45.6 (+0.6) | 47.4 (+0.9) | 42.8 (+0.7) |
| ResNeXt101-64x4d[67] 41.0 | 42.8 | 38.4 | |
| PVT-Large [60] | 42.6 | 42.9 | 39.5 |
| ViL-Base[76] | 44.3 | 45.1 | 41.0 |
| Swin-Base [43] | 45.0 | 46.9 | 42.3 |
| Focal-Base (Ours) | 46.3 (+1.3) | 47.8 (+0.9) | 43.2 (+0.9) |
| Model | #Params. FLOPs | Top-1 (%) |
| ResNet-50 [33] | 25.0 4.1 | 76.2 |
| DeiT-Small/16 [55] | 22.1 4.6 | 79.9 |
| PVT-Small [60] | 24.5 3.8 | 79.8 |
| ViL-Small [76] | 24.6 5.1 | 82.0 |
| CvT-13 [64] | 20.0 4.5 | 81.6 |
| Swin-Tiny [43] | 28.3 4.5 | 81.2 |
| Focal-Tiny (Ours) | 28.9 4.9 | 82.2 |
| ResNet-101[33] | 45.0 7.9 | 77.4 |
| PVT-Medium [60] | 44.2 6.7 | 81.2 |
| CvT-21 [64] | 32.0 7.1 | 82.5 |
| ViL-Medium [76] | 39.7 9.1 | 83.3 |
| Swin-Small [43] | 49.6 8.7 | 83.1 |
| Focal-Small (Ours) | 51.1 9.4 | 83.6 |
| ResNet-152[33] | 60.0 11.0 | 78.3 |
| ViT-Base/16 [21] | 86.6 17.6 | 77.9 |
| DeiT-Base/16 [55] | 17.5 | 81.8 |
| 86.6 | ||
| PVT-Large [60] | 61.4 9.8 | 81.7 |
| ViL-Base[76] | 55.7 13.4 | 83.2 |
| Swin-Base [43] | 87.8 15.4 | 83.4 |
| Focal-Base (Ours) | 89.8 | 16.4 84.0 |
| Backbone | RetinaNet | Mask R-CNN | |
| APb | Apb | APm | |
| ResNet-50 [33] | 36.3 | 38.0 | 34.4 |
| PVT-Small | 40.4 | 40.4 | 37.8 |
| ViL-Small [76] | 41.6 | 41.8 | 38.5 |
| Swin-Tiny [43] | 42.0 | 43.7 | 39.8 |
| Focal-Tiny (Ours) | 43.7 (+1.7) | 44.8 (+1.1) | 41.0 (+1.3) |
| ResNet-101[33] | 38.5 | 40.4 | 36.4 |
| ResNeXt101-32x4d [67] | 39.9 | 41.9 | 37.5 |
| PVT-Medium [60] | 41.9 | 42.0 | 39.0 |
| ViL-Medium [76] | 42.9 | 43.4 | 39.7 |
| Swin-Small [43] | 45.0 | 46.5 | 42.1 |
| Focal-Small (Ours) | 45.6 (+0.6) | 47.4 (+0.9) | 42.8 (+0.7) |
| ResNeXt101-64x4d[67] 41.0 | 42.8 | 38.4 | |
| PVT-Large [60] | 42.6 | 42.9 | 39.5 |
| ViL-Base[76] | 44.3 | 45.1 | 41.0 |
| Swin-Base [43] | 45.0 | 46.9 | 42.3 |
| Focal-Base (Ours) | 46.3 (+1.3) | 47.8 (+0.9) | 43.2 (+0.9) |
| Backbone | #Params (M) | FLOPs (G) | RetinaNet 3x schedule + MS | Mask R-CNN 3x schedule + MS | ||||||||||
| AP | AP5 | AP | APs | APM | APL | AP6 | AP | AP | Apm | AP | AP | |||
| ResNet50 [33] | 37.7/44.2 | 239/260 | 39.0 | 58.4 | 41.8 | 22.4 | 42.8 | 51.6 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| PVT-Small[60] | 34.2/44.1 | 226/245 | 42.2 | 62.7 | 45.0 | 26.2 | 45.2 | 57.2 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| ViL-Small [76] | 35.7/45.0 | 252/174 42.9 | 63.8 | 45.6 | 27.8 | 46.4 | 56.3 | 43.4 | 64.9 | 47.0 | 39.6 | 62.1 | 42.4 | |
| Swin-Tiny [43] | 38.5/47.8 | 245/264 45.0 | 65.9 | 48.4 | 29.7 | 48.9 | 58.1 | 46.0 | 68.1 | 50.3 | 41.6 | 65.1 | 44.9 | |
| Focal-Tiny (Ours) | 39.4/48.8 | 265/291 | 45.5 | 66.3 | 48.8 | 31.2 | 49.2 | 58.7 | 47.2 | 69.4 | 51.9 | 42.7 | 66.5 | 45.9 |
| ResNet101 [33] | 56.7/63.2 | 315/33640.9 | 60.1 | 44.0 | 23.7 | 45.0 | 53.8 | 42.8 | 63.2 | 47.1 | 38.5 | 60.1 | 41.3 | |
| ResNeXt101-32x4d [67] | 56.4/62.8 | 319/340 | 41.4 | 61.0 | 44.3 | 23.9 | 45.5 | 53.7 | 44.0 | 64.4 | 48.0 | 39.2 | 61.4 | 41.9 |
| PVT-Medium [60] | 53.9/63.9 | 283/302 | 43.2 | 63.8 | 46.1 | 27.3 | 46.3 | 58.9 | 44.2 | 66.0 | 48.2 | 40.5 | 63.1 | 43.5 |
| ViL-Medium [76] | 50.8/60.1 | 339/261 | 43.7 | 64.6 | 46.4 | 27.9 | 47.1 | 56.9 | 44.6 | 66.3 | 48.5 | 40.7 | 63.8 | 43.7 |
| Swin-Small [43] | 59.8/69.1 | 335/354 46.4 | 67.0 | 50.1 | 31.0 | 50.1 | 60.3 | 48.5 | 70.2 | 53.5 | 43.3 | 67.3 | 46.6 | |
| Focal-Small (Ours) | 61.7/71.2 | 367/401 | 47.3 | 67.8 | 51.0 | 31.6 | 50.9 | 61.1 | 48.8 | 70.5 | 53.6 | 43.8 | 67.7 | 47.2 |
| ResNeXt101-64x4d [67] | 95.5/102 | 473/493 | 41.8 | 61.5 | 44.4 | 25.2 | 45.4 | 54.6 | 44.4 | 64.9 | 48.8 | 39.7 | 61.9 | 42.6 |
| PVT-Large[60] | 71.1/81.0 | 345/364 43.4 | 63.6 | 46.1 | 26.1 | 46.0 | 59.5 | 44.5 | 66.0 | 48.3 | 40.7 | 63.4 | 43.7 | |
| ViL-Base [76] | 66.7/76.1 | 443/365 44.7 | 65.5 | 47.6 | 29.9 | 48.0 | 58.1 | 45.7 | 67.2 | 49.9 | 41.3 | 64.4 | 44.5 | |
| Swin-Base 43] | 98.4/107 | 477/496 45.8 | 66.4 | 49.1 | 29.9 | 49.4 | 60.3 | 48.5 | 69.8 | 53.2 | 43.4 | 66.8 | 46.9 | |
| Focal-Base (Ours) | 100.8/110.0 514/533 46.9 | 67.8 | 50.3 | 31.9 | 50.3 | 61.5 | 49.0 | 70.1 | 53.6 | 43.7 | 67.6 | 47.0 |
| Backbone | #Params (M) | FLOPs (G) | RetinaNet 3x schedule + MS | Mask R-CNN 3x schedule + MS | ||||||||||
| AP | AP5 | AP | APs | APM | APL | AP6 | AP | AP | Apm | AP | AP | |||
| ResNet50 [33] | 37.7/44.2 | 239/260 | 39.0 | 58.4 | 41.8 | 22.4 | 42.8 | 51.6 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| PVT-Small[60] | 34.2/44.1 | 226/245 | 42.2 | 62.7 | 45.0 | 26.2 | 45.2 | 57.2 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| ViL-Small [76] | 35.7/45.0 | 252/174 42.9 | 63.8 | 45.6 | 27.8 | 46.4 | 56.3 | 43.4 | 64.9 | 47.0 | 39.6 | 62.1 | 42.4 | |
| Swin-Tiny [43] | 38.5/47.8 | 245/264 45.0 | 65.9 | 48.4 | 29.7 | 48.9 | 58.1 | 46.0 | 68.1 | 50.3 | 41.6 | 65.1 | 44.9 | |
| Focal-Tiny (Ours) | 39.4/48.8 | 265/291 | 45.5 | 66.3 | 48.8 | 31.2 | 49.2 | 58.7 | 47.2 | 69.4 | 51.9 | 42.7 | 66.5 | 45.9 |
| ResNet101 [33] | 56.7/63.2 | 315/33640.9 | 60.1 | 44.0 | 23.7 | 45.0 | 53.8 | 42.8 | 63.2 | 47.1 | 38.5 | 60.1 | 41.3 | |
| ResNeXt101-32x4d [67] | 56.4/62.8 | 319/340 | 41.4 | 61.0 | 44.3 | 23.9 | 45.5 | 53.7 | 44.0 | 64.4 | 48.0 | 39.2 | 61.4 | 41.9 |
| PVT-Medium [60] | 53.9/63.9 | 283/302 | 43.2 | 63.8 | 46.1 | 27.3 | 46.3 | 58.9 | 44.2 | 66.0 | 48.2 | 40.5 | 63.1 | 43.5 |
| ViL-Medium [76] | 50.8/60.1 | 339/261 | 43.7 | 64.6 | 46.4 | 27.9 | 47.1 | 56.9 | 44.6 | 66.3 | 48.5 | 40.7 | 63.8 | 43.7 |
| Swin-Small [43] | 59.8/69.1 | 335/354 46.4 | 67.0 | 50.1 | 31.0 | 50.1 | 60.3 | 48.5 | 70.2 | 53.5 | 43.3 | 67.3 | 46.6 | |
| Focal-Small (Ours) | 61.7/71.2 | 367/401 | 47.3 | 67.8 | 51.0 | 31.6 | 50.9 | 61.1 | 48.8 | 70.5 | 53.6 | 43.8 | 67.7 | 47.2 |
| ResNeXt101-64x4d [67] | 95.5/102 | 473/493 | 41.8 | 61.5 | 44.4 | 25.2 | 45.4 | 54.6 | 44.4 | 64.9 | 48.8 | 39.7 | 61.9 | 42.6 |
| PVT-Large[60] | 71.1/81.0 | 345/364 43.4 | 63.6 | 46.1 | 26.1 | 46.0 | 59.5 | 44.5 | 66.0 | 48.3 | 40.7 | 63.4 | 43.7 | |
| ViL-Base [76] | 66.7/76.1 | 443/365 44.7 | 65.5 | 47.6 | 29.9 | 48.0 | 58.1 | 45.7 | 67.2 | 49.9 | 41.3 | 64.4 | 44.5 | |
| Swin-Base 43] | 98.4/107 | 477/496 45.8 | 66.4 | 49.1 | 29.9 | 49.4 | 60.3 | 48.5 | 69.8 | 53.2 | 43.4 | 66.8 | 46.9 | |
| Focal-Base (Ours) | 100.8/110.0 514/533 46.9 | 67.8 | 50.3 | 31.9 | 50.3 | 61.5 | 49.0 | 70.1 | 53.6 | 43.7 | 67.6 | 47.0 |
| Method | #Param FLOPs | mini-val | test-dev | |||
| Apb | APm | Apb | Apm | |||
| X101-64x4d [67] | 155M | 1033G 52.3 | 46.0 | |||
| EfficientNet-D7 [54] | 77M | 410G | 54.4 | - | 55.1 | = |
| GCNet*[7] | - | 1041G | 51.8 | 44.7 | 52.3 | 45.4 |
| ResNeSt-200 [75] | = | 52.5 | = | 53.3 | 47.1 | |
| Copy-paste [28] | 185M | 1440G 55.9 | 47.2 | 56.0 | 47.4 | |
| BoTNet-200 [51] | - | 49.7 | - | |||
| SpineNet-190 [22] | 164M | 1885G 52.6 | 52.8 | |||
| CenterNet2 [84] | - | = | - | - | 56.4 | = |
| Swin-L (HTC++) [43] | 284M | 1470G 57.1 | 49.5 | 57.7 | 50.2 | |
| Swin-L (DyHead)[17] | 213M | 965G | 56.2 | - | - | - |
| Swin-L† (HTC++) [43] | 284M | 58.0 | 50.4 | 58.7 | 51.1 | |
| Swin-L† (DyHead) [17] | 213M | 58.4 | - | 58.7 | ||
| Swin-L† (QueryInst) [25] | - | 56.1 | 1 | 56.1 | ||
| Focal-L (HTC++) (Ours) | 265M | 1165G | 57.0 | 49.9 | - | = |
| Focal-L (DyHead) (Ours) | 229M | 1081G | 56.4 | - | - | = |
| Focal-L† (HTC++) (Ours) | 265M | - | 58.1 | 50.9 | 58.4 | 51.3 |
| Focal-L† (DyHead) (Ours) | 229M | - | 58.7 | - | 59.0 | - |
| Backbone | Method | #Param FLOPs mIoU +MS | |||
| ResNet-101 | DANet [45] | 69M | 1119G | 45.3 | |
| ResNet-101 | ACNet [26] | = | = | 45.9 | |
| ResNet-101 | DNL [69] | 69M | 1249G | 46.0 | |
| ResNet-101 | UperNet [65] | 86M | 1029G | 44.9 | |
| HRNet-w48 [53] | OCRNet [73] | 71M | 664G | 45.7 | = |
| ResNeSt-200 [75] | DLab.v3+ [12] | 88M | 1381G | 48.4 | = |
| Swin-T[43] | UperNet [65] | 60M | 945G | 44.5 | 45.8 |
| Swin-S [43] | UperNet [65] | 81M | 1038G | 47.6 | 49.5 |
| Swin-B [43] | UperNet [65] | 121M | 1188G | 48.1 | 49.7 |
| Twins-SVT-L[15] | UperNet [65] | 133M | 48.8 | 50.2 | |
| MiT-B5 [66] | SegFormer [66] | 85M | 51.0 | 51.8 | |
| ViT-L/16+ [21] | SETR[80] | 308M | 50.3 | = | |
| Swin-L* [43] | UperNet [65] | 234M | 3230G | 52.1 | 53.5 |
| ViT-L/16 [21] | Segmenter [52] | 334M | = | 51.8 | 53.6 |
| Swin-L‡ [43] | K-Net [77] | = | = | 54.3 | |
| Swin-L‡ [43] | PatchDiverse [29] | 234M | 53.1 | 54.4 | |
| VOLO-D5 [72] | UperNet [65] | = | - | 54.3 | |
| Focal-T (Ours) | UperNet [65] | 62M | 998G | 45.8 | 47.0 |
| Focal-S (Ours) | UperNet [65] | 85M | 1130G | 48.0 | 50.0 |
| Focal-B (Ours) | UperNet [65] | 126M | 1354G | 49.0 | 50.5 |
| Focal-L‡ (Ours) | UperNet [65] | 240M | 3376G | 54.0 | 55.4 |
| Model | W-Size FLOPs Top-1(%) APb APm | ||
| Swin-Tiny | 7 | 4.5 | 81.2 43.739.8 |
| 14 | 4.9 | 82.1 44.0 40.5 | |
| Focal-Tiny | 7 | 4.9 | 82.2 44.941.1 |
| 14 | 5.2 | 82.3 45.5 41.5 |
| Model | W-Shift Top-1(%) APb APm | |||
| Swin-Tiny | √ | 80.2 81.2 | 38.8 43.7 | 36.4 39.8 |
| Focal-Tiny | 82.2 | 44.8 | 41.0 | |
| √ | 81.9 | 44.9 | 41.1 |
| Method | #Param FLOPs | mini-val | test-dev | |||
| Apb | APm | Apb | Apm | |||
| X101-64x4d [67] | 155M | 1033G 52.3 | 46.0 | |||
| EfficientNet-D7 [54] | 77M | 410G | 54.4 | - | 55.1 | = |
| GCNet*[7] | - | 1041G | 51.8 | 44.7 | 52.3 | 45.4 |
| ResNeSt-200 [75] | = | 52.5 | = | 53.3 | 47.1 | |
| Copy-paste [28] | 185M | 1440G 55.9 | 47.2 | 56.0 | 47.4 | |
| BoTNet-200 [51] | - | 49.7 | - | |||
| SpineNet-190 [22] | 164M | 1885G 52.6 | 52.8 | |||
| CenterNet2 [84] | - | = | - | - | 56.4 | = |
| Swin-L (HTC++) [43] | 284M | 1470G 57.1 | 49.5 | 57.7 | 50.2 | |
| Swin-L (DyHead)[17] | 213M | 965G | 56.2 | - | - | - |
| Swin-L† (HTC++) [43] | 284M | 58.0 | 50.4 | 58.7 | 51.1 | |
| Swin-L† (DyHead) [17] | 213M | 58.4 | - | 58.7 | ||
| Swin-L† (QueryInst) [25] | - | 56.1 | 1 | 56.1 | ||
| Focal-L (HTC++) (Ours) | 265M | 1165G | 57.0 | 49.9 | - | = |
| Focal-L (DyHead) (Ours) | 229M | 1081G | 56.4 | - | - | = |
| Focal-L† (HTC++) (Ours) | 265M | - | 58.1 | 50.9 | 58.4 | 51.3 |
| Focal-L† (DyHead) (Ours) | 229M | - | 58.7 | - | 59.0 | - |
| Backbone | Method | #Param FLOPs mIoU +MS | |||
| ResNet-101 | DANet [45] | 69M | 1119G | 45.3 | |
| ResNet-101 | ACNet [26] | = | = | 45.9 | |
| ResNet-101 | DNL [69] | 69M | 1249G | 46.0 | |
| ResNet-101 | UperNet [65] | 86M | 1029G | 44.9 | |
| HRNet-w48 [53] | OCRNet [73] | 71M | 664G | 45.7 | = |
| ResNeSt-200 [75] | DLab.v3+ [12] | 88M | 1381G | 48.4 | = |
| Swin-T[43] | UperNet [65] | 60M | 945G | 44.5 | 45.8 |
| Swin-S [43] | UperNet [65] | 81M | 1038G | 47.6 | 49.5 |
| Swin-B [43] | UperNet [65] | 121M | 1188G | 48.1 | 49.7 |
| Twins-SVT-L[15] | UperNet [65] | 133M | 48.8 | 50.2 | |
| MiT-B5 [66] | SegFormer [66] | 85M | 51.0 | 51.8 | |
| ViT-L/16+ [21] | SETR[80] | 308M | 50.3 | = | |
| Swin-L* [43] | UperNet [65] | 234M | 3230G | 52.1 | 53.5 |
| ViT-L/16 [21] | Segmenter [52] | 334M | = | 51.8 | 53.6 |
| Swin-L‡ [43] | K-Net [77] | = | = | 54.3 | |
| Swin-L‡ [43] | PatchDiverse [29] | 234M | 53.1 | 54.4 | |
| VOLO-D5 [72] | UperNet [65] | = | - | 54.3 | |
| Focal-T (Ours) | UperNet [65] | 62M | 998G | 45.8 | 47.0 |
| Focal-S (Ours) | UperNet [65] | 85M | 1130G | 48.0 | 50.0 |
| Focal-B (Ours) | UperNet [65] | 126M | 1354G | 49.0 | 50.5 |
| Focal-L‡ (Ours) | UperNet [65] | 240M | 3376G | 54.0 | 55.4 |
| Model | W-Size FLOPs Top-1(%) APb APm | ||
| Swin-Tiny | 7 | 4.5 | 81.2 43.739.8 |
| 14 | 4.9 | 82.1 44.0 40.5 | |
| Focal-Tiny | 7 | 4.9 | 82.2 44.941.1 |
| 14 | 5.2 | 82.3 45.5 41.5 |
| Model | W-Shift Top-1(%) APb APm | |||
| Swin-Tiny | √ | 80.2 81.2 | 38.8 43.7 | 36.4 39.8 |
| Focal-Tiny | 82.2 | 44.8 | 41.0 | |
| √ | 81.9 | 44.9 | 41.1 |
| Depths Model #Params. FLOPs Top-1(%) APb Apm | |||||
| 2-2-2-2 | Swin | 21.2 | 3.1 | 78.7 | 38.2 35.7 |
| Focal | 21.7 | 3.4 | 79.9 | 40.5 37.6 | |
| 2-2-4-2 | Swin | 24.7 | 3.8 | 80.2 | 41.2 38.1 |
| Focal | 25.4 | 4.1 | 81.4 | 43.3 39.8 | |
| 2-2-6-2 | Swin | 28.3 | 4.5 | 81.2 | 43.7 39.8 |
| Focal | 29.1 | 4.9 | 82.2 | 44.8 41.0 |
| Depths Model #Params. FLOPs Top-1(%) APb Apm | |||||
| 2-2-2-2 | Swin | 21.2 | 3.1 | 78.7 | 38.2 35.7 |
| Focal | 21.7 | 3.4 | 79.9 | 40.5 37.6 | |
| 2-2-4-2 | Swin | 24.7 | 3.8 | 80.2 | 41.2 38.1 |
| Focal | 25.4 | 4.1 | 81.4 | 43.3 39.8 | |
| 2-2-6-2 | Swin | 28.3 | 4.5 | 81.2 | 43.7 39.8 |
| Focal | 29.1 | 4.9 | 82.2 | 44.8 41.0 |
| Output Size | Layer Name | Focal-Tiny | Focal-Small | Focal-Base | ||||
| stage 1 | 56×56 | Patch Embedding | p1= 4;c1 = 96 | p1=4;c1= 96 | p1 = 4;c1 = 128 | |||
| 56×56 | Transformer Block | {1,13} 三 s={7,7 | ×2 | 二 {1,13} ={7,7} | ×2 | {1,13} ={7,7} | ×2 | |
| stage 2 | 28×28 | Patch Embedding | P2=2;c=192 | P2=2;C=192 | P2=2;C= 256 | |||
| 28×28 | Transformer Block | {1,13} 三 swr={7,5} 1 | ×2 | ={1,13} sw,r={7,5} 1 | ×2 | {1,13} 二 su,r={7,5} | ×2 | |
| stage 3 | 14 × 14 | Patch Embedding | p3=2;c3=384 | p3=2; c3= 384 | p3=2; c3= 512 | |||
| 14 × 14 | Transformer Block | ={1,13} s={7,3} | ×6 | ={1,13} ={7,3} | ×18 | ={1,13} ={7,3} | ×18 | |
| stage 4 | 7×7 | Patch Embedding | P4=2;C4=768 | P4=2;C4=768 | P4= 2;C4=1024 | |||
| 7×7 | Transformer Block | 二 {1,7} | ×2 | {1,7} s 三 ={7,1} | ×2 | 二 {1,7} su,r {7,1} 二 | ×2 |
| Backbone | RetinaNet | Mask R-CNN | |
| APb | Apb | APm | |
| ResNet-50 [33] | 36.3 | 38.0 | 34.4 |
| PVT-Small | 40.4 | 40.4 | 37.8 |
| ViL-Small [76] | 41.6 | 41.8 | 38.5 |
| Swin-Tiny [43] | 42.0 | 43.7 | 39.8 |
| Focal-Tiny (Ours) | 43.7 (+1.7) | 44.8 (+1.1) | 41.0 (+1.3) |
| ResNet-101[33] | 38.5 | 40.4 | 36.4 |
| ResNeXt101-32x4d [67] | 39.9 | 41.9 | 37.5 |
| PVT-Medium [60] | 41.9 | 42.0 | 39.0 |
| ViL-Medium [76] | 42.9 | 43.4 | 39.7 |
| Swin-Small [43] | 45.0 | 46.5 | 42.1 |
| Focal-Small (Ours) | 45.6 (+0.6) | 47.4 (+0.9) | 42.8 (+0.7) |
| ResNeXt101-64x4d[67] 41.0 | 42.8 | 38.4 | |
| PVT-Large [60] | 42.6 | 42.9 | 39.5 |
| ViL-Base[76] | 44.3 | 45.1 | 41.0 |
| Swin-Base [43] | 45.0 | 46.9 | 42.3 |
| Focal-Base (Ours) | 46.3 (+1.3) | 47.8 (+0.9) | 43.2 (+0.9) |
| Model | #Params. FLOPs | Top-1 (%) |
| ResNet-50 [33] | 25.0 4.1 | 76.2 |
| DeiT-Small/16 [55] | 22.1 4.6 | 79.9 |
| PVT-Small [60] | 24.5 3.8 | 79.8 |
| ViL-Small [76] | 24.6 5.1 | 82.0 |
| CvT-13 [64] | 20.0 4.5 | 81.6 |
| Swin-Tiny [43] | 28.3 4.5 | 81.2 |
| Focal-Tiny (Ours) | 28.9 4.9 | 82.2 |
| ResNet-101[33] | 45.0 7.9 | 77.4 |
| PVT-Medium [60] | 44.2 6.7 | 81.2 |
| CvT-21 [64] | 32.0 7.1 | 82.5 |
| ViL-Medium [76] | 39.7 9.1 | 83.3 |
| Swin-Small [43] | 49.6 8.7 | 83.1 |
| Focal-Small (Ours) | 51.1 9.4 | 83.6 |
| ResNet-152[33] | 60.0 11.0 | 78.3 |
| ViT-Base/16 [21] | 86.6 17.6 | 77.9 |
| DeiT-Base/16 [55] | 17.5 | 81.8 |
| 86.6 | ||
| PVT-Large [60] | 61.4 9.8 | 81.7 |
| ViL-Base[76] | 55.7 13.4 | 83.2 |
| Swin-Base [43] | 87.8 15.4 | 83.4 |
| Focal-Base (Ours) | 89.8 | 16.4 84.0 |
| Backbone | #Params (M) | FLOPs (G) | RetinaNet 3x schedule + MS | Mask R-CNN 3x schedule + MS | ||||||||||
| AP | AP5 | AP | APs | APM | APL | AP6 | AP | AP | Apm | AP | AP | |||
| ResNet50 [33] | 37.7/44.2 | 239/260 | 39.0 | 58.4 | 41.8 | 22.4 | 42.8 | 51.6 | 41.0 | 61.7 | 44.9 | 37.1 | 58.4 | 40.1 |
| PVT-Small[60] | 34.2/44.1 | 226/245 | 42.2 | 62.7 | 45.0 | 26.2 | 45.2 | 57.2 | 43.0 | 65.3 | 46.9 | 39.9 | 62.5 | 42.8 |
| ViL-Small [76] | 35.7/45.0 | 252/174 42.9 | 63.8 | 45.6 | 27.8 | 46.4 | 56.3 | 43.4 | 64.9 | 47.0 | 39.6 | 62.1 | 42.4 | |
| Swin-Tiny [43] | 38.5/47.8 | 245/264 45.0 | 65.9 | 48.4 | 29.7 | 48.9 | 58.1 | 46.0 | 68.1 | 50.3 | 41.6 | 65.1 | 44.9 | |
| Focal-Tiny (Ours) | 39.4/48.8 | 265/291 | 45.5 | 66.3 | 48.8 | 31.2 | 49.2 | 58.7 | 47.2 | 69.4 | 51.9 | 42.7 | 66.5 | 45.9 |
| ResNet101 [33] | 56.7/63.2 | 315/33640.9 | 60.1 | 44.0 | 23.7 | 45.0 | 53.8 | 42.8 | 63.2 | 47.1 | 38.5 | 60.1 | 41.3 | |
| ResNeXt101-32x4d [67] | 56.4/62.8 | 319/340 | 41.4 | 61.0 | 44.3 | 23.9 | 45.5 | 53.7 | 44.0 | 64.4 | 48.0 | 39.2 | 61.4 | 41.9 |
| PVT-Medium [60] | 53.9/63.9 | 283/302 | 43.2 | 63.8 | 46.1 | 27.3 | 46.3 | 58.9 | 44.2 | 66.0 | 48.2 | 40.5 | 63.1 | 43.5 |
| ViL-Medium [76] | 50.8/60.1 | 339/261 | 43.7 | 64.6 | 46.4 | 27.9 | 47.1 | 56.9 | 44.6 | 66.3 | 48.5 | 40.7 | 63.8 | 43.7 |
| Swin-Small [43] | 59.8/69.1 | 335/354 46.4 | 67.0 | 50.1 | 31.0 | 50.1 | 60.3 | 48.5 | 70.2 | 53.5 | 43.3 | 67.3 | 46.6 | |
| Focal-Small (Ours) | 61.7/71.2 | 367/401 | 47.3 | 67.8 | 51.0 | 31.6 | 50.9 | 61.1 | 48.8 | 70.5 | 53.6 | 43.8 | 67.7 | 47.2 |
| ResNeXt101-64x4d [67] | 95.5/102 | 473/493 | 41.8 | 61.5 | 44.4 | 25.2 | 45.4 | 54.6 | 44.4 | 64.9 | 48.8 | 39.7 | 61.9 | 42.6 |
| PVT-Large[60] | 71.1/81.0 | 345/364 43.4 | 63.6 | 46.1 | 26.1 | 46.0 | 59.5 | 44.5 | 66.0 | 48.3 | 40.7 | 63.4 | 43.7 | |
| ViL-Base [76] | 66.7/76.1 | 443/365 44.7 | 65.5 | 47.6 | 29.9 | 48.0 | 58.1 | 45.7 | 67.2 | 49.9 | 41.3 | 64.4 | 44.5 | |
| Swin-Base 43] | 98.4/107 | 477/496 45.8 | 66.4 | 49.1 | 29.9 | 49.4 | 60.3 | 48.5 | 69.8 | 53.2 | 43.4 | 66.8 | 46.9 | |
| Focal-Base (Ours) | 100.8/110.0 514/533 46.9 | 67.8 | 50.3 | 31.9 | 50.3 | 61.5 | 49.0 | 70.1 | 53.6 | 43.7 | 67.6 | 47.0 |
| Model | W-Size FLOPs Top-1(%) APb APm | ||
| Swin-Tiny | 7 | 4.5 | 81.2 43.739.8 |
| 14 | 4.9 | 82.1 44.0 40.5 | |
| Focal-Tiny | 7 | 4.9 | 82.2 44.941.1 |
| 14 | 5.2 | 82.3 45.5 41.5 |
| Backbone | Method | #Param FLOPs mIoU +MS | |||
| ResNet-101 | DANet [45] | 69M | 1119G | 45.3 | |
| ResNet-101 | ACNet [26] | = | = | 45.9 | |
| ResNet-101 | DNL [69] | 69M | 1249G | 46.0 | |
| ResNet-101 | UperNet [65] | 86M | 1029G | 44.9 | |
| HRNet-w48 [53] | OCRNet [73] | 71M | 664G | 45.7 | = |
| ResNeSt-200 [75] | DLab.v3+ [12] | 88M | 1381G | 48.4 | = |
| Swin-T[43] | UperNet [65] | 60M | 945G | 44.5 | 45.8 |
| Swin-S [43] | UperNet [65] | 81M | 1038G | 47.6 | 49.5 |
| Swin-B [43] | UperNet [65] | 121M | 1188G | 48.1 | 49.7 |
| Twins-SVT-L[15] | UperNet [65] | 133M | 48.8 | 50.2 | |
| MiT-B5 [66] | SegFormer [66] | 85M | 51.0 | 51.8 | |
| ViT-L/16+ [21] | SETR[80] | 308M | 50.3 | = | |
| Swin-L* [43] | UperNet [65] | 234M | 3230G | 52.1 | 53.5 |
| ViT-L/16 [21] | Segmenter [52] | 334M | = | 51.8 | 53.6 |
| Swin-L‡ [43] | K-Net [77] | = | = | 54.3 | |
| Swin-L‡ [43] | PatchDiverse [29] | 234M | 53.1 | 54.4 | |
| VOLO-D5 [72] | UperNet [65] | = | - | 54.3 | |
| Focal-T (Ours) | UperNet [65] | 62M | 998G | 45.8 | 47.0 |
| Focal-S (Ours) | UperNet [65] | 85M | 1130G | 48.0 | 50.0 |
| Focal-B (Ours) | UperNet [65] | 126M | 1354G | 49.0 | 50.5 |
| Focal-L‡ (Ours) | UperNet [65] | 240M | 3376G | 54.0 | 55.4 |
| Method | #Param FLOPs | mini-val | test-dev | |||
| Apb | APm | Apb | Apm | |||
| X101-64x4d [67] | 155M | 1033G 52.3 | 46.0 | |||
| EfficientNet-D7 [54] | 77M | 410G | 54.4 | - | 55.1 | = |
| GCNet*[7] | - | 1041G | 51.8 | 44.7 | 52.3 | 45.4 |
| ResNeSt-200 [75] | = | 52.5 | = | 53.3 | 47.1 | |
| Copy-paste [28] | 185M | 1440G 55.9 | 47.2 | 56.0 | 47.4 | |
| BoTNet-200 [51] | - | 49.7 | - | |||
| SpineNet-190 [22] | 164M | 1885G 52.6 | 52.8 | |||
| CenterNet2 [84] | - | = | - | - | 56.4 | = |
| Swin-L (HTC++) [43] | 284M | 1470G 57.1 | 49.5 | 57.7 | 50.2 | |
| Swin-L (DyHead)[17] | 213M | 965G | 56.2 | - | - | - |
| Swin-L† (HTC++) [43] | 284M | 58.0 | 50.4 | 58.7 | 51.1 | |
| Swin-L† (DyHead) [17] | 213M | 58.4 | - | 58.7 | ||
| Swin-L† (QueryInst) [25] | - | 56.1 | 1 | 56.1 | ||
| Focal-L (HTC++) (Ours) | 265M | 1165G | 57.0 | 49.9 | - | = |
| Focal-L (DyHead) (Ours) | 229M | 1081G | 56.4 | - | - | = |
| Focal-L† (HTC++) (Ours) | 265M | - | 58.1 | 50.9 | 58.4 | 51.3 |
| Focal-L† (DyHead) (Ours) | 229M | - | 58.7 | - | 59.0 | - |
| Model | W-Shift Top-1(%) APb APm | |||
| Swin-Tiny | √ | 80.2 81.2 | 38.8 43.7 | 36.4 39.8 |
| Focal-Tiny | 82.2 | 44.8 | 41.0 | |
| √ | 81.9 | 44.9 | 41.1 |
| Depths Model #Params. FLOPs Top-1(%) APb Apm | |||||
| 2-2-2-2 | Swin | 21.2 | 3.1 | 78.7 | 38.2 35.7 |
| Focal | 21.7 | 3.4 | 79.9 | 40.5 37.6 | |
| 2-2-4-2 | Swin | 24.7 | 3.8 | 80.2 | 41.2 38.1 |
| Focal | 25.4 | 4.1 | 81.4 | 43.3 39.8 | |
| 2-2-6-2 | Swin | 28.3 | 4.5 | 81.2 | 43.7 39.8 |
| Focal | 29.1 | 4.9 | 82.2 | 44.8 41.0 |
| Singularity in | 2nd Layer Trained (RF) | Vanishing Init. | Non-vanishing Init. |
| Bias | 1: No; Y2: Yes | γ1: No; γ2: No | γ1: No; 2: No |
| Variance | Y1: No; 2: Yes | 1: Yes; Y2: No | Y1: No; 2: No |
| Singularity in | 2nd Layer Trained (RF) | Vanishing Init. | Non-vanishing Init. |
| Bias | 1: No; Y2: Yes | γ1: No; γ2: No | γ1: No; 2: No |
| Variance | Y1: No; 2: Yes | 1: Yes; Y2: No | Y1: No; 2: No |
| Singularity in | 2nd Layer Trained (RF) | Vanishing Init. | Non-vanishing Init. |
| Bias | 1: No; Y2: Yes | γ1: No; γ2: No | γ1: No; 2: No |
| Variance | Y1: No; 2: Yes | 1: Yes; Y2: No | Y1: No; 2: No |
| Singularity in | 2nd Layer Trained (RF) | Vanishing Init. | Non-vanishing Init. |
| Bias | 1: No; Y2: Yes | γ1: No; γ2: No | γ1: No; 2: No |
| Variance | Y1: No; 2: Yes | 1: Yes; Y2: No | Y1: No; 2: No |
| Singularity in | 2nd Layer Trained (RF) | Vanishing Init. | Non-vanishing Init. |
| Bias | 1: No; Y2: Yes | γ1: No; γ2: No | γ1: No; 2: No |
| Variance | Y1: No; 2: Yes | 1: Yes; Y2: No | Y1: No; 2: No |
| Source | Flows | MOS |
| Real | 1 | 4.27 ± 0.13 |
| Flowtron | 2 | 3.66 ± 0.16 |
| Tacotron 2 | 1 | 3.52 ± 0.17 |
| Pitch Mean | Pitch Standard Deviation | |||||
| Model | Style Expressive | High Pitch | Surprised | Expressive | High Pitch | Surprised |
| Reference | 53.6 | 55.2 | 58.2 | 4.5 | 2.3 | 1.0 |
| FTA Posterior | 53.4 | 53.3 | 55.5 | 2.5 | 2.3 | 3.0 |
| FTA Baseline | 53.1 | 52.6 | 52.8 | 2.2 | 1.9 | 1.9 |
| Tacotron 2 GST | 51.7 | 53.6 | 51.6 | 2.0 | 2.4 | 1.7 |
| Source | Flows | MOS |
| Real | 1 | 4.27 ± 0.13 |
| Flowtron | 2 | 3.66 ± 0.16 |
| Tacotron 2 | 1 | 3.52 ± 0.17 |
| Pitch Mean | Pitch Standard Deviation | |||||
| Model | Style Expressive | High Pitch | Surprised | Expressive | High Pitch | Surprised |
| Reference | 53.6 | 55.2 | 58.2 | 4.5 | 2.3 | 1.0 |
| FTA Posterior | 53.4 | 53.3 | 55.5 | 2.5 | 2.3 | 3.0 |
| FTA Baseline | 53.1 | 52.6 | 52.8 | 2.2 | 1.9 | 1.9 |
| Tacotron 2 GST | 51.7 | 53.6 | 51.6 | 2.0 | 2.4 | 1.7 |
| Real | DCGAN | WGAN | WGAN-GP | LSGAN | ||
| Conv Space | MMD | 0.019 | 0.205 | 0.270 | 0.194 | 0.232 |
| 1-NN Accuracy | 0.499 | 0.825 | 0.920 | 0.812 | 0.871 | |
| 1-NN Accuracy (real) | 0.495 | 0.759 | 0.880 | 0.765 | 0.804 | |
| 1-NN Accuracy (fake) | 0.503 | 0.892 | 0.961 | 0.860 | 0.938 | |
| Real | DCGAN | WGAN | WGAN-GP | LSGAN | ||
| Conv Space | MMD | 0.019 | 0.205 | 0.270 | 0.194 | 0.232 |
| 1-NN Accuracy | 0.499 | 0.825 | 0.920 | 0.812 | 0.871 | |
| 1-NN Accuracy (real) | 0.495 | 0.759 | 0.880 | 0.765 | 0.804 | |
| 1-NN Accuracy (fake) | 0.503 | 0.892 | 0.961 | 0.860 | 0.938 |
| Real | DCGAN | WGAN | WGAN-GP | LSGAN | ||
| Conv Space | MMD | 0.019 | 0.205 | 0.270 | 0.194 | 0.232 |
| 1-NN Accuracy | 0.499 | 0.825 | 0.920 | 0.812 | 0.871 | |
| 1-NN Accuracy (real) | 0.495 | 0.759 | 0.880 | 0.765 | 0.804 | |
| 1-NN Accuracy (fake) | 0.503 | 0.892 | 0.961 | 0.860 | 0.938 |
| Real | DCGAN | WGAN | WGAN-GP | LSGAN | ||
| Conv Space | MMD | 0.019 | 0.205 | 0.270 | 0.194 | 0.232 |
| 1-NN Accuracy | 0.499 | 0.825 | 0.920 | 0.812 | 0.871 | |
| 1-NN Accuracy (real) | 0.495 | 0.759 | 0.880 | 0.765 | 0.804 | |
| 1-NN Accuracy (fake) | 0.503 | 0.892 | 0.961 | 0.860 | 0.938 |
| Real | DCGAN | WGAN | WGAN-GP | LSGAN | ||
| Conv Space | MMD | 0.019 | 0.205 | 0.270 | 0.194 | 0.232 |
| 1-NN Accuracy | 0.499 | 0.825 | 0.920 | 0.812 | 0.871 | |
| 1-NN Accuracy (real) | 0.495 | 0.759 | 0.880 | 0.765 | 0.804 | |
| 1-NN Accuracy (fake) | 0.503 | 0.892 | 0.961 | 0.860 | 0.938 |
| Experiment | Theoretical Upper Bound | Exp. Convergence Time (in seconds) | Metric | ||||
| (in seconds) | L1 | L2 | Lyap. | L1 | L2 | Lyap. | |
| SingleNeuron (acc) | ~3.4e3 | 0.065 | 0.064 | 0.025 | 0.95 | 0.95 | 1.0 |
| MLP (rmse) | ~ 1.4e10 | 4.3e3 | 3.4e3 | 3.1e3 | 0.091 | 0.179 | 0.085 |
| Experiment for single neuron case on Iris dataset | Theoretical Upper Bound (in seconds) | Exp. Convergence Time (in seconds) | Accuracy on Test Set | ||||
| L1 | L2 | Lyap. | L1 | L2 | Lyap. | ||
| k=0.001 | ~ 37213.848 | 0.312 | 0.310 | 0.0918 | 0.6 | 0.95 | 0.95 |
| k = 0.005 | ~7442.769 | 0.0943 | 0.0942 | 0.0344 | 0.95 | 1.0 | 1.0 |
| k= 0.01 | ~ 3721.385 | 0.0566 | 0.0573 | 0.0221 | 0.95 | 1.0 | 1.0 |
| Experiment | Theoretical Upper Bound | Exp. Convergence Time (in seconds) | Metric | ||||
| (in seconds) | L1 | L2 | Lyap. | L1 | rmse L2 | Lyap. | |
| IMDBWiki | 8.3e6 | 980.40 | 712.99 | 467.96 | 0.414 | 0.415 | 0.416 |
| Experiment for MLP case on Boston | Theoretical Upper Bound (in seconds) | Exp. Convergence Time to within 10e-9 (in seconds) | Metric rmse | ||||
| L1 | L2 | Lyap. | L1 | L2 | Lyap. | ||
| dataset M=0.1 | ~1.97e11 | 1277.66 | 906.61 | 755.59 | 0.095 | 0.145 | 0.092 |
| M= 0.2 | ~ 5.67e10 | 1297.11 | 1097.62 | 914.78 | 0.096 | 0.146 | 0.093 |
| M= 0.3 | ~2.73e10 | 1290.48 | 1197.53 | 998.05 | 0.093 | 0.147 | 0.101 |
| Experiment | Theoretical Upper Bound | Exp. Convergence Time (in seconds) | Metric | ||||
| (in seconds) | L1 | L2 | Lyap. | L1 | L2 | Lyap. | |
| SingleNeuron (acc) | ~3.4e3 | 0.065 | 0.064 | 0.025 | 0.95 | 0.95 | 1.0 |
| MLP (rmse) | ~ 1.4e10 | 4.3e3 | 3.4e3 | 3.1e3 | 0.091 | 0.179 | 0.085 |
| Experiment for single neuron case on Iris dataset | Theoretical Upper Bound (in seconds) | Exp. Convergence Time (in seconds) | Accuracy on Test Set | ||||
| L1 | L2 | Lyap. | L1 | L2 | Lyap. | ||
| k=0.001 | ~ 37213.848 | 0.312 | 0.310 | 0.0918 | 0.6 | 0.95 | 0.95 |
| k = 0.005 | ~7442.769 | 0.0943 | 0.0942 | 0.0344 | 0.95 | 1.0 | 1.0 |
| k= 0.01 | ~ 3721.385 | 0.0566 | 0.0573 | 0.0221 | 0.95 | 1.0 | 1.0 |
| Experiment | Theoretical Upper Bound | Exp. Convergence Time (in seconds) | Metric | ||||
| (in seconds) | L1 | L2 | Lyap. | L1 | rmse L2 | Lyap. | |
| IMDBWiki | 8.3e6 | 980.40 | 712.99 | 467.96 | 0.414 | 0.415 | 0.416 |
| Experiment for MLP case on Boston | Theoretical Upper Bound (in seconds) | Exp. Convergence Time to within 10e-9 (in seconds) | Metric rmse | ||||
| L1 | L2 | Lyap. | L1 | L2 | Lyap. | ||
| dataset M=0.1 | ~1.97e11 | 1277.66 | 906.61 | 755.59 | 0.095 | 0.145 | 0.092 |
| M= 0.2 | ~ 5.67e10 | 1297.11 | 1097.62 | 914.78 | 0.096 | 0.146 | 0.093 |
| M= 0.3 | ~2.73e10 | 1290.48 | 1197.53 | 998.05 | 0.093 | 0.147 | 0.101 |
| Input Size ² | MobileNet | ResNet-18 | ResNet-34 | ResNet-50 | ResNet-101 |
| 224×224 | 68.19 (88.44) | 69.93 (89.22) | 73.30 (91.42) | 75.65 (92.47) | 77.37 (93.56) |
| 225×225 | 68.80 (88.78) | 70.27 (89.52) | 73.72 (91.58) | 76.01 (92.90) | 77.67 (93.81) |
| Average Precision (AP) | AP@.20I0U | AP@ .50I0U | AP@.75I0U | AP@.90I0U |
| Zero Padding | 80.24% | 49.58% | 3.7% | 0.007% |
| Mirror Padding | 83.20% | 57% | 8.44% | 0.02% |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| 1 | 2 | 3 | 3 | 3 |
| 2 | 4 | 6 | 6 | 6 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| 0 | 0 | 0 | • · | ||
| 0 | a | b | |||
| 0 | C | d | |||
| 0 | · | ||||
| • = | |||||
| 46 | 66 | 6 | ||
| 69 | 99 | 9 | ||
| 69 | 9 | 9 | ||
| 6999 | 9 | |||
| 6999 | 9 |
| a | b | ·· | ||
| C | d | |||
| · | ||||
| Original Input | Padded at top-leftPadded at bottom-Padded at top-rightPadded at bottom left corner | ||||||||||||||||||||||||||||
| e | d | d | e f | d | d | e | f | right corner | |||||||||||||||||||||
| a | b | C | b | a | b | a | a | b | a | C | |||||||||||||||||||
| d | e | e | d | b e | C f | b | C f | a d | a d | e | C f | a | a | b | |||||||||||||||
| h | h | g | d g | h | i | e h | d g | d g | e h | i | g | h | d | e | |||||||||||||||
| g | g | g | h | ||||||||||||||||||||||||||
| Padded at top-left | Padded at bottom-left | Padded at top-right | Padded at bottom-right | Average (grouped padding strategy) | ||||||||||||||||||||||||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | ||||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | ||||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | ||||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | ||||||||||||||||
| 20 | 20 | 16 | 16 16 | 20 | 20 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | ||||||||||||||||||
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| • · | ||||
| e | d | e | f | . • | . • |
| b | a | b | C | = = | |
| e | d | e | f | ||
| h | g | h | |||
| = = | |||||
| 4 | 8 | 6 | 6 | 6 |
| 8 | 16 | 12 | 12 | 12 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| 6.25 | 8.75 | 7.5 | 7.5 | 7.5 |
| 8.75 12.25 | 10.5 10.510.5 | |||
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| Input Size ² | MobileNet | ResNet-18 | ResNet-34 | ResNet-50 | ResNet-101 |
| 224×224 | 68.19 (88.44) | 69.93 (89.22) | 73.30 (91.42) | 75.65 (92.47) | 77.37 (93.56) |
| 225×225 | 68.80 (88.78) | 70.27 (89.52) | 73.72 (91.58) | 76.01 (92.90) | 77.67 (93.81) |
| Average Precision (AP) | AP@.20I0U | AP@ .50I0U | AP@.75I0U | AP@.90I0U |
| Zero Padding | 80.24% | 49.58% | 3.7% | 0.007% |
| Mirror Padding | 83.20% | 57% | 8.44% | 0.02% |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| 1 | 2 | 3 | 3 | 3 |
| 2 | 4 | 6 | 6 | 6 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| 0 | 0 | 0 | • · | ||
| 0 | a | b | |||
| 0 | C | d | |||
| 0 | · | ||||
| • = | |||||
| 46 | 66 | 6 | ||
| 69 | 99 | 9 | ||
| 69 | 9 | 9 | ||
| 6999 | 9 | |||
| 6999 | 9 |
| a | b | ·· | ||
| C | d | |||
| · | ||||
| Original Input | Padded at top-leftPadded at bottom-Padded at top-rightPadded at bottom left corner | |||||||||||||||||||||||||||
| e | d | d | e f | d | d | e | f | right corner | ||||||||||||||||||||
| a | b | C | b | a | b | a | a | b | a | C | ||||||||||||||||||
| d | e | e | d | b e | C f | b | C f | a d | a d | e | C f | a | a | b | ||||||||||||||
| h | h | g | d g | h | i | e h | d g | d g | e h | i | g | h | d | e | ||||||||||||||
| g | g | g | h |
| Padded at top-left | Padded at bottom-left | Padded at top-right | Padded at bottom-right | Average (grouped padding strategy) | |||||||||||||||||||||||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 16 | 20 | 20 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| • · | ||||
| e | d | e | f | . • | . • |
| b | a | b | C | = = | |
| e | d | e | f | ||
| h | g | h | |||
| = = | |||||
| 4 | 8 | 6 | 6 | 6 |
| 8 | 16 | 12 | 12 | 12 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| 6.25 | 8.75 | 7.5 | 7.5 | 7.5 |
| 8.75 12.25 | 10.5 10.510.5 | |||
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| Input Size ² | MobileNet | ResNet-18 | ResNet-34 | ResNet-50 | ResNet-101 |
| 224×224 | 68.19 (88.44) | 69.93 (89.22) | 73.30 (91.42) | 75.65 (92.47) | 77.37 (93.56) |
| 225×225 | 68.80 (88.78) | 70.27 (89.52) | 73.72 (91.58) | 76.01 (92.90) | 77.67 (93.81) |
| Input Size ² | MobileNet | ResNet-18 | ResNet-34 | ResNet-50 | ResNet-101 |
| 224×224 | 68.19 (88.44) | 69.93 (89.22) | 73.30 (91.42) | 75.65 (92.47) | 77.37 (93.56) |
| 225×225 | 68.80 (88.78) | 70.27 (89.52) | 73.72 (91.58) | 76.01 (92.90) | 77.67 (93.81) |
| Average Precision (AP) | AP@.20I0U | AP@ .50I0U | AP@.75I0U | AP@.90I0U |
| Zero Padding | 80.24% | 49.58% | 3.7% | 0.007% |
| Mirror Padding | 83.20% | 57% | 8.44% | 0.02% |
| Average Precision (AP) | AP@.20I0U | AP@ .50I0U | AP@.75I0U | AP@.90I0U |
| Zero Padding | 80.24% | 49.58% | 3.7% | 0.007% |
| Mirror Padding | 83.20% | 57% | 8.44% | 0.02% |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| 1 | 2 | 3 | 3 | 3 |
| 2 | 4 | 6 | 6 | 6 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| 1 | 2 | 3 | 3 | 3 |
| 2 | 4 | 6 | 6 | 6 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| 0 | 0 | 0 | • · | ||
| 0 | a | b | |||
| 0 | C | d | |||
| 0 | · | ||||
| • = | |||||
| 46 | 66 | 6 | ||
| 69 | 99 | 9 | ||
| 69 | 9 | 9 | ||
| 6999 | 9 | |||
| 6999 | 9 |
| a | b | ·· | ||
| C | d | |||
| · | ||||
| 0 | 0 | 0 | • · | ||
| 0 | a | b | |||
| 0 | C | d | |||
| 0 | · | ||||
| • = | |||||
| 46 | 66 | 6 | ||
| 69 | 99 | 9 | ||
| 69 | 9 | 9 | ||
| 6999 | 9 | |||
| 6999 | 9 |
| a | b | ·· | ||
| C | d | |||
| · | ||||
| Original Input | Padded at top-leftPadded at bottom-Padded at top-rightPadded at bottom left corner | |||||||||||||||||||||||||||
| e | d | d | e f | d | d | e | f | right corner | ||||||||||||||||||||
| a | b | C | b | a | b | a | a | b | a | C | ||||||||||||||||||
| d | e | e | d | b e | C f | b | C f | a d | a d | e | C f | a | a | b | ||||||||||||||
| h | h | g | d g | h | i | e h | d g | d g | e h | i | g | h | d | e | ||||||||||||||
| g | g | g | h |
| Padded at top-left | Padded at bottom-left | Padded at top-right | Padded at bottom-right | Average (grouped padding strategy) | |||||||||||||||||||||||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 16 | 20 | 20 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 |
| Original Input | Padded at top-leftPadded at bottom-Padded at top-rightPadded at bottom left corner | |||||||||||||||||||||||||||
| e | d | d | e f | d | d | e | f | right corner | ||||||||||||||||||||
| a | b | C | b | a | b | a | a | b | a | C | ||||||||||||||||||
| d | e | e | d | b e | C f | b | C f | a d | a d | e | C f | a | a | b | ||||||||||||||
| h | h | g | d g | h | i | e h | d g | d g | e h | i | g | h | d | e | ||||||||||||||
| g | g | g | h |
| Padded at top-left | Padded at bottom-left | Padded at top-right | Padded at bottom-right | Average (grouped padding strategy) | |||||||||||||||||||||||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 16 | 20 | 20 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| • · | ||||
| e | d | e | f | . • | . • |
| b | a | b | C | = = | |
| e | d | e | f | ||
| h | g | h | |||
| = = | |||||
| 4 | 8 | 6 | 6 | 6 |
| 8 | 16 | 12 | 12 | 12 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| • · | ||||
| e | d | e | f | . • | . • |
| b | a | b | C | = = | |
| e | d | e | f | ||
| h | g | h | |||
| = = | |||||
| 4 | 8 | 6 | 6 | 6 |
| 8 | 16 | 12 | 12 | 12 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| 6.25 | 8.75 | 7.5 | 7.5 | 7.5 |
| 8.75 12.25 | 10.5 10.510.5 | |||
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| 6.25 | 8.75 | 7.5 | 7.5 | 7.5 |
| 8.75 12.25 | 10.5 10.510.5 | |||
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| Input Size ² | MobileNet | ResNet-18 | ResNet-34 | ResNet-50 | ResNet-101 |
| 224×224 | 68.19 (88.44) | 69.93 (89.22) | 73.30 (91.42) | 75.65 (92.47) | 77.37 (93.56) |
| 225×225 | 68.80 (88.78) | 70.27 (89.52) | 73.72 (91.58) | 76.01 (92.90) | 77.67 (93.81) |
| Average Precision (AP) | AP@.20I0U | AP@ .50I0U | AP@.75I0U | AP@.90I0U |
| Zero Padding | 80.24% | 49.58% | 3.7% | 0.007% |
| Mirror Padding | 83.20% | 57% | 8.44% | 0.02% |
| 1 | 2 | 3 | 3 | 3 |
| 2 | 4 | 6 | 6 | 6 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| 3 | 6 | 9 | 9 | 9 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| a | b | ·· | ||
| C | d | |||
| · | ||||
| 46 | 66 | 6 | ||
| 69 | 99 | 9 | ||
| 69 | 9 | 9 | ||
| 6999 | 9 | |||
| 6999 | 9 |
| 0 | 0 | 0 | • · | ||
| 0 | a | b | |||
| 0 | C | d | |||
| 0 | · | ||||
| • = | |||||
| a | 1 | 1 | 1 | b | 1 | 1 | 1 |
| 1 | 1 | 1 | 1 | 1 | 1 | ||
| 1 | 1 | 1 | 1 | 1 | 1 | ||
| sum=9 | sum=9 | ||||||
| uniform | uniform |
| a | a | b | C | aa | b | C | a | a | b | C | a | a b | C | ||||
| a | a | b | C | a | a | b C | a d | a | b | C | a | a | b | C f | |||
| d | d | e | f | d | d | e | f | d | e | f | d | d | e | ||||
| g | g | h | i | g | g | h | i | g | g | h | i | g | g | h ： |
| a | a | b | a a | b | C | a a | b | C | a a | b | C | a | a | b C | a | a | b | C | ||||||
| a | a | b | a | a | C | a | a b | C | a | a b | C | a | a | b | C | a | a b | C | ||||||
| d | d | e | d | e | f | d | e | d | e | f | d d | e | f | d | d | f | ||||||||
| g | g | h | g | h | i | g | h | g | h | g | g h | g | g | h | ||||||||||
| a | a | b C | a | a | b C | a | a | b | C | a | d | e f | a | a | b | C | a | a | b C | |||||
| a | a | b C | a | a | b | C | a | a | b C | a | a | b | C | a a | b | C | a | a | b | C | ||||
| d | d | e | d | d | e f | d | d | e | f | d d | e | f | d | d e | f | d | d | e | f | |||||
| g | g | h i | g | g | h i | g | g | h | g g | h | ： | g | g | h i | g | h | ： | |||||||
| g |
| Padded at top- left corner | Padded at bottom- left corner | Padded at top- right corner | Padded at bottom- right corner | Average (grouped padding strategy) | |
| Convolutions involving (a) | 3 2 | 2 1 | 2 | 1 | 2 0.75 |
| 2 2 | 1 | 0.75 0.5 | |||
| sum=9 | sum=3 | sum=3 | sum =1 | sum = 4 | |
| Convolutions involving (b) | 2 2 | 1 1 | 2 2 | 1 1 | 1.5 1.5 |
| 1 1 | 1 1 | 0.5 0.5 | |||
| sum=6 | sum=2 | sum=6 | sum=2 | sum =4 | |
| Convolutions involving (c) | 2 1 | 2 1 | 1 | 1 | 1.5 0.5 |
| 2 1 | 2 1 | 1 | 1 | 1.5 0.5 | |
| sum=6 | sum=6 | sum=2 | sum=2 | sum = 4 | |
| Convolutions involving (d) | 1 1 | 1 1 | 1 1 | 1 1 | 1 1 |
| 1 1 | 1 1 | 1 1 | 1 1 | 1 1 | |
| sum=4 | sum=4 | sum=4 | sum =4 | sum = 4 | |
| uniform | uniform | uniform | uniform | uniform |
| Original Input | Padded at top- left corner | Padded at bottom- Padded at top- left corner | right corner b | Padded at bottom- right corner | ||||
| a b | a b a b | a | a b | a b | a | b | ||
| C d | d | C d | C d | C d | ||||
| C | ||||||||
| Padded at top-left | Padded at bottom-left | Padded at top-right | Padded at bottom-right | Average (grouped padding strategy) | |||||||||||||||||||||||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 25 | 25 | 20 | 20 | 20 | 15 | 15 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 9 | 9 | 12 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 | 16 | 20 | 20 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | |||||||||||||||
| 20 | 20 | 16 | 16 16 | 20 | 20 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 12 | 12 | 16 | 16 | 16 | 16 | 16 | 16 | 16 | 16 |
| Original Input | Padded at top-leftPadded at bottom-Padded at top-rightPadded at bottom left corner | |||||||||||||||||||||||||||
| e | d | d | e f | d | d | e | f | right corner | ||||||||||||||||||||
| a | b | C | b | a | b | a | a | b | a | C | ||||||||||||||||||
| d | e | e | d | b e | C f | b | C f | a d | a d | e | C f | a | a | b | ||||||||||||||
| h | h | g | d g | h | i | e h | d g | d g | e h | i | g | h | d | e | ||||||||||||||
| g | g | g | h |
| a | b | C | ||
| d | e | f | ||
| g | h | |||
| • · | ||||
| 4 | 8 | 6 | 6 | 6 |
| 8 | 16 | 12 | 12 | 12 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| 6 | 12 | 9 | 9 | 9 |
| ede | edef | e | def | e | edef | |||||||
| b | a b | C | b | a b | C | b | a H C | b | a b | |||
| e | e | f | e | d e | f | e | d e f | e | d e | |||
| h | g h | i | h | g h | h | g h | h | g h | ||||
| e | d | e | f | e | d | e f | e | d | e | f | e | d | e | f | e | d | e | f | e | d | e | f | ||
| b | a | b | C | b | a | b C | b | a | b C | b | a | b C | b | a b | C | b | a | b C | ||||||
| e | d | e | e | d e | e | d | e f | e | d e | f | e | d e | f | e | d e | f | ||||||||
| h | g | h | h g | h | h | g | h | h | g | h ： | h | g | h | h | h | |||||||||
| g |
| e | d | e | f | . • | . • |
| b | a | b | C | = = | |
| e | d | e | f | ||
| h | g | h | |||
| = = | |||||
| e | d | e f | e | d | e f | e | d | e | f | e | d | e f | e | d | e | f | e d | e | f | |||||
| b | a | b C | b | a | b | C | b | a | b | C | b a | b | C | b | a | b C | b | a | b | C | ||||
| e | d | e f | e | d | e | f | e | d | e | f | e | d e | f | e | d | e | f | e | d | e | f | |||
| h | g | h | h | g | h | h | g | h | h | g h | ： | h | g | h | h | h | ： | |||||||
| g |
| a: | b: | C: | d: | e: | f: | g: | h: | |||||||||
| 1 1 1 1 | 2 1 | 1 | 1 | 2 2 | 4 | 2 | 1 1 | i: 1 | ||||||||
| 2 1 | 1 | 2 1 | 2 1 | 1 1 | 2 | 1 | 1 | |||||||||
| 1 | 1 | 1 1 | 1 | 1 | ||||||||||||
| 1 1 | 1 | 2 1 | ||||||||||||||
| sum=4 | sum =8 | sum=6 | sum =8 | sum =12 | sum = 16 | sum=6 | sum = 12 | sum=9 |
| 6.25 | 8.75 | 7.5 | 7.5 | 7.5 |
| 8.75 12.25 | 10.5 10.510.5 | |||
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| 7.5 | 10.5 | 9 | 9 | 9 |
| a | b | C | ||
| d | e | f | ||
| g | h | |||