| Feature source | R@1↑ R@5 | 个 MdR↓ |
| R-152 | 20.8 | 46.2 6.0 |
| R(2+1)D-34 | 23.7 | 53.2 4.0 |
| R(2+1)D-34 +R-152 | 27.2 | 55.2 3.0 |
| Temporal reduction R@1 ↑ R@5↑MdR↓ | ||
| Max | 21.8 | 49.5 8.0 |
| Mean | 22.5 | 51.3 6.0 |
| Multi-Head Attn | 27.2 55.2 | 3.0 |
| Text Encoder | R@1↑R@5↑ MdR↓ | ||
| W2V (GloVe) | 22.1 | 49.8 | 6.0 |
| T5-Small | 24.5 | 51.2 | 3.0 |
| T5-Base | 27.2 | 55.2 | 3.0 |
| Text Encoder Text Decoder R@1 ↑ R@5 ↑ MdR↓ | ||||
| T5-Base | T5-Small | 26.2 | 54.2 | 3.0 |
| T5-Base | T5-Base | 27.2 | 55.2 | 3.0 |
| Contrastive | R@1↑ R@5↑ | MdR↓ |
| InfoNCE (inter+intra) | 10.7 | 28.5 15.0 |
| InfoNCE (inter) | 10.8 | 29.0 14.5 |
| Triplet (inter+intra) | 26.8 | 56.2 3.0 |
| Triplet (inter) | 27.2 | 55.2 3.0 |
| Batch-size | Memory bank | ||||||||
| Size | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 2k | 8k |
| R@1/5 18.5/45.6 20.7/49.9 25.2/54.6 27.2/55.2 28.0/56.1 26.9/55.0 25.3/53.5 | 26.8/54.7 26.2/52.7 | ||||||||
| R@1↑ | R@5↑ MdR↓ | ||
| None | 25.9 | 53.0 | 4.0 4.0 3.0 |
| Identity | 26.4 | 51.9 | |
| Full | 25.8 | 53.9 | |
| Hybrid | 26.0 | 54.8 | 3.0 |
| Cross | 27.2 | 55.2 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑R@5↑ R@10↑MdR↓ | R@1↑ R@5↑ R@10↑MdR↓ | |||||||
| Random Baseline | 0.1 | 0.5 | 1.0 | 500.0 | 0.1 | 0.5 | 1.0 | 500.0 |
| JSFusion (Yu et al., 2018) | 10.2 | 31.2 | 43.2 | 13.0 | 1 | 1 | 1 | 1 |
| HT100M (Miech et al., 2019) | 12.1 | 35.0 | 48.0 | 12.0 | 1 | 一 | 一 | 一 |
| JPoSE(Wray et al., 2019) | 14.3 | 38.1 | 53.0 | 9.0 | 16.4 | 41.3 | 54.4 | 8.7 |
| CE (Liu et al., 2019) | 20.9 | 48.8 | 62.4 | 6.0 | 20.6 | 50.3 | 64.0 | 5.3 |
| MMT(Gabeur et al., 2020) | 24.6 | 54.0 | 67.1 | 4.0 | 24.4 | 56.0 | 67.8 | 4.0 |
| Ours | 27.4 | 56.3 | 67.7 | 3.0 | 26.6 | 55.1 | 67.5 | 3.0 |
| VidTranslate (Korbar etal., 2020) | 14.7 | 1 | 52.8 | 1 | 一 | 1 | ||
| HT100M (Miech et al.,2019) | 14.9 | 40.2 | 52.8 | 9.0 | 16.8 | 41.7 | 55.1 | 8.0 |
| NoiseEstimation (Amrani et al., 2020) | 17.4 | 41.6 | 53.6 | 8.0 | 1 | 一 | 1 | 1 |
| UniVL (Luo et al.,2020) | 21.2 | 49.6 | 63.1 | 6.0 | 一 | 一 | 一 | 一 |
| AVLnet (Rouditchenko et al., 2020) | 27.1 | 55.6 | 66.6 | 4.0 | 28.5 | 54.6 | 65.2 | 4.0 |
| MMT(Gabeur et al., 2020) | 26.6 | 57.1 | 69.6 | 4.0 | 27.0 | 57.5 | 69.7 | 3.7 |
| Ours-pretrained | 30.1 | 58.5 | 69.3 | 3.0 | 28.5 | 58.6 | 71.6 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@10↑ MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||||
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 0.02 | 0.1 | 1.02 | 2100.5 | |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 1 | 1 | 1 | 1 |
| VSE++(Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 1 | 一 | 1 | 一 |
| Dual (Dong et al.,2019) | 31.1 | 67.4 | 78.9 | 3.0 | 1 | 1 | 1 | 1 |
| HGR(Chen et al., 2020b) | 35.1 | 73.5 | 83.5 | 2.0 | 一 | 一 | 一 | |
| Ours | 44.6 | 81.8 | 89.5 | 1.0 | 58.1 | 83.8 | 90.9 | 1.0 |
| Ours-pretrained | 45.9 | 82.4 | 90.4 | 1.0 | 61.2 | 85.2 | 91.8 | 1.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@50↑ MdR↓ R@1↑ R@5 ↑ R@50↑ MdR↓ | ||||||||
| Random Baseline | 0.02 | 0.1 | 1.02 | 2458 | 0.02 | 0.1 | 1.02 | 2458 |
| FSE(Zhang et al., 2018) | 18.2 | 44.8 | 89.1 | 7.0 | 16.7 | 43.1 | 88.4 | 7.0 |
| CE (Liu et al., 2019) | 18.2 | 47.7 | 91.4 | 6.0 | 17.7 | 46.6 | 90.9 | 6.0 |
| HSE (Zhang et al.,2018) | 20.5 | 49.3 | 1 | 1 | 18.7 | 48.1 | 1 | 1 |
| MMT (Gabeur et al.,2020) | 22.7 | 54.2 | 93.2 | 5.0 | 22.9 | 54.8 | 93.1 | 4.3 |
| Ours | 26.8 | 58.1 | 93.5 | 3.0 | 25.5 | 57.3 | 93.5 | 3.0 |
| MMT-pretrained (Gabeur et al., 2020) | 28.7 | 61.4 | 94.5 | 3.3 | 28.9 | 61.1 | 94.3 | 4.0 |
| Ours-pretrained | 29.2 | 61.6 | 94.7 | 3.0 | 28.7 | 60.8 | 94.8 | 2.0 |
| Text→Video | Video→Text | |||||
| R@1↑ R@5↑ R@10↑MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||
| VSE (Kiros et al.,2014) | 12.3 30.1 | 42.3 | 14.0 | 1 | ||
| VSE++ (Faghri et al., 2018) | 15.4 39.6 | 53.0 | 9.0 | 一 | ||
| Multi. Cues (Mithun et al.,2018) | 20.3 47.8 | 61.1 | 6.0 | 1 | 1 | 1 一 |
| CE (Liu et al., 2019) | 19.8 49.0 | 63.8 | 6.0 | 一 | ||
| Ours | 23.0 52.8 | 65.8 | 5.0 | 27.3 | 50.7 | 60.8 5.0 |
| Ours-pretrained | 28.4 60.0 | 72.9 | 4.0 | 34.7 | 59.9 | 70.0 3.0 |
| Captioning | ||||
| BLUE4 | METEOR | Rogue-L | CIDEr | |
| VidTranslate (Korbar et al., 2020) | 41.7 | 28.5 | 一 | 一 |
| POS+VCT (Hou et al., 2019) | 42.3 | 29.7 | 62.8 | 49.1 |
| ORG (Zhang et al., 2020) | 43.6 | 28.8 | 62.1 | 50.9 |
| Ours, MSR-VTT only | 39.7 | 28.3 | 60.5 | 46.5 |
| Ours,HT100M + MSR-VTT | 38.9 | 28.2 | 59.8 | 48.6 |
| Captioning | ||||
| Blue@4 METEORI | Rogue-L CIDEr | |||
| Shared Enc-Dec (Wang et al., 2019) | 28.4 | 21.7 | 47.0 | 45.1 |
| ORG (Zhang et al., 2020) | 32.1 | 22.2 | 48.9 | 49.7 |
| Ours, ,VATEX only | 32.8 | 24.4 | 49.1 | 51.2 |
| Ours,HT100M + Vatex | 32.5 | 24.1 | 48.9 | 50.5 |
| Captioning | ||||
| Blue@4 | METEOR | Rogue-L | CIDEr | |
| DENSE (Krishna et al.,2017) | 1.6 | 8.9 | ||
| DVC-D-A (Li et al., 2018) | 1.7 | 9.3 | ||
| Bi-LSTM+TempoAttn (Zhou et al., 2018b) | 2.1 | 10.0 | 一 | |
| Masked Transformer (Zhou et al.,2018b) | 2.8 | 11.1 | 1 | 1 |
| Ours, ActivityNet only | 1.5 | 6.9 | 17.8 | 3.2 |
| Ours,HT100M + ActivityNet | 1.4 | 6.9 | 17.5 | 3.1 |
| Text→Video | Video→Text | |||||||
| R@1↑ | R@5↑ | R@10↑ | MdR | R@1↑ | R@5↑ | R@10个 | MdR | |
| Zero-Shot | ||||||||
| ActivityNet | 0.06 | 0.2 | 0.5 | 1907.0 | 0.0 | 0.2 | 0.3 | 2238.0 |
| VATEX | 0.07 | 0.4 | 0.7 | 682.0 | 0.07 | 0.4 | 0.9 | 697 |
| MSVD | 8.9 | 26.0 | 37.9 | 18.0 | 21.4 | 46.2 | 57.7 | 6.0 |
| MSR-VTT | 8.7 | 23.0 | 31.1 | 31.0 | 12.7 | 27.5 | 36.2 | 24.0 |
| Method | Mod | Dataset | Model | FT? | H51 | U101 |
| Self-Supervised Pre-training | ||||||
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 53.1 | 82.7 | |
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 61.0 | 91.3 | |
| MMV(Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | 67.1 | 91.8 | |
| ELo (Piergiovanni et al.,2020) | V,F,A | YT8M | R(2+1)D-50x3 | x√xν | 67.4 | 93.8 |
| XDC (Alwassel et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 68.9 | 95.5 |
| GDT (Patrick et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 72.8 | 95.2 |
| MMV (Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | √ | 75.0 | 95.2 |
| Supervised Pre-training | ||||||
| P3D (Qiu et al., 2017) | V,I | S1M+IM | P3D | 88.6 | ||
| TSN (Wang et al.,2018) | V,I | IM | TSN | ? | 69.4 | 94.2 |
| I3D (Carreira & Zisserman,2017) | V,I | K400+IM | I3D | √ | 74.8 | 95.6 |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 74.5 | 96.8 | |
| S3D-G (Xie et al., 2018) | V,I | K400+IM | S3D-G | 75.9 | 96.8 | |
| I3D(Carreira & Zisserman,2017) | V,I | K400+IM | I3D | 77.1 | 96.7 | |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 76.4 | 95.5 | |
| R(2+1)D (Tran et al., 2018) | V,F | K400 | R(2+1)D-34x2 | 78.7 | 97.3 | |
| Omni (Duan et al., 2020) | V,I | K400+OS | Slow-8x8-R101 | 79.0 | 97.3 | |
| I3D (Carreira & Zisserman, 2017) | V,F,I | K400+IM | I3Dx2 | 80.7 | 98.0 | |
| Omni (Duan et al., 2020) | V,F,I | K400+OS | Slow-8x8-R101x2 | √ | 83.8 | 98.6 |
| Ours (Avg-pooling) | V,I | IG65M+IM | R(2+1)D-34+R152 | X | 73.7 | 64.3 |
| Ours (T-pooling) | V,I | HM+IG65M+IM | R(2+1)D-34+R152 | X | 81.3 | 98.0 |
| Text→Video | Video →Text | |||||||
| R@1↑ | R@5个 | R@10个 | MdR↓ | R@1↑ | R@5↑ | R@10个 | MdR | |
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 | 0.02 | 0.1 | 1.02 | 2100.5 |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 一 | |||
| VSE++ (Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 一 | 一 | 一 | |
| Dual (Dong et al., 2019) | 31.1 | 67.4 | 78.9 | 3.0 | ||||
| HGR (Chen et al.,2020b) | 35.1 | 73.5 | 83.5 | 2.0 | ||||
| Ours | 44.9±0.2 82.1±0.2 | 89.7±0.2 | 1.0 | 58.4±0.1 84.4±0.2 91.0±0.3 | 1.0 | |||
| Feature source | R@1↑ R@5 | 个 MdR↓ |
| R-152 | 20.8 | 46.2 6.0 |
| R(2+1)D-34 | 23.7 | 53.2 4.0 |
| R(2+1)D-34 +R-152 | 27.2 | 55.2 3.0 |
| Temporal reduction R@1 ↑ R@5↑MdR↓ | ||
| Max | 21.8 | 49.5 8.0 |
| Mean | 22.5 | 51.3 6.0 |
| Multi-Head Attn | 27.2 55.2 | 3.0 |
| Text Encoder | R@1↑R@5↑ MdR↓ | ||
| W2V (GloVe) | 22.1 | 49.8 | 6.0 |
| T5-Small | 24.5 | 51.2 | 3.0 |
| T5-Base | 27.2 | 55.2 | 3.0 |
| Text Encoder Text Decoder R@1 ↑ R@5 ↑ MdR↓ | ||||
| T5-Base | T5-Small | 26.2 | 54.2 | 3.0 |
| T5-Base | T5-Base | 27.2 | 55.2 | 3.0 |
| Contrastive | R@1↑ R@5↑ | MdR↓ |
| InfoNCE (inter+intra) | 10.7 | 28.5 15.0 |
| InfoNCE (inter) | 10.8 | 29.0 14.5 |
| Triplet (inter+intra) | 26.8 | 56.2 3.0 |
| Triplet (inter) | 27.2 | 55.2 3.0 |
| Batch-size | Memory bank | ||||||||
| Size | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 2k | 8k |
| R@1/5 18.5/45.6 20.7/49.9 25.2/54.6 27.2/55.2 28.0/56.1 26.9/55.0 25.3/53.5 | 26.8/54.7 26.2/52.7 |
| R@1↑ | R@5↑ MdR↓ | ||
| None | 25.9 | 53.0 | 4.0 4.0 3.0 |
| Identity | 26.4 | 51.9 | |
| Full | 25.8 | 53.9 | |
| Hybrid | 26.0 | 54.8 | 3.0 |
| Cross | 27.2 | 55.2 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑R@5↑ R@10↑MdR↓ | R@1↑ R@5↑ R@10↑MdR↓ | |||||||
| Random Baseline | 0.1 | 0.5 | 1.0 | 500.0 | 0.1 | 0.5 | 1.0 | 500.0 |
| JSFusion (Yu et al., 2018) | 10.2 | 31.2 | 43.2 | 13.0 | 1 | 1 | 1 | 1 |
| HT100M (Miech et al., 2019) | 12.1 | 35.0 | 48.0 | 12.0 | 1 | 一 | 一 | 一 |
| JPoSE(Wray et al., 2019) | 14.3 | 38.1 | 53.0 | 9.0 | 16.4 | 41.3 | 54.4 | 8.7 |
| CE (Liu et al., 2019) | 20.9 | 48.8 | 62.4 | 6.0 | 20.6 | 50.3 | 64.0 | 5.3 |
| MMT(Gabeur et al., 2020) | 24.6 | 54.0 | 67.1 | 4.0 | 24.4 | 56.0 | 67.8 | 4.0 |
| Ours | 27.4 | 56.3 | 67.7 | 3.0 | 26.6 | 55.1 | 67.5 | 3.0 |
| VidTranslate (Korbar etal., 2020) | 14.7 | 1 | 52.8 | 1 | 一 | 1 | ||
| HT100M (Miech et al.,2019) | 14.9 | 40.2 | 52.8 | 9.0 | 16.8 | 41.7 | 55.1 | 8.0 |
| NoiseEstimation (Amrani et al., 2020) | 17.4 | 41.6 | 53.6 | 8.0 | 1 | 一 | 1 | 1 |
| UniVL (Luo et al.,2020) | 21.2 | 49.6 | 63.1 | 6.0 | 一 | 一 | 一 | 一 |
| AVLnet (Rouditchenko et al., 2020) | 27.1 | 55.6 | 66.6 | 4.0 | 28.5 | 54.6 | 65.2 | 4.0 |
| MMT(Gabeur et al., 2020) | 26.6 | 57.1 | 69.6 | 4.0 | 27.0 | 57.5 | 69.7 | 3.7 |
| Ours-pretrained | 30.1 | 58.5 | 69.3 | 3.0 | 28.5 | 58.6 | 71.6 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@10↑ MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||||
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 0.02 | 0.1 | 1.02 | 2100.5 | |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 1 | 1 | 1 | 1 |
| VSE++(Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 1 | 一 | 1 | 一 |
| Dual (Dong et al.,2019) | 31.1 | 67.4 | 78.9 | 3.0 | 1 | 1 | 1 | 1 |
| HGR(Chen et al., 2020b) | 35.1 | 73.5 | 83.5 | 2.0 | 一 | 一 | 一 | |
| Ours | 44.6 | 81.8 | 89.5 | 1.0 | 58.1 | 83.8 | 90.9 | 1.0 |
| Ours-pretrained | 45.9 | 82.4 | 90.4 | 1.0 | 61.2 | 85.2 | 91.8 | 1.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@50↑ MdR↓ R@1↑ R@5 ↑ R@50↑ MdR↓ | ||||||||
| Random Baseline | 0.02 | 0.1 | 1.02 | 2458 | 0.02 | 0.1 | 1.02 | 2458 |
| FSE(Zhang et al., 2018) | 18.2 | 44.8 | 89.1 | 7.0 | 16.7 | 43.1 | 88.4 | 7.0 |
| CE (Liu et al., 2019) | 18.2 | 47.7 | 91.4 | 6.0 | 17.7 | 46.6 | 90.9 | 6.0 |
| HSE (Zhang et al.,2018) | 20.5 | 49.3 | 1 | 1 | 18.7 | 48.1 | 1 | 1 |
| MMT (Gabeur et al.,2020) | 22.7 | 54.2 | 93.2 | 5.0 | 22.9 | 54.8 | 93.1 | 4.3 |
| Ours | 26.8 | 58.1 | 93.5 | 3.0 | 25.5 | 57.3 | 93.5 | 3.0 |
| MMT-pretrained (Gabeur et al., 2020) | 28.7 | 61.4 | 94.5 | 3.3 | 28.9 | 61.1 | 94.3 | 4.0 |
| Ours-pretrained | 29.2 | 61.6 | 94.7 | 3.0 | 28.7 | 60.8 | 94.8 | 2.0 |
| Text→Video | Video→Text | |||||
| R@1↑ R@5↑ R@10↑MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||
| VSE (Kiros et al.,2014) | 12.3 30.1 | 42.3 | 14.0 | 1 | ||
| VSE++ (Faghri et al., 2018) | 15.4 39.6 | 53.0 | 9.0 | 一 | ||
| Multi. Cues (Mithun et al.,2018) | 20.3 47.8 | 61.1 | 6.0 | 1 | 1 | 1 一 |
| CE (Liu et al., 2019) | 19.8 49.0 | 63.8 | 6.0 | 一 | ||
| Ours | 23.0 52.8 | 65.8 | 5.0 | 27.3 | 50.7 | 60.8 5.0 |
| Ours-pretrained | 28.4 60.0 | 72.9 | 4.0 | 34.7 | 59.9 | 70.0 3.0 |
| Captioning | ||||
| BLUE4 | METEOR | Rogue-L | CIDEr | |
| VidTranslate (Korbar et al., 2020) | 41.7 | 28.5 | 一 | 一 |
| POS+VCT (Hou et al., 2019) | 42.3 | 29.7 | 62.8 | 49.1 |
| ORG (Zhang et al., 2020) | 43.6 | 28.8 | 62.1 | 50.9 |
| Ours, MSR-VTT only | 39.7 | 28.3 | 60.5 | 46.5 |
| Ours,HT100M + MSR-VTT | 38.9 | 28.2 | 59.8 | 48.6 |
| Captioning | ||||
| Blue@4 METEORI | Rogue-L CIDEr | |||
| Shared Enc-Dec (Wang et al., 2019) | 28.4 | 21.7 | 47.0 | 45.1 |
| ORG (Zhang et al., 2020) | 32.1 | 22.2 | 48.9 | 49.7 |
| Ours, ,VATEX only | 32.8 | 24.4 | 49.1 | 51.2 |
| Ours,HT100M + Vatex | 32.5 | 24.1 | 48.9 | 50.5 |
| Captioning | ||||
| Blue@4 | METEOR | Rogue-L | CIDEr | |
| DENSE (Krishna et al.,2017) | 1.6 | 8.9 | ||
| DVC-D-A (Li et al., 2018) | 1.7 | 9.3 | ||
| Bi-LSTM+TempoAttn (Zhou et al., 2018b) | 2.1 | 10.0 | 一 | |
| Masked Transformer (Zhou et al.,2018b) | 2.8 | 11.1 | 1 | 1 |
| Ours, ActivityNet only | 1.5 | 6.9 | 17.8 | 3.2 |
| Ours,HT100M + ActivityNet | 1.4 | 6.9 | 17.5 | 3.1 |
| Text→Video | Video→Text | |||||||
| R@1↑ | R@5↑ | R@10↑ | MdR | R@1↑ | R@5↑ | R@10个 | MdR | |
| Zero-Shot | ||||||||
| ActivityNet | 0.06 | 0.2 | 0.5 | 1907.0 | 0.0 | 0.2 | 0.3 | 2238.0 |
| VATEX | 0.07 | 0.4 | 0.7 | 682.0 | 0.07 | 0.4 | 0.9 | 697 |
| MSVD | 8.9 | 26.0 | 37.9 | 18.0 | 21.4 | 46.2 | 57.7 | 6.0 |
| MSR-VTT | 8.7 | 23.0 | 31.1 | 31.0 | 12.7 | 27.5 | 36.2 | 24.0 |
| Method | Mod | Dataset | Model | FT? | H51 | U101 |
| Self-Supervised Pre-training | ||||||
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 53.1 | 82.7 | |
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 61.0 | 91.3 | |
| MMV(Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | 67.1 | 91.8 | |
| ELo (Piergiovanni et al.,2020) | V,F,A | YT8M | R(2+1)D-50x3 | x√xν | 67.4 | 93.8 |
| XDC (Alwassel et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 68.9 | 95.5 |
| GDT (Patrick et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 72.8 | 95.2 |
| MMV (Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | √ | 75.0 | 95.2 |
| Supervised Pre-training | ||||||
| P3D (Qiu et al., 2017) | V,I | S1M+IM | P3D | 88.6 | ||
| TSN (Wang et al.,2018) | V,I | IM | TSN | ? | 69.4 | 94.2 |
| I3D (Carreira & Zisserman,2017) | V,I | K400+IM | I3D | √ | 74.8 | 95.6 |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 74.5 | 96.8 | |
| S3D-G (Xie et al., 2018) | V,I | K400+IM | S3D-G | 75.9 | 96.8 | |
| I3D(Carreira & Zisserman,2017) | V,I | K400+IM | I3D | 77.1 | 96.7 | |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 76.4 | 95.5 | |
| R(2+1)D (Tran et al., 2018) | V,F | K400 | R(2+1)D-34x2 | 78.7 | 97.3 | |
| Omni (Duan et al., 2020) | V,I | K400+OS | Slow-8x8-R101 | 79.0 | 97.3 | |
| I3D (Carreira & Zisserman, 2017) | V,F,I | K400+IM | I3Dx2 | 80.7 | 98.0 | |
| Omni (Duan et al., 2020) | V,F,I | K400+OS | Slow-8x8-R101x2 | √ | 83.8 | 98.6 |
| Ours (Avg-pooling) | V,I | IG65M+IM | R(2+1)D-34+R152 | X | 73.7 | 64.3 |
| Ours (T-pooling) | V,I | HM+IG65M+IM | R(2+1)D-34+R152 | X | 81.3 | 98.0 |
| Text→Video | Video →Text | |||||||
| R@1↑ | R@5个 | R@10个 | MdR↓ | R@1↑ | R@5↑ | R@10个 | MdR | |
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 | 0.02 | 0.1 | 1.02 | 2100.5 |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 一 | |||
| VSE++ (Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 一 | 一 | 一 | |
| Dual (Dong et al., 2019) | 31.1 | 67.4 | 78.9 | 3.0 | ||||
| HGR (Chen et al.,2020b) | 35.1 | 73.5 | 83.5 | 2.0 | ||||
| Ours | 44.9±0.2 82.1±0.2 | 89.7±0.2 | 1.0 | 58.4±0.1 84.4±0.2 91.0±0.3 | 1.0 |
| Feature source | R@1↑ R@5 | 个 MdR↓ |
| R-152 | 20.8 | 46.2 6.0 |
| R(2+1)D-34 | 23.7 | 53.2 4.0 |
| R(2+1)D-34 +R-152 | 27.2 | 55.2 3.0 |
| Temporal reduction R@1 ↑ R@5↑MdR↓ | ||
| Max | 21.8 | 49.5 8.0 |
| Mean | 22.5 | 51.3 6.0 |
| Multi-Head Attn | 27.2 55.2 | 3.0 |
| Text Encoder | R@1↑R@5↑ MdR↓ | ||
| W2V (GloVe) | 22.1 | 49.8 | 6.0 |
| T5-Small | 24.5 | 51.2 | 3.0 |
| T5-Base | 27.2 | 55.2 | 3.0 |
| Text Encoder Text Decoder R@1 ↑ R@5 ↑ MdR↓ | ||||
| T5-Base | T5-Small | 26.2 | 54.2 | 3.0 |
| T5-Base | T5-Base | 27.2 | 55.2 | 3.0 |
| Contrastive | R@1↑ R@5↑ | MdR↓ |
| InfoNCE (inter+intra) | 10.7 | 28.5 15.0 |
| InfoNCE (inter) | 10.8 | 29.0 14.5 |
| Triplet (inter+intra) | 26.8 | 56.2 3.0 |
| Triplet (inter) | 27.2 | 55.2 3.0 |
| Batch-size | Memory bank | ||||||||
| Size | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 2k | 8k |
| R@1/5 18.5/45.6 20.7/49.9 25.2/54.6 27.2/55.2 28.0/56.1 26.9/55.0 25.3/53.5 | 26.8/54.7 26.2/52.7 |
| R@1↑ | R@5↑ MdR↓ | ||
| None | 25.9 | 53.0 | 4.0 4.0 3.0 |
| Identity | 26.4 | 51.9 | |
| Full | 25.8 | 53.9 | |
| Hybrid | 26.0 | 54.8 | 3.0 |
| Cross | 27.2 | 55.2 | 3.0 |
| Feature source | R@1↑ R@5 | 个 MdR↓ |
| R-152 | 20.8 | 46.2 6.0 |
| R(2+1)D-34 | 23.7 | 53.2 4.0 |
| R(2+1)D-34 +R-152 | 27.2 | 55.2 3.0 |
| Temporal reduction R@1 ↑ R@5↑MdR↓ | ||
| Max | 21.8 | 49.5 8.0 |
| Mean | 22.5 | 51.3 6.0 |
| Multi-Head Attn | 27.2 55.2 | 3.0 |
| Text Encoder | R@1↑R@5↑ MdR↓ | ||
| W2V (GloVe) | 22.1 | 49.8 | 6.0 |
| T5-Small | 24.5 | 51.2 | 3.0 |
| T5-Base | 27.2 | 55.2 | 3.0 |
| Text Encoder Text Decoder R@1 ↑ R@5 ↑ MdR↓ | ||||
| T5-Base | T5-Small | 26.2 | 54.2 | 3.0 |
| T5-Base | T5-Base | 27.2 | 55.2 | 3.0 |
| Contrastive | R@1↑ R@5↑ | MdR↓ |
| InfoNCE (inter+intra) | 10.7 | 28.5 15.0 |
| InfoNCE (inter) | 10.8 | 29.0 14.5 |
| Triplet (inter+intra) | 26.8 | 56.2 3.0 |
| Triplet (inter) | 27.2 | 55.2 3.0 |
| Batch-size | Memory bank | ||||||||
| Size | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 2k | 8k |
| R@1/5 18.5/45.6 20.7/49.9 25.2/54.6 27.2/55.2 28.0/56.1 26.9/55.0 25.3/53.5 | 26.8/54.7 26.2/52.7 |
| R@1↑ | R@5↑ MdR↓ | ||
| None | 25.9 | 53.0 | 4.0 4.0 3.0 |
| Identity | 26.4 | 51.9 | |
| Full | 25.8 | 53.9 | |
| Hybrid | 26.0 | 54.8 | 3.0 |
| Cross | 27.2 | 55.2 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑R@5↑ R@10↑MdR↓ | R@1↑ R@5↑ R@10↑MdR↓ | |||||||
| Random Baseline | 0.1 | 0.5 | 1.0 | 500.0 | 0.1 | 0.5 | 1.0 | 500.0 |
| JSFusion (Yu et al., 2018) | 10.2 | 31.2 | 43.2 | 13.0 | 1 | 1 | 1 | 1 |
| HT100M (Miech et al., 2019) | 12.1 | 35.0 | 48.0 | 12.0 | 1 | 一 | 一 | 一 |
| JPoSE(Wray et al., 2019) | 14.3 | 38.1 | 53.0 | 9.0 | 16.4 | 41.3 | 54.4 | 8.7 |
| CE (Liu et al., 2019) | 20.9 | 48.8 | 62.4 | 6.0 | 20.6 | 50.3 | 64.0 | 5.3 |
| MMT(Gabeur et al., 2020) | 24.6 | 54.0 | 67.1 | 4.0 | 24.4 | 56.0 | 67.8 | 4.0 |
| Ours | 27.4 | 56.3 | 67.7 | 3.0 | 26.6 | 55.1 | 67.5 | 3.0 |
| VidTranslate (Korbar etal., 2020) | 14.7 | 1 | 52.8 | 1 | 一 | 1 | ||
| HT100M (Miech et al.,2019) | 14.9 | 40.2 | 52.8 | 9.0 | 16.8 | 41.7 | 55.1 | 8.0 |
| NoiseEstimation (Amrani et al., 2020) | 17.4 | 41.6 | 53.6 | 8.0 | 1 | 一 | 1 | 1 |
| UniVL (Luo et al.,2020) | 21.2 | 49.6 | 63.1 | 6.0 | 一 | 一 | 一 | 一 |
| AVLnet (Rouditchenko et al., 2020) | 27.1 | 55.6 | 66.6 | 4.0 | 28.5 | 54.6 | 65.2 | 4.0 |
| MMT(Gabeur et al., 2020) | 26.6 | 57.1 | 69.6 | 4.0 | 27.0 | 57.5 | 69.7 | 3.7 |
| Ours-pretrained | 30.1 | 58.5 | 69.3 | 3.0 | 28.5 | 58.6 | 71.6 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑R@5↑ R@10↑MdR↓ | R@1↑ R@5↑ R@10↑MdR↓ | |||||||
| Random Baseline | 0.1 | 0.5 | 1.0 | 500.0 | 0.1 | 0.5 | 1.0 | 500.0 |
| JSFusion (Yu et al., 2018) | 10.2 | 31.2 | 43.2 | 13.0 | 1 | 1 | 1 | 1 |
| HT100M (Miech et al., 2019) | 12.1 | 35.0 | 48.0 | 12.0 | 1 | 一 | 一 | 一 |
| JPoSE(Wray et al., 2019) | 14.3 | 38.1 | 53.0 | 9.0 | 16.4 | 41.3 | 54.4 | 8.7 |
| CE (Liu et al., 2019) | 20.9 | 48.8 | 62.4 | 6.0 | 20.6 | 50.3 | 64.0 | 5.3 |
| MMT(Gabeur et al., 2020) | 24.6 | 54.0 | 67.1 | 4.0 | 24.4 | 56.0 | 67.8 | 4.0 |
| Ours | 27.4 | 56.3 | 67.7 | 3.0 | 26.6 | 55.1 | 67.5 | 3.0 |
| VidTranslate (Korbar etal., 2020) | 14.7 | 1 | 52.8 | 1 | 一 | 1 | ||
| HT100M (Miech et al.,2019) | 14.9 | 40.2 | 52.8 | 9.0 | 16.8 | 41.7 | 55.1 | 8.0 |
| NoiseEstimation (Amrani et al., 2020) | 17.4 | 41.6 | 53.6 | 8.0 | 1 | 一 | 1 | 1 |
| UniVL (Luo et al.,2020) | 21.2 | 49.6 | 63.1 | 6.0 | 一 | 一 | 一 | 一 |
| AVLnet (Rouditchenko et al., 2020) | 27.1 | 55.6 | 66.6 | 4.0 | 28.5 | 54.6 | 65.2 | 4.0 |
| MMT(Gabeur et al., 2020) | 26.6 | 57.1 | 69.6 | 4.0 | 27.0 | 57.5 | 69.7 | 3.7 |
| Ours-pretrained | 30.1 | 58.5 | 69.3 | 3.0 | 28.5 | 58.6 | 71.6 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@10↑ MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||||
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 0.02 | 0.1 | 1.02 | 2100.5 | |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 1 | 1 | 1 | 1 |
| VSE++(Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 1 | 一 | 1 | 一 |
| Dual (Dong et al.,2019) | 31.1 | 67.4 | 78.9 | 3.0 | 1 | 1 | 1 | 1 |
| HGR(Chen et al., 2020b) | 35.1 | 73.5 | 83.5 | 2.0 | 一 | 一 | 一 | |
| Ours | 44.6 | 81.8 | 89.5 | 1.0 | 58.1 | 83.8 | 90.9 | 1.0 |
| Ours-pretrained | 45.9 | 82.4 | 90.4 | 1.0 | 61.2 | 85.2 | 91.8 | 1.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@50↑ MdR↓ R@1↑ R@5 ↑ R@50↑ MdR↓ | ||||||||
| Random Baseline | 0.02 | 0.1 | 1.02 | 2458 | 0.02 | 0.1 | 1.02 | 2458 |
| FSE(Zhang et al., 2018) | 18.2 | 44.8 | 89.1 | 7.0 | 16.7 | 43.1 | 88.4 | 7.0 |
| CE (Liu et al., 2019) | 18.2 | 47.7 | 91.4 | 6.0 | 17.7 | 46.6 | 90.9 | 6.0 |
| HSE (Zhang et al.,2018) | 20.5 | 49.3 | 1 | 1 | 18.7 | 48.1 | 1 | 1 |
| MMT (Gabeur et al.,2020) | 22.7 | 54.2 | 93.2 | 5.0 | 22.9 | 54.8 | 93.1 | 4.3 |
| Ours | 26.8 | 58.1 | 93.5 | 3.0 | 25.5 | 57.3 | 93.5 | 3.0 |
| MMT-pretrained (Gabeur et al., 2020) | 28.7 | 61.4 | 94.5 | 3.3 | 28.9 | 61.1 | 94.3 | 4.0 |
| Ours-pretrained | 29.2 | 61.6 | 94.7 | 3.0 | 28.7 | 60.8 | 94.8 | 2.0 |
| Text→Video | Video→Text | |||||
| R@1↑ R@5↑ R@10↑MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||
| VSE (Kiros et al.,2014) | 12.3 30.1 | 42.3 | 14.0 | 1 | ||
| VSE++ (Faghri et al., 2018) | 15.4 39.6 | 53.0 | 9.0 | 一 | ||
| Multi. Cues (Mithun et al.,2018) | 20.3 47.8 | 61.1 | 6.0 | 1 | 1 | 1 一 |
| CE (Liu et al., 2019) | 19.8 49.0 | 63.8 | 6.0 | 一 | ||
| Ours | 23.0 52.8 | 65.8 | 5.0 | 27.3 | 50.7 | 60.8 5.0 |
| Ours-pretrained | 28.4 60.0 | 72.9 | 4.0 | 34.7 | 59.9 | 70.0 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@10↑ MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||||
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 0.02 | 0.1 | 1.02 | 2100.5 | |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 1 | 1 | 1 | 1 |
| VSE++(Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 1 | 一 | 1 | 一 |
| Dual (Dong et al.,2019) | 31.1 | 67.4 | 78.9 | 3.0 | 1 | 1 | 1 | 1 |
| HGR(Chen et al., 2020b) | 35.1 | 73.5 | 83.5 | 2.0 | 一 | 一 | 一 | |
| Ours | 44.6 | 81.8 | 89.5 | 1.0 | 58.1 | 83.8 | 90.9 | 1.0 |
| Ours-pretrained | 45.9 | 82.4 | 90.4 | 1.0 | 61.2 | 85.2 | 91.8 | 1.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@50↑ MdR↓ R@1↑ R@5 ↑ R@50↑ MdR↓ | ||||||||
| Random Baseline | 0.02 | 0.1 | 1.02 | 2458 | 0.02 | 0.1 | 1.02 | 2458 |
| FSE(Zhang et al., 2018) | 18.2 | 44.8 | 89.1 | 7.0 | 16.7 | 43.1 | 88.4 | 7.0 |
| CE (Liu et al., 2019) | 18.2 | 47.7 | 91.4 | 6.0 | 17.7 | 46.6 | 90.9 | 6.0 |
| HSE (Zhang et al.,2018) | 20.5 | 49.3 | 1 | 1 | 18.7 | 48.1 | 1 | 1 |
| MMT (Gabeur et al.,2020) | 22.7 | 54.2 | 93.2 | 5.0 | 22.9 | 54.8 | 93.1 | 4.3 |
| Ours | 26.8 | 58.1 | 93.5 | 3.0 | 25.5 | 57.3 | 93.5 | 3.0 |
| MMT-pretrained (Gabeur et al., 2020) | 28.7 | 61.4 | 94.5 | 3.3 | 28.9 | 61.1 | 94.3 | 4.0 |
| Ours-pretrained | 29.2 | 61.6 | 94.7 | 3.0 | 28.7 | 60.8 | 94.8 | 2.0 |
| Text→Video | Video→Text | |||||
| R@1↑ R@5↑ R@10↑MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||
| VSE (Kiros et al.,2014) | 12.3 30.1 | 42.3 | 14.0 | 1 | ||
| VSE++ (Faghri et al., 2018) | 15.4 39.6 | 53.0 | 9.0 | 一 | ||
| Multi. Cues (Mithun et al.,2018) | 20.3 47.8 | 61.1 | 6.0 | 1 | 1 | 1 一 |
| CE (Liu et al., 2019) | 19.8 49.0 | 63.8 | 6.0 | 一 | ||
| Ours | 23.0 52.8 | 65.8 | 5.0 | 27.3 | 50.7 | 60.8 5.0 |
| Ours-pretrained | 28.4 60.0 | 72.9 | 4.0 | 34.7 | 59.9 | 70.0 3.0 |
| Captioning | ||||
| BLUE4 | METEOR | Rogue-L | CIDEr | |
| VidTranslate (Korbar et al., 2020) | 41.7 | 28.5 | 一 | 一 |
| POS+VCT (Hou et al., 2019) | 42.3 | 29.7 | 62.8 | 49.1 |
| ORG (Zhang et al., 2020) | 43.6 | 28.8 | 62.1 | 50.9 |
| Ours, MSR-VTT only | 39.7 | 28.3 | 60.5 | 46.5 |
| Ours,HT100M + MSR-VTT | 38.9 | 28.2 | 59.8 | 48.6 |
| Captioning | ||||
| Blue@4 METEORI | Rogue-L CIDEr | |||
| Shared Enc-Dec (Wang et al., 2019) | 28.4 | 21.7 | 47.0 | 45.1 |
| ORG (Zhang et al., 2020) | 32.1 | 22.2 | 48.9 | 49.7 |
| Ours, ,VATEX only | 32.8 | 24.4 | 49.1 | 51.2 |
| Ours,HT100M + Vatex | 32.5 | 24.1 | 48.9 | 50.5 |
| Captioning | ||||
| BLUE4 | METEOR | Rogue-L | CIDEr | |
| VidTranslate (Korbar et al., 2020) | 41.7 | 28.5 | 一 | 一 |
| POS+VCT (Hou et al., 2019) | 42.3 | 29.7 | 62.8 | 49.1 |
| ORG (Zhang et al., 2020) | 43.6 | 28.8 | 62.1 | 50.9 |
| Ours, MSR-VTT only | 39.7 | 28.3 | 60.5 | 46.5 |
| Ours,HT100M + MSR-VTT | 38.9 | 28.2 | 59.8 | 48.6 |
| Captioning | ||||
| Blue@4 METEORI | Rogue-L CIDEr | |||
| Shared Enc-Dec (Wang et al., 2019) | 28.4 | 21.7 | 47.0 | 45.1 |
| ORG (Zhang et al., 2020) | 32.1 | 22.2 | 48.9 | 49.7 |
| Ours, ,VATEX only | 32.8 | 24.4 | 49.1 | 51.2 |
| Ours,HT100M + Vatex | 32.5 | 24.1 | 48.9 | 50.5 |
| Captioning | ||||
| Blue@4 | METEOR | Rogue-L | CIDEr | |
| DENSE (Krishna et al.,2017) | 1.6 | 8.9 | ||
| DVC-D-A (Li et al., 2018) | 1.7 | 9.3 | ||
| Bi-LSTM+TempoAttn (Zhou et al., 2018b) | 2.1 | 10.0 | 一 | |
| Masked Transformer (Zhou et al.,2018b) | 2.8 | 11.1 | 1 | 1 |
| Ours, ActivityNet only | 1.5 | 6.9 | 17.8 | 3.2 |
| Ours,HT100M + ActivityNet | 1.4 | 6.9 | 17.5 | 3.1 |
| Text→Video | Video→Text | |||||||
| R@1↑ | R@5↑ | R@10↑ | MdR | R@1↑ | R@5↑ | R@10个 | MdR | |
| Zero-Shot | ||||||||
| ActivityNet | 0.06 | 0.2 | 0.5 | 1907.0 | 0.0 | 0.2 | 0.3 | 2238.0 |
| VATEX | 0.07 | 0.4 | 0.7 | 682.0 | 0.07 | 0.4 | 0.9 | 697 |
| MSVD | 8.9 | 26.0 | 37.9 | 18.0 | 21.4 | 46.2 | 57.7 | 6.0 |
| MSR-VTT | 8.7 | 23.0 | 31.1 | 31.0 | 12.7 | 27.5 | 36.2 | 24.0 |
| Captioning | ||||
| Blue@4 | METEOR | Rogue-L | CIDEr | |
| DENSE (Krishna et al.,2017) | 1.6 | 8.9 | ||
| DVC-D-A (Li et al., 2018) | 1.7 | 9.3 | ||
| Bi-LSTM+TempoAttn (Zhou et al., 2018b) | 2.1 | 10.0 | 一 | |
| Masked Transformer (Zhou et al.,2018b) | 2.8 | 11.1 | 1 | 1 |
| Ours, ActivityNet only | 1.5 | 6.9 | 17.8 | 3.2 |
| Ours,HT100M + ActivityNet | 1.4 | 6.9 | 17.5 | 3.1 |
| Text→Video | Video→Text | |||||||
| R@1↑ | R@5↑ | R@10↑ | MdR | R@1↑ | R@5↑ | R@10个 | MdR | |
| Zero-Shot | ||||||||
| ActivityNet | 0.06 | 0.2 | 0.5 | 1907.0 | 0.0 | 0.2 | 0.3 | 2238.0 |
| VATEX | 0.07 | 0.4 | 0.7 | 682.0 | 0.07 | 0.4 | 0.9 | 697 |
| MSVD | 8.9 | 26.0 | 37.9 | 18.0 | 21.4 | 46.2 | 57.7 | 6.0 |
| MSR-VTT | 8.7 | 23.0 | 31.1 | 31.0 | 12.7 | 27.5 | 36.2 | 24.0 |
| Method | Mod | Dataset | Model | FT? | H51 | U101 |
| Self-Supervised Pre-training | ||||||
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 53.1 | 82.7 | |
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 61.0 | 91.3 | |
| MMV(Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | 67.1 | 91.8 | |
| ELo (Piergiovanni et al.,2020) | V,F,A | YT8M | R(2+1)D-50x3 | x√xν | 67.4 | 93.8 |
| XDC (Alwassel et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 68.9 | 95.5 |
| GDT (Patrick et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 72.8 | 95.2 |
| MMV (Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | √ | 75.0 | 95.2 |
| Supervised Pre-training | ||||||
| P3D (Qiu et al., 2017) | V,I | S1M+IM | P3D | 88.6 | ||
| TSN (Wang et al.,2018) | V,I | IM | TSN | ? | 69.4 | 94.2 |
| I3D (Carreira & Zisserman,2017) | V,I | K400+IM | I3D | √ | 74.8 | 95.6 |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 74.5 | 96.8 | |
| S3D-G (Xie et al., 2018) | V,I | K400+IM | S3D-G | 75.9 | 96.8 | |
| I3D(Carreira & Zisserman,2017) | V,I | K400+IM | I3D | 77.1 | 96.7 | |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 76.4 | 95.5 | |
| R(2+1)D (Tran et al., 2018) | V,F | K400 | R(2+1)D-34x2 | 78.7 | 97.3 | |
| Omni (Duan et al., 2020) | V,I | K400+OS | Slow-8x8-R101 | 79.0 | 97.3 | |
| I3D (Carreira & Zisserman, 2017) | V,F,I | K400+IM | I3Dx2 | 80.7 | 98.0 | |
| Omni (Duan et al., 2020) | V,F,I | K400+OS | Slow-8x8-R101x2 | √ | 83.8 | 98.6 |
| Ours (Avg-pooling) | V,I | IG65M+IM | R(2+1)D-34+R152 | X | 73.7 | 64.3 |
| Ours (T-pooling) | V,I | HM+IG65M+IM | R(2+1)D-34+R152 | X | 81.3 | 98.0 |
| Text→Video | Video →Text | |||||||
| R@1↑ | R@5个 | R@10个 | MdR↓ | R@1↑ | R@5↑ | R@10个 | MdR | |
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 | 0.02 | 0.1 | 1.02 | 2100.5 |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 一 | |||
| VSE++ (Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 一 | 一 | 一 | |
| Dual (Dong et al., 2019) | 31.1 | 67.4 | 78.9 | 3.0 | ||||
| HGR (Chen et al.,2020b) | 35.1 | 73.5 | 83.5 | 2.0 | ||||
| Ours | 44.9±0.2 82.1±0.2 | 89.7±0.2 | 1.0 | 58.4±0.1 84.4±0.2 91.0±0.3 | 1.0 |
| Method | Mod | Dataset | Model | FT? | H51 | U101 |
| Self-Supervised Pre-training | ||||||
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 53.1 | 82.7 | |
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 61.0 | 91.3 | |
| MMV(Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | 67.1 | 91.8 | |
| ELo (Piergiovanni et al.,2020) | V,F,A | YT8M | R(2+1)D-50x3 | x√xν | 67.4 | 93.8 |
| XDC (Alwassel et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 68.9 | 95.5 |
| GDT (Patrick et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 72.8 | 95.2 |
| MMV (Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | √ | 75.0 | 95.2 |
| Supervised Pre-training | ||||||
| P3D (Qiu et al., 2017) | V,I | S1M+IM | P3D | 88.6 | ||
| TSN (Wang et al.,2018) | V,I | IM | TSN | ? | 69.4 | 94.2 |
| I3D (Carreira & Zisserman,2017) | V,I | K400+IM | I3D | √ | 74.8 | 95.6 |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 74.5 | 96.8 | |
| S3D-G (Xie et al., 2018) | V,I | K400+IM | S3D-G | 75.9 | 96.8 | |
| I3D(Carreira & Zisserman,2017) | V,I | K400+IM | I3D | 77.1 | 96.7 | |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 76.4 | 95.5 | |
| R(2+1)D (Tran et al., 2018) | V,F | K400 | R(2+1)D-34x2 | 78.7 | 97.3 | |
| Omni (Duan et al., 2020) | V,I | K400+OS | Slow-8x8-R101 | 79.0 | 97.3 | |
| I3D (Carreira & Zisserman, 2017) | V,F,I | K400+IM | I3Dx2 | 80.7 | 98.0 | |
| Omni (Duan et al., 2020) | V,F,I | K400+OS | Slow-8x8-R101x2 | √ | 83.8 | 98.6 |
| Ours (Avg-pooling) | V,I | IG65M+IM | R(2+1)D-34+R152 | X | 73.7 | 64.3 |
| Ours (T-pooling) | V,I | HM+IG65M+IM | R(2+1)D-34+R152 | X | 81.3 | 98.0 |
| Text→Video | Video →Text | |||||||
| R@1↑ | R@5个 | R@10个 | MdR↓ | R@1↑ | R@5↑ | R@10个 | MdR | |
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 | 0.02 | 0.1 | 1.02 | 2100.5 |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 一 | |||
| VSE++ (Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 一 | 一 | 一 | |
| Dual (Dong et al., 2019) | 31.1 | 67.4 | 78.9 | 3.0 | ||||
| HGR (Chen et al.,2020b) | 35.1 | 73.5 | 83.5 | 2.0 | ||||
| Ours | 44.9±0.2 82.1±0.2 | 89.7±0.2 | 1.0 | 58.4±0.1 84.4±0.2 91.0±0.3 | 1.0 |
| Batch-size | Memory bank | ||||||||
| Size | 8 | 16 | 32 | 64 | 128 | 256 | 512 | 2k | 8k |
| R@1/5 18.5/45.6 20.7/49.9 25.2/54.6 27.2/55.2 28.0/56.1 26.9/55.0 25.3/53.5 | 26.8/54.7 26.2/52.7 |
| R@1↑ | R@5↑ MdR↓ | ||
| None | 25.9 | 53.0 | 4.0 4.0 3.0 |
| Identity | 26.4 | 51.9 | |
| Full | 25.8 | 53.9 | |
| Hybrid | 26.0 | 54.8 | 3.0 |
| Cross | 27.2 | 55.2 | 3.0 |
| Feature source | R@1↑ R@5 | 个 MdR↓ |
| R-152 | 20.8 | 46.2 6.0 |
| R(2+1)D-34 | 23.7 | 53.2 4.0 |
| R(2+1)D-34 +R-152 | 27.2 | 55.2 3.0 |
| Temporal reduction R@1 ↑ R@5↑MdR↓ | ||
| Max | 21.8 | 49.5 8.0 |
| Mean | 22.5 | 51.3 6.0 |
| Multi-Head Attn | 27.2 55.2 | 3.0 |
| Contrastive | R@1↑ R@5↑ | MdR↓ |
| InfoNCE (inter+intra) | 10.7 | 28.5 15.0 |
| InfoNCE (inter) | 10.8 | 29.0 14.5 |
| Triplet (inter+intra) | 26.8 | 56.2 3.0 |
| Triplet (inter) | 27.2 | 55.2 3.0 |
| Text Encoder | R@1↑R@5↑ MdR↓ | ||
| W2V (GloVe) | 22.1 | 49.8 | 6.0 |
| T5-Small | 24.5 | 51.2 | 3.0 |
| T5-Base | 27.2 | 55.2 | 3.0 |
| Text Encoder Text Decoder R@1 ↑ R@5 ↑ MdR↓ | ||||
| T5-Base | T5-Small | 26.2 | 54.2 | 3.0 |
| T5-Base | T5-Base | 27.2 | 55.2 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑R@5↑ R@10↑MdR↓ | R@1↑ R@5↑ R@10↑MdR↓ | |||||||
| Random Baseline | 0.1 | 0.5 | 1.0 | 500.0 | 0.1 | 0.5 | 1.0 | 500.0 |
| JSFusion (Yu et al., 2018) | 10.2 | 31.2 | 43.2 | 13.0 | 1 | 1 | 1 | 1 |
| HT100M (Miech et al., 2019) | 12.1 | 35.0 | 48.0 | 12.0 | 1 | 一 | 一 | 一 |
| JPoSE(Wray et al., 2019) | 14.3 | 38.1 | 53.0 | 9.0 | 16.4 | 41.3 | 54.4 | 8.7 |
| CE (Liu et al., 2019) | 20.9 | 48.8 | 62.4 | 6.0 | 20.6 | 50.3 | 64.0 | 5.3 |
| MMT(Gabeur et al., 2020) | 24.6 | 54.0 | 67.1 | 4.0 | 24.4 | 56.0 | 67.8 | 4.0 |
| Ours | 27.4 | 56.3 | 67.7 | 3.0 | 26.6 | 55.1 | 67.5 | 3.0 |
| VidTranslate (Korbar etal., 2020) | 14.7 | 1 | 52.8 | 1 | 一 | 1 | ||
| HT100M (Miech et al.,2019) | 14.9 | 40.2 | 52.8 | 9.0 | 16.8 | 41.7 | 55.1 | 8.0 |
| NoiseEstimation (Amrani et al., 2020) | 17.4 | 41.6 | 53.6 | 8.0 | 1 | 一 | 1 | 1 |
| UniVL (Luo et al.,2020) | 21.2 | 49.6 | 63.1 | 6.0 | 一 | 一 | 一 | 一 |
| AVLnet (Rouditchenko et al., 2020) | 27.1 | 55.6 | 66.6 | 4.0 | 28.5 | 54.6 | 65.2 | 4.0 |
| MMT(Gabeur et al., 2020) | 26.6 | 57.1 | 69.6 | 4.0 | 27.0 | 57.5 | 69.7 | 3.7 |
| Ours-pretrained | 30.1 | 58.5 | 69.3 | 3.0 | 28.5 | 58.6 | 71.6 | 3.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@10↑ MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||||
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 0.02 | 0.1 | 1.02 | 2100.5 | |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 1 | 1 | 1 | 1 |
| VSE++(Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 1 | 一 | 1 | 一 |
| Dual (Dong et al.,2019) | 31.1 | 67.4 | 78.9 | 3.0 | 1 | 1 | 1 | 1 |
| HGR(Chen et al., 2020b) | 35.1 | 73.5 | 83.5 | 2.0 | 一 | 一 | 一 | |
| Ours | 44.6 | 81.8 | 89.5 | 1.0 | 58.1 | 83.8 | 90.9 | 1.0 |
| Ours-pretrained | 45.9 | 82.4 | 90.4 | 1.0 | 61.2 | 85.2 | 91.8 | 1.0 |
| Text→Video | Video→Text | |||||||
| R@1↑ R@5↑ R@50↑ MdR↓ R@1↑ R@5 ↑ R@50↑ MdR↓ | ||||||||
| Random Baseline | 0.02 | 0.1 | 1.02 | 2458 | 0.02 | 0.1 | 1.02 | 2458 |
| FSE(Zhang et al., 2018) | 18.2 | 44.8 | 89.1 | 7.0 | 16.7 | 43.1 | 88.4 | 7.0 |
| CE (Liu et al., 2019) | 18.2 | 47.7 | 91.4 | 6.0 | 17.7 | 46.6 | 90.9 | 6.0 |
| HSE (Zhang et al.,2018) | 20.5 | 49.3 | 1 | 1 | 18.7 | 48.1 | 1 | 1 |
| MMT (Gabeur et al.,2020) | 22.7 | 54.2 | 93.2 | 5.0 | 22.9 | 54.8 | 93.1 | 4.3 |
| Ours | 26.8 | 58.1 | 93.5 | 3.0 | 25.5 | 57.3 | 93.5 | 3.0 |
| MMT-pretrained (Gabeur et al., 2020) | 28.7 | 61.4 | 94.5 | 3.3 | 28.9 | 61.1 | 94.3 | 4.0 |
| Ours-pretrained | 29.2 | 61.6 | 94.7 | 3.0 | 28.7 | 60.8 | 94.8 | 2.0 |
| Text→Video | Video→Text | |||||
| R@1↑ R@5↑ R@10↑MdR↓ R@1↑ R@5↑ R@10↑ MdR↓ | ||||||
| VSE (Kiros et al.,2014) | 12.3 30.1 | 42.3 | 14.0 | 1 | ||
| VSE++ (Faghri et al., 2018) | 15.4 39.6 | 53.0 | 9.0 | 一 | ||
| Multi. Cues (Mithun et al.,2018) | 20.3 47.8 | 61.1 | 6.0 | 1 | 1 | 1 一 |
| CE (Liu et al., 2019) | 19.8 49.0 | 63.8 | 6.0 | 一 | ||
| Ours | 23.0 52.8 | 65.8 | 5.0 | 27.3 | 50.7 | 60.8 5.0 |
| Ours-pretrained | 28.4 60.0 | 72.9 | 4.0 | 34.7 | 59.9 | 70.0 3.0 |
| Captioning | ||||
| Blue@4 METEORI | Rogue-L CIDEr | |||
| Shared Enc-Dec (Wang et al., 2019) | 28.4 | 21.7 | 47.0 | 45.1 |
| ORG (Zhang et al., 2020) | 32.1 | 22.2 | 48.9 | 49.7 |
| Ours, ,VATEX only | 32.8 | 24.4 | 49.1 | 51.2 |
| Ours,HT100M + Vatex | 32.5 | 24.1 | 48.9 | 50.5 |
| Captioning | ||||
| BLUE4 | METEOR | Rogue-L | CIDEr | |
| VidTranslate (Korbar et al., 2020) | 41.7 | 28.5 | 一 | 一 |
| POS+VCT (Hou et al., 2019) | 42.3 | 29.7 | 62.8 | 49.1 |
| ORG (Zhang et al., 2020) | 43.6 | 28.8 | 62.1 | 50.9 |
| Ours, MSR-VTT only | 39.7 | 28.3 | 60.5 | 46.5 |
| Ours,HT100M + MSR-VTT | 38.9 | 28.2 | 59.8 | 48.6 |
| Text→Video | Video→Text | |||||||
| R@1↑ | R@5↑ | R@10↑ | MdR | R@1↑ | R@5↑ | R@10个 | MdR | |
| Zero-Shot | ||||||||
| ActivityNet | 0.06 | 0.2 | 0.5 | 1907.0 | 0.0 | 0.2 | 0.3 | 2238.0 |
| VATEX | 0.07 | 0.4 | 0.7 | 682.0 | 0.07 | 0.4 | 0.9 | 697 |
| MSVD | 8.9 | 26.0 | 37.9 | 18.0 | 21.4 | 46.2 | 57.7 | 6.0 |
| MSR-VTT | 8.7 | 23.0 | 31.1 | 31.0 | 12.7 | 27.5 | 36.2 | 24.0 |
| Captioning | ||||
| Blue@4 | METEOR | Rogue-L | CIDEr | |
| DENSE (Krishna et al.,2017) | 1.6 | 8.9 | ||
| DVC-D-A (Li et al., 2018) | 1.7 | 9.3 | ||
| Bi-LSTM+TempoAttn (Zhou et al., 2018b) | 2.1 | 10.0 | 一 | |
| Masked Transformer (Zhou et al.,2018b) | 2.8 | 11.1 | 1 | 1 |
| Ours, ActivityNet only | 1.5 | 6.9 | 17.8 | 3.2 |
| Ours,HT100M + ActivityNet | 1.4 | 6.9 | 17.5 | 3.1 |
| Method | Mod | Dataset | Model | FT? | H51 | U101 |
| Self-Supervised Pre-training | ||||||
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 53.1 | 82.7 | |
| MIL-NCE (Miech et al.,2020) | V,T | HM | S3D-G | 61.0 | 91.3 | |
| MMV(Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | 67.1 | 91.8 | |
| ELo (Piergiovanni et al.,2020) | V,F,A | YT8M | R(2+1)D-50x3 | x√xν | 67.4 | 93.8 |
| XDC (Alwassel et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 68.9 | 95.5 |
| GDT (Patrick et al., 2020) | V,A | IG65M | R(2+1)D-18 | √ | 72.8 | 95.2 |
| MMV (Alayrac et al., 2020) | V,T,A | HM+AS | TSM-50x2 | √ | 75.0 | 95.2 |
| Supervised Pre-training | ||||||
| P3D (Qiu et al., 2017) | V,I | S1M+IM | P3D | 88.6 | ||
| TSN (Wang et al.,2018) | V,I | IM | TSN | ? | 69.4 | 94.2 |
| I3D (Carreira & Zisserman,2017) | V,I | K400+IM | I3D | √ | 74.8 | 95.6 |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 74.5 | 96.8 | |
| S3D-G (Xie et al., 2018) | V,I | K400+IM | S3D-G | 75.9 | 96.8 | |
| I3D(Carreira & Zisserman,2017) | V,I | K400+IM | I3D | 77.1 | 96.7 | |
| R(2+1)D (Tran et al., 2018) | V | K400 | R(2+1)D-34 | 76.4 | 95.5 | |
| R(2+1)D (Tran et al., 2018) | V,F | K400 | R(2+1)D-34x2 | 78.7 | 97.3 | |
| Omni (Duan et al., 2020) | V,I | K400+OS | Slow-8x8-R101 | 79.0 | 97.3 | |
| I3D (Carreira & Zisserman, 2017) | V,F,I | K400+IM | I3Dx2 | 80.7 | 98.0 | |
| Omni (Duan et al., 2020) | V,F,I | K400+OS | Slow-8x8-R101x2 | √ | 83.8 | 98.6 |
| Ours (Avg-pooling) | V,I | IG65M+IM | R(2+1)D-34+R152 | X | 73.7 | 64.3 |
| Ours (T-pooling) | V,I | HM+IG65M+IM | R(2+1)D-34+R152 | X | 81.3 | 98.0 |
| Text→Video | Video →Text | |||||||
| R@1↑ | R@5个 | R@10个 | MdR↓ | R@1↑ | R@5↑ | R@10个 | MdR | |
| Random Baseline | 0.2 | 0.7 | 1.05 | 2000.5 | 0.02 | 0.1 | 1.02 | 2100.5 |
| VSE (Kiros et al., 2014) | 28.0 | 64.3 | 76.9 | 3.0 | 一 | |||
| VSE++ (Faghri et al.,2018) | 33.7 | 70.1 | 81.0 | 2.0 | 一 | 一 | 一 | |
| Dual (Dong et al., 2019) | 31.1 | 67.4 | 78.9 | 3.0 | ||||
| HGR (Chen et al.,2020b) | 35.1 | 73.5 | 83.5 | 2.0 | ||||
| Ours | 44.9±0.2 82.1±0.2 | 89.7±0.2 | 1.0 | 58.4±0.1 84.4±0.2 91.0±0.3 | 1.0 |
| Algorithm2 Client Update (FEDAVG) input initial 0o,loss fi(0),optimizer CLIENTOPT |
| 1:for k =1,...,K do 2:0k ←CLIENTOPT(0k-1,fi(0k-1)) 3:end for output △ := 0o -0k,client weight qi |
| Algorithm 3 Client Update (FEDPA) input initial 0o,loss f(0),sampler CLIENTMCMC |
| 1:for k=1,...,K do 2:0k ~ CLIENTMCMC(0k-1,fi) 3:end for output △ := ∑-1(0o- 𝜇),client weight qi |
| Dim | △FEDAVG| | △(DP) | △e(exact) | ||
| 100 | 72 | 91 | +26% | 82 | +12% |
| 1K | 76 | 92 | +21% | 104 | +36% |
| 10K | 80 | 93 | +16% | 797 | +896% |
| 100K | 149 | 155 | +4% | 丨 | |
| Dataset | Task | # classes | # clients (train/test) | # examples p/ client (train/test) |
| EMNIST-62 | CR | 62 | 3,400 / 3,400 | 198 ± 77 /23±9 |
| CIFAR-100 | IR | 100 | 500/100 | 100 ±0/100±0 |
| StackOverflow | LR | 500 | 342,477 / 204,088 | 397 ± 1279 /81± 301 |
| NWP | 10,000 |
| Method \@ | accuracy (%, 个) 500R | 1500R | rounds (#,↓) 84% 86% |
| AFO t | 80.4 | 86.8 | 546 1291 |
| MIME $ | 83.1 | *84.9 | 464 * |
| FEDAVG-1E | 83.9 | 86.5 | 451 1360 |
| FEDAVG-ME | 85.8 | 85.9 | 86 |
| FEDPA-ME | 86.5 | 87.3 | 84 92 |
| Method \@ | accuracy (%, 个) 1000R | 1500R | rounds (#,↓) 30% | 40% |
| AFO t | 31.9 | 41.1 | 898 | 1401 |
| MIME t | 33.2 | *33.9 | 680 | * |
| FEDAVG-1E | 24.2 | 31.7 | 1379 | |
| FEDAVG-ME | 40.2 | 42.1 | 348 | 896 |
| FEDPA-ME | 44.3 | 46.3 | 348 | 543 |
| Method \Metric | NWP | LR (all metrics in %,↑) | ||||
| accuracy (%,†↑) | rounds (#,↓) | precision | recall@5 | ma-F1 | mi-F1 | |
| AFO + | 23.4 | 1049 | 68.0 | 1 | 1 | |
| FEDAVG-1E | 22.8 | 1074 | 74.58 | 69.1 | 14.9 | 43.8 |
| FEDAVG-ME | 23.0 | 870 | 78.65 | 68.7 | 15.6 | 43.3 |
| FEDPA-ME | 23.4 | 805 | 72.8 | 68.6 | 17.3 | 44.0 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflowNWP | StackOverflow LR |
| SERVEROPTCLIENTOPT# clients p/round | SGD (m = 0.9)SGD(m = 0.9)100 | SGD(m = 0.9)SGD(m = 0.9)20 | Adam(τ =10-3)SGD (m = 0.0)10 | Adagrad (τ = 10-5)SGD(m = 0.9)10 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate Client learning rate Client epochs | {0.01,0.05,0.1,0.5,1, 5} {0.001,0.005,0.01,0.05,0.1} | {0.01,0.05,0.1,0.5,1} {0.1,0.5,1,5,10} {0.01,0.05,0.1} {1,5,10,50,100} {2,5,10,20} | ||
| FEDPA burn-in FEDPA shrinkage | {100,200,400,600,800} {0.0001,0.001,0.01,0.1,1} | |||
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate | 0.5 | 0.5 | 1.0 | 5.0 |
| Client learning rate | 0.01 | 0.01 | 0.1 | 50.0 |
| Client epochs | 5 | 10 | 5 | 5 |
| FEDPA burn-in | 100 | 400 | 800 | 800 |
| FEDPA shrinkage | 0.1 | 0.01 | 0.01 | 0.01 |
| Algorithm2 Client Update (FEDAVG) input initial 0o,loss fi(0),optimizer CLIENTOPT |
| 1:for k =1,...,K do 2:0k ←CLIENTOPT(0k-1,fi(0k-1)) 3:end for output △ := 0o -0k,client weight qi |
| Algorithm 3 Client Update (FEDPA) input initial 0o,loss f(0),sampler CLIENTMCMC |
| 1:for k=1,...,K do 2:0k ~ CLIENTMCMC(0k-1,fi) 3:end for output △ := ∑-1(0o- 𝜇),client weight qi |
| Dim | △FEDAVG| | △(DP) | △e(exact) | ||
| 100 | 72 | 91 | +26% | 82 | +12% |
| 1K | 76 | 92 | +21% | 104 | +36% |
| 10K | 80 | 93 | +16% | 797 | +896% |
| 100K | 149 | 155 | +4% | 丨 |
| Dataset | Task | # classes | # clients (train/test) | # examples p/ client (train/test) |
| EMNIST-62 | CR | 62 | 3,400 / 3,400 | 198 ± 77 /23±9 |
| CIFAR-100 | IR | 100 | 500/100 | 100 ±0/100±0 |
| StackOverflow | LR | 500 | 342,477 / 204,088 | 397 ± 1279 /81± 301 |
| NWP | 10,000 |
| Method \\@ | accuracy (%, 个) 500R | 1500R | rounds (#,↓) 84% 86% |
| AFO t | 80.4 | 86.8 | 546 1291 |
| MIME $ | 83.1 | *84.9 | 464 * |
| FEDAVG-1E | 83.9 | 86.5 | 451 1360 |
| FEDAVG-ME | 85.8 | 85.9 | 86 |
| FEDPA-ME | 86.5 | 87.3 | 84 92 |
| Method \\@ | accuracy (%, 个) 1000R | 1500R | rounds (#,↓) 30% | 40% |
| AFO t | 31.9 | 41.1 | 898 | 1401 |
| MIME t | 33.2 | *33.9 | 680 | * |
| FEDAVG-1E | 24.2 | 31.7 | 1379 | |
| FEDAVG-ME | 40.2 | 42.1 | 348 | 896 |
| FEDPA-ME | 44.3 | 46.3 | 348 | 543 |
| Method \\Metric | NWP | LR (all metrics in %,↑) | ||||
| accuracy (%,†↑) | rounds (#,↓) | precision | recall@5 | ma-F1 | mi-F1 | |
| AFO + | 23.4 | 1049 | 68.0 | 1 | 1 | |
| FEDAVG-1E | 22.8 | 1074 | 74.58 | 69.1 | 14.9 | 43.8 |
| FEDAVG-ME | 23.0 | 870 | 78.65 | 68.7 | 15.6 | 43.3 |
| FEDPA-ME | 23.4 | 805 | 72.8 | 68.6 | 17.3 | 44.0 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflowNWP | StackOverflow LR |
| SERVEROPTCLIENTOPT# clients p/round | SGD (m = 0.9)SGD(m = 0.9)100 | SGD(m = 0.9)SGD(m = 0.9)20 | Adam(τ =10-3)SGD (m = 0.0)10 | Adagrad (τ = 10-5)SGD(m = 0.9)10 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate Client learning rate Client epochs | {0.01,0.05,0.1,0.5,1, 5} {0.001,0.005,0.01,0.05,0.1} | {0.01,0.05,0.1,0.5,1} {0.1,0.5,1,5,10} {0.01,0.05,0.1} {1,5,10,50,100} {2,5,10,20} | ||
| FEDPA burn-in FEDPA shrinkage | {100,200,400,600,800} {0.0001,0.001,0.01,0.1,1} |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate | 0.5 | 0.5 | 1.0 | 5.0 |
| Client learning rate | 0.01 | 0.01 | 0.1 | 50.0 |
| Client epochs | 5 | 10 | 5 | 5 |
| FEDPA burn-in | 100 | 400 | 800 | 800 |
| FEDPA shrinkage | 0.1 | 0.01 | 0.01 | 0.01 |
| Algorithm2 Client Update (FEDAVG) input initial 0o,loss fi(0),optimizer CLIENTOPT |
| 1:for k =1,...,K do 2:0k ←CLIENTOPT(0k-1,fi(0k-1)) 3:end for output △ := 0o -0k,client weight qi |
| Algorithm 3 Client Update (FEDPA) input initial 0o,loss f(0),sampler CLIENTMCMC |
| 1:for k=1,...,K do 2:0k ~ CLIENTMCMC(0k-1,fi) 3:end for output △ := ∑-1(0o- 𝜇),client weight qi |
| Algorithm2 Client Update (FEDAVG) input initial 0o,loss fi(0),optimizer CLIENTOPT |
| 1:for k =1,...,K do 2:0k ←CLIENTOPT(0k-1,fi(0k-1)) 3:end for output △ := 0o -0k,client weight qi |
| Algorithm 3 Client Update (FEDPA) input initial 0o,loss f(0),sampler CLIENTMCMC |
| 1:for k=1,...,K do 2:0k ~ CLIENTMCMC(0k-1,fi) 3:end for output △ := ∑-1(0o- 𝜇),client weight qi |
| Dim | △FEDAVG| | △(DP) | △e(exact) | ||
| 100 | 72 | 91 | +26% | 82 | +12% |
| 1K | 76 | 92 | +21% | 104 | +36% |
| 10K | 80 | 93 | +16% | 797 | +896% |
| 100K | 149 | 155 | +4% | 丨 |
| Dim | △FEDAVG| | △(DP) | △e(exact) | ||
| 100 | 72 | 91 | +26% | 82 | +12% |
| 1K | 76 | 92 | +21% | 104 | +36% |
| 10K | 80 | 93 | +16% | 797 | +896% |
| 100K | 149 | 155 | +4% | 丨 |
| Dataset | Task | # classes | # clients (train/test) | # examples p/ client (train/test) |
| EMNIST-62 | CR | 62 | 3,400 / 3,400 | 198 ± 77 /23±9 |
| CIFAR-100 | IR | 100 | 500/100 | 100 ±0/100±0 |
| StackOverflow | LR | 500 | 342,477 / 204,088 | 397 ± 1279 /81± 301 |
| NWP | 10,000 |
| Dataset | Task | # classes | # clients (train/test) | # examples p/ client (train/test) |
| EMNIST-62 | CR | 62 | 3,400 / 3,400 | 198 ± 77 /23±9 |
| CIFAR-100 | IR | 100 | 500/100 | 100 ±0/100±0 |
| StackOverflow | LR | 500 | 342,477 / 204,088 | 397 ± 1279 /81± 301 |
| NWP | 10,000 |
| Method \\@ | accuracy (%, 个) 500R | 1500R | rounds (#,↓) 84% 86% |
| AFO t | 80.4 | 86.8 | 546 1291 |
| MIME $ | 83.1 | *84.9 | 464 * |
| FEDAVG-1E | 83.9 | 86.5 | 451 1360 |
| FEDAVG-ME | 85.8 | 85.9 | 86 |
| FEDPA-ME | 86.5 | 87.3 | 84 92 |
| Method \\@ | accuracy (%, 个) 1000R | 1500R | rounds (#,↓) 30% | 40% |
| AFO t | 31.9 | 41.1 | 898 | 1401 |
| MIME t | 33.2 | *33.9 | 680 | * |
| FEDAVG-1E | 24.2 | 31.7 | 1379 | |
| FEDAVG-ME | 40.2 | 42.1 | 348 | 896 |
| FEDPA-ME | 44.3 | 46.3 | 348 | 543 |
| Method \\Metric | NWP | LR (all metrics in %,↑) | ||||
| accuracy (%,†↑) | rounds (#,↓) | precision | recall@5 | ma-F1 | mi-F1 | |
| AFO + | 23.4 | 1049 | 68.0 | 1 | 1 | |
| FEDAVG-1E | 22.8 | 1074 | 74.58 | 69.1 | 14.9 | 43.8 |
| FEDAVG-ME | 23.0 | 870 | 78.65 | 68.7 | 15.6 | 43.3 |
| FEDPA-ME | 23.4 | 805 | 72.8 | 68.6 | 17.3 | 44.0 |
| Method \\@ | accuracy (%, 个) 500R | 1500R | rounds (#,↓) 84% 86% |
| AFO t | 80.4 | 86.8 | 546 1291 |
| MIME $ | 83.1 | *84.9 | 464 * |
| FEDAVG-1E | 83.9 | 86.5 | 451 1360 |
| FEDAVG-ME | 85.8 | 85.9 | 86 |
| FEDPA-ME | 86.5 | 87.3 | 84 92 |
| Method \\@ | accuracy (%, 个) 1000R | 1500R | rounds (#,↓) 30% | 40% |
| AFO t | 31.9 | 41.1 | 898 | 1401 |
| MIME t | 33.2 | *33.9 | 680 | * |
| FEDAVG-1E | 24.2 | 31.7 | 1379 | |
| FEDAVG-ME | 40.2 | 42.1 | 348 | 896 |
| FEDPA-ME | 44.3 | 46.3 | 348 | 543 |
| Method \\Metric | NWP | LR (all metrics in %,↑) | ||||
| accuracy (%,†↑) | rounds (#,↓) | precision | recall@5 | ma-F1 | mi-F1 | |
| AFO + | 23.4 | 1049 | 68.0 | 1 | 1 | |
| FEDAVG-1E | 22.8 | 1074 | 74.58 | 69.1 | 14.9 | 43.8 |
| FEDAVG-ME | 23.0 | 870 | 78.65 | 68.7 | 15.6 | 43.3 |
| FEDPA-ME | 23.4 | 805 | 72.8 | 68.6 | 17.3 | 44.0 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflowNWP | StackOverflow LR |
| SERVEROPTCLIENTOPT# clients p/round | SGD (m = 0.9)SGD(m = 0.9)100 | SGD(m = 0.9)SGD(m = 0.9)20 | Adam(τ =10-3)SGD (m = 0.0)10 | Adagrad (τ = 10-5)SGD(m = 0.9)10 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate Client learning rate Client epochs | {0.01,0.05,0.1,0.5,1, 5} {0.001,0.005,0.01,0.05,0.1} | {0.01,0.05,0.1,0.5,1} {0.1,0.5,1,5,10} {0.01,0.05,0.1} {1,5,10,50,100} {2,5,10,20} | ||
| FEDPA burn-in FEDPA shrinkage | {100,200,400,600,800} {0.0001,0.001,0.01,0.1,1} |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflowNWP | StackOverflow LR |
| SERVEROPTCLIENTOPT# clients p/round | SGD (m = 0.9)SGD(m = 0.9)100 | SGD(m = 0.9)SGD(m = 0.9)20 | Adam(τ =10-3)SGD (m = 0.0)10 | Adagrad (τ = 10-5)SGD(m = 0.9)10 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate Client learning rate Client epochs | {0.01,0.05,0.1,0.5,1, 5} {0.001,0.005,0.01,0.05,0.1} | {0.01,0.05,0.1,0.5,1} {0.1,0.5,1,5,10} {0.01,0.05,0.1} {1,5,10,50,100} {2,5,10,20} | ||
| FEDPA burn-in FEDPA shrinkage | {100,200,400,600,800} {0.0001,0.001,0.01,0.1,1} |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate | 0.5 | 0.5 | 1.0 | 5.0 |
| Client learning rate | 0.01 | 0.01 | 0.1 | 50.0 |
| Client epochs | 5 | 10 | 5 | 5 |
| FEDPA burn-in | 100 | 400 | 800 | 800 |
| FEDPA shrinkage | 0.1 | 0.01 | 0.01 | 0.01 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate | 0.5 | 0.5 | 1.0 | 5.0 |
| Client learning rate | 0.01 | 0.01 | 0.1 | 50.0 |
| Client epochs | 5 | 10 | 5 | 5 |
| FEDPA burn-in | 100 | 400 | 800 | 800 |
| FEDPA shrinkage | 0.1 | 0.01 | 0.01 | 0.01 |
| Algorithm2 Client Update (FEDAVG) input initial 0o,loss fi(0),optimizer CLIENTOPT |
| 1:for k =1,...,K do 2:0k ←CLIENTOPT(0k-1,fi(0k-1)) 3:end for output △ := 0o -0k,client weight qi |
| Algorithm 3 Client Update (FEDPA) input initial 0o,loss f(0),sampler CLIENTMCMC |
| 1:for k=1,...,K do 2:0k ~ CLIENTMCMC(0k-1,fi) 3:end for output △ := ∑-1(0o- 𝜇),client weight qi |
| Dim | △FEDAVG| | △(DP) | △e(exact) | ||
| 100 | 72 | 91 | +26% | 82 | +12% |
| 1K | 76 | 92 | +21% | 104 | +36% |
| 10K | 80 | 93 | +16% | 797 | +896% |
| 100K | 149 | 155 | +4% | 丨 |
| Dataset | Task | # classes | # clients (train/test) | # examples p/ client (train/test) |
| EMNIST-62 | CR | 62 | 3,400 / 3,400 | 198 ± 77 /23±9 |
| CIFAR-100 | IR | 100 | 500/100 | 100 ±0/100±0 |
| StackOverflow | LR | 500 | 342,477 / 204,088 | 397 ± 1279 /81± 301 |
| NWP | 10,000 |
| Method \\Metric | NWP | LR (all metrics in %,↑) | ||||
| accuracy (%,†↑) | rounds (#,↓) | precision | recall@5 | ma-F1 | mi-F1 | |
| AFO + | 23.4 | 1049 | 68.0 | 1 | 1 | |
| FEDAVG-1E | 22.8 | 1074 | 74.58 | 69.1 | 14.9 | 43.8 |
| FEDAVG-ME | 23.0 | 870 | 78.65 | 68.7 | 15.6 | 43.3 |
| FEDPA-ME | 23.4 | 805 | 72.8 | 68.6 | 17.3 | 44.0 |
| Method \\@ | accuracy (%, 个) 500R | 1500R | rounds (#,↓) 84% 86% |
| AFO t | 80.4 | 86.8 | 546 1291 |
| MIME $ | 83.1 | *84.9 | 464 * |
| FEDAVG-1E | 83.9 | 86.5 | 451 1360 |
| FEDAVG-ME | 85.8 | 85.9 | 86 |
| FEDPA-ME | 86.5 | 87.3 | 84 92 |
| Method \\@ | accuracy (%, 个) 1000R | 1500R | rounds (#,↓) 30% | 40% |
| AFO t | 31.9 | 41.1 | 898 | 1401 |
| MIME t | 33.2 | *33.9 | 680 | * |
| FEDAVG-1E | 24.2 | 31.7 | 1379 | |
| FEDAVG-ME | 40.2 | 42.1 | 348 | 896 |
| FEDPA-ME | 44.3 | 46.3 | 348 | 543 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate Client learning rate Client epochs | {0.01,0.05,0.1,0.5,1, 5} {0.001,0.005,0.01,0.05,0.1} | {0.01,0.05,0.1,0.5,1} {0.1,0.5,1,5,10} {0.01,0.05,0.1} {1,5,10,50,100} {2,5,10,20} | ||
| FEDPA burn-in FEDPA shrinkage | {100,200,400,600,800} {0.0001,0.001,0.01,0.1,1} |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflowNWP | StackOverflow LR |
| SERVEROPTCLIENTOPT# clients p/round | SGD (m = 0.9)SGD(m = 0.9)100 | SGD(m = 0.9)SGD(m = 0.9)20 | Adam(τ =10-3)SGD (m = 0.0)10 | Adagrad (τ = 10-5)SGD(m = 0.9)10 |
| Hyperparameter | EMNIST-62 | CIFAR-100 | StackOverflow NWP | StackOverflow LR |
| Server learning rate | 0.5 | 0.5 | 1.0 | 5.0 |
| Client learning rate | 0.01 | 0.01 | 0.1 | 50.0 |
| Client epochs | 5 | 10 | 5 | 5 |
| FEDPA burn-in | 100 | 400 | 800 | 800 |
| FEDPA shrinkage | 0.1 | 0.01 | 0.01 | 0.01 |
| CROSS-SPEAKER | SPEAKER-DEPENDENT | |||||
| METHOD | DEV AcC | TEST AcC | REC ERROR | DEV AcC | TEST Acc | REC ERROR |
| MFCC | 48.89 | 49.28 | 66.27 | 66.22 | ||
| DCCA | 45.40 | 46.06 | 65.88 | 65.81 | ||
| GCCA | 49.59 | 50.18 | 40.67 | 69.52 | 69.78 | 40.39 |
| DGCCA | 53.78 | 54.22 | 35.89 | 72.62 | 72.33 | 20.52 |
| FRIEND | HASHTAG | |||
| ALGORITHM | P@1000 | R@1000 | P@1000 | R@1000 |
| PCA[TEXT+NET] | 0.445/0.439 | 0.149/0.147 | 0.011/0.008 | 0.312/0.290 |
| GCCA[TEXT] | 0.244/0.249 | 0.080/0.081 | 0.012/0.009 | 0.351/0.326 |
| GCCA[TEXT+NET] | 0.271/0.276 | 0.088/0.089 | 0.012/0.010 | 0.359/0.334 |
| DGCCA[TEXT+NET] | 0.297/0.268 | 0.099/0.090 | 0.013/0.010 | 0.385/0.373 |
| WGCCA[TEXT] WGCCA[TEXT+NET] | 0.269/0.279 0.376/0.364 | 0.089/0.091 0.123/0.120 | 0.012/0.009 0.013/0.009 | 0.357/0.325 0.360/0.346 |
| CROSS-SPEAKER | SPEAKER-DEPENDENT | |||||
| METHOD | DEV AcC | TEST AcC | REC ERROR | DEV AcC | TEST Acc | REC ERROR |
| MFCC | 48.89 | 49.28 | 66.27 | 66.22 | ||
| DCCA | 45.40 | 46.06 | 65.88 | 65.81 | ||
| GCCA | 49.59 | 50.18 | 40.67 | 69.52 | 69.78 | 40.39 |
| DGCCA | 53.78 | 54.22 | 35.89 | 72.62 | 72.33 | 20.52 |
| FRIEND | HASHTAG | |||
| ALGORITHM | P@1000 | R@1000 | P@1000 | R@1000 |
| PCA[TEXT+NET] | 0.445/0.439 | 0.149/0.147 | 0.011/0.008 | 0.312/0.290 |
| GCCA[TEXT] | 0.244/0.249 | 0.080/0.081 | 0.012/0.009 | 0.351/0.326 |
| GCCA[TEXT+NET] | 0.271/0.276 | 0.088/0.089 | 0.012/0.010 | 0.359/0.334 |
| DGCCA[TEXT+NET] | 0.297/0.268 | 0.099/0.090 | 0.013/0.010 | 0.385/0.373 |
| WGCCA[TEXT] WGCCA[TEXT+NET] | 0.269/0.279 0.376/0.364 | 0.089/0.091 0.123/0.120 | 0.012/0.009 0.013/0.009 | 0.357/0.325 0.360/0.346 |
| CROSS-SPEAKER | SPEAKER-DEPENDENT | |||||
| METHOD | DEV AcC | TEST AcC | REC ERROR | DEV AcC | TEST Acc | REC ERROR |
| MFCC | 48.89 | 49.28 | 66.27 | 66.22 | ||
| DCCA | 45.40 | 46.06 | 65.88 | 65.81 | ||
| GCCA | 49.59 | 50.18 | 40.67 | 69.52 | 69.78 | 40.39 |
| DGCCA | 53.78 | 54.22 | 35.89 | 72.62 | 72.33 | 20.52 |
| CROSS-SPEAKER | SPEAKER-DEPENDENT | |||||
| METHOD | DEV AcC | TEST AcC | REC ERROR | DEV AcC | TEST Acc | REC ERROR |
| MFCC | 48.89 | 49.28 | 66.27 | 66.22 | ||
| DCCA | 45.40 | 46.06 | 65.88 | 65.81 | ||
| GCCA | 49.59 | 50.18 | 40.67 | 69.52 | 69.78 | 40.39 |
| DGCCA | 53.78 | 54.22 | 35.89 | 72.62 | 72.33 | 20.52 |
| FRIEND | HASHTAG | |||
| ALGORITHM | P@1000 | R@1000 | P@1000 | R@1000 |
| PCA[TEXT+NET] | 0.445/0.439 | 0.149/0.147 | 0.011/0.008 | 0.312/0.290 |
| GCCA[TEXT] | 0.244/0.249 | 0.080/0.081 | 0.012/0.009 | 0.351/0.326 |
| GCCA[TEXT+NET] | 0.271/0.276 | 0.088/0.089 | 0.012/0.010 | 0.359/0.334 |
| DGCCA[TEXT+NET] | 0.297/0.268 | 0.099/0.090 | 0.013/0.010 | 0.385/0.373 |
| WGCCA[TEXT] WGCCA[TEXT+NET] | 0.269/0.279 0.376/0.364 | 0.089/0.091 0.123/0.120 | 0.012/0.009 0.013/0.009 | 0.357/0.325 0.360/0.346 |
| FRIEND | HASHTAG | |||
| ALGORITHM | P@1000 | R@1000 | P@1000 | R@1000 |
| PCA[TEXT+NET] | 0.445/0.439 | 0.149/0.147 | 0.011/0.008 | 0.312/0.290 |
| GCCA[TEXT] | 0.244/0.249 | 0.080/0.081 | 0.012/0.009 | 0.351/0.326 |
| GCCA[TEXT+NET] | 0.271/0.276 | 0.088/0.089 | 0.012/0.010 | 0.359/0.334 |
| DGCCA[TEXT+NET] | 0.297/0.268 | 0.099/0.090 | 0.013/0.010 | 0.385/0.373 |
| WGCCA[TEXT] WGCCA[TEXT+NET] | 0.269/0.279 0.376/0.364 | 0.089/0.091 0.123/0.120 | 0.012/0.009 0.013/0.009 | 0.357/0.325 0.360/0.346 |
| CROSS-SPEAKER | SPEAKER-DEPENDENT | |||||
| METHOD | DEV AcC | TEST AcC | REC ERROR | DEV AcC | TEST Acc | REC ERROR |
| MFCC | 48.89 | 49.28 | 66.27 | 66.22 | ||
| DCCA | 45.40 | 46.06 | 65.88 | 65.81 | ||
| GCCA | 49.59 | 50.18 | 40.67 | 69.52 | 69.78 | 40.39 |
| DGCCA | 53.78 | 54.22 | 35.89 | 72.62 | 72.33 | 20.52 |
| FRIEND | HASHTAG | |||
| ALGORITHM | P@1000 | R@1000 | P@1000 | R@1000 |
| PCA[TEXT+NET] | 0.445/0.439 | 0.149/0.147 | 0.011/0.008 | 0.312/0.290 |
| GCCA[TEXT] | 0.244/0.249 | 0.080/0.081 | 0.012/0.009 | 0.351/0.326 |
| GCCA[TEXT+NET] | 0.271/0.276 | 0.088/0.089 | 0.012/0.010 | 0.359/0.334 |
| DGCCA[TEXT+NET] | 0.297/0.268 | 0.099/0.090 | 0.013/0.010 | 0.385/0.373 |
| WGCCA[TEXT] WGCCA[TEXT+NET] | 0.269/0.279 0.376/0.364 | 0.089/0.091 0.123/0.120 | 0.012/0.009 0.013/0.009 | 0.357/0.325 0.360/0.346 |
| Require: e | |
| Require: η 1:procedure | Learning rate for corrective step |
| 2: 0←00 | Initialize parameters |
| 3: while θt not converged do | Draw training batch |
| 4: | draw X~Px |
| 5: | J← VθCo(X) |
| 6: | △0←-∈J |
| 7: | drawXv ~ Px N |
| 8: | 12 gL²←△（ M Ifθt(xi)-fθt+△θ(xi)|2)1/2 N |
| 9: | xiEXv △0'←△0o-n(gL2) |
| 10: | 0t←0t-1+△0 |
| 11: | return 0t |
| Algorithm 2: Hilbert-constrained gradient descent. Implements Equation 7. | |
| Require: n ≥ 1 | Number of corrective steps. May be 1. |
| Require: E | Overall learning rate |
| Require: n | Learning rate for corrective step |
| Require: β | Momentum |
| 1:procedure | |
| 2: | θ←00 |
| 3: v↑0 | Initialize momentum buffer |
| 4: | while 0t not converged do |
| 5: | reset dropout mask, if using |
| 6: | draw X~Px |
| 7: | J← VeCo(X) |
| 8: | U←βu+∈J |
| 9: | △0←-u |
| 10: | drawXv ~ Px Draw validation batch |
| 11: | gL²←∀△θ( M lfθ(xi)-fθ+△θ(xi)|2)1/2 N i=0 First correction |
| 12: 13: | △01←△0o-n(gL²) U←U+n(gl²) |
| 14: | for1<j<n do > Optional additional correc- tions |
| 15: | N gL²←J+∀△θ（%²） M Ifet(xi)- |
| 16: | i=0 fθt+△0j-1(xi)|2)1/2 |
| 17: | △0j←△0j-1-n(gL2) |
| 18: | U ←v+n(gl²) |
| 19: | 0t←0t-1+△0 |
| 20: | return 0t |
| Algorithm 3: Natural gradient by gradient descent. This algorithm can be paired with any optimizer to increase its similarity to the natural gradient. | |
| Require: n Require: η | Number of corrective steps.May be 1. |
| 1:procedure | Learning rate for corrective step |
| 2: θ←00 | >Initialize parameters |
| 3: while 0t not converged do | |
| 4: △0o←RMSprop(0t) | Use any optimizer to get proposed update |
| 5: fori<ndo | |
| 6: | Step towards F-1J |
| △0i+1=△0i-n(J+λF△0) | |
| 7: | θ←θ+△0 |
| 8: return 0t | |
| Require: e | |
| Require: η 1:procedure | Learning rate for corrective step |
| 2: 0←00 | Initialize parameters |
| 3: while θt not converged do | Draw training batch |
| 4: | draw X~Px |
| 5: | J← VθCo(X) |
| 6: | △0←-∈J |
| 7: | drawXv ~ Px N |
| 8: | 12 gL²←△（ M Ifθt(xi)-fθt+△θ(xi)|2)1/2 N |
| 9: | xiEXv △0'←△0o-n(gL2) |
| 10: | 0t←0t-1+△0 |
| 11: | return 0t |
| Algorithm 2: Hilbert-constrained gradient descent. Implements Equation 7. | |
| Require: n ≥ 1 | Number of corrective steps. May be 1. |
| Require: E | Overall learning rate |
| Require: n | Learning rate for corrective step |
| Require: β | Momentum |
| 1:procedure | |
| 2: | θ←00 |
| 3: v↑0 | Initialize momentum buffer |
| 4: | while 0t not converged do |
| 5: | reset dropout mask, if using |
| 6: | draw X~Px |
| 7: | J← VeCo(X) |
| 8: | U←βu+∈J |
| 9: | △0←-u |
| 10: | drawXv ~ Px Draw validation batch |
| 11: | gL²←∀△θ( M lfθ(xi)-fθ+△θ(xi)|2)1/2 N i=0 First correction |
| 12: 13: | △01←△0o-n(gL²) U←U+n(gl²) |
| 14: | for1<j<n do > Optional additional correc- tions |
| 15: | N gL²←J+∀△θ（%²） M Ifet(xi)- |
| 16: | i=0 fθt+△0j-1(xi)|2)1/2 |
| 17: | △0j←△0j-1-n(gL2) |
| 18: | U ←v+n(gl²) |
| 19: | 0t←0t-1+△0 |
| 20: | return 0t |
| Algorithm 3: Natural gradient by gradient descent. This algorithm can be paired with any optimizer to increase its similarity to the natural gradient. | |
| Require: n Require: η | Number of corrective steps.May be 1. |
| 1:procedure | Learning rate for corrective step |
| 2: θ←00 | >Initialize parameters |
| 3: while 0t not converged do | |
| 4: △0o←RMSprop(0t) | Use any optimizer to get proposed update |
| 5: fori<ndo | |
| 6: | Step towards F-1J |
| △0i+1=△0i-n(J+λF△0) | |
| 7: | θ←θ+△0 |
| 8: return 0t |
| Require: e | |
| Require: η 1:procedure | Learning rate for corrective step |
| 2: 0←00 | Initialize parameters |
| 3: while θt not converged do | Draw training batch |
| 4: | draw X~Px |
| 5: | J← VθCo(X) |
| 6: | △0←-∈J |
| 7: | drawXv ~ Px N |
| 8: | 12 gL²←△（ M Ifθt(xi)-fθt+△θ(xi)|2)1/2 N |
| 9: | xiEXv △0'←△0o-n(gL2) |
| 10: | 0t←0t-1+△0 |
| 11: | return 0t |
| Require: e | |
| Require: η 1:procedure | Learning rate for corrective step |
| 2: 0←00 | Initialize parameters |
| 3: while θt not converged do | Draw training batch |
| 4: | draw X~Px |
| 5: | J← VθCo(X) |
| 6: | △0←-∈J |
| 7: | drawXv ~ Px N |
| 8: | 12 gL²←△（ M Ifθt(xi)-fθt+△θ(xi)|2)1/2 N |
| 9: | xiEXv △0'←△0o-n(gL2) |
| 10: | 0t←0t-1+△0 |
| 11: | return 0t |
| Algorithm 2: Hilbert-constrained gradient descent. Implements Equation 7. | |
| Require: n ≥ 1 | Number of corrective steps. May be 1. |
| Require: E | Overall learning rate |
| Require: n | Learning rate for corrective step |
| Require: β | Momentum |
| 1:procedure | |
| 2: | θ←00 |
| 3: v↑0 | Initialize momentum buffer |
| 4: | while 0t not converged do |
| 5: | reset dropout mask, if using |
| 6: | draw X~Px |
| 7: | J← VeCo(X) |
| 8: | U←βu+∈J |
| 9: | △0←-u |
| 10: | drawXv ~ Px Draw validation batch |
| 11: | gL²←∀△θ( M lfθ(xi)-fθ+△θ(xi)|2)1/2 N i=0 First correction |
| 12: 13: | △01←△0o-n(gL²) U←U+n(gl²) |
| 14: | for1<j<n do > Optional additional correc- tions |
| 15: | N gL²←J+∀△θ（%²） M Ifet(xi)- |
| 16: | i=0 fθt+△0j-1(xi)|2)1/2 |
| 17: | △0j←△0j-1-n(gL2) |
| 18: | U ←v+n(gl²) |
| 19: | 0t←0t-1+△0 |
| 20: | return 0t |
| Algorithm 2: Hilbert-constrained gradient descent. Implements Equation 7. | |
| Require: n ≥ 1 | Number of corrective steps. May be 1. |
| Require: E | Overall learning rate |
| Require: n | Learning rate for corrective step |
| Require: β | Momentum |
| 1:procedure | |
| 2: | θ←00 |
| 3: v↑0 | Initialize momentum buffer |
| 4: | while 0t not converged do |
| 5: | reset dropout mask, if using |
| 6: | draw X~Px |
| 7: | J← VeCo(X) |
| 8: | U←βu+∈J |
| 9: | △0←-u |
| 10: | drawXv ~ Px Draw validation batch |
| 11: | gL²←∀△θ( M lfθ(xi)-fθ+△θ(xi)|2)1/2 N i=0 First correction |
| 12: 13: | △01←△0o-n(gL²) U←U+n(gl²) |
| 14: | for1<j<n do > Optional additional correc- tions |
| 15: | N gL²←J+∀△θ（%²） M Ifet(xi)- |
| 16: | i=0 fθt+△0j-1(xi)|2)1/2 |
| 17: | △0j←△0j-1-n(gL2) |
| 18: | U ←v+n(gl²) |
| 19: | 0t←0t-1+△0 |
| 20: | return 0t |
| Algorithm 3: Natural gradient by gradient descent. This algorithm can be paired with any optimizer to increase its similarity to the natural gradient. | |
| Require: n Require: η | Number of corrective steps.May be 1. |
| 1:procedure | Learning rate for corrective step |
| 2: θ←00 | >Initialize parameters |
| 3: while 0t not converged do | |
| 4: △0o←RMSprop(0t) | Use any optimizer to get proposed update |
| 5: fori<ndo | |
| 6: | Step towards F-1J |
| △0i+1=△0i-n(J+λF△0) | |
| 7: | θ←θ+△0 |
| 8: return 0t |
| Algorithm 3: Natural gradient by gradient descent. This algorithm can be paired with any optimizer to increase its similarity to the natural gradient. | |
| Require: n Require: η | Number of corrective steps.May be 1. |
| 1:procedure | Learning rate for corrective step |
| 2: θ←00 | >Initialize parameters |
| 3: while 0t not converged do | |
| 4: △0o←RMSprop(0t) | Use any optimizer to get proposed update |
| 5: fori<ndo | |
| 6: | Step towards F-1J |
| △0i+1=△0i-n(J+λF△0) | |
| 7: | θ←θ+△0 |
| 8: return 0t |
| Require: e | |
| Require: η 1:procedure | Learning rate for corrective step |
| 2: 0←00 | Initialize parameters |
| 3: while θt not converged do | Draw training batch |
| 4: | draw X~Px |
| 5: | J← VθCo(X) |
| 6: | △0←-∈J |
| 7: | drawXv ~ Px N |
| 8: | 12 gL²←△（ M Ifθt(xi)-fθt+△θ(xi)|2)1/2 N |
| 9: | xiEXv △0'←△0o-n(gL2) |
| 10: | 0t←0t-1+△0 |
| 11: | return 0t |
| Algorithm 2: Hilbert-constrained gradient descent. Implements Equation 7. | |
| Require: n ≥ 1 | Number of corrective steps. May be 1. |
| Require: E | Overall learning rate |
| Require: n | Learning rate for corrective step |
| Require: β | Momentum |
| 1:procedure | |
| 2: | θ←00 |
| 3: v↑0 | Initialize momentum buffer |
| 4: | while 0t not converged do |
| 5: | reset dropout mask, if using |
| 6: | draw X~Px |
| 7: | J← VeCo(X) |
| 8: | U←βu+∈J |
| 9: | △0←-u |
| 10: | drawXv ~ Px Draw validation batch |
| 11: | gL²←∀△θ( M lfθ(xi)-fθ+△θ(xi)|2)1/2 N i=0 First correction |
| 12: 13: | △01←△0o-n(gL²) U←U+n(gl²) |
| 14: | for1<j<n do > Optional additional correc- tions |
| 15: | N gL²←J+∀△θ（%²） M Ifet(xi)- |
| 16: | i=0 fθt+△0j-1(xi)|2)1/2 |
| 17: | △0j←△0j-1-n(gL2) |
| 18: | U ←v+n(gl²) |
| 19: | 0t←0t-1+△0 |
| 20: | return 0t |
| Algorithm 3: Natural gradient by gradient descent. This algorithm can be paired with any optimizer to increase its similarity to the natural gradient. | |
| Require: n Require: η | Number of corrective steps.May be 1. |
| 1:procedure | Learning rate for corrective step |
| 2: θ←00 | >Initialize parameters |
| 3: while 0t not converged do | |
| 4: △0o←RMSprop(0t) | Use any optimizer to get proposed update |
| 5: fori<ndo | |
| 6: | Step towards F-1J |
| △0i+1=△0i-n(J+λF△0) | |
| 7: | θ←θ+△0 |
| 8: return 0t |