[tab] appendix_c_nodes_video_noise.md (markdown)
# Investigation on brittleness of embeddings


## Additive embeddings

### no noise

### noise std=0.1

### noise std=0.2

### noise std=0.5

## Concat
Step 200000, validation loss: 0.7374703884124756
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.8475988051470589), 'val_cross_entropy_loss': np.float64(0.7374703171206456), 'val_entropy': np.float64(0.8575162127906201), 'val_masked_token_top16_accuracy': np.float64(0.9825415529456794), 'val_masked_token_top1_accuracy': np.float64(0.776269306154812), 'val_masked_token_top2_accuracy': np.float64(0.8820458533717137), 'val_masked_token_top5_accuracy': np.float64(0.949582414299834), 'val_psnr': np.float64(22.455391640756645), 'val_select_logit': np.float64(15.983110203462488), 'val_select_p': np.float64(0.7558641293469597), 'val_ssim': np.float64(0.6962924330842262), 'val_total_loss': np.float64(0.7374703171206456), 'val_z_loss': np.float64(313.3120548023897), 'val_loss': np.float32(0.7374704), 'val_full_frame_codebook_usage_lam': np.float64(1.0), 'val_full_frame_codebook_usage_tokenizer': np.float64(0.2629250919117647), 'val_full_frame_cross_entropy_loss': np.float64(1.7930428303924262), 'val_full_frame_entropy': np.float64(0.252041938550332), 'val_full_frame_masked_token_top16_accuracy': np.float64(0.9929032676360187), 'val_full_frame_masked_token_top1_accuracy': np.float64(0.8329210959228814), 'val_full_frame_masked_token_top2_accuracy': np.float64(0.9222704674683365), 'val_full_frame_masked_token_top5_accuracy': np.float64(0.9736630788036421), 'val_full_frame_psnr': np.float64(28.751719717885933), 'val_full_frame_select_logit': np.float64(100.21908793729894), 'val_full_frame_select_p': np.float64(0.912218968073527), 'val_full_frame_ssim': np.float64(0.8437704747798396), 'val_full_frame_z_loss': np.float64(51192.01493566176), 'val_full_frame_loss': np.float32(1.7930428)}

## noise std 0.05
Step 200000, validation loss: 1.3161627054214478
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.8595281862745098), 'val_cross_entropy_loss': np.float64(1.3161625441382914), 'val_entropy': np.float64(0.9603639922890008), 'val_masked_token_top16_accuracy': np.float64(0.9656095154145184), 'val_masked_token_top1_accuracy': np.float64(0.6909338095608879), 'val_masked_token_top2_accuracy': np.float64(0.8155956373495215), 'val_masked_token_top5_accuracy': np.float64(0.9094531045240515), 'val_psnr': np.float64(22.258947148042566), 'val_select_logit': np.float64(15.273398137560077), 'val_select_p': np.float64(0.7302459712122001), 'val_ssim': np.float64(0.6844308913922778), 'val_total_loss': np.float64(1.3161625441382914), 'val_z_loss': np.float64(289.0865448596431), 'val_loss': np.float32(1.3161627), 'val_full_frame_codebook_usage_lam': np.float64(1.0), 'val_full_frame_codebook_usage_tokenizer': np.float64(0.2633463541666667), 'val_full_frame_cross_entropy_loss': np.float64(1.7980740304086722), 'val_full_frame_entropy': np.float64(0.252041938550332), 'val_full_frame_masked_token_top16_accuracy': np.float64(0.9928698411174849), 'val_full_frame_masked_token_top1_accuracy': np.float64(0.8328876740792218), 'val_full_frame_masked_token_top2_accuracy': np.float64(0.9221479238248339), 'val_full_frame_masked_token_top5_accuracy': np.float64(0.9736742201973411), 'val_full_frame_psnr': np.float64(28.751719717885933), 'val_full_frame_select_logit': np.float64(100.21908793729894), 'val_full_frame_select_p': np.float64(0.912218968073527), 'val_full_frame_ssim': np.float64(0.8437704747798396), 'val_full_frame_z_loss': np.float64(51192.01493566176), 'val_full_frame_loss': np.float32(1.798074)}

## noise std 0.1
Step 200000, validation loss: 3.47092342376709
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.9107689950980392), 'val_cross_entropy_loss': np.float64(3.470923194698259), 'val_entropy': np.float64(2.102112695282581), 'val_masked_token_top16_accuracy': np.float64(0.7756070003790014), 'val_masked_token_top1_accuracy': np.float64(0.36497432636279686), 'val_masked_token_top2_accuracy': np.float64(0.4784945939101425), 'val_masked_token_top5_accuracy': np.float64(0.6185943133690778), 'val_psnr': np.float64(18.93759428286085), 'val_select_logit': np.float64(10.699732406466614), 'val_select_p': np.float64(0.4912407164480172), 'val_ssim': np.float64(0.5805023651497037), 'val_total_loss': np.float64(3.470923194698259), 'val_z_loss': np.float64(154.57306955374924), 'val_loss': np.float32(3.4709234), 'val_full_frame_codebook_usage_lam': np.float64(1.0), 'val_full_frame_codebook_usage_tokenizer': np.float64(0.2633463541666667), 'val_full_frame_cross_entropy_loss': np.float64(1.7980740304086722), 'val_full_frame_entropy': np.float64(0.252041938550332), 'val_full_frame_masked_token_top16_accuracy': np.float64(0.9928698411174849), 'val_full_frame_masked_token_top1_accuracy': np.float64(0.8328876740792218), 'val_full_frame_masked_token_top2_accuracy': np.float64(0.9221479238248339), 'val_full_frame_masked_token_top5_accuracy': np.float64(0.9736742201973411), 'val_full_frame_psnr': np.float64(28.751719717885933), 'val_full_frame_select_logit': np.float64(100.21908793729894), 'val_full_frame_select_p': np.float64(0.912218968073527), 'val_full_frame_ssim': np.float64(0.8437704747798396), 'val_full_frame_z_loss': np.float64(51192.01493566176), 'val_full_frame_loss': np.float32(1.798074)}

## noise std 0.2
Step 200000, validation loss: 5.663453578948975
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.9687117034313726), 'val_cross_entropy_loss': np.float64(5.6634534480525), 'val_entropy': np.float64(3.8459870207543467), 'val_masked_token_top16_accuracy': np.float64(0.39807266756600024), 'val_masked_token_top1_accuracy': np.float64(0.10833961239048079), 'val_masked_token_top2_accuracy': np.float64(0.16518428921699524), 'val_masked_token_top5_accuracy': np.float64(0.2562381183984233), 'val_psnr': np.float64(15.170352804894542), 'val_select_logit': np.float64(6.860248369329116), 'val_select_p': np.float64(0.22353572529904983), 'val_ssim': np.float64(0.4300605286570156), 'val_total_loss': np.float64(5.6634534480525), 'val_z_loss': np.float64(81.19780237534466), 'val_loss': np.float32(5.6634536), 'val_full_frame_codebook_usage_lam': np.float64(1.0), 'val_full_frame_codebook_usage_tokenizer': np.float64(0.2633463541666667), 'val_full_frame_cross_entropy_loss': np.float64(1.7980740304086722), 'val_full_frame_entropy': np.float64(0.252041938550332), 'val_full_frame_masked_token_top16_accuracy': np.float64(0.9928698411174849), 'val_full_frame_masked_token_top1_accuracy': np.float64(0.8328876740792218), 'val_full_frame_masked_token_top2_accuracy': np.float64(0.9221479238248339), 'val_full_frame_masked_token_top5_accuracy': np.float64(0.9736742201973411), 'val_full_frame_psnr': np.float64(28.751719717885933), 'val_full_frame_select_logit': np.float64(100.21908793729894), 'val_full_frame_select_p': np.float64(0.912218968073527), 'val_full_frame_ssim': np.float64(0.8437704747798396), 'val_full_frame_z_loss': np.float64(51192.01493566176), 'val_full_frame_loss': np.float32(1.798074)}