[tab] appendix_c_nodes_embeddings_noise.md (markdown)



## Additive embeddings

### no noise
Step 200000, validation loss: 0.7587440609931946
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.8475988051470589), 'val_cross_entropy_loss': np.float64(0.758744008400861), 'val_entropy': np.float64(0.8734586110302046), 'val_masked_token_top16_accuracy': np.float64(0.9815394200530707), 'val_masked_token_top1_accuracy': np.float64(0.772024557870977), 'val_masked_token_top2_accuracy': np.float64(0.8777434533717585), 'val_masked_token_top5_accuracy': np.float64(0.9463883007273954), 'val_psnr': np.float64(18.16088799869313), 'val_select_logit': np.float64(15.902265399110084), 'val_select_p': np.float64(0.7548150642245424), 'val_ssim': np.float64(0.6326266468739977), 'val_total_loss': np.float64(0.758744008400861), 'val_z_loss': np.float64(310.9372079886642), 'val_loss': np.float32(0.75874406), '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(20.045630099726658), 'val_full_frame_entropy': np.float64(1.0269374473422181), 'val_full_frame_masked_token_top16_accuracy': np.float64(0.7251559460864347), 'val_full_frame_masked_token_top1_accuracy': np.float64(0.38186273446270064), 'val_full_frame_masked_token_top2_accuracy': np.float64(0.47075533224087135), 'val_full_frame_masked_token_top5_accuracy': np.float64(0.5903074694614784), 'val_full_frame_psnr': np.float64(16.088213939292757), 'val_full_frame_select_logit': np.float64(84.10442965638404), 'val_full_frame_select_p': np.float64(0.7601301389582017), 'val_full_frame_ssim': np.float64(0.5480527725874209), 'val_full_frame_z_loss': np.float64(108920.47901348039), 'val_full_frame_loss': np.float32(20.045631)}

### noise std=0.1
Step 200000, validation loss: 1.9375224113464355
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.8475988051470589), 'val_cross_entropy_loss': np.float64(1.9375225586049698), 'val_entropy': np.float64(2.236036305334054), 'val_masked_token_top16_accuracy': np.float64(0.8798762057341781), 'val_masked_token_top1_accuracy': np.float64(0.5657584152969659), 'val_masked_token_top2_accuracy': np.float64(0.689856609877418), 'val_masked_token_top5_accuracy': np.float64(0.798516615933063), 'val_psnr': np.float64(15.530764074886546), 'val_select_logit': np.float64(10.11456164191751), 'val_select_p': np.float64(0.501306425707013), 'val_ssim': np.float64(0.5097568672077328), 'val_total_loss': np.float64(1.9375225586049698), 'val_z_loss': np.float64(149.545166015625), 'val_loss': np.float32(1.9375224), '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(20.045630099726658), 'val_full_frame_entropy': np.float64(1.0269374473422181), 'val_full_frame_masked_token_top16_accuracy': np.float64(0.7251559460864347), 'val_full_frame_masked_token_top1_accuracy': np.float64(0.38186273446270064), 'val_full_frame_masked_token_top2_accuracy': np.float64(0.47075533224087135), 'val_full_frame_masked_token_top5_accuracy': np.float64(0.5903074694614784), 'val_full_frame_psnr': np.float64(16.088213939292757), 'val_full_frame_select_logit': np.float64(84.10442965638404), 'val_full_frame_select_p': np.float64(0.7601301389582017), 'val_full_frame_ssim': np.float64(0.5480527725874209), 'val_full_frame_z_loss': np.float64(108920.47901348039), 'val_full_frame_loss': np.float32(20.045631)}

### noise std=0.2
Step 200000, validation loss: 4.311364650726318
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.8475988051470589), 'val_cross_entropy_loss': np.float64(4.3113649312187645), 'val_entropy': np.float64(4.482920328776042), 'val_masked_token_top16_accuracy': np.float64(0.5900948678745943), 'val_masked_token_top1_accuracy': np.float64(0.24632565764819875), 'val_masked_token_top2_accuracy': np.float64(0.33755794225954544), 'val_masked_token_top5_accuracy': np.float64(0.4589417284610225), 'val_psnr': np.float64(12.573247198965035), 'val_select_logit': np.float64(6.313630515453863), 'val_select_p': np.float64(0.16665662007004606), 'val_ssim': np.float64(0.3333607175770928), 'val_total_loss': np.float64(4.3113649312187645), 'val_z_loss': np.float64(77.57380646350337), 'val_loss': np.float32(4.3113647), '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(20.045630099726658), 'val_full_frame_entropy': np.float64(1.0269374473422181), 'val_full_frame_masked_token_top16_accuracy': np.float64(0.7251559460864347), 'val_full_frame_masked_token_top1_accuracy': np.float64(0.38186273446270064), 'val_full_frame_masked_token_top2_accuracy': np.float64(0.47075533224087135), 'val_full_frame_masked_token_top5_accuracy': np.float64(0.5903074694614784), 'val_full_frame_psnr': np.float64(16.088213939292757), 'val_full_frame_select_logit': np.float64(84.10442965638404), 'val_full_frame_select_p': np.float64(0.7601301389582017), 'val_full_frame_ssim': np.float64(0.5480527725874209), 'val_full_frame_z_loss': np.float64(108920.47901348039), 'val_full_frame_loss': np.float32(20.045631)}

### noise std=0.5
Step 200000, validation loss: 6.960869312286377
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.8475988051470589), 'val_cross_entropy_loss': np.float64(6.960869602128571), 'val_entropy': np.float64(5.414477582071342), 'val_masked_token_top16_accuracy': np.float64(0.18385726447198905), 'val_masked_token_top1_accuracy': np.float64(0.0353936998940566), 'val_masked_token_top2_accuracy': np.float64(0.05846153243499644), 'val_masked_token_top5_accuracy': np.float64(0.10274799825514064), 'val_psnr': np.float64(10.914788994134641), 'val_select_logit': np.float64(5.507573454987769), 'val_select_p': np.float64(0.07029049901985655), 'val_ssim': np.float64(0.2510850712949154), 'val_total_loss': np.float64(6.960869602128571), 'val_z_loss': np.float64(69.57815611596202), 'val_loss': np.float32(6.9608693), '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(20.045630099726658), 'val_full_frame_entropy': np.float64(1.0269374473422181), 'val_full_frame_masked_token_top16_accuracy': np.float64(0.7251559460864347), 'val_full_frame_masked_token_top1_accuracy': np.float64(0.38186273446270064), 'val_full_frame_masked_token_top2_accuracy': np.float64(0.47075533224087135), 'val_full_frame_masked_token_top5_accuracy': np.float64(0.5903074694614784), 'val_full_frame_psnr': np.float64(16.088213939292757), 'val_full_frame_select_logit': np.float64(84.10442965638404), 'val_full_frame_select_p': np.float64(0.7601301389582017), 'val_full_frame_ssim': np.float64(0.5480527725874209), 'val_full_frame_z_loss': np.float64(108920.47901348039), 'val_full_frame_loss': np.float32(20.045631)}

## 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 0.1
Step 200000, validation loss: 3.6271512508392334
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.8475988051470589), 'val_cross_entropy_loss': np.float64(3.6271509796965358), 'val_entropy': np.float64(4.294355560751522), 'val_masked_token_top16_accuracy': np.float64(0.7079328228445614), 'val_masked_token_top1_accuracy': np.float64(0.29852578511425093), 'val_masked_token_top2_accuracy': np.float64(0.41297777552230686), 'val_masked_token_top5_accuracy': np.float64(0.5610486105376599), 'val_psnr': np.float64(14.66877135108499), 'val_select_logit': np.float64(5.881039871889002), 'val_select_p': np.float64(0.18452119885706433), 'val_ssim': np.float64(0.4027574781109305), 'val_total_loss': np.float64(3.6271509796965358), 'val_z_loss': np.float64(67.83754580628639), 'val_loss': np.float32(3.6271513), '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 0.2
Step 200000, validation loss: 6.788418769836426
{'val_codebook_usage_lam': np.float64(1.0), 'val_codebook_usage_tokenizer': np.float64(0.8475988051470589), 'val_cross_entropy_loss': np.float64(6.788418115354052), 'val_entropy': np.float64(5.4373855964810245), 'val_masked_token_top16_accuracy': np.float64(0.19955201680753745), 'val_masked_token_top1_accuracy': np.float64(0.032450725634892784), 'val_masked_token_top2_accuracy': np.float64(0.05669430161223692), 'val_masked_token_top5_accuracy': np.float64(0.10574950832946628), 'val_psnr': np.float64(10.75548319723092), 'val_select_logit': np.float64(4.335007929334454), 'val_select_p': np.float64(0.06822160222366744), 'val_ssim': np.float64(0.25764136659164055), 'val_total_loss': np.float64(6.788418115354052), 'val_z_loss': np.float64(54.11139491960114), 'val_loss': np.float32(6.788419), '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)}