[tab] appendix_c_nodes.md (markdown)


        noise_stddev = 0.5  # Standard deviation for the Gaussian noise
        noise = jax.random.normal(batch["mask_rng"], vid_embed_BTNM.shape) * noise_stddev
        vid_embed_BTNM += noise

## 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