papers/hi-mar/sau.json

{
  "paper_id": "hi-mar",
  "paper_title": "Hi-MAR: Hierarchical Masked Autoregressive Models with Low-Resolution Token Pivots",
  "D1": [
    {
      "id": "hi-mar-D1-001",
      "claim": "Hi-MAR Transformer layers: n_layers=24 (B) / 32 (L) / 40 (H)",
      "source": "Section 4.2, Table 1"
    },
    {
      "id": "hi-mar-D1-002",
      "claim": "Hi-MAR Transformer hidden size: d_model=768 (B) / 1024 (L) / 1280 (H)",
      "source": "Section 4.2, Table 1"
    },
    {
      "id": "hi-mar-D1-003",
      "claim": "Diffusion Head Phase 1 layers: diff_head1_layers=6 (B) / 8 (L) / 12 (H)",
      "source": "Section 4.2, Table 1"
    },
    {
      "id": "hi-mar-D1-004",
      "claim": "Diffusion Head Phase 1 hidden size: diff_head1_hidden=1024 (B) / 1280 (L) / 1536 (H)",
      "source": "Section 4.2, Table 1"
    },
    {
      "id": "hi-mar-D1-005",
      "claim": "Diffusion Head Phase 2 layers: diff_head2_layers=6 (B) / 8 (L) / 12 (H)",
      "source": "Section 4.2, Table 1"
    },
    {
      "id": "hi-mar-D1-006",
      "claim": "Diffusion Head Phase 2 hidden size: diff_head2_hidden=512 (B) / 512 (L) / 768 (H)",
      "source": "Section 4.2, Table 1"
    },
    {
      "id": "hi-mar-D1-007",
      "claim": "Total parameter count: n_params=244M (B) / 529M (L) / 1090M (H)",
      "source": "Section 4.2, Table 1"
    },
    {
      "id": "hi-mar-D1-008",
      "claim": "Number of hierarchical phases in Hi-MAR: num_phases=2",
      "source": "Section 3.2"
    },
    {
      "id": "hi-mar-D1-009",
      "claim": "ImageNet class-conditional training configuration: AdamW optimizer (beta1=0.9, beta2=0.95, weight_decay=0.02), constant learning rate lr=1e-4 with 100-epoch linear warmup, total 800 epochs. Evaluation uses 50K generated samples for FID/IS/Precision/Recall.",
      "source": "Section 4.2"
    },
    {
      "id": "hi-mar-D1-010",
      "claim": "Masking ratio configuration: Phase 1 uniformly sampled from [0.7, 1.0] (same as MAR); Phase 2 uses cosine masking schedule (MaskGIT).",
      "source": "Section 4.2"
    },
    {
      "id": "hi-mar-D1-011",
      "claim": "MS-COCO text-to-image training configuration: masking ratio sampled from Beta(alpha=4, beta=1) for both phases, AdamW optimizer (lr=8e-4, weight_decay=0.03), 8K-step linear warmup. Captions encoded via CLIP text encoder as context tokens. Evaluation uses 30K randomly drawn prompts from the validation set.",
      "source": "Section 4.2, Section 4.1"
    },
    {
      "id": "hi-mar-D1-012",
      "claim": "Exponential moving average momentum: ema_momentum=0.9999 (applied to both ImageNet and MS-COCO training)",
      "source": "Section 4.2"
    },
    {
      "id": "hi-mar-D1-013",
      "claim": "Inference configuration: Phase 1 uses 32 autoregressive steps, Phase 2 uses 4 autoregressive steps, both with cosine schedule. Chosen as optimal speed/accuracy trade-off: Phase 1 FID saturates at 32 steps, Phase 2 FID nearly saturates at 4 steps given strong Phase 1 global structure guidance.",
      "source": "Section 4.2, Section 4.5"
    },
    {
      "id": "hi-mar-D1-014",
      "claim": "ImageNet dataset: 256x256 resolution, 1,281,167 training images from 1,000 classes.",
      "source": "Section 4.1"
    },
    {
      "id": "hi-mar-D1-015",
      "claim": "MS-COCO dataset: 256x256 resolution, 82,783 training images, 40,504 validation images, each image annotated with 5 captions.",
      "source": "Section 4.1"
    },
    {
      "id": "hi-mar-D1-016",
      "claim": "Low-resolution image size for Phase 1: 128x128 (half of the full 256x256 resolution)",
      "source": "Section 4.2"
    },
    {
      "id": "hi-mar-D1-017",
      "claim": "VAE encoder type and downsampling ratio: KL-16 (from MAR, 16x spatial downsampling). Shared encoder for both 128x128 and 256x256 inputs.",
      "source": "Section 4.2"
    },
    {
      "id": "hi-mar-D1-018",
      "claim": "GPU type used for experiments: H100-80GB (all training and inference speed measurements)",
      "source": "Section 4.2, Section 4.5"
    },
    {
      "id": "hi-mar-D1-019",
      "claim": "Speed/accuracy trade-off measurement configuration: measured on 1 H100 GPU with batch size 128 on ImageNet 256x256. DiT-XL/2 evaluated at diffusion steps [50, 75, 100, 250]; MAR-B evaluated at autoregressive steps [16, 32, 64, 128, 256]; Hi-MAR-B evaluated with Phase 1 fixed at 32 steps, Phase 2 varying [1, 2, 4, 6, 8].",
      "source": "Section 4.5"
    },
    {
      "id": "hi-mar-D1-020",
      "claim": "Latent token counts (KL-16 VAE): Phase 1 (128x128 input -> 8x8 latent grid) = 64 tokens; Phase 2 (256x256 input -> 16x16 latent grid) = 256 tokens.",
      "source": "Section 4.2"
    },
    {
      "id": "hi-mar-D1-021",
      "claim": "Hi-MAR-B ImageNet 256x256 benchmark results: w/o CFG: FID=2.44, IS=251.46, Precision=0.80, Recall=0.59; w/ CFG: FID=1.93, IS=293.0, Precision=0.81, Recall=0.59. Absolute FID improvement over MAR-B (FID=2.31 w/ CFG, 208M vs Hi-MAR-B 244M): 0.38.",
      "source": "Section 4.3, Table 2"
    },
    {
      "id": "hi-mar-D1-022",
      "claim": "Hi-MAR-L ImageNet 256x256 benchmark results: w/o CFG: FID=2.11, IS=278.63, Precision=0.79, Recall=0.62; w/ CFG: FID=1.66, IS=322.3, Precision=0.79, Recall=0.61.",
      "source": "Section 4.3, Table 2"
    },
    {
      "id": "hi-mar-D1-023",
      "claim": "Hi-MAR-H ImageNet 256x256 benchmark results: w/o CFG: FID=1.55, IS=300.72, Precision=0.80, Recall=0.63; w/ CFG: FID=1.52, IS=322.78, Precision=0.80, Recall=0.63.",
      "source": "Section 4.3, Table 2"
    },
    {
      "id": "hi-mar-D1-024",
      "claim": "Hi-MAR-S MS-COCO 256x256 text-to-image benchmark results: FID=4.77. Absolute FID improvement over best competitor AutoNAT-S (FID=5.36): 0.59. Comparison: AutoNAT-S FID=5.36, MAR FID=6.36, U-ViT-S/2 Deep FID=5.48.",
      "source": "Section 4.4, Table 3"
    },
    {
      "id": "hi-mar-D1-025",
      "claim": "Hi-MAR-S T2I-CompBench compositional alignment results: Attribute Binding (Color=0.3862, Shape=0.2782, Texture=0.3945); Object Relationship (Spatial=0.0409, Non-Spatial=0.2690); Complex=0.2313. Outperforms U-ViT-S/2 Deep and AutoNAT-S across all metrics.",
      "source": "Section 4.4, Table 4"
    },
    {
      "id": "hi-mar-D1-026",
      "claim": "Ablation study results (Hi-MAR-B, ImageNet w/ CFG): baseline MAR-B FID=2.31 (208M); +hierarchical pivots with visual tokens FID=2.28; +conditional tokens (mitigating train-inference discrepancy) FID=2.07; +Diffusion Transformer head Phase 2 only FID=1.98 (239M); +Diffusion Transformer head both phases FID=1.98 (233M); full Hi-MAR with scale vector FID=1.93 (242M).",
      "source": "Section 4.5, Table 5"
    },
    {
      "id": "hi-mar-D1-027",
      "claim": "Speed/accuracy trade-off result: Hi-MAR-B achieves a better Pareto frontier than both DiT-XL/2 and MAR-B. Phase 2 steps can be reduced from 8 to 1 with small FID degradation due to strong Phase 1 global structure guidance. Computational cost: 54% of MAR's cost at comparable quality.",
      "source": "Section 4.5, Figure 3; Abstract"
    },
    {
      "id": "hi-mar-D1-028",
      "claim": "Autoregressive steps impact: Phase 1 FID decreases with more steps, reaching optimal at 32 steps; Phase 2 FID nearly saturates at just 4 steps (when Phase 1 is fixed at 32). Optimal configuration chosen for production: Phase 1=32 steps, Phase 2=4 steps.",
      "source": "Section 4.5, Figure 4"
    }
  ],
  "D2": [
    {
      "id": "hi-mar-D2-001",
      "claim": "Hi-MAR employs a two-phase hierarchical masked autoregressive framework: Phase 1 predicts low-resolution tokens (64 tokens, 8x8 grid) to capture global structure; Phase 2 predicts dense tokens (256 tokens, 16x16 grid) guided by Phase 1 conditional token pivots. Formula: X'_s = mask(X_s, ceil(r_1*N_s)), r_1~Uniform[0.7,1.0]; Z^s = T_theta(X'_s, C); X'_l = mask(X_l, ceil(r_2*N_l)); Z^l = T_theta([C, Z^s, X'_l]). Diffusion loss: L(z_i, x_i) = E_{epsilon,t}[||epsilon - epsilon_theta(x_i^t | t, z_i)||^2], epsilon~N(0,I). (Sec 3.1-3.2)",
      "source": "Section 3.2, Section 1"
    },
    {
      "id": "hi-mar-D2-002",
      "claim": "Phase 1 performs bidirectional autoregressive modeling over low-resolution tokens (128x128 input), producing conditional tokens Z^s that reflect global structure. Formula: I_s in R^{128x128x3} -> VAE_enc -> I'_s in R^{8x8xd}, N_s=64. Masked tokens: X'_s = {x_i if i not in M, m_mask if i in M}, |M|=ceil(r*N_s). Z^s = Transformer(X'_s, C) = {z^s_1,...,z^s_64}. Per-token diffusion loss: L(z^s_i, x^s_i) = E_{epsilon,t}[||epsilon - epsilon_theta(x^t_i | t, z^s_i)||^2]. (Sec 3.1-3.2)",
      "source": "Section 3.2"
    },
    {
      "id": "hi-mar-D2-003",
      "claim": "Phase 2 conditions on conditional tokens Z^s from Transformer output (not ground-truth visual tokens X^s), mitigating training-inference discrepancy. Formula: training: Z^l_cond = T_theta([C, Z^s, X'_l]) where Z^s=T_theta(X'_s,C). inference: Z^l_cond = T_theta([C, Z_hat^s, X'_l]) where Z_hat^s=T_theta(X'_s,C). Both use Transformer-generated conditional tokens (not ground-truth X^s), ensuring P_train(Z^s|X_s) ~ P_infer(Z_hat^s|X_s). (Sec 3.2)",
      "source": "Section 3.2"
    },
    {
      "id": "hi-mar-D2-004",
      "claim": "Hi-MAR operates in continuous-valued space using pre-trained KL-16 VAE, avoiding vector quantization and its information loss. Formula: I in R^{HxWx3} -> VAE_enc(I) = I' in R^{hxwxd}, with h=H/16, w=W/16. Token sequence: X = reshape(I') = {x_1,...,x_N}, N=h*w. All tokens are real-valued vectors x_i in R^d (no discrete codebook). Decoder: I_hat = VAE_dec(rescale(X_hat)). Shared VAE for both Phase 1 (128x128->8x8, d) and Phase 2 (256x256->16x16, d). (Sec 3.1)",
      "source": "Section 3.1, Section 4.2"
    },
    {
      "id": "hi-mar-D2-005",
      "claim": "Scale-aware Transformer blocks with adaLN-Zero inject phase identity via learnable scale vector v = MLP(sinusoidal(phase_id)). Formula: v_tilde = a*v + b; alpha1,beta1,gamma1,alpha2,beta2,gamma2 = split(v_tilde); z_a = z^i + gamma1*Attn(alpha1*LN(z^i) + beta1); z^{i+1} = z_a + gamma2*FFN(alpha2*LN(z_a) + beta2). Different scale vectors for Phase 1 vs Phase 2 provide explicit resolution-specific guidance to the shared Transformer backbone. a,b are learnable parameters; split operates along channel dim. (Sec 3.2, Eq 2)",
      "source": "Section 3.2"
    },
    {
      "id": "hi-mar-D2-006",
      "claim": "Diffusion Transformer head replaces MLP-based diffusion head in Phase 2, using self-attention over all masked+unmasked conditional tokens. Formula: c = time_emb(t) + Z_cond (sum of time step embedding and conditional tokens); alpha1,beta1,gamma1,alpha2,beta2,gamma2 = split(c); y_a = y^i + gamma1*Attn(alpha1*LN(y^i) + beta1); y^{i+1} = y_a + gamma2*FFN(alpha2*LN(y_a) + beta2). Input y^0 = x^t (noise-corrupted vector). Stack of K blocks. Loss: L = E_{epsilon,t}[||epsilon - epsilon_theta^{DiT}(x^t | t, Z_cond)||^2]. (Sec 3.3, Eq 3)",
      "source": "Section 3.3"
    },
    {
      "id": "hi-mar-D2-007",
      "claim": "Phase 1 retains an MLP-based diffusion head (lighter weight) since its primary role is optimizing low-resolution conditional tokens as pivots. Phase 2 uses the heavier Diffusion Transformer head. Formula (MLP head): epsilon_theta^{MLP}(x_i^t | t, z_i) = MLP([t_emb; z_i]), predicting epsilon per-token independently. Formula (DiT head): epsilon_theta^{DiT}(x^t | t, Z_cond) = DiT_blocks(x^t + t_emb), using self-attention across all tokens. MLP head: O(N*d^2) per token; DiT head: O(N^2*d) attention complexity. (Sec 3.3)",
      "source": "Section 3.3"
    },
    {
      "id": "hi-mar-D2-008",
      "claim": "Training masking: Phase 1 masking ratio r_1 ~ Uniform[0.7, 1.0] (same as MAR's p(r)); Phase 2 uses cosine schedule r_2(t) = cos(pi*t / 2T) following MaskGIT. For MS-COCO text-to-image training: both phases sample r ~ Beta(alpha=4, beta=1). Formula: mask set M subset of {1..N}, |M| = ceil(r*N); X'_i = x_i if i not in M, else m_mask (learnable). Phase 1: N=64, Phase 2: N=256. Cosine schedule: r(step) = cos(pi * step / (2 * total_steps)). (Sec 4.2, Sec 3.1)",
      "source": "Section 4.2"
    },
    {
      "id": "hi-mar-D2-009",
      "claim": "Inference: Phase 1 uses T_1=32 AR steps (optimal, FID saturates beyond), Phase 2 uses T_2=4 AR steps (nearly saturated FID given Phase 1 guidance), both with cosine schedule. Formula: At step k in {1..T}, predict tau_k = ceil(cos(pi*k/2T) * N) tokens. For each masked position i: (a) predict x_hat_i, (b) compute confidence score, (c) keep top-tau_k most confident predictions, (d) re-mask remaining ceil(r*N)-tau_k tokens. Total inference steps: T_1+T_2=36 vs MAR's typical 64+. (Sec 4.5, Fig 3-4)",
      "source": "Section 4.2, Section 4.5"
    },
    {
      "id": "hi-mar-D2-010",
      "claim": "Hi-MAR instantiated in three scales (B/L/H) matching MAR backbone sizes, adding ~15-17% parameters for hierarchical components. Formula: Hi-MAR-B: 24 layers * d_model=768 -> 244M (vs MAR-B 208M, +17.3%); Hi-MAR-L: 32 layers * d_model=1024 -> 529M (vs MAR-L 479M, +10.4%); Hi-MAR-H: 40 layers * d_model=1280 -> 1090M (vs MAR-H 943M, +15.6%). Diff.Head_1 layers: 6/8/12; Diff.Head_2 layers: 6/8/12. All share the same KL-16 VAE tokenizer. (Sec 4.2, Table 1)",
      "source": "Section 4.2, Table 1"
    },
    {
      "id": "hi-mar-D2-011",
      "claim": "Hi-MAR integrates three key designs: (1) hierarchical two-phase Transformer with conditional token pivots, (2) scale-aware adaLN-Zero blocks, (3) Diffusion Transformer head. Formula: L_total = L_phase1 + L_phase2, where L_phase1 = E[||epsilon - epsilon^{MLP}_theta(x_i^t | t, z_i^s)||^2] over low-res tokens, L_phase2 = E[||epsilon - epsilon^{DiT}_theta(x_j^t | t, Z^s, z_j^l)||^2] over dense tokens. Ablation FID: baseline 2.31 -> +pivots 2.28 -> +cond 2.07 -> +DiT_head 1.98 -> +scale_vector 1.93. (Sec 3.1-3.3, Table 5)",
      "source": "Section 4.5, Table 5"
    },
    {
      "id": "hi-mar-D2-012",
      "claim": "Hi-MAR-B achieves FID=1.93 on ImageNet 256x256 w/ CFG (delta=0.38 over MAR-B) and FID=4.77 on MS-COCO 256x256 (delta=0.59 over AutoNAT-S). Computational cost: C_HiMAR/C_MAR approx 54%. Formula: FID = ||mu_r - mu_g||^2 + Tr(Sigma_r + Sigma_g - 2*(Sigma_r * Sigma_g)^{1/2}) where (mu_r, Sigma_r) and (mu_g, Sigma_g) are Inception-v3 feature statistics of real vs generated images. Phase 2 only needs 4 steps vs Phase 1's 32, yielding 54% cost while improving FID. (Sec 4.3-4.5, Abstract)",
      "source": "Abstract, Section 4.3, Section 4.4, Section 4.5"
    }
  ],
  "D3": [
    {
      "id": "hi-mar-D3-001",
      "claim": "Class-conditional image generation benchmark on ImageNet 256x256. Purpose: Compare Hi-MAR (B/L/H variants) against state-of-the-art models across GAN, diffusion, autoregressive, and masked autoregressive families under both w/o CFG and w/ CFG settings. For Hi-MAR under w/o CFG, CFG is turned off only during Phase 2 dense token prediction. Datasets: ImageNet (1,281,167 training images, 1,000 classes, 256x256 resolution). Baselines: GAN-based (BigGAN, GigaGAN, StyleGAN-XL); Diffusion-based (ADM, CDM, LDM-4-G, U-ViT-H/2, DiT-XL/2); Autoregressive (VQGAN, VQGAN-re, RQTransformer, GIVT, LlamaGen-L/XL/XXL, VAR-d16/d20/d24); Masked Autoregressive (MaskGIT, AutoNAT-L, MAR-B/L/H). Metrics: FID (lower better), Inception Score (higher better), Precision (higher better), Recall (higher better). Evaluation uses 50K generated samples.",
      "source": "Section 4.3, Table 2"
    },
    {
      "id": "hi-mar-D3-002",
      "claim": "Text-to-image generation benchmark on MS-COCO 256x256. Purpose: Compare a lightweight Hi-MAR-S (comparable size to U-ViT-S/2 Deep) against GAN, diffusion, and masked autoregressive baselines. Datasets: MS-COCO (82,783 training images, 40,504 validation images, each image annotated with 5 captions). Captions are converted to text embeddings via CLIP text encoder and fed as context tokens. Baselines: GAN (AttnGAN, DM-GAN, DF-GAN, XMC-GAN, LAFITE); Diffusion (VQ-Diffusion, Friro, U-ViT-S/2 Deep); Masked AR (AutoNAT-S, MAR). Metrics: FID (lower better, main metric), evaluated on 30K randomly drawn prompts from the validation set.",
      "source": "Section 4.4, Table 3"
    },
    {
      "id": "hi-mar-D3-003",
      "claim": "Compositional text-to-image alignment evaluation on T2I-CompBench. Purpose: Assess fine-grained compositional alignment between generated images and input text captions. Compare Hi-MAR-S against other MS-COCO-trained methods with similar parameter size. Datasets: T2I-CompBench (Huang et al., 2023), a comprehensive benchmark for open-world compositional text-to-image generation. Baselines: U-ViT-S/2 Deep, AutoNAT-S. Metrics: Attribute Binding (Color, Shape, Texture scores, higher better); Object Relationship (Spatial, Non-Spatial scores, higher better); Complex composition score (higher better).",
      "source": "Section 4.4, Table 4"
    },
    {
      "id": "hi-mar-D3-004",
      "claim": "Ablation study on ImageNet class-conditional generation. Purpose: Isolate the contribution of each Hi-MAR design component: (a) Hi-MAR Transformer with hierarchical pivots, (b) conditional tokens vs. visual tokens for cross-phase guidance, (c) MLP-based vs. Diffusion Transformer head per phase, (d) scale-aware Transformer block (scale vector). Datasets: ImageNet 256x256. Configurations: 6 ablated variants starting from baseline MAR-B (208M, FID=2.31 w/ CFG) and progressively adding components. Metrics: FID (lower better) and parameter count. The full Hi-MAR with all three key designs achieves FID=1.93.",
      "source": "Section 4.5, Table 5"
    },
    {
      "id": "hi-mar-D3-005",
      "claim": "Speed/accuracy trade-off analysis. Purpose: Compare the throughput-FID Pareto frontier of Hi-MAR-B against DiT-XL/2 and MAR-B. Datasets: ImageNet 256x256, measured on 1 H100 GPU with batch size 128. Baselines: DiT-XL/2 (varying diffusion steps: 50, 75, 100, 250); MAR-B (varying autoregressive steps: 16, 32, 64, 128, 256). Hi-MAR-B config: Phase 1 fixed at 32 steps, Phase 2 varying (1, 2, 4, 6, 8 steps). Metrics: FID vs. relative speed (samples/second or throughput).",
      "source": "Section 4.5, Figure 3"
    },
    {
      "id": "hi-mar-D3-006",
      "claim": "Impact of autoregressive steps analysis. Purpose: Study how the number of autoregressive steps in each phase affects generation quality. Datasets: ImageNet 256x256, using Hi-MAR-B. Sub-experiment (a): Vary Phase 1 steps while fixing Phase 2 at 4 steps -- FID decreases with more Phase 1 steps, optimal at 32. Sub-experiment (b): Vary Phase 2 steps while fixing Phase 1 at 32 steps -- FID nearly saturates at just 4 Phase 2 steps. Metrics: FID (lower better). Result: Phase 1=32 and Phase 2=4 chosen as optimal trade-off between generation quality and inference speed.",
      "source": "Section 4.5, Figure 4"
    }
  ],
  "D4": [
    {
      "id": "hi-mar-D4-001",
      "claim": "Hi-MAR Full Method Execution Pipeline: (1) Input image resized to 128x128 and 256x256 -- both encoded via shared KL-16 VAE into latent token sequences (64 tokens for Phase 1, 256 tokens for Phase 2); (2) Phase 1 -- masked low-resolution tokens concatenated with context tokens (class/text embeddings) fed into Hi-MAR Transformer with scale-aware adaLN-Zero blocks, MLP-based diffusion head denoises and reconstructs conditional tokens Z^s; (3) Phase 2 -- input sequence [context tokens, Z^s from Phase 1, masked dense tokens] processed by same Hi-MAR Transformer (different scale vector), Diffusion Transformer head with self-attention over all tokens predicts final dense token sequence; (4) Output -- VAE decoder reconstructs 256x256 image from Phase 2 dense tokens.",
      "source": "Section 3.2, Section 3.3, Figure 2"
    },
    {
      "id": "hi-mar-D4-002",
      "claim": "Phase 1: Low-Resolution Sub-Pipeline -- (a) Input: image resized to 128x128; (b) Encoding: KL-16 VAE encoder produces 64 latent tokens (8x8 grid); (c) Masking: r ~ Uniform[0.7, 1.0] for ImageNet, or Beta(4,1) for MS-COCO; (d) Context preparation: class tokens (ImageNet via learnable embedding) or CLIP text embeddings (MS-COCO) appended; (e) Transformer: Hi-MAR Transformer with scale-aware blocks (sinusoidal embedding -> MLP -> scale vector v -> adaLN-Zero: alpha1,beta1,gamma1 for self-attention, alpha2,beta2,gamma2 for FFN) outputs conditional tokens Z^s; (f) Diffusion: MLP-based diffusion head conditioned on Z^s performs denoising (standard epsilon-prediction, randomly sampled timestep t) to reconstruct low-resolution latent tokens; (g) Phase 1 loss: L(z_i^s, x_i^s) = E_{epsilon,t}[||epsilon - epsilon_theta(x_i^t | t, z_i^s)||^2].",
      "source": "Section 3.2, Section 4.2, Figure 2(b)(c)(d)"
    },
    {
      "id": "hi-mar-D4-003",
      "claim": "Phase 2: High-Resolution Sub-Pipeline -- (a) Input: full 256x256 image; (b) Encoding: same KL-16 VAE encoder produces 256 latent tokens (16x16 grid); (c) Masking: cosine schedule (ImageNet) or Beta(4,1) distribution (MS-COCO); (d) Context preparation: concatenate [context tokens, Z^s conditional tokens from Phase 1 output, masked dense tokens] into single input sequence; (e) Transformer: same Hi-MAR Transformer backbone (different scale vector for Phase 2) processes full sequence, producing dense conditional tokens; (f) Diffusion: Diffusion Transformer head (stack of Transformer blocks with adaLN conditioned on time step embedding + conditional tokens) applies self-attention over all masked and unmasked tokens to model inter-token dependencies; (g) Phase 2 loss: same epsilon-prediction diffusion loss as Phase 1 but applied over dense token sequence.",
      "source": "Section 3.2, Section 3.3, Section 4.2, Figure 2(b)(c)(e)"
    },
    {
      "id": "hi-mar-D4-004",
      "claim": "Ordered Experimental Protocols -- (1) Class-conditional training on ImageNet 256x256: AdamW(beta1=0.9, beta2=0.95, wd=0.02), constant lr=1e-4, 100-epoch warmup, 800 epochs, uniform masking Phase 1 + cosine masking Phase 2; (2) Text-to-image training on MS-COCO 256x256: CLIP text encoder for caption embeddings, Beta(4,1) masking, AdamW(lr=8e-4, wd=0.03), 8K-step warmup; (3) ImageNet evaluation: 50K samples, CFG turned off only in Phase 2 for w/o CFG setting, metrics=FID/IS/Precision/Recall; (4) MS-COCO evaluation: 30K prompts from validation set, FID only; (5) Ablation study: 6 configurations sequentially adding hierarchical pivots, conditional tokens, Diffusion Transformer head per phase, and scale vector; (6) Speed/accuracy: fix Phase 1=32, vary Phase 2=[1,2,4,6,8] on 1 H100, batch 128; (7) AR steps analysis: sweep Phase 1 and Phase 2 steps independently.",
      "source": "Section 4.2, Section 4.3, Section 4.4, Section 4.5"
    }
  ]
}