{
  "paper_id": "nfig",
  "paper_title": "NFIG: Multi-Scale Autoregressive Image Generation via Frequency Ordering",
  "D1": [
    {
      "id": "nfig-D1-001",
      "claim": "ImageNet ILSVRC 2012: 1.2M train / 50k val / 100k test images, 1000 categories, 256x256x3 resolution",
      "source": "Section 4.1"
    },
    {
      "id": "nfig-D1-002",
      "claim": "FR-VAE tokenizer: VQGAN framework, DINO discriminator, DINOv2-base encoder, XQGAN implementation strategy, codebook K=4096, n=10 frequency bands, scale_factors [1,2,3,4,5,6,8,10,13,16], 680 total tokens",
      "source": "Section 3.1, Section 4.1"
    },
    {
      "id": "nfig-D1-003",
      "claim": "NFIG Transformer: VAR backbone (decoder-only), depth 16, block-wise causal attention, Next-Frequency Prediction (coarse-to-fine), model sizes 310M/600M, token sequence length 680 (vs AR baseline 256)",
      "source": "Section 3.2, Section 4.1"
    },
    {
      "id": "nfig-D1-004",
      "claim": "Frequency band division: n=10 frequency bands with increasing scale sequence, lower-frequency bands get fewer tokens (smaller h_i*w_i), higher-frequency bands get more tokens (larger h_i*w_i), bandwidth per band proportional to its token count ratio h_i*w_i / sum_j(h_j*w_j), with h_n=H', w_n=W'",
      "source": "Section 3.2, Eq. 9"
    },
    {
      "id": "nfig-D1-005",
      "claim": "NFIG training: PyTorch, NVIDIA H100, Adam optimizer, lr=8e-5, batch_size=768, 350 epochs (VAR baseline: 200ep for 310M, 250ep for 600M, 300ep for 1B, 350ep for 2B); scaling study at 55 epochs; epoch comparison at 200/250/300/350 epochs",
      "source": "Section 4.1, Section 4.2"
    },
    {
      "id": "nfig-D1-006",
      "claim": "FR-VAE loss weights: reconstruction_loss=1.0, frequency_quantized_loss=1.0, LPIPS perceptual loss=1.0, GAN loss=0.5",
      "source": "Appendix B.1, Eq. 10"
    },
    {
      "id": "nfig-D1-007",
      "claim": "NFIG inference: CFG=4.5, top_k=990, 10 inference steps",
      "source": "Section 4.1"
    }
  ],
  "D2": [
    {
      "id": "nfig-D2-001",
      "claim": "f_hat_i = F^{-1}(F(f) .* M_i) — Frequency-guided Decomposer: decomposes encoder feature map f into n frequency components via FFT-based masking and inverse FFT, each mask M_i selects a specific frequency band",
      "source": "Section 3.1.1, Eq. 1"
    },
    {
      "id": "nfig-D2-002",
      "claim": "f_tilde = sum_{i=1}^{n} T(f_hat_i, H', W') — Frequency-guided Composer: merges frequency components of potentially different resolutions back into a unified feature map by interpolating each to H'xW' and summing",
      "source": "Section 3.1.1, Eq. 2"
    },
    {
      "id": "nfig-D2-003",
      "claim": "v_0 = argmin ||f_hat_0 - Z(v_0)||^2; R_0 = f_hat_0 - Z(v_0); for i>=1: v_i = argmin ||(R_{i-1}+f_hat_i) - Z(v_i)||^2; R_i = R_{i-1} + (f_hat_i - Z(v_i)) — Residual Token Extraction: progressive frequency-band quantization with cumulative residual R_i tracking unencoded signal through level i",
      "source": "Section 3.1.2, Eq. 4"
    },
    {
      "id": "nfig-D2-004",
      "claim": "t^{(j,k)} = lookup(Z, argmin_{z in Z} ||z - v_i^{(j,k)}||_2) — Vector Quantization: converts continuous feature vectors to discrete codebook indices via nearest-neighbor L2 lookup in learnable codebook Z (KxC)",
      "source": "Section 3.1.2, Eq. 5"
    },
    {
      "id": "nfig-D2-005",
      "claim": "p(T_1,...,T_n) = prod_{i=1}^{n} p(T_i | T_1,...,T_{i-1}) — Next-Frequency Autoregressive Prediction: factorizes joint token distribution as product of conditionals from low to high frequency (coarse-to-fine), with block-wise causal attention enforcing band-level autoregressive ordering",
      "source": "Section 3.2, Eq. 7"
    },
    {
      "id": "nfig-D2-006",
      "claim": "sigma_i = sigma_{i-1} + (h_i*w_i / sum_j(h_j*w_j)) * sigma_max — Frequency Band Division Strategy: allocates bandwidth proportionally to token count (h_i*w_i) of each band; low-frequency bands get narrower bandwidth, high-frequency bands get wider bandwidth",
      "source": "Section 3.2, Eq. 9"
    },
    {
      "id": "nfig-D2-007",
      "claim": "L = ||I - I_hat||_2^2 + ||f - f_hat||_2^2 + L_p(I) + 0.5 * L_g(I) — FR-VAE Total Loss: pixel MSE + feature MSE + LPIPS perceptual loss + 0.5x GAN adversarial loss (DINO discriminator); additional VQ codebook/commitment losses not shown",
      "source": "Appendix B.1, Eq. 10"
    },
    {
      "id": "nfig-D2-008",
      "claim": "L(T, T_tilde) = -sum_{i=1}^{n} t_i * log(t_tilde_i) — NFIG Transformer Cross-Entropy Loss: standard autoregressive next-token prediction loss over all frequency-band tokens with block-wise causal masking",
      "source": "Appendix B.1, Eq. 11"
    },
    {
      "id": "nfig-D2-009",
      "claim": "Block-wise Causal Attention (referenced from VAR [19]): decoder-only transformer enforces autoregressive ordering across frequency bands — tokens in lower-frequency bands (1..i-1) are visible to band i, while higher-frequency bands (i+1..n) are masked; attention within each frequency block follows VAR's block-wise scheme",
      "source": "Section 3.2"
    }
  ],
  "D3": [
    {
      "id": "nfig-D3-001",
      "claim": "Main Generation Experiment: class-conditional ImageNet 256x256 generation, train FR-VAE tokenizer then NFIG-310M Transformer (350 epochs, Adam lr=8e-5, batch=768, H100), inference with CFG=4.5 top_k=990 in 10 steps; compared against GAN (BigGAN, GigaGAN, StyleGAN-XL), Diffusion (ADM, CDM, LDM-4-G, DiT-L/2, DiT-XL/2, L-DiT-3B/7B), Mask Diffusion (MaskGIT, RCG), AR (VQVAE-2, VQGAN, ViTVQ, RQTransformer, FAR-B/H, XQGAN-310M, VAR-d16/d20); metrics: gFID, rFID, IS, Precision, Recall, params, steps, relative inference time",
      "source": "Section 4.1, Section 4.2, Table 2"
    },
    {
      "id": "nfig-D3-002",
      "claim": "Ablation Study: incremental component contribution on ImageNet val 50k — baseline AR (seq_len=256) → +FR-Quantizer (seq_len=680) → +DINO-Disc → +AdaLN Transformer → +Top_k → +CFG=full NFIG; each variant trained from scratch with same FR-VAE; evaluated by rFID and gFID",
      "source": "Section 4.3, Table 5"
    },
    {
      "id": "nfig-D3-003",
      "claim": "Scaling Study: NFIG-310M vs NFIG-600M trained for 55 epochs (limited compute budget), same FR-VAE tokenizer, Adam lr=8e-5 batch=768; compare FID/IS/Precision/Recall between scales to validate scaling behavior",
      "source": "Section 4.2, Table 3"
    },
    {
      "id": "nfig-D3-004",
      "claim": "Epoch Efficiency Comparison: NFIG-310M trained at 200/250/300/350 epochs vs VAR-d16 (310M, 200ep) and VAR-d20 (600M, 250ep); validate that NFIG-310M at 200ep outperforms VAR-d16 and at 350ep matches VAR-d20 despite 2x fewer params; metrics: FID, IS, Precision, Recall",
      "source": "Section 4.2, Table 4"
    },
    {
      "id": "nfig-D3-005",
      "claim": "Frequency Distribution Analysis: generate images with NFIG and visualize intermediate results at steps 2/4/6/8/10; compute FFT frequency spectrum at each step to show progressive low-to-high refinement; compare VQ loss across scale factors between NFIG and VAR to demonstrate more balanced feature learning",
      "source": "Section 4.4, Figure 4, Figure 5"
    },
    {
      "id": "nfig-D3-006",
      "claim": "Frequency Keep Ability Analysis: compare NFIG vs VAR-16 on ImageNet using PSD (Power Spectral Density, lower is better) and FKS (Frequency Keep Score, weighted: Low 0.57, Mid 0.28, High 0.15, higher is better) across low/mid/high frequency bands",
      "source": "Appendix B.2"
    },
    {
      "id": "nfig-D3-007",
      "claim": "Cross-Dataset FR-VAE Reconstruction: evaluate zero-shot reconstruction on DTD, QRCODE, Diagrams, Chest-X, CelebA-HQ, COCO, LSUN-Bedroom using ImageNet-pretrained FR-VAE; compute rFID between original and reconstructed images per dataset",
      "source": "Appendix B.4"
    }
  ],
  "D4": [
    {
      "id": "nfig-D4-001",
      "claim": "NFIG main pipeline (paper-specified generation workflow): (1) Train FR-VAE image tokenizer with frequency-guided residual quantization + VQGAN losses → (2) Train NFIG Transformer on FR-VAE ground-truth frequency tokens with cross-entropy loss → (3) Inference: generate tokens autoregressively from low to high frequency (10 steps), decode via FR-VAE decoder",
      "source": "Section 4.1"
    },
    {
      "id": "nfig-D4-002",
      "claim": "Ablation experiment sequence (paper-specified): (1) Incrementally add components to baseline AR model (FR-Quantizer → DINO-Disc → AdaLN → Top_k → CFG) → (2) Train each variant from scratch with same FR-VAE tokenizer → (3) Evaluate rFID and gFID on ImageNet validation set",
      "source": "Section 4.3"
    },
    {
      "id": "nfig-D4-003",
      "claim": "Scaling study sequence: (1) Train NFIG-310M for 55 epochs → (2) Train NFIG-600M for 55 epochs → (3) Compare FID/IS/Precision/Recall between the two scales under same limited compute budget",
      "source": "Section 4.2"
    },
    {
      "id": "nfig-D4-004",
      "claim": "Epoch efficiency comparison sequence: (1) Train NFIG-310M for multiple epoch budgets (200, 250, 300, 350) → (2) Compare against VAR-d16 (310M, 200ep) and VAR-d20 (600M, 250ep) → (3) Validate NFIG-310M at 200ep already outperforms VAR-d16, and at 350ep matches VAR-d20 despite 2x fewer parameters",
      "source": "Section 4.2"
    },
    {
      "id": "nfig-D4-005",
      "claim": "Frequency visualization sequence: (1) Generate images with NFIG, capture intermediates at steps 2/4/6/8/10 → (2) Compute FFT frequency spectrum at each step to visualize progressive low-to-high frequency refinement → (3) Compare VQ loss per scale factor between NFIG and VAR to demonstrate balanced feature learning",
      "source": "Section 4.4"
    },
    {
      "id": "nfig-D4-006",
      "claim": "Frequency Keep Ability analysis sequence: (1) Generate images from both NFIG and VAR-16 → (2) Compute Power Spectral Density (PSD) for both → (3) Compute Frequency Keep Score (FKS) with weighted per-band similarity (Low 0.57, Mid 0.28, High 0.15) → (4) Compare per-band fidelity between models",
      "source": "Appendix B.2"
    },
    {
      "id": "nfig-D4-007",
      "claim": "Cross-dataset FR-VAE evaluation sequence: (1) Load ImageNet-pretrained FR-VAE tokenizer → (2) Encode and decode images from each target dataset (DTD, QRCODE, Diagrams, Chest-X, CelebA-HQ, COCO, LSUN-Bedroom) → (3) Compute rFID between original and reconstructed images per dataset",
      "source": "Appendix B.4"
    }
  ]
}