{
  "paper_id": "moe-pot",
  "paper_title": "MoE-POT: Mixture-of-Experts Operator Transformer for Large-Scale PDE Pre-Training",
  "D1": [
    {
      "id": "moe-pot-D1-001",
      "claim": "Model architecture (size-invariant, confirmed by Table 5): N_r=16 routed experts, N_s=2 shared experts, Top-K=4, total 6 activated experts per input (4 routed + 2 shared); N_r, N_s, K invariant across Tiny/Small/Medium",
      "source": "Section 4 (lines 128, 134, 142), Section 1 (line 26), Section 3.2 (lines 81-83), Table 5"
    },
    {
      "id": "moe-pot-D1-002",
      "claim": "Per-size attention dimension (Table 5): attention_dim=512 (Tiny) / 1024 (Small) / 1024 (Medium)",
      "source": "Table 5 (Appendix B.3)"
    },
    {
      "id": "moe-pot-D1-003",
      "claim": "Per-size MLP hidden dimension (Table 5): mlp_dim=512 (Tiny) / 1024 (Small) / 2048 (Medium)",
      "source": "Table 5 (Appendix B.3)"
    },
    {
      "id": "moe-pot-D1-004",
      "claim": "Per-size transformer layers (Table 5): num_layers=4 (Tiny) / 6 (Small) / 8 (Medium)",
      "source": "Table 5 (Appendix B.3)"
    },
    {
      "id": "moe-pot-D1-005",
      "claim": "Per-size attention heads (Table 5): num_heads=4 (Tiny) / 8 (Small) / 8 (Medium)",
      "source": "Table 5 (Appendix B.3)"
    },
    {
      "id": "moe-pot-D1-006",
      "claim": "Per-size total parameters (Table 5): 30M (Tiny) / 166M (Small) / 489M (Medium)",
      "source": "Table 5, Section 5 (line 188)"
    },
    {
      "id": "moe-pot-D1-007",
      "claim": "Activated params (T/S/M): 17M / 90M / 288M. Note: Section 5 body text says 188M for Medium but Table 3 and Table 5 consistently show 288M — the 188M value is a typo in the MoE-POT paper",
      "source": "Table 5, Table 3, Section 5 (line 188)"
    },
    {
      "id": "moe-pot-D1-008",
      "claim": "Pre-training config: Adam optimizer (β1=0.9, β2=0.9), lr=1e-3, One-cycle schedule, weight_decay=1e-6, 1000 epochs (200 warmup), batch_size=20 on 8x RTX 4090 (24GB), T=10 input timesteps, load_balance_weight w_bal=0.1, dataset_sampling_weight w_k=1",
      "source": "Section 5 (line 180), Section B.3 (lines 401-403), Section 4 (line 160)"
    },
    {
      "id": "moe-pot-D1-009",
      "claim": "Fine-tuning config: lr=1e-3, One-cycle schedule, 200 epochs (40 warmup), router-gating network parameters frozen, only expert networks updated",
      "source": "Section B.3 (line 408), Section 5.1 (line 192)"
    },
    {
      "id": "moe-pot-D1-010",
      "claim": "Downstream task config: lr=1e-3, One-cycle schedule, 500 epochs (100 warmup)",
      "source": "Section 5.2 (line 198), Section B.3 (line 408)"
    },
    {
      "id": "moe-pot-D1-011",
      "claim": "Data preprocessing: spatial resolution H=128 (lower-res upscaled, higher-res downscaled), patch_size P=8 (Conv2D kernel PxP stride P), padding_constant=1 for unused channel entries",
      "source": "Section B.1 (lines 373-375), Section B.3 (line 403), Section C.1 (line 500)"
    },
    {
      "id": "moe-pot-D1-012",
      "claim": "Pre-training dataset splits (train/test): FNO-NS(1e-5)=1000/200, FNO-NS(1e-3)=1000/200, PDEBench-CNS(0.1,0.01)=9000/200, PDEBench-SWE=900/60, PDEBench-DR=900/60, CFDBench=9000/1000; total 6 datasets from 3 benchmark collections",
      "source": "Table 6, Section 5 (line 178)"
    },
    {
      "id": "moe-pot-D1-013",
      "claim": "Downstream dataset splits (train/test): NS(1e-4)=2000/200, CNS(1,0.01)=2000/200, PDEArena=2000/200",
      "source": "Table 7"
    },
    {
      "id": "moe-pot-D1-014",
      "claim": "Dataset mixture counts (Appendix C.5 negative transfer analysis): 6-dataset (base: NS(1e-5), NS(1e-3), CNS(0.1,0.01), SWE, DR, CFDBench); 10-dataset (base + NS(1e-4), CNS(1,0.1), 2x PDEArena NS tasks); 12-dataset (10-set + CNS(1,0.01), CNS(0.1,0.1))",
      "source": "Section C.5 (lines 579-581)"
    },
    {
      "id": "moe-pot-D1-015",
      "claim": "N_r (routed experts per layer) ablation: tested [8, 16, 32], selected 16 — error stable when N_r sufficiently large, balance of performance and computational cost",
      "source": "Table 4, Section 5.6 (line 235)"
    },
    {
      "id": "moe-pot-D1-016",
      "claim": "Top-K ablation: tested [1, 2, 4], selected 4 — larger K reduces error with diminishing returns, 4 is optimal trade-off",
      "source": "Table 4, Section 5.6 (line 235)"
    },
    {
      "id": "moe-pot-D1-017",
      "claim": "Number of heads h ablation: tested [2, 4, 8], selected 4 — minimal impact on error but affects computational cost",
      "source": "Table 8, Section C.1 (line 500)"
    },
    {
      "id": "moe-pot-D1-018",
      "claim": "Patch size P ablation: tested [4, 8, 16], selected 8 — medium patch sizes reduce error, 8 chosen for optimal performance",
      "source": "Table 8, Section C.1 (line 500)"
    },
    {
      "id": "moe-pot-D1-019",
      "claim": "Few-shot sample sizes — in-distribution (NS(1e-4)): [16, 32, 64, 128, 512, 2000]; models fine-tuned 500 epochs at each sample size",
      "source": "Table 13, Section C.4 (line 557)"
    },
    {
      "id": "moe-pot-D1-020",
      "claim": "Few-shot sample sizes — out-of-distribution (Wave-Layer): [16, 32, 64, 128]; models fine-tuned 500 epochs at each sample size",
      "source": "Table 14, Section C.4 (line 557)"
    },
    {
      "id": "moe-pot-D1-021",
      "claim": "Classification emergence eval epochs: [50, 150, 250] — router classification accuracy tracked over pre-training to measure emergence of dataset identification capability",
      "source": "Table 16, Section C.6 (line 599)"
    },
    {
      "id": "moe-pot-D1-022",
      "claim": "Poseidon baseline activated params (used in Appendix C.2.2 comparison): Poseidon-T=21M, Poseidon-B=158M",
      "source": "Table 10, Section C.2.2"
    }
  ],
  "D2": [
    {
      "id": "moe-pot-D2-001",
      "claim": "Balanced Data Sampling Probability: p_k = w_k / (K * |D_k| * sum_{j=1}^{K} w_j), where w_k is importance weight (w_k=1 for all datasets), |D_k| is dataset size, K=6 datasets. Ensures proportional representation of datasets with fewer samples.",
      "source": "B.1"
    },
    {
      "id": "moe-pot-D2-002",
      "claim": "Noise Injection for Denoising Pre-training: epsilon ~ N(0, epsilon_bar * ||u^{<t}|| * I), input = u^{<t} + epsilon. Applied only during pre-training (not fine-tuning/inference) to improve robustness and reduce train-inference discrepancy.",
      "source": "2.2"
    },
    {
      "id": "moe-pot-D2-003",
      "claim": "Patchification with Learnable Positional Encoding: Z_p^t = P(u^t + p^t) for t=1..T, where P is Conv2D (kernel PxP, stride P), p^t encodes spatial (x_i,y_j) and temporal (t) coordinates via learnable matrix W_p. Partitions spatial domain into non-overlapping patches.",
      "source": "4"
    },
    {
      "id": "moe-pot-D2-004",
      "claim": "Temporal Aggregation with Fourier Features: z_agg = sum_{t=1}^{T} W_t(z_p^t) * exp(-i * gamma * t), aggregating T input frames weighted by learned Fourier-modulated convolution. Real-valued implementation splits into sin/cos components.",
      "source": "4"
    },
    {
      "id": "moe-pot-D2-005",
      "claim": "Multi-head Fourier Layer (AFNO-style): Split input into h heads, apply MLP in Fourier domain per head — z_{0i}^l(x) = F^{-1}[W_{2,i}^l * sigma(W_{1,i}^l * F[z_i^l] + b_{1,i}^l) + b_{2,i}^l](x). Translation-invariant kernel integral operator in frequency domain.",
      "source": "4"
    },
    {
      "id": "moe-pot-D2-006",
      "claim": "MoE Router Gating (Softmax over Routing Logits): s^l(z_0^l(x)) = G^l(z_0^l(x)), w^l(z_0^l(x)) = Softmax(s^l(z_0^l(x))) in R^{N_r}. Router CNN G^l preserves spatial information; softmax normalizes across N_r=16 routed experts.",
      "source": "4"
    },
    {
      "id": "moe-pot-D2-007",
      "claim": "MoE TopK Expert Selection: TopK(w^l) = {(i_k, w_k^l)}_{k=1}^{K}, selecting K=4 largest entries from softmax distribution. Non-selected experts masked to zero; 4/16 = 25% activation per input.",
      "source": "4"
    },
    {
      "id": "moe-pot-D2-008",
      "claim": "MoE Output Aggregation (Shared + TopK Routed Experts): z^{l+1}(x) = (1/N_s) * sum_{i=1}^{N_s} E_i^{l(s)}(z_0^l(x)) + sum_{k=1}^{K} w_k^l * E_{i_k}^{l(r)}(z_0^l(x)). N_s=2 shared experts always activated capture universal PDE properties; K=4 routed experts specialize in dataset-specific features.",
      "source": "4"
    },
    {
      "id": "moe-pot-D2-009",
      "claim": "Load Balancing Loss (per-layer CV-based): Importance_i^l = sum_{b=1}^{B} w_{i,b}^l(x), L_balance^l = w_bal * CV({Importance_i^l}_{i=1}^{N_r})^2 with w_bal=0.1. Uses full softmax (before TopK masking) to regularize uniform expert utilization and prevent routing collapse.",
      "source": "4"
    },
    {
      "id": "moe-pot-D2-010",
      "claim": "Final Training Loss (Next-Frame MSE + Load Balancing): L = sum_{t=1}^{T} ||G_w(u^{<t} + epsilon) - u^t||_2^2 + sum_{l=1}^{N} L_balance^l. Auto-regressive denoising prediction + per-block auxiliary load balancing loss; only prediction loss used during inference.",
      "source": "4"
    },
    {
      "id": "moe-pot-D2-011",
      "claim": "Auto-regressive Inference Rollout: u^{i+T} = G_w(u^i, ..., u^{i+T-1}) for i=0..M-T. Sliding window of T=10 frames; model feeds own predictions as input for subsequent steps. No noise injection at inference.",
      "source": "B.3"
    },
    {
      "id": "moe-pot-D2-012",
      "claim": "L2 Relative Error (L2RE) Evaluation Metric: Rel-l2 = ||x_pred - x_gt||_2 / ||x_gt||_2. Primary evaluation metric throughout all experiments; equivalent to normalized root-mean-square error (NRMSE).",
      "source": "5"
    },
    {
      "id": "moe-pot-D2-013",
      "claim": "Average Expert Distribution per Dataset (Interpretability Step 1): Y_i = (1/N_i) * sum_{j=1}^{N_i} Y_{ij} in R^{16}. Computes representative expert activation fingerprint for each pre-training dataset using full softmax output (before TopK).",
      "source": "B.4"
    },
    {
      "id": "moe-pot-D2-014",
      "claim": "Cross-entropy Distance for Dataset Identification (Interpretability Step 2): f(I_0, Y_i) = -sum_{k=1}^{16} I_{0,k} * log(Y_{i,k}). Measures similarity between new input's routing distribution I_0 and dataset i's reference distribution Y_i.",
      "source": "B.4"
    },
    {
      "id": "moe-pot-D2-015",
      "claim": "Nearest Dataset Classification via Argmin (Interpretability Step 3): i_0 = argmin_{i in {1..6}} f(I_0, Y_i). Classifies input X to the dataset i_0 whose pre-computed average routing distribution Y_i has the minimum cross-entropy distance to the input's routing distribution I_0.",
      "source": "B.4"
    }
  ],
  "D3": [
    {
      "id": "moe-pot-D3-001",
      "claim": "Evaluate small (non-pre-trained) neural operators trained individually on each single PDE dataset from scratch. Datasets: FNO-NS(1e-5), FNO-NS(1e-3), PDEBench-CNS(0.1,0.01), PDEBench-SWE, PDEBench-DR, CFDBench. Baselines: FNO (0.5M), UNet (25M), FFNO (1.2M), GK-T (1.1M), Oformer (1.8M), GNOT (2.2M). Metric: L2RE.",
      "source": "Section 5.1 Main Experiments (Table 1, Small Model part)"
    },
    {
      "id": "moe-pot-D3-002",
      "claim": "Evaluate zero-shot performance of pre-trained models on 6 PDE datasets after joint pre-training (auto-regressive denoising, T=10, noise injection, balanced sampling w_k=1). Preprocessing: spatial resolution H=128, channel padding, patchification P=8. Training: Adam lr=1e-3, weight_decay=1e-6, one-cycle 1000 epochs (200 warm-up), batch size 20, 8x RTX 4090, w_bal=0.1. Datasets: FNO-NS(1e-5), FNO-NS(1e-3), PDEBench-CNS(0.1,0.01), PDEBench-SWE, PDEBench-DR, CFDBench. Baselines: FNO-T/S/M, DPOT-T/S/M, MoE-POT-T/S/M. Metric: L2RE.",
      "source": "Section 5.1 Main Experiments (Table 1, Pre-trained part), Section B.1, Section B.3"
    },
    {
      "id": "moe-pot-D3-003",
      "claim": "Evaluate fine-tuned performance: after joint pre-training, each model fine-tuned separately on each individual dataset (200 epochs, one-cycle lr=1e-3, 40 warm-up). Router-gating frozen; only expert networks updated. Datasets: same 6. Baselines: DPOT-T/S/M, MoE-POT-T/S/M (fine-tuned). Metric: L2RE.",
      "source": "Section 5.1 Main Experiments (Table 1, Fine-tuned part), Section B.3"
    },
    {
      "id": "moe-pot-D3-004",
      "claim": "Evaluate knowledge transfer to downstream PDE tasks (NS(1e-4), CNS(1,0.01), PDEArena) comparing train-from-scratch vs. pre-train+fine-tune. Downstream fine-tuning: 500 epochs, one-cycle (100 warm-up), lr=1e-3. Datasets: NS(1e-4) train=2000/test=200, CNS(1,0.01) train=2000/test=200, PDEArena train=2000/test=200. Baselines: Geo-FNO, U-Net, FFNO (scratch), DPOT-S w/o and w/ pre-train, MoE-POT-S w/o and w/ pre-train. Metric: L2RE.",
      "source": "Section 5.2 Downstream Tasks Experiments (Table 2), Section B.3"
    },
    {
      "id": "moe-pot-D3-005",
      "claim": "Study scaling laws: compare dense scaling (DPOT-T/S/M/L: 7.5M-493M) vs. sparse MoE scaling (MoE-POT-T/S/M: 17M-288M activated). Plot L2RE vs. activated parameters for both zero-shot and fine-tuned settings across 6 pre-training datasets. Datasets: FNO-NS(1e-5), FNO-NS(1e-3), PDEBench-CNS(0.1,0.01), PDEBench-SWE, PDEBench-DR, CFDBench. Metric: L2RE(zero-shot, fine-tuned).",
      "source": "Section 5.3 Scaling Experiments (Figure 4 a,b)"
    },
    {
      "id": "moe-pot-D3-006",
      "claim": "Compare average single-step inference time (ms) across model variants on NS(1e-5). Demonstrates MoE achieves lower inference time at equivalent total parameter counts via sparse activation. Baselines: DPOT-T/S/M/L. Metrics: inference time (ms/step), activated parameters (M), total parameters (M).",
      "source": "Section 5.5 Inference Time Analysis (Table 3)"
    },
    {
      "id": "moe-pot-D3-007",
      "claim": "Ablation on N_r (routed experts): train MoE-POT-T with N_r in {8, 16, 32}, compare averaged zero-shot L2RE across 6 datasets. Selected: N_r=16. Metric: L2RE (averaged zero-shot).",
      "source": "Section 5.6 Ablation Experiments (Table 4, left part)"
    },
    {
      "id": "moe-pot-D3-008",
      "claim": "Ablation on Top-K (expert selections): train MoE-POT-T with Top-K in {1, 2, 4} (N_r=16 fixed), compare averaged zero-shot L2RE across 6 datasets. Selected: K=4. Metric: L2RE (averaged zero-shot).",
      "source": "Section 5.6 Ablation Experiments (Table 4, right part)"
    },
    {
      "id": "moe-pot-D3-009",
      "claim": "Ablation on attention heads (h): train MoE-POT-T with h in {2, 4, 8}, compare averaged zero-shot L2RE across 6 datasets. Selected: h=4. Metric: L2RE (averaged zero-shot).",
      "source": "Appendix C.1 Partial Hyperparameter Ablation Experiment (Table 8, left part)"
    },
    {
      "id": "moe-pot-D3-010",
      "claim": "Ablation on patch size (P): train MoE-POT-T with P in {4, 8, 16}, compare averaged zero-shot L2RE across 6 datasets. Selected: P=8. Metric: L2RE (averaged zero-shot).",
      "source": "Appendix C.1 Partial Hyperparameter Ablation Experiment (Table 8, right part)"
    },
    {
      "id": "moe-pot-D3-011",
      "claim": "Compare MoE-POT zero-shot L2RE against DPOT-L (493M dense, largest DPOT variant) on 6 pre-training datasets. Demonstrates MoE-POT with fewer activated parameters achieves competitive/superior zero-shot performance vs. much larger dense models. Datasets: 6 pre-training datasets. Baselines: DPOT-S/M/L. Metric: L2RE (zero-shot).",
      "source": "Appendix C.2.1 Experimental Results with DPOT-L (Table 9)"
    },
    {
      "id": "moe-pot-D3-012",
      "claim": "Compare MoE-POT vs. Poseidon on Wave-Layer and Wave-Gauss in auto-regressive setting (models predict future states from solution trajectories only, no PDE parameters). MoE-POT: pre-train on 6 datasets then fine-tune. Poseidon: adapted to auto-regressive setting. Datasets: Wave-Layer, Wave-Gauss. Baselines: Poseidon-T (21M), Poseidon-B (158M). Metric: L2RE.",
      "source": "Appendix C.2.2 Experimental Results with Poseidon, Setting 1 (Table 10)"
    },
    {
      "id": "moe-pot-D3-013",
      "claim": "Compare MoE-POT vs. Poseidon on Wave-Layer and Wave-Gauss in parameter-informed setting (models receive explicit PDE parameters as additional input). MoE-POT adapted to accept PDE parameters. Poseidon evaluated in native setting. Datasets: Wave-Layer, Wave-Gauss. Baselines: Poseidon-T (21M), Poseidon-B (158M). Metric: L2RE.",
      "source": "Appendix C.2.2 Experimental Results with Poseidon, Setting 2 (Table 11)"
    },
    {
      "id": "moe-pot-D3-014",
      "claim": "Analyze L2RE error accumulation over auto-regressive rollout on SWE dataset: measure single-step L2RE at frames 50, 70, 100 during 100-step rollout. Datasets: PDEBench-SWE. Baselines: DPOT-S (30.8M). Metrics: L2RE at frames 50/70/100, average L2RE.",
      "source": "Appendix C.3 Rollout Error at Different Timesteps (Table 12)"
    },
    {
      "id": "moe-pot-D3-015",
      "claim": "Analyze few-shot fine-tuning sample efficiency on in-distribution downstream task NS(1e-4): fine-tune MoE-POT-S and DPOT-S for 500 epochs with varying training samples {16, 32, 64, 128, 512, 2000}. Datasets: NS(1e-4). Baselines: DPOT-S (30.8M). Metric: L2RE (final).",
      "source": "Appendix C.4 Analysis of Fine-Tuning Sample Efficiency (Table 13)"
    },
    {
      "id": "moe-pot-D3-016",
      "claim": "Analyze few-shot fine-tuning sample efficiency on OOD downstream task Wave-Layer: fine-tune MoE-POT-S and DPOT-S for 500 epochs with varying training samples {16, 32, 64, 128}. Datasets: Wave-Layer (Poseidon benchmark). Baselines: DPOT-S (30.8M). Metric: L2RE (final).",
      "source": "Appendix C.4 Analysis of Fine-Tuning Sample Efficiency (Table 14)"
    },
    {
      "id": "moe-pot-D3-017",
      "claim": "Study negative transfer from pre-training data heterogeneity: DPOT-S and MoE-POT-S pre-trained from scratch on progressively larger mixtures (6, 10, 12 datasets), zero-shot evaluated on 6 base datasets. Tests MoE mitigation of negative transfer from conflicting PDE dynamics. Datasets: 6/10/12 dataset mixtures (see description). Baselines: DPOT-S (30.8M dense). Metric: L2RE (zero-shot on 6 base datasets).",
      "source": "Appendix C.5 Performance with Increasing Dataset (Table 15)"
    }
  ],
  "D4": [
    {
      "id": "moe-pot-D4-001",
      "claim": "MoE-POT model forward pass pipeline: Balanced Data Sampling -> Noise Injection -> Patchification with Learnable Positional Encoding -> Temporal Aggregation with Fourier Features -> Multi-head Fourier Layer (AFNO-style frequency-domain MLP) -> MoE Router Gating (Softmax over CNN routing logits) -> MoE TopK Expert Selection -> MoE Output Aggregation (shared experts average + weighted routed experts) + Load Balancing Loss (CV-based auxiliary) -> Final Training Loss (MSE + per-layer load balance) -> Auto-regressive Inference Rollout (no noise, sliding window T=10).",
      "source": "Section 4 (derived from D2 ordering_before/ordering_after annotations)"
    },
    {
      "id": "moe-pot-D4-002",
      "claim": "Router interpretability classification pipeline (Section B.4): Step 1 — Compute average expert distribution Y_i for each pre-training dataset i from full softmax router output over all 16 experts. Step 2 — For new input X, compute cross-entropy distance f(I_0, Y_i) between its routing distribution I_0 and each dataset reference Y_i. Step 3 — Classify X to dataset i_0 = argmin_i f(I_0, Y_i).",
      "source": "Section B.4 (derived from D2 ordering_before/ordering_after annotations)"
    },
    {
      "id": "moe-pot-D4-003",
      "claim": "Zero-shot evaluation protocol (Section 5.1): Phase 1 — Data preprocessing (spatial resolution unification to H=128, channel padding, mask channel for irregular geometries, patchification P=8). Phase 2 — Joint pre-training on all 6 datasets (auto-regressive next-frame prediction, T=10, noise injection, balanced sampling w_k=1, Adam lr=1e-3, 1000 epochs, 200 warm-up). Phase 3 — Zero-shot evaluation on each individual dataset test split.",
      "source": "Section 5.1 (derived from D3 phase_ordering)"
    },
    {
      "id": "moe-pot-D4-004",
      "claim": "Fine-tuning evaluation protocol (Section 5.1): Phase 1 — Joint pre-training on all 6 datasets (1000 epochs). Phase 2 — Fine-tune separately on each individual dataset (200 epochs, one-cycle lr=1e-3, 40 warm-up, freeze router-gating, update expert networks only). Phase 3 — Evaluate on same dataset test split.",
      "source": "Section 5.1, Section B.3 (derived from D3 phase_ordering)"
    },
    {
      "id": "moe-pot-D4-005",
      "claim": "Downstream transfer evaluation protocol (Section 5.2): Phase 1 — Joint pre-training on 6 datasets (1000 epochs). Phase 2 — Fine-tune on downstream task (NS(1e-4), CNS(1,0.01), or PDEArena) for 500 epochs (one-cycle lr=1e-3, 100 warm-up). Phase 3 — Evaluate on downstream task test split. Compared against train-from-scratch baseline (no pre-training).",
      "source": "Section 5.2, Section B.3 (derived from D3 phase_ordering)"
    },
    {
      "id": "moe-pot-D4-006",
      "claim": "Scaling law analysis protocol (Section 5.3): Phase 1 — Pre-train each model variant (T/S/M for MoE-POT, T/S/M/L for DPOT) on all 6 datasets. Phase 2 — Evaluate zero-shot L2RE on test splits. Phase 3 — Fine-tune each model variant on individual datasets. Phase 4 — Evaluate fine-tuned L2RE on test splits. Phase 5 — Plot L2RE vs. activated parameters to characterize scaling behavior for dense vs. sparse architectures.",
      "source": "Section 5.3 (derived from D3 phase_ordering)"
    },
    {
      "id": "moe-pot-D4-007",
      "claim": "Negative transfer analysis protocol (Appendix C.5): Phase 1 — Pre-train DPOT-S (dense) and MoE-POT-S (sparse) from scratch on progressively larger dataset mixtures: 6 datasets (base) -> 10 datasets (base + NS(1e-4), CNS(1,0.1), 2x PDEArena) -> 12 datasets (10-set + CNS(1,0.01), CNS(0.1,0.1)). Phase 2 — Zero-shot evaluate both models on the original 6 base dataset test splits to measure whether dense models suffer negative transfer while MoE remains stable.",
      "source": "Appendix C.5 (derived from D3 phase_ordering)"
    }
  ]
}