{
  "project": "PhaseSAE",
  "author": "Conner Kupferberg",
  "date": "2026-09-22",
  "dataset": "TinyStories-1M (blocks.0.hook_resid_post, 16k tokens of NeelNanda/c4-10k)",
  "evaluation_harness": "sae_lens.evals",
  "head_to_head_k16": {
    "sparsity_l0": 16.0,
    "monolithic_topk_baseline": {
      "ce_loss_recovered_pct": 24.42,
      "explained_variance_r2": 0.1758,
      "mse_reconstruction_error": 0.2023,
      "peak_parameter_slice_mb": 0.0625,
      "training_time_seconds": 4.23
    },
    "phase_sae_p4": {
      "ce_loss_recovered_pct": 40.51,
      "explained_variance_r2": 0.2913,
      "mse_reconstruction_error": 0.174,
      "peak_parameter_slice_mb": 0.0156,
      "training_time_seconds": 5.37,
      "relative_ce_gain_pct": 65.9,
      "relative_r2_gain_pct": 65.7,
      "relative_bandwidth_reduction": "4.0x"
    }
  },
  "pareto_frontier_sweep": [
    {
      "k": 8,
      "architecture": "Top-K Baseline",
      "ce_recovery_pct": -1.16,
      "r2": 0.0709,
      "mse": 0.2281,
      "param_slice_mb": 0.0625
    },
    {
      "k": 8,
      "architecture": "PhaseSAE (P=4)",
      "ce_recovery_pct": 5.46,
      "r2": 0.1054,
      "mse": 0.2196,
      "param_slice_mb": 0.0156
    },
    {
      "k": 16,
      "architecture": "Top-K Baseline",
      "ce_recovery_pct": 2.37,
      "r2": 0.1322,
      "mse": 0.213,
      "param_slice_mb": 0.0625
    },
    {
      "k": 16,
      "architecture": "PhaseSAE (P=4)",
      "ce_recovery_pct": 44.52,
      "r2": 0.2717,
      "mse": 0.1788,
      "param_slice_mb": 0.0156
    },
    {
      "k": 24,
      "architecture": "Top-K Baseline",
      "ce_recovery_pct": 38.61,
      "r2": 0.2662,
      "mse": 0.1801,
      "param_slice_mb": 0.0625
    },
    {
      "k": 24,
      "architecture": "PhaseSAE (P=4)",
      "ce_recovery_pct": 58.1,
      "r2": 0.3974,
      "mse": 0.1479,
      "param_slice_mb": 0.0156
    }
  ],
  "hardware_roofline_triton_kernel": [
    {
      "batch_size": 1,
      "monolithic_topk_ms": 7.67,
      "unfused_phasesae_ms": 9.37,
      "fused_tdm_triton_ms": 10.39,
      "speedup_vs_unfused": 0.9,
      "peak_slice_mb": 18.0
    },
    {
      "batch_size": 4,
      "monolithic_topk_ms": 17.95,
      "unfused_phasesae_ms": 22.85,
      "fused_tdm_triton_ms": 20.07,
      "speedup_vs_unfused": 1.14,
      "peak_slice_mb": 18.0
    },
    {
      "batch_size": 16,
      "monolithic_topk_ms": 40.28,
      "unfused_phasesae_ms": 78.61,
      "fused_tdm_triton_ms": 41.73,
      "speedup_vs_unfused": 1.88,
      "peak_slice_mb": 18.0
    },
    {
      "batch_size": 64,
      "monolithic_topk_ms": 103.09,
      "unfused_phasesae_ms": 155.0,
      "fused_tdm_triton_ms": 109.89,
      "speedup_vs_unfused": 1.41,
      "peak_slice_mb": 18.0
    }
  ],
  "hierarchical_residual_contraction": [
    {
      "stage": "Input (x - b_dec)",
      "residual_norm": 6.136,
      "cumulative_reduction_pct": 0.0
    },
    {
      "stage": "Phase 0 (Tick 1)",
      "residual_norm": 3.5901,
      "cumulative_reduction_pct": 41.5
    },
    {
      "stage": "Phase 1 (Tick 2)",
      "residual_norm": 1.7797,
      "cumulative_reduction_pct": 71.0
    },
    {
      "stage": "Phase 2 (Tick 3)",
      "residual_norm": 0.9798,
      "cumulative_reduction_pct": 84.0
    },
    {
      "stage": "Phase 3 (Tick 4)",
      "residual_norm": 0.5835,
      "cumulative_reduction_pct": 90.5
    }
  ]
}