wave3/results.json

{
  "approximation_and_gradient": {
    "cells": 144,
    "maximum_based_lower_bound_cells": 100,
    "maximum_density_to_cap_ratio": 0.9998171678925967,
    "maximum_finite_difference_gradient_error": 3.55237506077799e-11,
    "maximum_gradient_sum_error": 4.440892098500626e-16,
    "maximum_maximum_based_lower_bound_violation": 0.0,
    "maximum_proposition_lower_bound_violation": 0.0,
    "maximum_upper_bound_violation": 0.0,
    "median_gap_by_rho": {
      "0.001": 0.004124181976492225,
      "0.003": 0.012369519496368886,
      "0.01": 0.04118052531982552,
      "0.03": 0.12512893452027574,
      "0.1": 0.4221889072966081,
      "0.3": 1.0649100162692093
    },
    "monotonicity_violations": 0,
    "proposition_lower_bound_cells": 106,
    "rho_values": [
      0.3,
      0.1,
      0.03,
      0.01,
      0.003,
      0.001
    ],
    "small_rho_loglog_gap_rate": 1.0028321462740508
  },
  "curvature": {
    "all_smoothness_checks_pass": true,
    "all_strong_convexity_checks_pass": true,
    "cells": 5,
    "observed_maximum_smoothness_ratio": 0.2499999999997276,
    "observed_minimum_curvature_ratio": 4.0
  },
  "cvar": {
    "all_proposition_bounds_pass": true,
    "cells": 6,
    "cvar": 2.4081532216795076,
    "gap_at_temperature_0.02": 0.0010575311257263742,
    "gap_at_temperature_1": 1.6888539571690582,
    "gap_reduction_factor": 1596.9780142490413,
    "rho": 0.1
  },
  "limitations": [
    "Finite-distribution mechanism audit, not a proof of the paper's theorems.",
    "Does not rerun the paper's neural OT, California Housing, or MNIST training."
  ],
  "paper": {
    "arxiv": "2509.24894",
    "official_repository": "https://github.com/egorgladin/logsumexp-approx",
    "openreview": "TzQElzflxR",
    "title": "Improved Stochastic Optimization of LogSumExp"
  },
  "projected_sgd": {
    "all_median_excess_values_decrease": true,
    "cells": 4,
    "median_excess_loglog_slope": -0.8191471243684091,
    "median_excess_reduction_factor": 32.33692980500027,
    "objective_star": 0.8900366743986718,
    "repetitions_per_cell": 64,
    "rho": 0.1,
    "theta_star": 0.12212949298705902
  },
  "stochastic_oracle": {
    "alpha": 0.9478397173100979,
    "batch_comparison_cells": 4,
    "exact_logsumexp_gradient": -6.286448053284757,
    "exact_safe_gradient": -1.0488805716454876,
    "largest_batch_logsumexp_bias": 6.119328107362518,
    "oracle_rmse_loglog_slope": -0.5010725902015449,
    "oracle_scaling": [
      {
        "repetitions": 500,
        "rmse": 2.137753166935301,
        "samples": 32
      },
      {
        "repetitions": 500,
        "rmse": 1.1547325186175323,
        "samples": 128
      },
      {
        "repetitions": 500,
        "rmse": 0.5523393521687044,
        "samples": 512
      },
      {
        "repetitions": 500,
        "rmse": 0.2800278271929918,
        "samples": 2048
      },
      {
        "repetitions": 500,
        "rmse": 0.13465387776047513,
        "samples": 8192
      }
    ],
    "oracle_scaling_cells": 5,
    "rho": 0.05,
    "smallest_proposed_bias": 0.003918594175956969
  }
}