SabaPivot's picture
download
raw
3.98 kB
{
"arxiv_id": "2508.09628",
"checks": {
"exit_time_log_linear_r_squared_above_0_99": true,
"first_phase_exceeds_paper_lower_bound": true,
"positive_exponential_slope": true
},
"hardware": {
"device_count": 1,
"gpu_memory_bytes": 15828320256,
"gpu_name": "Tesla T4"
},
"implementation": "independent PyTorch vectorization of stochastic SA_P Eq. (5.3)",
"openreview_id": "zrn7rRuvhW",
"paper": "Attention's forward pass and Frank-Wolfe",
"schema_version": 1,
"seed": 809704,
"simulation_dtype": "float32",
"software": {
"cuda_runtime": "12.8",
"python": "3.11.13",
"torch": "2.7.1+cu128"
},
"theorem_5_2_first_phase": {
"T1": 5,
"beta": 1000000.0,
"empirical_success_probability": 1.0,
"gamma": 0.1,
"moderate_beta_sweep": [
{"beta": 2.0, "correct_cell_fraction": 0.8888905843098958, "mean_distance_to_assigned_vertex": 0.8103741407394409},
{"beta": 4.0, "correct_cell_fraction": 0.9251810709635416, "mean_distance_to_assigned_vertex": 0.7234433889389038},
{"beta": 8.0, "correct_cell_fraction": 0.9843190511067708, "mean_distance_to_assigned_vertex": 0.5446025729179382},
{"beta": 16.0, "correct_cell_fraction": 0.9997914632161458, "mean_distance_to_assigned_vertex": 0.4528283476829529},
{"beta": 32.0, "correct_cell_fraction": 1.0, "mean_distance_to_assigned_vertex": 0.4431050419807434},
{"beta": 64.0, "correct_cell_fraction": 1.0, "mean_distance_to_assigned_vertex": 0.44286832213401794}
],
"moderate_beta_sweep_replicas": 65536,
"paper_lower_bound": 0.8221720589961077,
"replicas": 262144,
"successes": 262144,
"tau": 0.43301270189221935,
"tested_C": 1.1
},
"theorem_5_4_metastability": {
"c0": 0.375,
"epsilon": 0.034641016151377546,
"epsilon_over_gamma": 1.7320508075688772,
"gamma": 0.02,
"geometry": "three singleton clusters at an equilateral triangle of radius 0.5",
"log_linear_fit_r_squared": 0.9963311191434563,
"log_median_exit_vs_beta_slope": 0.33073748446408396,
"max_steps": 25000,
"replicas_per_beta": 16384,
"required_minimum_2diameter": 1.7320508075688772,
"rows": [
{"beta": 4.0, "censored_fraction": 0.0, "empirical_survival_at_t5": 0.71710205078125, "mean_exit_time_uncensored": 5.92352294921875, "median_exit_time_uncensored": 6.0, "q10_exit_time_uncensored": 4.0, "q90_exit_time_uncensored": 9.0, "replicas": 16384, "steps_executed": 19},
{"beta": 8.0, "censored_fraction": 0.0, "empirical_survival_at_t5": 0.987060546875, "mean_exit_time_uncensored": 16.8463134765625, "median_exit_time_uncensored": 16.0, "q10_exit_time_uncensored": 8.0, "q90_exit_time_uncensored": 27.0, "replicas": 16384, "steps_executed": 63},
{"beta": 12.0, "censored_fraction": 0.0, "empirical_survival_at_t5": 0.999755859375, "mean_exit_time_uncensored": 62.757568359375, "median_exit_time_uncensored": 58.0, "q10_exit_time_uncensored": 27.0, "q90_exit_time_uncensored": 105.0, "replicas": 16384, "steps_executed": 225},
{"beta": 16.0, "censored_fraction": 0.0, "empirical_survival_at_t5": 1.0, "mean_exit_time_uncensored": 250.796630859375, "median_exit_time_uncensored": 233.0, "q10_exit_time_uncensored": 107.0, "q90_exit_time_uncensored": 422.0, "replicas": 16384, "steps_executed": 1006},
{"beta": 20.0, "censored_fraction": 0.0, "empirical_survival_at_t5": 1.0, "mean_exit_time_uncensored": 1045.4474487304688, "median_exit_time_uncensored": 963.0, "q10_exit_time_uncensored": 427.0, "q90_exit_time_uncensored": 1769.7000000000007, "replicas": 16384, "steps_executed": 4471},
{"beta": 24.0, "censored_fraction": 0.0, "empirical_survival_at_t5": 1.0, "mean_exit_time_uncensored": 4416.9473876953125, "median_exit_time_uncensored": 4088.0, "q10_exit_time_uncensored": 1838.0, "q90_exit_time_uncensored": 7427.0, "replicas": 16384, "steps_executed": 18528}
],
"total_particle_updates": 1194983424
},
"wall_time_seconds": 53.05153066
}

Xet Storage Details

Size:
3.98 kB
·
Xet hash:
529cbecd1d3357a5840b0e9cc8f95bfe6ba1de7572f02dd6819ac30e777fdf56

Xet efficiently stores files, intelligently splitting them into unique chunks and accelerating uploads and downloads. More info.