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Field study: updating steps vs score (131 runs), with pre-registered recheck

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+ "user": "dnakhla",
1580
+ "submission_id": "terminal-desk-v5",
1581
+ "run_id": "c571a091047b4600ad689fc6",
1582
+ "solved": 3,
1583
+ "steps": 153,
1584
+ "logged": 153,
1585
+ "grad_steps": 93,
1586
+ "grad_norm_sum": 124.947,
1587
+ "mean_reward": 0.508,
1588
+ "scores": {
1589
+ "industrial-physical-systems": 1,
1590
+ "office-white-collar": 1,
1591
+ "software-engineering": 1
1592
+ }
1593
+ },
1594
+ {
1595
+ "user": "nice-bill",
1596
+ "submission_id": "shiftdesk-v7",
1597
+ "run_id": "b0bb05008a20ac4d35a728d3",
1598
+ "solved": 4,
1599
+ "steps": 189,
1600
+ "logged": 189,
1601
+ "grad_steps": 68,
1602
+ "grad_norm_sum": 31.244,
1603
+ "mean_reward": 0.808,
1604
+ "scores": {
1605
+ "industrial-physical-systems": 1,
1606
+ "office-white-collar": 2,
1607
+ "software-engineering": 1
1608
+ }
1609
+ },
1610
+ {
1611
+ "user": "jjmachan",
1612
+ "submission_id": "pool-desk-v3-20261017-1127",
1613
+ "run_id": "cb49526bd4011974ec0d0b76",
1614
+ "solved": 1,
1615
+ "steps": 164,
1616
+ "logged": 164,
1617
+ "grad_steps": 87,
1618
+ "grad_norm_sum": 40.424,
1619
+ "mean_reward": 0.75,
1620
+ "scores": {
1621
+ "office-white-collar": 1
1622
+ }
1623
+ },
1624
+ {
1625
+ "user": "bochencs",
1626
+ "submission_id": "bochencs-science-v7",
1627
+ "run_id": "3a8f035c246df592bf923b0a",
1628
+ "solved": 2,
1629
+ "steps": 104,
1630
+ "logged": 104,
1631
+ "grad_steps": 60,
1632
+ "grad_norm_sum": 27.712,
1633
+ "mean_reward": 0.495,
1634
+ "scores": {
1635
+ "industrial-physical-systems": 1,
1636
+ "office-white-collar": 1
1637
+ }
1638
+ },
1639
+ {
1640
+ "user": "distributedtensor",
1641
+ "submission_id": "posttrain-m4-b",
1642
+ "run_id": "d442a2a22ffca01f49855de5",
1643
+ "solved": 2,
1644
+ "steps": 147,
1645
+ "logged": 147,
1646
+ "grad_steps": 83,
1647
+ "grad_norm_sum": 40.73,
1648
+ "mean_reward": 0.68,
1649
+ "scores": {
1650
+ "industrial-physical-systems": 1,
1651
+ "office-white-collar": 1
1652
+ }
1653
+ },
1654
+ {
1655
+ "user": "rca-umb",
1656
+ "submission_id": "five-desks-v9",
1657
+ "run_id": "8eceb03347c6f626626db1c4",
1658
+ "solved": 3,
1659
+ "steps": 82,
1660
+ "logged": 82,
1661
+ "grad_steps": 45,
1662
+ "grad_norm_sum": 18.775,
1663
+ "mean_reward": 0.296,
1664
+ "scores": {
1665
+ "industrial-physical-systems": 2,
1666
+ "office-white-collar": 1
1667
+ }
1668
+ },
1669
+ {
1670
+ "user": "Syndicate604",
1671
+ "submission_id": "science-desk-v5",
1672
+ "run_id": "30416be58a587e6cdc589944",
1673
+ "solved": 3,
1674
+ "steps": 148,
1675
+ "logged": 148,
1676
+ "grad_steps": 60,
1677
+ "grad_norm_sum": 34.659,
1678
+ "mean_reward": 0.794,
1679
+ "scores": {
1680
+ "office-white-collar": 3
1681
+ }
1682
+ },
1683
+ {
1684
+ "user": "cmunley",
1685
+ "submission_id": "mixed-skills-v7",
1686
+ "run_id": "6fa6e836d5bb24c8d2195030",
1687
+ "solved": 3,
1688
+ "steps": 31,
1689
+ "logged": 31,
1690
+ "grad_steps": 28,
1691
+ "grad_norm_sum": 8.222,
1692
+ "mean_reward": 0.305,
1693
+ "scores": {
1694
+ "industrial-physical-systems": 2,
1695
+ "office-white-collar": 1
1696
+ }
1697
+ },
1698
+ {
1699
+ "user": "ruv",
1700
+ "submission_id": "metaharness-mix8-20261018",
1701
+ "run_id": "bc710b4807e062b5d26cd8fc",
1702
+ "solved": 4,
1703
+ "steps": 275,
1704
+ "logged": 275,
1705
+ "grad_steps": 147,
1706
+ "grad_norm_sum": 149.157,
1707
+ "mean_reward": 0.182,
1708
+ "scores": {
1709
+ "industrial-physical-systems": 2,
1710
+ "natural-science": 1,
1711
+ "office-white-collar": 1
1712
+ }
1713
+ },
1714
+ {
1715
+ "user": "ajinkyamulay",
1716
+ "submission_id": "analyst-workbench-v8",
1717
+ "run_id": "33176b4d5a53cb604e776537",
1718
+ "solved": 3,
1719
+ "steps": 157,
1720
+ "logged": 157,
1721
+ "grad_steps": 71,
1722
+ "grad_norm_sum": 38.042,
1723
+ "mean_reward": 0.762,
1724
+ "scores": {
1725
+ "industrial-physical-systems": 2,
1726
+ "office-white-collar": 1
1727
+ }
1728
+ },
1729
+ {
1730
+ "user": "Profa-QE",
1731
+ "submission_id": "profa-qe-arena-v5r2",
1732
+ "run_id": "6fb817d2648bd1b24bff42de",
1733
+ "solved": 2,
1734
+ "steps": 173,
1735
+ "logged": 173,
1736
+ "grad_steps": 93,
1737
+ "grad_norm_sum": 48.775,
1738
+ "mean_reward": 0.578,
1739
+ "scores": {
1740
+ "industrial-physical-systems": 1,
1741
+ "office-white-collar": 1
1742
+ }
1743
+ },
1744
+ {
1745
+ "user": "dnakhla",
1746
+ "submission_id": "terminal-desk-v5-rd20261018",
1747
+ "run_id": "21872f55b50537fc4650c821",
1748
+ "solved": 3,
1749
+ "steps": 151,
1750
+ "logged": 151,
1751
+ "grad_steps": 84,
1752
+ "grad_norm_sum": 46.359,
1753
+ "mean_reward": 0.563,
1754
+ "scores": {
1755
+ "industrial-physical-systems": 1,
1756
+ "mathematics-or-formal-reasoning": 1,
1757
+ "office-white-collar": 1
1758
+ }
1759
+ },
1760
+ {
1761
+ "user": "arshy",
1762
+ "submission_id": "eval-rules-desk-v1",
1763
+ "run_id": "8b8f055414db4dac7adff019",
1764
+ "solved": 3,
1765
+ "steps": 114,
1766
+ "logged": 114,
1767
+ "grad_steps": 90,
1768
+ "grad_norm_sum": 51.014,
1769
+ "mean_reward": 0.397,
1770
+ "scores": {
1771
+ "industrial-physical-systems": 1,
1772
+ "office-white-collar": 2
1773
+ }
1774
+ },
1775
+ {
1776
+ "user": "nice-bill",
1777
+ "submission_id": "shiftdesk-v8",
1778
+ "run_id": "77411448767f7f8e27ef37e4",
1779
+ "solved": 5,
1780
+ "steps": 175,
1781
+ "logged": 135,
1782
+ "grad_steps": 61,
1783
+ "grad_norm_sum": 26.992,
1784
+ "mean_reward": 0.8,
1785
+ "scores": {
1786
+ "finance-economics": 1,
1787
+ "industrial-physical-systems": 2,
1788
+ "office-white-collar": 2
1789
+ }
1790
+ },
1791
+ {
1792
+ "user": "Codcordance",
1793
+ "submission_id": "concordance-maths-20261018-v1",
1794
+ "run_id": "0fe94468c9a15d6c78c97457",
1795
+ "solved": 2,
1796
+ "steps": 182,
1797
+ "logged": 107,
1798
+ "grad_steps": 24,
1799
+ "grad_norm_sum": 15.076,
1800
+ "mean_reward": 0.159,
1801
+ "scores": {
1802
+ "industrial-physical-systems": 1,
1803
+ "office-white-collar": 1
1804
+ }
1805
+ },
1806
+ {
1807
+ "user": "bochencs",
1808
+ "submission_id": "bochencs-terminal-priority-v8",
1809
+ "run_id": "4a68f48e58d14469b7319f86",
1810
+ "solved": 3,
1811
+ "steps": 139,
1812
+ "logged": 76,
1813
+ "grad_steps": 47,
1814
+ "grad_norm_sum": 29.413,
1815
+ "mean_reward": 0.76,
1816
+ "scores": {
1817
+ "industrial-physical-systems": 1,
1818
+ "office-white-collar": 1,
1819
+ "software-engineering": 1
1820
+ }
1821
+ },
1822
+ {
1823
+ "user": "stoiclion",
1824
+ "submission_id": "agent-workbench-v1",
1825
+ "run_id": "3be16030019bfca3b2dfe372",
1826
+ "solved": 4,
1827
+ "steps": 194,
1828
+ "logged": 78,
1829
+ "grad_steps": 45,
1830
+ "grad_norm_sum": 27.959,
1831
+ "mean_reward": 0.84,
1832
+ "scores": {
1833
+ "industrial-physical-systems": 2,
1834
+ "office-white-collar": 1,
1835
+ "software-engineering": 1
1836
+ }
1837
+ },
1838
+ {
1839
+ "user": "NoeFlandre",
1840
+ "submission_id": "workbench-gym-v3",
1841
+ "run_id": "99908f0c348c181c87f9a087",
1842
+ "solved": 3,
1843
+ "steps": 202,
1844
+ "logged": 96,
1845
+ "grad_steps": 30,
1846
+ "grad_norm_sum": 14.745,
1847
+ "mean_reward": 0.882,
1848
+ "scores": {
1849
+ "office-white-collar": 2,
1850
+ "software-engineering": 1
1851
+ }
1852
+ },
1853
+ {
1854
+ "user": "distributedtensor",
1855
+ "submission_id": "posttrain-m4-c",
1856
+ "run_id": "50f8c181ca24d7a72e33bec4",
1857
+ "solved": 3,
1858
+ "steps": 134,
1859
+ "logged": 70,
1860
+ "grad_steps": 43,
1861
+ "grad_norm_sum": 23.988,
1862
+ "mean_reward": 0.672,
1863
+ "scores": {
1864
+ "finance-economics": 1,
1865
+ "office-white-collar": 2
1866
+ }
1867
+ },
1868
+ {
1869
+ "user": "rca-umb",
1870
+ "submission_id": "five-desks-v10",
1871
+ "run_id": "ab4d729e0946348182d0ab1c",
1872
+ "solved": 2,
1873
+ "steps": 76,
1874
+ "logged": 51,
1875
+ "grad_steps": 31,
1876
+ "grad_norm_sum": 12.358,
1877
+ "mean_reward": 0.309,
1878
+ "scores": {
1879
+ "industrial-physical-systems": 1,
1880
+ "office-white-collar": 1
1881
+ }
1882
+ },
1883
+ {
1884
+ "user": "Syndicate604",
1885
+ "submission_id": "evidence-desk-math-v4-rerun",
1886
+ "run_id": "df794d8796d63710a208f9ba",
1887
+ "solved": 3,
1888
+ "steps": 195,
1889
+ "logged": 195,
1890
+ "grad_steps": 105,
1891
+ "grad_norm_sum": 77.371,
1892
+ "mean_reward": 0.7,
1893
+ "scores": {
1894
+ "industrial-physical-systems": 2,
1895
+ "office-white-collar": 1
1896
+ }
1897
+ },
1898
+ {
1899
+ "user": "cmunley",
1900
+ "submission_id": "mixed-skills-v8",
1901
+ "run_id": "bb18cca416d850f02c05b482",
1902
+ "solved": 4,
1903
+ "steps": 21,
1904
+ "logged": 21,
1905
+ "grad_steps": 18,
1906
+ "grad_norm_sum": 6.835,
1907
+ "mean_reward": 0.4,
1908
+ "scores": {
1909
+ "industrial-physical-systems": 2,
1910
+ "office-white-collar": 2
1911
+ }
1912
+ },
1913
+ {
1914
+ "user": "GlobalBusinessAdvisors",
1915
+ "submission_id": "decision-ledger-software-d2-20261018",
1916
+ "run_id": "9f129154f9335c7e21f4dd6e",
1917
+ "solved": 3,
1918
+ "steps": 291,
1919
+ "logged": 291,
1920
+ "grad_steps": 189,
1921
+ "grad_norm_sum": 137.216,
1922
+ "mean_reward": 0.204,
1923
+ "scores": {
1924
+ "industrial-physical-systems": 1,
1925
+ "office-white-collar": 2
1926
+ }
1927
+ },
1928
+ {
1929
+ "user": "ruv",
1930
+ "submission_id": "metaharness-darwin-2026-10-18-redraw-36468965c9",
1931
+ "run_id": "130b1b1c74dfd37b074c7b6b",
1932
+ "solved": 3,
1933
+ "steps": 244,
1934
+ "logged": 244,
1935
+ "grad_steps": 122,
1936
+ "grad_norm_sum": 100.688,
1937
+ "mean_reward": 0.175,
1938
+ "scores": {
1939
+ "industrial-physical-systems": 1,
1940
+ "office-white-collar": 2
1941
+ }
1942
+ },
1943
+ {
1944
+ "user": "ajinkyamulay",
1945
+ "submission_id": "analyst-workbench-v7-r2",
1946
+ "run_id": "23e0988c2f5d4abff0a4d79e",
1947
+ "solved": 4,
1948
+ "steps": 94,
1949
+ "logged": 70,
1950
+ "grad_steps": 20,
1951
+ "grad_norm_sum": 9.008,
1952
+ "mean_reward": 0.063,
1953
+ "scores": {
1954
+ "finance-economics": 1,
1955
+ "industrial-physical-systems": 1,
1956
+ "office-white-collar": 2
1957
+ }
1958
+ },
1959
+ {
1960
+ "user": "dnakhla",
1961
+ "submission_id": "terminal-desk-v5-rd20261019",
1962
+ "run_id": "ade9de19553709cfe0787fa3",
1963
+ "solved": 1,
1964
+ "steps": 142,
1965
+ "logged": 142,
1966
+ "grad_steps": 93,
1967
+ "grad_norm_sum": 167.469,
1968
+ "mean_reward": 0.518,
1969
+ "scores": {
1970
+ "office-white-collar": 1
1971
+ }
1972
+ }
1973
+ ],
1974
+ "missing": []
1975
+ }
analysis/2026-10-19/field-gradients.md ADDED
@@ -0,0 +1,51 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ # Does the amount of real training predict the score? (2026-10-19)
2
+
3
+ Data: all 131 heldout-v2 runs on the leaderboard at 14:00 EDT (`leaderboard-2026-10-19-1400.json`), joined with each
4
+ run's public Trackio metrics (`scripts/field_gradients.py`, per-run summary `field-gradients-2026-10-19.json`). A step
5
+ changed the model if its `grad_norm` was above 0; steps where every rollout in the group scored the same have zero
6
+ advantage, zero loss and zero `grad_norm`. Trackio logged under 90% of the steps for 46 runs, so for those the counts
7
+ are lower bounds.
8
+
9
+ ## Results
10
+
11
+ Score by the number of steps that changed the model (bucket edges chosen before looking at the scores):
12
+
13
+ | Updating steps | Runs | Mean solved | Distribution |
14
+ |---|---|---|---|
15
+ | 0 | 5 | 1.60 | 0:1, 1:1, 2:2, 3:1 |
16
+ | 1–25 | 21 | 3.14 | 2:7, 3:6, 4:6, 5:2 |
17
+ | 26–50 | 25 | 3.20 | 1:1, 2:2, 3:14, 4:7, 5:1 |
18
+ | 51–100 | 59 | 2.59 | 0:3, 1:8, 2:16, 3:19, 4:9, 5:4 |
19
+ | 101–150 | 14 | 3.14 | 1:1, 2:2, 3:5, 4:6 |
20
+ | 151+ | 7 | 2.29 | 1:1, 2:3, 3:3 |
21
+
22
+ By the share of logged steps that changed the model: 0% 1.60 (5), 1–20% 3.21 (14), 21–40% 2.80 (20), 41–60% 2.76
23
+ (55), 61–80% 3.00 (26), 81–100% 2.55 (11).
24
+
25
+ Across all runs the correlation between updating steps and score is about zero (Pearson -0.07, Spearman -0.06).
26
+
27
+ Split chosen after seeing the table, so exploratory:
28
+
29
+ | Subset | 0 updates | 1–50 updates | 51+ updates | 1–50 minus 51+ | One-sided permutation p |
30
+ |---|---|---|---|---|---|
31
+ | All 131 runs | 1.60 (5) | 3.17 (46) | 2.66 (80) | +0.51 | 0.008 |
32
+ | 85 runs with ≥90% of steps logged | 1.67 (3) | 3.22 (18) | 2.62 (64) | +0.60 | 0.031 |
33
+
34
+ Averaging within each user first (so prolific users do not dominate): 1–50 updates 3.08 over 25 users, 51+ updates 2.73
35
+ over 22 users.
36
+
37
+ ## Reading
38
+
39
+ 1. Runs that never changed the model score lowest (1.60, n=5). Training at all helps, as naklitechie found (#229).
40
+ 2. Runs with 1–50 updating steps scored about half a point more than runs with more. That supports a weaker form of
41
+ light-touch: a few real updates, not none. The table is not a clean dose-response (101–150 is back at 3.14), the
42
+ 1–50/51+ split was picked after looking, and runs from one user are not independent, so this is a hypothesis.
43
+ 3. Our own runs fit loosely: v4 (29 updating steps) 5/40, v9 (45) 3/40, v10 (at least 31) 2/40; v1 (208) 2/40, v5 (186)
44
+ 3/40, v6 (95) 0/40.
45
+
46
+ ## Pre-registered check
47
+
48
+ To test point 2 on data it was not fitted to, the same script will be rerun on runs evaluated after this snapshot
49
+ (`evaluated_at` later than 2026-10-19 14:00 EDT) once at least 30 new runs exist. Prediction: runs with 1–50 updating
50
+ steps score higher on average than runs with 51 or more (one-sided permutation p < 0.05 counts as support; a difference of
51
+ 0 or below counts against). Zero-update runs are reported separately.
analysis/2026-10-19/field_gradients.py ADDED
@@ -0,0 +1,111 @@
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
+ """How much did each leaderboard run actually train? Fetches every run's public Trackio metrics and counts the steps
2
+ that changed the model (grad_norm > 0), then compares that with the run's held-out score.
3
+
4
+ A step changes the model only if its group of rollouts had some reward variance; steps where every rollout scored the
5
+ same have zero advantage, zero loss and zero grad_norm. Trackio sometimes logs fewer steps than the run made, so the
6
+ counts are lower bounds and the logged coverage is reported alongside.
7
+
8
+ Usage: python3 scripts/field_gradients.py <leaderboard snapshot json> [--after <epoch>] [--cache reports/field-gradients]
9
+ [--out x.json]
10
+ --after keeps only runs evaluated after that time (for the pre-registered check in reports/field-gradients-2026-10-19.md:
11
+ 1792432800 = 2026-10-19 14:00 EDT).
12
+ """
13
+
14
+ import argparse
15
+ import json
16
+ import os
17
+ import statistics as st
18
+ import time
19
+ import urllib.request
20
+
21
+ API = "https://openenvarena-training.hf.space/api/get_metric_values"
22
+ METRICS = ["grad_norm", "frac_reward_zero_std", "reward"]
23
+
24
+
25
+ def metric(project, run, name):
26
+ body = json.dumps({"project": project, "run": run, "run_id": run, "metric_name": name}).encode()
27
+ req = urllib.request.Request(API, data=body, headers={"Content-Type": "application/json",
28
+ "User-Agent": "five-desks-tracker/1.0"})
29
+ with urllib.request.urlopen(req, timeout=60) as r:
30
+ data = json.load(r)
31
+ rows = data.get("data", data) if isinstance(data, dict) else data
32
+ return {p["step"]: p["value"] for p in rows if isinstance(p, dict) and "step" in p}
33
+
34
+
35
+ def fetch(run, cache):
36
+ path = os.path.join(cache, run["run_id"] + ".json")
37
+ if os.path.exists(path):
38
+ return json.load(open(path))
39
+ got = {}
40
+ for name in METRICS:
41
+ try:
42
+ got[name] = metric(run["user"], run["run_id"], name)
43
+ except Exception as e: # a missing project or metric is recorded, not fatal
44
+ got[name] = {"error": str(e)}
45
+ time.sleep(0.3)
46
+ json.dump(got, open(path, "w"))
47
+ return got
48
+
49
+
50
+ def summarise(run, m):
51
+ g = m.get("grad_norm", {})
52
+ if not isinstance(g, dict) or "error" in g or not g:
53
+ return None
54
+ vals = list(g.values())
55
+ rew = [v for v in m.get("reward", {}).values()] if "error" not in m.get("reward", {}) else []
56
+ return {
57
+ "user": run["user"], "submission_id": run["submission_id"], "run_id": run["run_id"],
58
+ "solved": run["solved"], "steps": run.get("steps") or 0, "logged": len(vals),
59
+ "grad_steps": sum(1 for v in vals if v and abs(v) > 0),
60
+ "grad_norm_sum": round(sum(abs(v) for v in vals if v), 3),
61
+ "mean_reward": round(st.mean(rew), 3) if rew else None,
62
+ "scores": {k: v["solved"] for k, v in run["scores"].items() if v["solved"]},
63
+ }
64
+
65
+
66
+ def bucket_table(rows, key, edges, label):
67
+ print(f"\n{label}")
68
+ print(f"{'range':>12s} {'runs':>5s} {'mean':>5s} distribution")
69
+ for lo, hi in edges:
70
+ v = [r["solved"] for r in rows if lo <= key(r) <= hi]
71
+ if v:
72
+ dist = {s: v.count(s) for s in sorted(set(v))}
73
+ print(f"{f'{lo}-{hi}':>12s} {len(v):5d} {st.mean(v):5.2f} {dist}")
74
+
75
+
76
+ def main():
77
+ ap = argparse.ArgumentParser()
78
+ ap.add_argument("snapshot")
79
+ ap.add_argument("--cache", default="reports/field-gradients")
80
+ ap.add_argument("--out")
81
+ ap.add_argument("--after", type=float, default=0)
82
+ args = ap.parse_args()
83
+ os.makedirs(args.cache, exist_ok=True)
84
+ runs = [r for r in json.load(open(args.snapshot))["runs"] if r.get("benchmark") == "heldout-v2"
85
+ and (r.get("evaluated_at") or 0) > args.after]
86
+ rows, missing = [], []
87
+ for r in runs:
88
+ s = summarise(r, fetch(r, args.cache))
89
+ (rows.append(s) if s else missing.append(r["submission_id"]))
90
+ print(f"runs {len(runs)}, with Trackio grad_norm {len(rows)}, missing {len(missing)}")
91
+ if not rows:
92
+ return
93
+ cov = [r["logged"] / r["steps"] for r in rows if r["steps"]]
94
+ print(f"logged coverage: median {st.median(cov):.2f}, runs under 90% logged: {sum(c < 0.9 for c in cov)}")
95
+ bucket_table(rows, lambda r: r["grad_steps"], [(0, 0), (1, 25), (26, 50), (51, 100), (101, 150), (151, 10_000)],
96
+ "score by steps that changed the model (grad_norm > 0)")
97
+ bucket_table(rows, lambda r: round(100 * r["grad_steps"] / r["logged"]) if r["logged"] else 0,
98
+ [(0, 0), (1, 20), (21, 40), (41, 60), (61, 80), (81, 100)],
99
+ "score by percent of logged steps that changed the model")
100
+ xs = [r["grad_steps"] for r in rows]
101
+ ys = [r["solved"] for r in rows]
102
+ if len(set(xs)) > 1:
103
+ print(f"\nPearson r(grad_steps, solved) = {st.correlation(xs, ys):.3f} over {len(rows)} runs")
104
+ ranks = lambda a: [sorted(a).index(x) + (a.count(x) - 1) / 2 for x in a]
105
+ print(f"Spearman rho = {st.correlation(ranks(xs), ranks(ys)):.3f}")
106
+ if args.out:
107
+ json.dump({"rows": rows, "missing": missing}, open(args.out, "w"), indent=1)
108
+
109
+
110
+ if __name__ == "__main__":
111
+ main()