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Historical Baseline — Findings

Author: automated analysis pipeline Date: 2026-05-02 Status: Historical baseline complete. Supply-capacity handoff parameters at the bottom.

1. Summary

Under the recommended Frontier Rule A (top-10 by training compute at release), 2018+ window, the historical record from Epoch AI says:

Metric Annual multiplier Doubling R² n
Training compute (FLOP) 5.97× 4.7 mo 0.84 113
Training cost (2023 USD) 4.89× 5.2 mo 0.72 74
Cost per FLOP (2023 USD/FLOP) 0.76× n/a (decline) 0.21 74

In plain English: from 2018 through early 2026, frontier training runs grew by roughly 6× per year in raw compute and 5× per year in inflation- adjusted dollars, while the price per training FLOP fell ~24%/yr.

The single most important historical-baseline caveat is that these numbers are moderately sensitive to frontier definition and very sensitive to cost variant. Sections 6–8 quantify both.

2. Data sources

  • Primary: Epoch AI "Notable AI Models" CSV (https://epoch.ai/data/notable_ai_models.csv), retrieved 2026-05-02. 1,011 model rows, 1950–2026.
  • Cross-checks: Epoch's frontier_ai_models.csv and large_scale_ai_models.csv (downloaded but not used in headline fits; Epoch's own frontier subset is replicated in our epoch_frontier_flag column).
  • Local snapshot: data/raw/epoch_*.csv (immutable).
  • Processed dataset: data/processed/historical_models.{csv,parquet} (1,011 rows × 35 cols).

Mappings from Epoch column names to historical-baseline schema names: docs/data_dictionary.md.

3. Inclusion criteria

  • All 1,011 notable models retained in the processed dataset (full row preservation).
  • For trend fits, rows are dropped only when the relevant y column is missing.
  • Compute coverage: 521 / 1,011 models have a known training_compute_flop. Coverage is strong post-2018 (≥30/year through 2025).
  • Cost coverage is sparser: 179 models with the headline 2023-USD cost figure, 33 with explicit upfront cost, 25 with explicit cloud-rental cost.
  • Date quality: 1,007 / 1,011 rows have a parseable publication date.
  • Confidence flags: Epoch's Confidence field is mapped to compute_estimate_quality (high / medium / low).

4. Frontier definitions

We use three independent rules plus Epoch's own flag as a sanity check. There is no neutral definition of "frontier" and treating any single rule as authoritative is precisely the kind of unforced error this project is trying to avoid.

Rule Definition n flagged (full) n flagged (2018+)
A Top 10 by training compute within the 1-year window ending at release 245 113
B Highest-compute model per organization per calendar year 378 264
C training_compute_flop ≥ 1e23 137 137
(Epoch) Epoch's curated Frontier model boolean 123 —

Rule C is the most restrictive but also the most fragile — by truncating the lower tail it removes most within-year variation, which collapses both its slope estimate and its R².

5. Historical compute trend

Full table: outputs/tables/historical_trend_estimates.csv. Compute rows below.

Window Rule n ×/yr Doubling (mo) R²
2018+ all models 370 6.30 4.5 0.50
2018+ A (top-10) 113 5.97 4.7 0.84
2018+ B (top/org/yr) 264 6.38 4.5 0.46
2018+ C (≥1e23) 137 2.00 12.0 0.30
Full all models 521 2.12 11.1 0.76
Full A 245 2.14 10.9 0.83
Full B 378 2.02 11.9 0.75
Full Epoch flag 113 2.05 11.6 0.89

Headline reading: the modern (2018+) frontier-compute trend is ~6× per year under Rule A or B and converges with the all-models trend. The long-run trend (1950–2026) is ~2× per year. The two regimes are real and visible in the chart outputs/charts/historical_compute_over_time.png.

Rule C's 2× answer for 2018+ is a selection artifact rather than a disagreement — once you require ≥1e23 FLOP, the bottom of the post-2018 distribution disappears and you are left fitting a shorter dynamic range. Treat it as an upper-bound floor, not a "slow" estimate.

6. Historical cost trend

Window Rule n ×/yr Doubling (mo) R²
2018+ all models 155 3.13 7.3 0.27
2018+ A 74 4.89 5.2 0.72
2018+ B 121 3.02 7.5 0.23
2018+ C 51 3.03 7.5 0.50
Full A 98 3.16 7.2 0.73
Full Epoch flag 56 3.28 7.0 0.91

Headline cost reading: under Rule A 2018+, frontier training costs grew ~5× per year, doubling about every 5 months. Under Epoch's own flag the fit is even cleaner (R² = 0.91) at ~3.3× per year, doubling ~7 months.

Note the spread: 3× to 5×. We'll treat ~4× as the central estimate.

Chart: outputs/charts/historical_cost_over_time.png.

Cost variant sensitivity (historical-baseline critical finding)

Epoch publishes three cost columns. Under Rule A 2018+, the same trend looks very different depending on which one you fit:

Cost variant ×/yr Doubling (mo) R² n
Headline (2023 USD) 4.89 5.2 0.72 74
Cloud-rental 3.41 6.8 0.85 22
Upfront-hardware 2.49 9.1 0.84 27

The headline figure grows almost twice as fast as the upfront-hardware figure. This is not noise — it is a real divergence:

  • Upfront cost captures the price of the chips actually installed. Hardware prices (especially per-FLOP) have fallen, so total upfront cost grows more slowly than total compute.
  • Cloud-rental cost is what you'd pay a hyperscaler at posted rates; it is closer to opportunity cost.
  • Headline 2023 USD is Epoch's blended figure, closest to cloud-rental but with broader coverage.

For the supply capacity model we recommend carrying all three cost variants forward, with the headline 2023-USD figure as the base case and explicit fast/slow bounds that reflect cost-variant disagreement.

7. Cost per FLOP trend

Window Rule n ×/yr Annual decline R²
2018+ A 74 0.76 24.2% 0.21
2018+ C 51 0.88 11.7% 0.10
Full A 98 0.69 31.1% 0.46
Full Epoch flag 56 0.72 27.8% 0.68

Cost per FLOP declines roughly 25–30% per year across most reasonable cuts of the data. R² is materially lower than for compute or cost in isolation — unsurprising, because cost-per-FLOP combines the noise of two already-uncertain estimates and the dataset thins to ~50–100 rows.

The historical base estimate is ~25%/yr decline (0.75×/yr) for the modern window, with bounds at ~12% and ~30% reflecting the rule sensitivity.

Chart: outputs/charts/historical_cost_per_flop_over_time.png.

8. Key uncertainties

  1. Cost variant divergence (largest single uncertainty). Same models, same window, same regression — but the implied annual cost-growth multiplier ranges 2.5× → 4.9× depending on which cost column you use. the supply capacity model must not silently average these.
  2. Cost coverage is thin. 74 frontier-rule-A rows have headline cost, only 22–27 have the more hardware-grounded variants. Late 2025 / 2026 are particularly sparse.
  3. 2026 partial year. Only 2 models with known compute disclosed so far. Strong negative residuals for 2026 in residuals_compute_trend.png probably reflect right-truncation, not a deceleration.
  4. OLS, no error model. Epoch's Confidence field is collected but not yet used in fitting. A WLS variant using inverse-confidence weights would tighten standard errors but would not change central estimates materially given how concentrated Confident ratings are post-2020.
  5. Selection artifacts in Rule C. Already discussed.
  6. Organization-level structure. The residual-by-org chart shows OpenAI, Google, Meta, DeepMind, NVIDIA, and xAI sit consistently above the trend line under Rule A 2018+; Alibaba, Anthropic, Google Brain sit below. the supply capacity model should not assume one global rate fits all labs.
  7. Long-tail pre-1990 data. Including pre-deep-learning systems pulls the long-run slope down. The two-regime (slow until ~2010, fast after) structure is visible in every chart and is one of the cleaner findings in this dataset.
  8. Hardware quality / cluster scale data is too sparse for a model. 199 frontier rows with accelerator counts and 204 with training duration give a credible descriptive timeline (outputs/charts/historical_hardware_timeline.png) but not enough for a reliable multivariate fit yet.

These are the explicit handoff parameters. Each is a recommendation, not a forecast — the corresponding fast/slow bounds are intentionally wide enough to bracket the rule-sensitivity and variant-sensitivity exposed in Sections 5–7.

Base compute growth assumption:           6.0×/yr        (Rule A, 2018+)
Fast compute growth assumption:           6.4×/yr        (Rule B, 2018+)
Slow compute growth assumption:           2.0×/yr        (long-run, 1950+)

Base training-cost growth assumption:     4.0×/yr        (mid of Rule A 2018+ vs Epoch-flag full)
Fast training-cost growth assumption:     4.9×/yr        (Rule A 2018+, headline 2023 USD)
Slow training-cost growth assumption:     2.5×/yr        (Rule A 2018+, upfront-hardware variant)

Base cost-per-FLOP decline assumption:    0.75×/yr  (~25% / yr decline)
Fast cost-per-FLOP decline assumption:    0.69×/yr  (~31% / yr decline)
Slow cost-per-FLOP decline assumption:    0.88×/yr  (~12% / yr decline)

Recommended historical window:            2018-01-01 → most recent full quarter
Recommended frontier definition:          Rule A (top-10 at release)
                                          with Rule B + Epoch flag as cross-checks

Known weaknesses

  • Cost-variant divergence (2.5× ↔ 4.9×) is wider than rule-choice divergence and is not captured by quoting a single 2023-USD figure with a CI. the supply capacity model must explicitly track at least the cloud and upfront variants in parallel.
  • The cost-per-FLOP fit is the noisiest of the three trends (R² = 0.21 under the headline rule). Treat its central estimate as ±10 percentage points on the annual decline rate, not ±2.
  • Right-truncation: late-2025 and 2026 disclosures will continue to arrive for months. Re-fitting in Q3 2026 should tighten the modern-window slopes and may revise the headline numbers slightly upward (reporting bias historically favors high-compute systems).
  • Organization-level residual structure is not modeled. the supply capacity model may need lab-level effects rather than a single global rate.

10. Open questions

  1. Should Rule A use a top-N percentile (e.g. top 10%) rather than a fixed top-10? The current rule under-counts the modern era when many more frontier-grade models are released per year.
  2. Should the fits be WLS with Confidence as inverse variance? Likely small effect, but worth confirming.
  3. Should we collect non-Epoch cost figures (lab disclosures, hardware purchase reports, public cloud pricing) as a follow-up cross-check on the cost-variant divergence?
  4. Do we need a separate "training compute including post-training" trend? RLHF/RLAIF and inference-time scaling are now non-negligible and Epoch's Finetune compute column is sparse but populated for some recent models.
  5. Should the next phase formalize the two-regime finding (slow pre-2010, fast post-2010) with a piecewise fit and a structural break test rather than assuming a single 2018+ window?

Appendix: deliverable checklist

Spec deliverable File Status
Clean dataset (parquet) data/processed/historical_models.parquet ✓
Clean dataset (CSV) data/processed/historical_models.csv ✓
Data dictionary docs/data_dictionary.md ✓
Compute over time outputs/charts/historical_compute_over_time.png ✓
Cost over time outputs/charts/historical_cost_over_time.png ✓
Cost per FLOP outputs/charts/historical_cost_per_flop_over_time.png ✓
Compute by organization outputs/charts/historical_compute_by_organization.png ✓
Cost by organization outputs/charts/historical_cost_by_organization.png ✓
Residuals (compute) outputs/charts/historical_residuals_compute.png ✓
Residuals (cost) outputs/charts/historical_residuals_cost.png ✓
Hardware timeline outputs/charts/historical_hardware_timeline.png ✓ (bonus)
Trend estimates table outputs/tables/historical_trend_estimates.csv ✓ (45 rows)
Hardware summary outputs/tables/historical_hardware_summary.csv ✓ (bonus)
historical-baseline memo docs/historical_findings.md ✓ (this file)