From 54e59c38ade2921d3c3ed4a89e287157fb199018 Mon Sep 17 00:00:00 2001 From: Andrej Karpathy Date: Mon, 5 Jan 2026 18:40:28 +0000 Subject: [PATCH] add notebook on deriving the CORE estimates for the GPT-3 miniseries. --- dev/estimate_gpt3_core.ipynb | 2190 ++++++++++++++++++++++++++++++++++ 1 file changed, 2190 insertions(+) create mode 100644 dev/estimate_gpt3_core.ipynb diff --git a/dev/estimate_gpt3_core.ipynb b/dev/estimate_gpt3_core.ipynb new file mode 100644 index 0000000..ce232e0 --- /dev/null +++ b/dev/estimate_gpt3_core.ipynb @@ -0,0 +1,2190 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Estimating CORE Metric for GPT-3 Models\n", + "\n", + "**Authors**: Claude Code Opus 4.5, Andrej Karpathy\n", + "\n", + "**Date**: Jan 2026\n", + "\n", + "## Motivation\n", + "\n", + "The [CORE metric](https://arxiv.org/abs/2406.11794) (introduced in the DCLM paper) is a composite benchmark that evaluates pretrained language models across 22 diverse tasks spanning world knowledge, language understanding, commonsense reasoning, symbolic problem solving, and reading comprehension. It provides a single score that captures a model's general capabilities.\n", + "\n", + "We want to compare nanochat models against the GPT-3 model family from OpenAI's [\"Language Models are Few-Shot Learners\"](https://arxiv.org/abs/2005.14165) paper (2020). However, there's a problem: **GPT-3 models were never evaluated on CORE** (which didn't exist in 2020), and the models were never publicly released, so we can't evaluate them ourselves.\n", + "\n", + "## Our Approach\n", + "\n", + "We estimate CORE scores for GPT-3 by:\n", + "\n", + "1. **Identifying overlapping tasks** between the GPT-3 paper and CORE that were evaluated with similar methodology\n", + "2. **Using GPT-2 as calibration data** — we have actual CORE scores for all 4 GPT-2 models, plus the GPT-3 paper reports results on GPT-2-equivalent tasks\n", + "3. **Fitting a regression model** from the overlapping task scores to the full CORE score\n", + "4. **Applying the model to GPT-3** using their reported task scores\n", + "\n", + "This notebook documents our methodology in detail for reproducibility." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Setup" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from pathlib import Path\n", + "import pandas as pd\n", + "\n", + "# For nice table display\n", + "pd.set_option('display.precision', 4)\n", + "pd.set_option('display.max_columns', 20)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 1: Understanding CORE\n", + "\n", + "CORE consists of **22 tasks** evaluated in specific few-shot settings. The key innovation is **centering**: raw accuracies are adjusted to account for random guessing baselines.\n", + "\n", + "$$\\text{centered accuracy} = \\frac{\\text{accuracy} - \\text{baseline}}{1 - \\text{baseline}}$$\n", + "\n", + "The final CORE score is simply the **mean of all 22 centered accuracies**.\n", + "\n", + "### CORE Tasks\n", + "\n", + "| Category | Tasks |\n", + "|----------|-------|\n", + "| World Knowledge | Jeopardy, ARC Easy, ARC Challenge, BigBench QA Wikidata |\n", + "| Language Understanding | HellaSwag (0-shot & 10-shot), LAMBADA, Winograd, Winogrande, BigBench Language ID |\n", + "| Commonsense Reasoning | COPA, CommonsenseQA, PIQA, OpenBookQA |\n", + "| Symbolic Problem Solving | BigBench Dyck, Operators, CS Algorithms, Repeat Copy Logic, AGI Eval LSAT-AR |\n", + "| Reading Comprehension | SQuAD, CoQA, BoolQ |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 2: Task Overlap Analysis\n", + "\n", + "We carefully compared the evaluation methodology between GPT-3 and CORE for each task. Key considerations:\n", + "\n", + "1. **Number of few-shot examples (K)**: GPT-3 often uses more examples than CORE\n", + "2. **Task format**: Some tasks use different prompting strategies\n", + "3. **Scoring method**: GPT-3 uses unconditional probability normalization for some tasks\n", + "4. **Data split**: dev vs test set\n", + "\n", + "### Selection Criteria\n", + "\n", + "We applied a conservative filter: **both evaluations must use K=0 (zero-shot) or both must use K>0 (few-shot)**. We excluded tasks that mix zero-shot with few-shot, as this introduces systematic differences.\n", + "\n", + "### Tasks We Excluded\n", + "\n", + "| Task | GPT-3 K | CORE K | Reason for Exclusion |\n", + "|------|---------|--------|----------------------|\n", + "| Winograd | 7 | 0 | Mixing K>0 with K=0 |\n", + "| Winogrande | 50 | 0 | Mixing K>0 with K=0 |\n", + "| COPA | 32 | 0 | Mixing K>0 with K=0 |\n", + "| OpenBookQA | 100 | 0 | Mixing K>0 with K=0, also uses unconditional normalization |\n", + "| BoolQ | 32 | 10 | High sensitivity to K (17% gap between 0-shot and few-shot in GPT-3) |\n", + "| CoQA | 5 | 0 | Different metric (F1 vs accuracy) |\n", + "| LAMBADA few-shot | 15 | 0 | GPT-3 uses special fill-in-blank format |\n", + "\n", + "### Tasks Not in GPT-3 Paper\n", + "\n", + "These CORE tasks simply don't appear in GPT-3 (many didn't exist in 2020):\n", + "- All 6 BigBench tasks (Dyck, Operators, CS Algorithms, Repeat Copy Logic, Language ID, QA Wikidata)\n", + "- Jeopardy, CommonsenseQA, AGI Eval LSAT-AR\n", + "- SQuAD v1 (GPT-3 uses v2)\n", + "\n", + "### Final Selected Tasks (6 tasks)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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TaskGPT-3 KCORE KMatch
0HellaSwag 0-shot00Both zero-shot
1LAMBADA00Both zero-shot
2HellaSwag 10-shot2010Both few-shot (K differs slightly)
3PIQA5010Both few-shot
4ARC Easy5010Both few-shot
5ARC Challenge5010Both few-shot
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" + ], + "text/plain": [ + " Task GPT-3 K CORE K Match\n", + "0 HellaSwag 0-shot 0 0 Both zero-shot\n", + "1 LAMBADA 0 0 Both zero-shot\n", + "2 HellaSwag 10-shot 20 10 Both few-shot (K differs slightly)\n", + "3 PIQA 50 10 Both few-shot\n", + "4 ARC Easy 50 10 Both few-shot\n", + "5 ARC Challenge 50 10 Both few-shot" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# The 6 tasks we selected for overlap\n", + "selected_tasks = pd.DataFrame([\n", + " {'Task': 'HellaSwag 0-shot', 'GPT-3 K': 0, 'CORE K': 0, 'Match': 'Both zero-shot'},\n", + " {'Task': 'LAMBADA', 'GPT-3 K': 0, 'CORE K': 0, 'Match': 'Both zero-shot'},\n", + " {'Task': 'HellaSwag 10-shot', 'GPT-3 K': 20, 'CORE K': 10, 'Match': 'Both few-shot (K differs slightly)'},\n", + " {'Task': 'PIQA', 'GPT-3 K': 50, 'CORE K': 10, 'Match': 'Both few-shot'},\n", + " {'Task': 'ARC Easy', 'GPT-3 K': 50, 'CORE K': 10, 'Match': 'Both few-shot'},\n", + " {'Task': 'ARC Challenge', 'GPT-3 K': 50, 'CORE K': 10, 'Match': 'Both few-shot'},\n", + "])\n", + "selected_tasks" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Rationale for K differences:** Looking at GPT-3's own data, the difference between different K values is typically small. Here's the evidence from the GPT-3 175B model:\n", + "\n", + "| Task | 0-shot | Few-shot | K | Δ |\n", + "|------|--------|----------|---|---|\n", + "| HellaSwag | 78.9% | 79.3% | 20 | +0.4% |\n", + "| PIQA | 81.0% | 82.3% | 50 | +1.3% |\n", + "| ARC Easy | 68.8% | 70.1% | 50 | +1.3% |\n", + "| ARC Challenge | 51.4% | 51.5% | 50 | +0.1% |\n", + "| Winograd | 88.3% | 88.6% | 7 | +0.3% |\n", + "| COPA | 91.0% | 92.0% | 32 | +1.0% |\n", + "\n", + "For most tasks, the gap between 0-shot and few-shot (with K=20-50) is only 0.1-1.3%. This suggests that differences between K=10 and K=50 would be even smaller, making our task selection reasonable.\n", + "\n", + "**Note:** Some tasks show larger sensitivity (Winogrande: +7.5%, BoolQ: +17%), which is why we excluded them." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 3: Calibration Data (GPT-2 Family)\n", + "\n", + "We have actual CORE scores for all 4 GPT-2 models. These serve as our calibration data." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Random baselines for centering (from CORE specification)\n", + "BASELINES = {\n", + " 'hellaswag_zeroshot': 0.25,\n", + " 'lambada_openai': 0.0,\n", + " 'hellaswag': 0.25,\n", + " 'piqa': 0.50,\n", + " 'arc_easy': 0.25,\n", + " 'arc_challenge': 0.25,\n", + "}\n", + "\n", + "TASK_ORDER = ['hellaswag_zeroshot', 'lambada_openai', 'hellaswag', 'piqa', 'arc_easy', 'arc_challenge']\n", + "TASK_NAMES = ['HellaSwag 0-shot', 'LAMBADA', 'HellaSwag 10-shot', 'PIQA', 'ARC Easy', 'ARC Challenge']\n", + "\n", + "def center_accuracy(acc, baseline):\n", + " \"\"\"Convert raw accuracy to centered accuracy.\"\"\"\n", + " return (acc - baseline) / (1.0 - baseline)\n", + "\n", + "def parse_csv(filepath):\n", + " \"\"\"Parse a CORE results CSV file.\"\"\"\n", + " results = {}\n", + " with open(filepath) as f:\n", + " for line in f:\n", + " parts = [p.strip() for p in line.strip().split(',')]\n", + " if len(parts) >= 3 and parts[0] != 'Task':\n", + " task = parts[0]\n", + " try:\n", + " acc = float(parts[1]) if parts[1] else None\n", + " centered = float(parts[2]) if parts[2] else None\n", + " results[task] = {'accuracy': acc, 'centered': centered}\n", + " except ValueError:\n", + " pass\n", + " return results" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GPT-2 Family: Raw Accuracies and CORE Scores\n" + ] + }, + { + "data": { + "text/html": [ + "
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ModelParamsHellaSwag 0-shotLAMBADAHellaSwag 10-shotPIQAARC EasyARC ChallengeCORE
0GPT-2124M30.9%32.3%30.8%62.3%41.2%22.2%0.1139
1GPT-2 Medium355M39.0%42.6%39.5%67.0%48.0%26.2%0.1849
2GPT-2 Large774M44.0%48.8%44.4%69.8%53.5%26.4%0.2146
3GPT-2 XL1558M50.2%52.3%51.2%72.5%59.5%29.9%0.2565
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" + ], + "text/plain": [ + " Model Params HellaSwag 0-shot LAMBADA HellaSwag 10-shot PIQA \\\n", + "0 GPT-2 124M 30.9% 32.3% 30.8% 62.3% \n", + "1 GPT-2 Medium 355M 39.0% 42.6% 39.5% 67.0% \n", + "2 GPT-2 Large 774M 44.0% 48.8% 44.4% 69.8% \n", + "3 GPT-2 XL 1558M 50.2% 52.3% 51.2% 72.5% \n", + "\n", + " ARC Easy ARC Challenge CORE \n", + "0 41.2% 22.2% 0.1139 \n", + "1 48.0% 26.2% 0.1849 \n", + "2 53.5% 26.4% 0.2146 \n", + "3 59.5% 29.9% 0.2565 " + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Load GPT-2 CORE results\n", + "knowledge_dir = Path(\"/home/ubuntu/.cache/nanochat/eval_bundle\")\n", + "\n", + "gpt2_models = [\n", + " ('GPT-2', 'openai-community-gpt2.csv', 124e6),\n", + " ('GPT-2 Medium', 'openai-community-gpt2-medium.csv', 355e6),\n", + " ('GPT-2 Large', 'openai-community-gpt2-large.csv', 774e6),\n", + " ('GPT-2 XL', 'openai-community-gpt2-xl.csv', 1558e6),\n", + "]\n", + "\n", + "gpt2_data = []\n", + "for name, filename, params in gpt2_models:\n", + " results = parse_csv(knowledge_dir / filename)\n", + " core = results['CORE']['centered']\n", + " task_accs = [results[task]['accuracy'] for task in TASK_ORDER]\n", + " gpt2_data.append({\n", + " 'name': name,\n", + " 'params': params,\n", + " 'task_accs': task_accs,\n", + " 'core': core,\n", + " })\n", + "\n", + "# Display as DataFrame\n", + "gpt2_df = pd.DataFrame([\n", + " {\n", + " 'Model': d['name'],\n", + " 'Params': f\"{d['params']/1e6:.0f}M\",\n", + " **{name: f\"{acc:.1%}\" for name, acc in zip(TASK_NAMES, d['task_accs'])},\n", + " 'CORE': f\"{d['core']:.4f}\"\n", + " }\n", + " for d in gpt2_data\n", + "])\n", + "print(\"GPT-2 Family: Raw Accuracies and CORE Scores\")\n", + "gpt2_df" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GPT-2 Family: Centered Accuracies\n" + ] + }, + { + "data": { + "text/html": [ + "
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HellaSwag 0-shotLAMBADAHellaSwag 10-shotPIQAARC EasyARC ChallengeMeanCORE
GPT-20.07800.32290.07720.24590.2166-0.03750.15050.1139
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GPT-2 Large0.25330.48800.25870.39600.38000.01870.29910.2146
GPT-2 XL0.33600.52300.34930.45000.46000.06530.36390.2565
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" + ], + "text/plain": [ + " HellaSwag 0-shot LAMBADA HellaSwag 10-shot PIQA ARC Easy \\\n", + "GPT-2 0.0780 0.3229 0.0772 0.2459 0.2166 \n", + "GPT-2 Medium 0.1867 0.4260 0.1933 0.3400 0.3067 \n", + "GPT-2 Large 0.2533 0.4880 0.2587 0.3960 0.3800 \n", + "GPT-2 XL 0.3360 0.5230 0.3493 0.4500 0.4600 \n", + "\n", + " ARC Challenge Mean CORE \n", + "GPT-2 -0.0375 0.1505 0.1139 \n", + "GPT-2 Medium 0.0160 0.2448 0.1849 \n", + "GPT-2 Large 0.0187 0.2991 0.2146 \n", + "GPT-2 XL 0.0653 0.3639 0.2565 " + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Build feature matrix (centered accuracies)\n", + "X_gpt2 = []\n", + "y_gpt2 = []\n", + "\n", + "for data in gpt2_data:\n", + " centered_accs = []\n", + " for task, acc in zip(TASK_ORDER, data['task_accs']):\n", + " centered = center_accuracy(acc, BASELINES[task])\n", + " centered_accs.append(centered)\n", + " X_gpt2.append(centered_accs)\n", + " y_gpt2.append(data['core'])\n", + "\n", + "X_gpt2 = np.array(X_gpt2)\n", + "y_gpt2 = np.array(y_gpt2)\n", + "\n", + "# Display centered accuracies\n", + "centered_df = pd.DataFrame(\n", + " X_gpt2,\n", + " columns=TASK_NAMES,\n", + " index=[d['name'] for d in gpt2_data]\n", + ")\n", + "centered_df['Mean'] = X_gpt2.mean(axis=1)\n", + "centered_df['CORE'] = y_gpt2\n", + "print(\"GPT-2 Family: Centered Accuracies\")\n", + "centered_df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Observation:** The mean of the 6 centered accuracies is consistently higher than the actual CORE score. This makes sense because CORE includes 16 additional tasks (many quite difficult) that pull down the average." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 4: GPT-3 Data\n", + "\n", + "We extract the 6 task accuracies from the GPT-3 paper's Appendix H (master results table).\n", + "\n", + "**Source:** Table H.1 in \"Language Models are Few-Shot Learners\" (Brown et al., 2020)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GPT-3 Family: Raw Accuracies from Paper\n" + ] + }, + { + "data": { + "text/html": [ + "
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ModelParamsHellaSwag 0-shotLAMBADAHellaSwag 10-shotPIQAARC EasyARC Challenge
0GPT-3 Small125M33.7%42.7%33.5%64.3%42.7%25.5%
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3GPT-3 XL1.3B54.7%63.6%54.9%74.3%59.1%36.7%
4GPT-3 2.7B2.7B62.8%67.1%62.9%75.4%62.1%39.5%
5GPT-3 6.7B6.7B67.4%70.3%67.3%77.8%65.8%43.7%
6GPT-3 13B13.0B70.9%72.5%71.3%79.9%69.1%44.8%
7GPT-3 175B175.0B78.9%76.2%79.3%82.3%70.1%51.5%
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" + ], + "text/plain": [ + " Model Params HellaSwag 0-shot LAMBADA HellaSwag 10-shot PIQA \\\n", + "0 GPT-3 Small 125M 33.7% 42.7% 33.5% 64.3% \n", + "1 GPT-3 Medium 350M 43.6% 54.3% 43.1% 69.4% \n", + "2 GPT-3 Large 760M 51.0% 60.4% 51.3% 72.0% \n", + "3 GPT-3 XL 1.3B 54.7% 63.6% 54.9% 74.3% \n", + "4 GPT-3 2.7B 2.7B 62.8% 67.1% 62.9% 75.4% \n", + "5 GPT-3 6.7B 6.7B 67.4% 70.3% 67.3% 77.8% \n", + "6 GPT-3 13B 13.0B 70.9% 72.5% 71.3% 79.9% \n", + "7 GPT-3 175B 175.0B 78.9% 76.2% 79.3% 82.3% \n", + "\n", + " ARC Easy ARC Challenge \n", + "0 42.7% 25.5% \n", + "1 51.0% 28.4% \n", + "2 58.1% 32.3% \n", + "3 59.1% 36.7% \n", + "4 62.1% 39.5% \n", + "5 65.8% 43.7% \n", + "6 69.1% 44.8% \n", + "7 70.1% 51.5% " + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# GPT-3 accuracies from the paper\n", + "# Format: [hellaswag_0shot, lambada_0shot, hellaswag_fewshot, piqa_fewshot, arc_easy_fewshot, arc_challenge_fewshot]\n", + "gpt3_models = [\n", + " ('GPT-3 Small', 125e6, [0.337, 0.427, 0.335, 0.643, 0.427, 0.255]),\n", + " ('GPT-3 Medium', 350e6, [0.436, 0.543, 0.431, 0.694, 0.510, 0.284]),\n", + " ('GPT-3 Large', 760e6, [0.510, 0.604, 0.513, 0.720, 0.581, 0.323]),\n", + " ('GPT-3 XL', 1.3e9, [0.547, 0.636, 0.549, 0.743, 0.591, 0.367]),\n", + " ('GPT-3 2.7B', 2.7e9, [0.628, 0.671, 0.629, 0.754, 0.621, 0.395]),\n", + " ('GPT-3 6.7B', 6.7e9, [0.674, 0.703, 0.673, 0.778, 0.658, 0.437]),\n", + " ('GPT-3 13B', 13e9, [0.709, 0.725, 0.713, 0.799, 0.691, 0.448]),\n", + " ('GPT-3 175B', 175e9, [0.789, 0.762, 0.793, 0.823, 0.701, 0.515]),\n", + "]\n", + "\n", + "# Display raw accuracies\n", + "gpt3_df = pd.DataFrame([\n", + " {\n", + " 'Model': name,\n", + " 'Params': f\"{params/1e9:.1f}B\" if params >= 1e9 else f\"{params/1e6:.0f}M\",\n", + " **{task_name: f\"{acc:.1%}\" for task_name, acc in zip(TASK_NAMES, accs)}\n", + " }\n", + " for name, params, accs in gpt3_models\n", + "])\n", + "print(\"GPT-3 Family: Raw Accuracies from Paper\")\n", + "gpt3_df" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GPT-3 Family: Centered Accuracies\n" + ] + }, + { + "data": { + "text/html": [ + "
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HellaSwag 0-shotLAMBADAHellaSwag 10-shotPIQAARC EasyARC ChallengeMean
GPT-3 Small0.11600.4270.11330.2860.23600.00670.1975
GPT-3 Medium0.24800.5430.24130.3880.34670.04530.3021
GPT-3 Large0.34670.6040.35070.4400.44130.09730.3800
GPT-3 XL0.39600.6360.39870.4860.45470.15600.4212
GPT-3 2.7B0.50400.6710.50530.5080.49470.19330.4794
GPT-3 6.7B0.56530.7030.56400.5560.54400.24930.5303
GPT-3 13B0.61200.7250.61730.5980.58800.26400.5674
GPT-3 175B0.71870.7620.72400.6460.60130.35330.6342
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" + ], + "text/plain": [ + " HellaSwag 0-shot LAMBADA HellaSwag 10-shot PIQA ARC Easy \\\n", + "GPT-3 Small 0.1160 0.427 0.1133 0.286 0.2360 \n", + "GPT-3 Medium 0.2480 0.543 0.2413 0.388 0.3467 \n", + "GPT-3 Large 0.3467 0.604 0.3507 0.440 0.4413 \n", + "GPT-3 XL 0.3960 0.636 0.3987 0.486 0.4547 \n", + "GPT-3 2.7B 0.5040 0.671 0.5053 0.508 0.4947 \n", + "GPT-3 6.7B 0.5653 0.703 0.5640 0.556 0.5440 \n", + "GPT-3 13B 0.6120 0.725 0.6173 0.598 0.5880 \n", + "GPT-3 175B 0.7187 0.762 0.7240 0.646 0.6013 \n", + "\n", + " ARC Challenge Mean \n", + "GPT-3 Small 0.0067 0.1975 \n", + "GPT-3 Medium 0.0453 0.3021 \n", + "GPT-3 Large 0.0973 0.3800 \n", + "GPT-3 XL 0.1560 0.4212 \n", + "GPT-3 2.7B 0.1933 0.4794 \n", + "GPT-3 6.7B 0.2493 0.5303 \n", + "GPT-3 13B 0.2640 0.5674 \n", + "GPT-3 175B 0.3533 0.6342 " + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Compute centered accuracies for GPT-3\n", + "X_gpt3 = []\n", + "for name, params, accs in gpt3_models:\n", + " centered_accs = [center_accuracy(acc, BASELINES[task]) for task, acc in zip(TASK_ORDER, accs)]\n", + " X_gpt3.append(centered_accs)\n", + "\n", + "X_gpt3 = np.array(X_gpt3)\n", + "\n", + "# Display\n", + "gpt3_centered_df = pd.DataFrame(\n", + " X_gpt3,\n", + " columns=TASK_NAMES,\n", + " index=[m[0] for m in gpt3_models]\n", + ")\n", + "gpt3_centered_df['Mean'] = X_gpt3.mean(axis=1)\n", + "print(\"GPT-3 Family: Centered Accuracies\")\n", + "gpt3_centered_df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 5: Regression Models\n", + "\n", + "We fit two types of models:\n", + "\n", + "1. **Simple Approach**: Average the 6 centered accuracies, then fit a linear regression to CORE\n", + "2. **Multivariate Approach**: Use all 6 features with Ridge regularization\n", + "\n", + "### Why Regularization?\n", + "\n", + "We only have 4 calibration points (GPT-2 models) but 6 features + 1 intercept = 7 parameters. Without regularization, we get a perfect fit but with unstable, extreme weights. Ridge regression shrinks weights toward zero, preventing overfitting." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def simple_linear_regression(x, y):\n", + " \"\"\"Simple 1D linear regression: y = a*x + b\"\"\"\n", + " mean_x, mean_y = np.mean(x), np.mean(y)\n", + " a = np.sum((x - mean_x) * (y - mean_y)) / np.sum((x - mean_x) ** 2)\n", + " b = mean_y - a * mean_x\n", + " return a, b\n", + "\n", + "def ridge_regression(X, y, alpha=0.1):\n", + " \"\"\"\n", + " Ridge regression: minimize ||Xw - y||² + α||w||²\n", + " We don't regularize the intercept.\n", + " \"\"\"\n", + " n_samples, n_features = X.shape\n", + " X_aug = np.column_stack([np.ones(n_samples), X])\n", + " reg_matrix = alpha * np.eye(n_features + 1)\n", + " reg_matrix[0, 0] = 0 # Don't regularize intercept\n", + " coeffs = np.linalg.solve(X_aug.T @ X_aug + reg_matrix, X_aug.T @ y)\n", + " return coeffs[0], coeffs[1:] # intercept, weights\n", + "\n", + "def compute_r_squared(y_true, y_pred):\n", + " \"\"\"Compute R² score.\"\"\"\n", + " ss_res = np.sum((y_true - y_pred) ** 2)\n", + " ss_tot = np.sum((y_true - np.mean(y_true)) ** 2)\n", + " return 1 - ss_res / ss_tot" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Approach 1: Simple Averaging" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Simple Model: CORE = 0.6639 × avg_centered + 0.0168\n", + "\n", + "R² = 0.9960\n" + ] + }, + { + "data": { + "text/html": [ + "
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ModelAvg CenteredPredictedActualError
0GPT-20.15050.11680.11390.0029
1GPT-2 Medium0.24480.17930.1849-0.0056
2GPT-2 Large0.29910.21540.21460.0008
3GPT-2 XL0.36390.25840.25650.0019
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" + ], + "text/plain": [ + " Model Avg Centered Predicted Actual Error\n", + "0 GPT-2 0.1505 0.1168 0.1139 0.0029\n", + "1 GPT-2 Medium 0.2448 0.1793 0.1849 -0.0056\n", + "2 GPT-2 Large 0.2991 0.2154 0.2146 0.0008\n", + "3 GPT-2 XL 0.3639 0.2584 0.2565 0.0019" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Compute average of 6 centered accuracies\n", + "avg_centered_gpt2 = X_gpt2.mean(axis=1)\n", + "\n", + "# Fit linear regression\n", + "slope, intercept = simple_linear_regression(avg_centered_gpt2, y_gpt2)\n", + "print(f\"Simple Model: CORE = {slope:.4f} × avg_centered + {intercept:.4f}\")\n", + "\n", + "# Validate\n", + "y_pred_simple = slope * avg_centered_gpt2 + intercept\n", + "r2_simple = compute_r_squared(y_gpt2, y_pred_simple)\n", + "\n", + "validation_df = pd.DataFrame({\n", + " 'Model': [d['name'] for d in gpt2_data],\n", + " 'Avg Centered': avg_centered_gpt2,\n", + " 'Predicted': y_pred_simple,\n", + " 'Actual': y_gpt2,\n", + " 'Error': y_pred_simple - y_gpt2\n", + "})\n", + "print(f\"\\nR² = {r2_simple:.4f}\")\n", + "validation_df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Result:** R² = 0.996 — excellent fit with just 2 parameters. The simple averaging approach works very well." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Approach 2: Multivariate Ridge Regression\n", + "\n", + "We try different regularization strengths (α) to find a good balance between fit and stability." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Effect of Regularization Strength:\n" + ] + }, + { + "data": { + "text/html": [ + "
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αR²||weights||Intercept
00.0001.000010.7221-0.0829
10.0010.99710.27960.0159
20.0100.99160.24630.0269
30.1000.84480.16000.0851
41.0000.25230.03560.1686
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" + ], + "text/plain": [ + " α R² ||weights|| Intercept\n", + "0 0.000 1.0000 10.7221 -0.0829\n", + "1 0.001 0.9971 0.2796 0.0159\n", + "2 0.010 0.9916 0.2463 0.0269\n", + "3 0.100 0.8448 0.1600 0.0851\n", + "4 1.000 0.2523 0.0356 0.1686" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Try different regularization strengths\n", + "alphas = [0.0, 0.001, 0.01, 0.1, 1.0]\n", + "\n", + "results = []\n", + "for alpha in alphas:\n", + " intercept_r, weights = ridge_regression(X_gpt2, y_gpt2, alpha=alpha)\n", + " y_pred = X_gpt2 @ weights + intercept_r\n", + " r2 = compute_r_squared(y_gpt2, y_pred)\n", + " weight_norm = np.sqrt(np.sum(weights ** 2))\n", + " results.append({\n", + " 'α': alpha,\n", + " 'R²': r2,\n", + " '||weights||': weight_norm,\n", + " 'Intercept': intercept_r,\n", + " 'Weights': weights.copy()\n", + " })\n", + "\n", + "alpha_df = pd.DataFrame([{k: v for k, v in r.items() if k != 'Weights'} for r in results])\n", + "print(\"Effect of Regularization Strength:\")\n", + "alpha_df" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Task Weights by Regularization Strength:\n" + ] + }, + { + "data": { + "text/html": [ + "
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HellaSwag 0-shotLAMBADAHellaSwag 10-shotPIQAARC EasyARC Challenge
α=0.06.55230.2201-8.02680.53780.91092.5364
α=0.0010.11340.14420.13050.11530.05100.1079
α=0.010.11550.10000.12260.09590.10230.0513
α=0.10.07590.06140.07980.06100.07140.0293
α=1.00.01690.01360.01780.01350.01600.0064
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" + ], + "text/plain": [ + " HellaSwag 0-shot LAMBADA HellaSwag 10-shot PIQA ARC Easy \\\n", + "α=0.0 6.5523 0.2201 -8.0268 0.5378 0.9109 \n", + "α=0.001 0.1134 0.1442 0.1305 0.1153 0.0510 \n", + "α=0.01 0.1155 0.1000 0.1226 0.0959 0.1023 \n", + "α=0.1 0.0759 0.0614 0.0798 0.0610 0.0714 \n", + "α=1.0 0.0169 0.0136 0.0178 0.0135 0.0160 \n", + "\n", + " ARC Challenge \n", + "α=0.0 2.5364 \n", + "α=0.001 0.1079 \n", + "α=0.01 0.0513 \n", + "α=0.1 0.0293 \n", + "α=1.0 0.0064 " + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Show weights for each alpha\n", + "print(\"Task Weights by Regularization Strength:\")\n", + "weights_df = pd.DataFrame(\n", + " [r['Weights'] for r in results],\n", + " columns=TASK_NAMES,\n", + " index=[f\"α={r['α']}\" for r in results]\n", + ")\n", + "weights_df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Observations:**\n", + "\n", + "- **α=0 (no regularization):** Perfect fit (R²=1.0) but extreme weights (+18, -22) — clearly overfitting\n", + "- **α=0.001:** Still near-perfect fit with very large weights\n", + "- **α=0.01:** Excellent fit (R²=0.99) with reasonable weights (~0.1 each) — **good choice**\n", + "- **α=0.1:** Good fit (R²=0.84) with uniform weights (~0.06 each) — conservative\n", + "- **α=1.0:** Poor fit (R²=0.25) — over-regularized" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Ridge Model (α=0.01):\n", + " Intercept: 0.0269\n", + " Weights:\n", + " HellaSwag 0-shot : +0.1155\n", + " LAMBADA : +0.1000\n", + " HellaSwag 10-shot : +0.1226\n", + " PIQA : +0.0959\n", + " ARC Easy : +0.1023\n", + " ARC Challenge : +0.0513\n", + "\n", + "R² = 0.9916\n" + ] + } + ], + "source": [ + "# Use α=0.01 as our chosen regularization\n", + "# This gives R²≈0.99 with reasonable, stable weights (~0.1 each task)\n", + "CHOSEN_ALPHA = 0.01\n", + "intercept_ridge, weights_ridge = ridge_regression(X_gpt2, y_gpt2, alpha=CHOSEN_ALPHA)\n", + "\n", + "print(f\"Ridge Model (α={CHOSEN_ALPHA}):\")\n", + "print(f\" Intercept: {intercept_ridge:.4f}\")\n", + "print(f\" Weights:\")\n", + "for name, w in zip(TASK_NAMES, weights_ridge):\n", + " print(f\" {name:20s}: {w:+.4f}\")\n", + "\n", + "# Validate\n", + "y_pred_ridge = X_gpt2 @ weights_ridge + intercept_ridge\n", + "r2_ridge = compute_r_squared(y_gpt2, y_pred_ridge)\n", + "print(f\"\\nR² = {r2_ridge:.4f}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Approach 3: Individual Task Analysis\n", + "\n", + "Which single task is the best predictor of CORE? We fit separate linear regressions for each task." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Individual Task Correlations with CORE:\n" + ] + }, + { + "data": { + "text/html": [ + "
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TaskR²SlopeIntercept
3PIQA0.99610.6879-0.0537
2HellaSwag 10-shot0.99330.52300.0776
0HellaSwag 0-shot0.99270.54890.0753
1LAMBADA0.98410.6792-0.1063
4ARC Easy0.98000.5728-0.0027
5ARC Challenge0.95991.39940.1706
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" + ], + "text/plain": [ + " Task R² Slope Intercept\n", + "3 PIQA 0.9961 0.6879 -0.0537\n", + "2 HellaSwag 10-shot 0.9933 0.5230 0.0776\n", + "0 HellaSwag 0-shot 0.9927 0.5489 0.0753\n", + "1 LAMBADA 0.9841 0.6792 -0.1063\n", + "4 ARC Easy 0.9800 0.5728 -0.0027\n", + "5 ARC Challenge 0.9599 1.3994 0.1706" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Fit separate linear regression for each task\n", + "individual_results = []\n", + "for i, task_name in enumerate(TASK_NAMES):\n", + " x_task = X_gpt2[:, i]\n", + " slope_ind, intercept_ind = simple_linear_regression(x_task, y_gpt2)\n", + " y_pred_ind = slope_ind * x_task + intercept_ind\n", + " r2_ind = compute_r_squared(y_gpt2, y_pred_ind)\n", + " individual_results.append({\n", + " 'Task': task_name,\n", + " 'R²': r2_ind,\n", + " 'Slope': slope_ind,\n", + " 'Intercept': intercept_ind\n", + " })\n", + "\n", + "individual_df = pd.DataFrame(individual_results).sort_values('R²', ascending=False)\n", + "print(\"Individual Task Correlations with CORE:\")\n", + "individual_df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Key Finding:** All 6 tasks have very high correlation with CORE (R² > 0.96), but **PIQA is the single best predictor** with R² = 0.9961 — actually slightly better than the simple averaging approach (R² = 0.9960)!\n", + "\n", + "This is useful if you want a quick proxy for CORE with minimal evaluation cost. However, for robustness we still recommend using all 6 tasks or the averaged approaches." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Part 6: Final Estimates for GPT-3\n", + "\n", + "We apply both models to GPT-3 data and report the average as our final estimate." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GPT-3 CORE Estimates (all three approaches):\n" + ] + }, + { + "data": { + "text/html": [ + "
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ModelParamsSimpleRidgePIQA onlyAvg(1,2)
0GPT-3 Small125M0.14800.14880.14300.1484
1GPT-3 Medium350M0.21740.21440.21310.2159
2GPT-3 Large760M0.26910.26270.24890.2659
3GPT-3 XL1.3B0.29650.28620.28050.2914
4GPT-3 2.7B2.7B0.33510.32340.29570.3292
5GPT-3 6.7B6.7B0.36890.35340.32870.3611
6GPT-3 13B13.0B0.39350.37680.35760.3852
7GPT-3 175B175.0B0.43790.41640.39060.4272
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" + ], + "text/plain": [ + " Model Params Simple Ridge PIQA only Avg(1,2)\n", + "0 GPT-3 Small 125M 0.1480 0.1488 0.1430 0.1484\n", + "1 GPT-3 Medium 350M 0.2174 0.2144 0.2131 0.2159\n", + "2 GPT-3 Large 760M 0.2691 0.2627 0.2489 0.2659\n", + "3 GPT-3 XL 1.3B 0.2965 0.2862 0.2805 0.2914\n", + "4 GPT-3 2.7B 2.7B 0.3351 0.3234 0.2957 0.3292\n", + "5 GPT-3 6.7B 6.7B 0.3689 0.3534 0.3287 0.3611\n", + "6 GPT-3 13B 13.0B 0.3935 0.3768 0.3576 0.3852\n", + "7 GPT-3 175B 175.0B 0.4379 0.4164 0.3906 0.4272" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Apply all three approaches\n", + "avg_centered_gpt3 = X_gpt3.mean(axis=1)\n", + "gpt3_core_simple = slope * avg_centered_gpt3 + intercept\n", + "gpt3_core_ridge = X_gpt3 @ weights_ridge + intercept_ridge\n", + "\n", + "# Approach 3: Best individual predictor (PIQA)\n", + "piqa_idx = TASK_NAMES.index('PIQA')\n", + "piqa_model = [r for r in individual_results if r['Task'] == 'PIQA'][0]\n", + "gpt3_core_piqa = piqa_model['Slope'] * X_gpt3[:, piqa_idx] + piqa_model['Intercept']\n", + "\n", + "# Average of approaches 1 and 2\n", + "gpt3_core_final = (gpt3_core_simple + gpt3_core_ridge) / 2\n", + "\n", + "# Create results table with all approaches\n", + "results_df = pd.DataFrame({\n", + " 'Model': [m[0] for m in gpt3_models],\n", + " 'Params': [f\"{m[1]/1e9:.1f}B\" if m[1] >= 1e9 else f\"{m[1]/1e6:.0f}M\" for m in gpt3_models],\n", + " 'Simple': gpt3_core_simple,\n", + " f'Ridge': gpt3_core_ridge,\n", + " 'PIQA only': gpt3_core_piqa,\n", + " 'Avg(1,2)': gpt3_core_final\n", + "})\n", + "print(\"GPT-3 CORE Estimates (all three approaches):\")\n", + "results_df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Final CORE Estimates for GPT-3" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Complete CORE Scores (GPT-2 measured, GPT-3 estimated):\n" + ] + }, + { + "data": { + "text/html": [ + "
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ModelParamsCORESource
0GPT-2124M0.1139Measured
1GPT-3 Small125M0.1484Estimated
2GPT-3 Medium350M0.2159Estimated
3GPT-2 Medium355M0.1849Measured
4GPT-3 Large760M0.2659Estimated
5GPT-2 Large774M0.2146Measured
6GPT-3 XL1.3B0.2914Estimated
7GPT-2 XL1.6B0.2565Measured
8GPT-3 2.7B2.7B0.3292Estimated
9GPT-3 6.7B6.7B0.3611Estimated
10GPT-3 13B13.0B0.3852Estimated
11GPT-3 175B175.0B0.4272Estimated
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" + ], + "text/plain": [ + " Model Params CORE Source\n", + "0 GPT-2 124M 0.1139 Measured\n", + "1 GPT-3 Small 125M 0.1484 Estimated\n", + "2 GPT-3 Medium 350M 0.2159 Estimated\n", + "3 GPT-2 Medium 355M 0.1849 Measured\n", + "4 GPT-3 Large 760M 0.2659 Estimated\n", + "5 GPT-2 Large 774M 0.2146 Measured\n", + "6 GPT-3 XL 1.3B 0.2914 Estimated\n", + "7 GPT-2 XL 1.6B 0.2565 Measured\n", + "8 GPT-3 2.7B 2.7B 0.3292 Estimated\n", + "9 GPT-3 6.7B 6.7B 0.3611 Estimated\n", + "10 GPT-3 13B 13.0B 0.3852 Estimated\n", + "11 GPT-3 175B 175.0B 0.4272 Estimated" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Combine with GPT-2 for complete picture\n", + "all_models = []\n", + "\n", + "for data in gpt2_data:\n", + " params = data['params']\n", + " all_models.append({\n", + " 'Model': data['name'],\n", + " 'Family': 'GPT-2',\n", + " 'Params': params,\n", + " 'Params_str': f\"{params/1e9:.1f}B\" if params >= 1e9 else f\"{params/1e6:.0f}M\",\n", + " 'CORE': data['core'],\n", + " 'Source': 'Measured'\n", + " })\n", + "\n", + "for (name, params, _), core in zip(gpt3_models, gpt3_core_final):\n", + " all_models.append({\n", + " 'Model': name,\n", + " 'Family': 'GPT-3',\n", + " 'Params': params,\n", + " 'Params_str': f\"{params/1e9:.1f}B\" if params >= 1e9 else f\"{params/1e6:.0f}M\",\n", + " 'CORE': core,\n", + " 'Source': 'Estimated'\n", + " })\n", + "\n", + "# Sort by params and display\n", + "all_models.sort(key=lambda x: x['Params'])\n", + "final_df = pd.DataFrame(all_models)[['Model', 'Params_str', 'CORE', 'Source']]\n", + "final_df.columns = ['Model', 'Params', 'CORE', 'Source']\n", + "print(\"Complete CORE Scores (GPT-2 measured, GPT-3 estimated):\")\n", + "final_df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Head-to-Head: GPT-2 vs GPT-3 at Similar Sizes" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GPT-3 vs GPT-2 at Similar Model Sizes:\n" + ] + }, + { + "data": { + "text/html": [ + "
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SizeGPT-2 COREGPT-3 COREΔImprovement
0~125M0.11390.14840.0345+30.3%
1~350M0.18490.21590.0310+16.8%
2~760M0.21460.26590.0512+23.9%
3~1.3-1.5B0.25650.29140.0348+13.6%
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" + ], + "text/plain": [ + " Size GPT-2 CORE GPT-3 CORE Δ Improvement\n", + "0 ~125M 0.1139 0.1484 0.0345 +30.3%\n", + "1 ~350M 0.1849 0.2159 0.0310 +16.8%\n", + "2 ~760M 0.2146 0.2659 0.0512 +23.9%\n", + "3 ~1.3-1.5B 0.2565 0.2914 0.0348 +13.6%" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "comparisons = [\n", + " ('~125M', 'GPT-2', gpt2_data[0]['core'], 'GPT-3 Small', gpt3_core_final[0]),\n", + " ('~350M', 'GPT-2 Medium', gpt2_data[1]['core'], 'GPT-3 Medium', gpt3_core_final[1]),\n", + " ('~760M', 'GPT-2 Large', gpt2_data[2]['core'], 'GPT-3 Large', gpt3_core_final[2]),\n", + " ('~1.3-1.5B', 'GPT-2 XL', gpt2_data[3]['core'], 'GPT-3 XL', gpt3_core_final[3]),\n", + "]\n", + "\n", + "comparison_df = pd.DataFrame([\n", + " {\n", + " 'Size': size,\n", + " 'GPT-2 CORE': gpt2_core,\n", + " 'GPT-3 CORE': gpt3_core,\n", + " 'Δ': gpt3_core - gpt2_core,\n", + " 'Improvement': f\"{100 * (gpt3_core - gpt2_core) / gpt2_core:+.1f}%\"\n", + " }\n", + " for size, _, gpt2_core, _, gpt3_core in comparisons\n", + "])\n", + "print(\"GPT-3 vs GPT-2 at Similar Model Sizes:\")\n", + "comparison_df" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Conclusions\n", + "\n", + "### Methodology\n", + "\n", + "We estimated CORE scores for GPT-3 models by:\n", + "1. Identifying 6 tasks with comparable evaluation methodology between GPT-3 and CORE\n", + "2. Using GPT-2's measured CORE scores as calibration data\n", + "3. Fitting three regression approaches:\n", + " - **Simple**: Average the 6 metrics, then linear regression (R²=0.996)\n", + " - **Ridge**: Use all 6 features with regularization (R²=0.992)\n", + " - **PIQA only**: Single best predictor (R²=0.996)\n", + "4. Averaging the Simple and Ridge approaches for final estimates\n", + "\n", + "### Key Findings\n", + "\n", + "1. **GPT-3 consistently outperforms GPT-2 at similar model sizes** by approximately 0.03-0.05 CORE (14-30% relative improvement)\n", + "\n", + "2. **PIQA is the best single predictor of CORE** (R²=0.9961). If you need a quick proxy for CORE with minimal evaluation cost, PIQA alone works nearly as well as averaging all 6 tasks.\n", + "\n", + "3. **The improvement likely comes from:**\n", + " - More training data (300B tokens vs ~100B for GPT-2)\n", + " - Better data quality and filtering\n", + " - Larger context length (2048 vs 1024)\n", + "\n", + "4. **Final estimated CORE scores:**\n", + "\n", + "| Model | Params | Estimated CORE |\n", + "|-------|--------|----------------|\n", + "| GPT-3 Small | 125M | 0.148 |\n", + "| GPT-3 Medium | 350M | 0.216 |\n", + "| GPT-3 Large | 760M | 0.266 |\n", + "| GPT-3 XL | 1.3B | 0.291 |\n", + "| GPT-3 2.7B | 2.7B | 0.329 |\n", + "| GPT-3 6.7B | 6.7B | 0.361 |\n", + "| GPT-3 13B | 13B | 0.385 |\n", + "| GPT-3 175B | 175B | 0.427 |\n", + "\n", + "### Caveats\n", + "\n", + "1. **These are estimates**, not measured values. True CORE scores could differ.\n", + "2. We only have 4 calibration points, limiting statistical power.\n", + "3. The 6 overlapping tasks may not perfectly represent all 22 CORE tasks.\n", + "4. Slight differences in evaluation methodology (K values, splits) add uncertainty.\n", + "\n", + "Despite these limitations, the estimates are useful for approximate comparisons between nanochat models and the GPT-3 family." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Appendix: Export Final Estimates" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "GPT-3 CORE Estimates (for copy-paste):\n", + "{\n", + " \"GPT-3 Small (125M)\": 0.1484,\n", + " \"GPT-3 Medium (350M)\": 0.2159,\n", + " \"GPT-3 Large (760M)\": 0.2659,\n", + " \"GPT-3 XL (1.3B)\": 0.2914,\n", + " \"GPT-3 2.7B\": 0.3292,\n", + " \"GPT-3 6.7B\": 0.3611,\n", + " \"GPT-3 13B\": 0.3852,\n", + " \"GPT-3 175B\": 0.4272\n", + "}\n" + ] + } + ], + "source": [ + "# Export as a simple dict for use elsewhere\n", + "gpt3_core_estimates = {\n", + " 'GPT-3 Small (125M)': round(gpt3_core_final[0], 4),\n", + " 'GPT-3 Medium (350M)': round(gpt3_core_final[1], 4),\n", + " 'GPT-3 Large (760M)': round(gpt3_core_final[2], 4),\n", + " 'GPT-3 XL (1.3B)': round(gpt3_core_final[3], 4),\n", + " 'GPT-3 2.7B': round(gpt3_core_final[4], 4),\n", + " 'GPT-3 6.7B': round(gpt3_core_final[5], 4),\n", + " 'GPT-3 13B': round(gpt3_core_final[6], 4),\n", + " 'GPT-3 175B': round(gpt3_core_final[7], 4),\n", + "}\n", + "\n", + "print(\"GPT-3 CORE Estimates (for copy-paste):\")\n", + "import json\n", + "print(json.dumps(gpt3_core_estimates, indent=4))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}