AI Model Accuracy vs Training Cost Tradeoff Calculator

ANA›Life Services Authority›National Calculator Authority›AI Model Accuracy vs Training Cost Tradeoff Calculator

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AI Model Accuracy vs Training Cost Tradeoff Calculator

Estimate model accuracy (as loss reduction) and training cost based on dataset size, model parameters, compute per token, and hardware cost. Uses neural scaling law relationships.

Model Parameters (millions)

Number of trainable parameters in millions (e.g. 125 for GPT-2 small)

Training Tokens (billions)

Total tokens used for training in billions (e.g. 300 for Chinchilla-optimal at 125M params)

FLOPs per Token per Parameter

Typically ~6 FLOPs per token per parameter for standard transformer training (forward + backward)

GPU FLOP/s (teraFLOPs/s)

Peak throughput of your GPU/TPU in TFLOP/s (e.g. 312 for A100 80GB BF16)

Hardware Utilization (%)

Effective utilization of peak FLOP/s (typically 30–50% in practice)

Number of GPUs

Total GPUs used in parallel training

GPU Cost per Hour (USD)

Cloud rental cost per GPU per hour (e.g. ~$3.00 for A100 on major clouds)

Irreducible (Entropy) Loss

Theoretical minimum loss (data entropy). ~1.69 nats for natural language (ln(5) approximation)

Calculate

function aiCalc() { const resultDiv = document.getElementById('ai-result');

const N = parseFloat(document.getElementById('ai-params').value); const D = parseFloat(document.getElementById('ai-tokens').value); const flopsPerTokenPerParam = parseFloat(document.getElementById('ai-flops-per-token').value); const gpuTFlops = parseFloat(document.getElementById('ai-gpu-flops').value); const utilPct = parseFloat(document.getElementById('ai-gpu-util').value); const numGPUs = parseFloat(document.getElementById('ai-num-gpus').value); const gpuCostPerHr = parseFloat(document.getElementById('ai-gpu-cost').value); const L_inf = parseFloat(document.getElementById('ai-irreducible-loss').value);

// Validation const fields = [ [N, 'Model Parameters', 1, 1e7], [D, 'Training Tokens', 0.1, 1e6], [flopsPerTokenPerParam, 'FLOPs per Token per Parameter', 1, 100], [gpuTFlops, 'GPU FLOP/s', 1, 10000], [utilPct, 'Hardware Utilization', 1, 100], [numGPUs, 'Number of GPUs', 1, 1e6], [gpuCostPerHr, 'GPU Cost per Hour', 0.01, 1000], [L_inf, 'Irreducible Loss', 0.01, 10] ];

for (const [val, name, lo, hi] of fields) { if (isNaN(val) || val hi) { resultDiv.innerHTML = '⚠️ Please enter a valid value for ' + name + ' (between ' + lo + ' and ' + hi + ').'; return; } }

// ── Scaling Law (Hoffmann et al. 2022 "Chinchilla") ────────────────────── // L(N, D) = L_inf + A / N^alpha + B / D^beta // Chinchilla best-fit constants: const A = 406.4; // nats const B = 410.7; // nats const alpha = 0.34; const beta = 0.28;

// N in actual parameters, D in actual tokens const N_actual = N * 1e6; // millions → units const D_actual = D * 1e9; // billions → units

const loss = L_inf + A / Math.pow(N_actual, alpha) + B / Math.pow(D_actual, beta);

// Perplexity (base-e) const perplexity = Math.exp(loss);

// Chinchilla-optimal token count for this N: D_opt = 20 * N const D_opt_billions = (20 * N_actual) / 1e9; const loss_opt = L_inf + A / Math.pow(N_actual, alpha) + B / Math.pow(20 * N_actual, beta); const perplexity_opt = Math.exp(loss_opt);

// ── Compute Cost ───────────────────────────────────────────────────────── // Total FLOPs = flopsPerTokenPerParam * N_actual * D_actual const totalFLOPs = flopsPerTokenPerParam * N_actual * D_actual; // FLOPs

// Effective cluster throughput (FLOP/s) const effectiveTFlops = gpuTFlops * (utilPct / 100) * numGPUs; // TFLOP/s const effectiveFLOPs_per_sec = effectiveTFlops * 1e12; // FLOP/s

// Training time in seconds, then hours const trainTimeSec = totalFLOPs / effectiveFLOPs_per_sec; const trainTimeHrs = trainTimeSec / 3600; const trainTimeDays = trainTimeHrs / 24;

// Total cost const totalCost = trainTimeHrs * numGPUs * gpuCostPerHr;

// Cost for Chinchilla-optimal run (same N, D_opt tokens) const D_opt_actual = 20 * N_actual; const totalFLOPs_opt = flopsPerTokenPerParam * N_actual * D_opt_actual; const trainTimeSec_opt = totalFLOPs_opt / effectiveFLOPs_per_sec; const trainTimeHrs_opt = trainTimeSec_opt / 3600; const totalCost_opt = trainTimeHrs_opt * numGPUs * gpuCostPerHr;

// Cost efficiency: loss reduction per $1000 const lossReduction = loss - L_inf; // reducible loss achieved const costEfficiency = totalCost > 0 ? (lossReduction / (totalCost / 1000)).toFixed(4) : 'N/A';

// PetaFLOP-days const petaFLOPdays = totalFLOPs / (1e15 * 86400);

// Format helpers const fmt = (n, d=2) => n.toLocaleString('en-US', {minimumFractionDigits: d, maximumFractionDigits: d}); const fmtCost = n => '$' + fmt(n, 0); const fmtSci = n => { if (n >= 1e15) return fmt(n/1e15, 2) + ' PetaFLOPs'; if (n >= 1e12) return fmt(n/1e12, 2) + ' TeraFLOPs'; if (n >= 1e9) return fmt(n/1e9, 2) + ' GigaFLOPs'; return fmt(n, 0) + ' FLOPs'; };

// Token ratio vs Chinchilla-optimal const tokenRatio = D_actual / D_opt_actual; let tokenStatus = ''; if (tokenRatio Model Loss (Scaling Law) Predicted Cross-Entropy Loss${fmt(loss, 4)} nats Irreducible (Entropy) Loss${fmt(L_inf, 4)} nats Reducible Loss Achieved${fmt(lossReduction, 4)} nats Perplexity (e^loss)${fmt(perplexity, 2)}

Chinchilla-Optimal Comparison (D = 20N) Optimal Tokens for This Model${fmt(D_opt_billions, 2)}B tokens Your Token Count${fmt(D, 2)}B tokens (${fmt(tokenRatio*100,1)}% of optimal) Token Adequacy${tokenStatus} Loss at Chinchilla-Optimal${fmt(loss_opt, 4)} nats (perplexity ${fmt(perplexity_opt,2)}) Cost at Chinchilla-Optimal${fmtCost(totalCost_opt)}

Compute & Cost Total Training FLOPs${fmtSci(totalFLOPs)} PetaFLOP-days${fmt(petaFLOPdays, 4)} Effective Cluster Throughput${fmt(effectiveTFlops, 1)} TFLOP/s Estimated Training Time${fmt(trainTimeHrs, 1)} hrs (${fmt(trainTimeDays, 2)} days) Total Training Cost${fmtCost(totalCost)} Cost per GPU-Hour${fmtCost(gpuCostPerHr)} × ${fmt(numGPUs,0)} GPUs

Efficiency Metric Loss Reduction per $1,000 Spent${costEfficiency} nats / $1K

`; }

#### Formulas Used

Neural Scaling Law (Hoffmann et al., 2022 — "Chinchilla"):

L(N, D) = L∞ + A / Nα + B / Dβ

Where: A = 406.4, B = 410.7, α = 0.34, β = 0.28 (fitted constants from Chinchilla paper)

N = number of parameters, D = number of training tokens, L∞ = irreducible entropy loss

Chinchilla-Optimal Token Count: Dopt = 20 × N

Total Training FLOPs: C = F × N × D (F ≈ 6 for standard transformer)

Training Time: T = C / (GPU_FLOP/s × utilization × num_GPUs)

Training Cost: Cost = Thours × num_GPUs × cost_per_GPU_hour

#### Assumptions & References

• Loss is measured in nats (natural log base); perplexity = eloss. For bits-per-character, divide by ln(2).

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References

• ANA
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