Inside the Machine: My Journey Reproducing the Scaling Laws for Language Models

After building my dual-RTX 4080 rig (which I covered in my previous post), I felt like a kid with a supercar stuck in a school zone. It was time to take it to the track. I decided to reproduce the foundational 2020 OpenAI paper: “Scaling Laws for Language Models.” Why this paper? Because it’s the “Old Testament” of modern AI. It’s the reason why GPT-4 and Llama 3 exist. If you don’t understand how loss scales with compute (C), dataset size (D), and parameters (N), you’re just guessing. I wanted to see if these “laws” held up on my own “bare-metal” Ubuntu setup.

Here is the report of my reproduction journey—the math, the code, and the thermal reality of running a local lab.

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The Goal of Scaling Laws for Language Models: Empirical Rigor Over Hype

The core of the paper is the power-law relationship: L(N)≈(Nc​/N)αN​ Essentially, the model’s performance (loss L) improves predictably as you scale parameters (N). My mission was to train a series of small-to-mid-sized Transformer models on the OpenWebText dataset and plot the loss curves to see if the power laws emerged.

The Hardware Tax: Budgeting My Compute

Reproducing OpenAI’s full scale would require an industrial cluster, but for my “TechnoDIY” purposes, I focused on models ranging from 10M to 150M parameters.

• GPU Utilization: Dual RTX 4080s (32GB VRAM combined).
• Time: About 72 hours of continuous training.
• Power: My 1000W PSU was pulling about 650-700W consistently.
• The Struggle: Heat. Even with a high-airflow case, the room temperature climbed by 5 degrees. Local AI is as much about HVAC as it is about CUDA.

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Setting Up the Environment (The “Do It Yourself” Bit)

If you want to try Scaling Laws for Language Models, don’t manually install every library. Use Docker. It ensures that the CUDA version in your container matches what your code expects.

Here is a simplified snippet of the training loop I used, leveraging torch.cuda.amp for mixed precision (to save VRAM on the 4080s) and a custom scaling logger:

Python

import torch
import torch.nn as nn
from torch.utils.data import DataLoader
from model import TransformerModel  # A standard GPT-style decoder

def train_scaling_series(model_configs):
    """
    Trains multiple models of varying sizes to find the scaling slope.
    """
    results = {}
    
    for config in model_configs:
        print(f"Starting training for {config['name']} ({config['params']} params)")
        
        # Move model to our dual GPUs using DataParallel for simplicity here
        model = TransformerModel(config).cuda()
        model = nn.DataParallel(model) 
        
        optimizer = torch.optim.AdamW(model.parameters(), lr=config['lr'])
        scaler = torch.cuda.amp.GradScaler() # Crucial for 40-series cards
        
        for epoch in range(10):
            for batch in train_loader:
                inputs, targets = batch
                inputs, targets = inputs.cuda(), targets.cuda()
                
                with torch.cuda.amp.autocast():
                    outputs = model(inputs)
                    loss = criterion(outputs, targets)
                
                scaler.scale(loss).backward()
                scaler.step(optimizer)
                scaler.update()
                optimizer.zero_grad()
                
        results[config['params']] = loss.item()
        
    return results

# Implementation Tip: Always log 'Compute' as Floating Point Operations (FLOPs)
# FLOPs approx = 6 * Parameters * Training Tokens

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The “Bare-Metal” Obstacles

Even with a high-end setup, I hit a few walls that the paper doesn’t warn you about:

1. The IO Bottleneck: During the first run, my GPU utilization was flickering between 30% and 90%. I realized my data augmentation was too heavy for a single CPU thread. I had to optimize the num_workers in my DataLoader and move to a faster mmap dataset format.
2. CUDA Out of Memory (OOM): When I tried to push the sequence length to 2048 on the 150M model, I hit the VRAM ceiling. This is where Activation Checkpointing saved me. It trades compute for memory by re-calculating the forward pass during backprop.

Python

# To save VRAM on your local GPUs, use this:
from torch.utils.checkpoint import checkpoint

def forward(self, x):
    # Instead of storing all activations, we checkpoint the layers
    for layer in self.layers:
        x = checkpoint(layer, x)
    return x

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The Results of Scaling Laws for Language Models: Does the Math Work?

After three days of the fans spinning at 80%, I plotted the data.

The Verdict: The Scaling Laws are real. Even on a consumer-grade local rig, the relationship between N (parameters) and L (loss) was nearly a straight line on a log-log plot. I found that for my setup, αN​ was roughly 0.07—very close to what OpenAI reported.

This confirms a vital lesson for every DIY AI enthusiast: Small models are not toys. If you can optimize a 10M parameter model to follow the scaling law, you have a high degree of certainty that scaling it up will work. This allows us to “fail fast” on cheap hardware before committing to massive training runs.

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The “TechnoDIY” Takeaway

If you want to reproduce this yourself, here is your checklist:

1. Monitor your FLOPs/watt: If your cards are under-utilized, you are literally burning money. Use nvidia-smi to ensure your power draw is consistent.
2. Use Mixed Precision: On RTX 4080s, FP16 or BF16 isn’t an option; it’s a requirement. It doubles your effective throughput.
3. Trust the Math, Not the Hype: Don’t chase the biggest model. Build a small model, verify the scaling law, and then scale incrementally.

Reproducing the Scaling Laws paper made me realize that AI isn’t some mystical entity. It is a predictable, mathematical machine. Owning the hardware to prove that is, in my opinion, the ultimate form of intellectual independence.

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Final Thoughts

Reproducing research Scaling Laws for Language Models is the only way to truly “own” the knowledge. My local Ubuntu workstation survived the 72-hour stress test, and I walked away with a deeper understanding of how intelligence scales.

In my next post, I’ll be looking at Data Scaling Laws—specifically, how much “junk” data you can feed a model before the scaling law breaks. Stay tuned, and keep building.

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Sömnez Hüseyin Implementation-First Research Lab

See also:

While Scaling Laws ensure that models get better at predicting the next token, they don’t necessarily solve the fundamental illusion of thinking, where a model can appear logical without genuine reasoning capabilities.

As established in the foundational work by Kaplan et al. (2020), Scaling Laws for Language Models, there is a clear empirical correlation between model scale and test loss. This research marked a turning point in the industry, shifting the focus from architectural tweaks to the strategic scaling of compute resources.