Quadtrix.cpp

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This project can be technically defined as an isomorphic, multi-backend implementation of a Generative Pre-trained Transformer (GPT) architecture, engineered to demonstrate the parity between high-level deep learning frameworks and low-level computational primitives.It functions as a comprehensive "vertical slice" of modern AI engineering, spanning from raw C++ pointer arithmetic to high-level Python abstractions

Hardware Execution Backends

Device	Technical Execution Pathway
CPU	Utilizes vectorized instructions (AVX/SSE) and multi-threading for sequential or small-batch inference.
CUDA	Leverages NVIDIA’s parallel computing platform for high-throughput training and inference on discrete GPUs.
iGPU	Targets Integrated GPUs (e.g., Intel Iris, AMD Radeon, or Apple Silicon M-series) via backends like Metal (MPS), DirectML, or oneAPI/SYCL, optimizing for power-efficient local execution.

What is this?

Quadtrix.cpp is a transformer learning laboratory. Write your own backprop, debug attention matrices, export to bare-metal C. If you've read the Attention paper and want to implement it rather than just call model.fit(), this is for you.

Philosophy: Frameworks hide the fundamentals. This project reveals them. Every gradient, every checkpoint, every matrix multiply lives in code you can step through with a debugger.

Parallel tracks: Native C++ training path (educational), PyTorch path (faster iteration), DirectML path (Windows iGPU), pure C inference (deployment), web frontend (chat UI).

Quick Start

# Native C++ path - train from scratch
g++ -std=c++17 -O2 -I. -Iinclude -o quadtrix main.cpp
./quadtrix data/input.txt

# PyTorch path - faster experimentation
pip install torch tiktoken numpy
python engine/main.py

# Interactive chat
./quadtrix data/input.txt --chat
python engine/inference.py

Architecture

Decoder-only transformer with clean fundamentals:

Input → Token Embedding → Position Embedding
  ↓
[Transformer Block] × n_layer
  ├─ Multi-Head Self-Attention (n_head=4)
  ├─ Layer Normalization
  ├─ Feed-Forward Network (4× expansion)
  └─ Residual Connections
  ↓
Layer Norm → Linear Head → Logits

Default hyperparameters (C++ path):

• Context: block_size=64
• Model: n_embd=128, n_head=4, n_layer=4
• Training: batch_size=4, lr=3e-4, max_iters=3000
• Optimizer: AdamW with gradient clipping

PyTorch path uses GPT-2 tokenization:

• Context: block_size=32
• Model: n_embd=64, n_head=4, n_layer=4
• Training: batch_size=16, lr=1e-3, max_iters=2000

Repository Structure

quadtrix.cpp/
│
├── main.cpp                          # C++ training/inference entry point
├── config/
│   └── config.h                      # Hyperparameters and system config
├── include/                          # Transformer implementation
│   ├── dataloader.h                  # Text corpus handling
│   ├── model.h                       # GPT model architecture
│   ├── layers.h                      # Attention, FFN, LayerNorm
│   ├── backward.h                    # Analytical gradient computation
│   └── tensor.h                      # N-dimensional array operations
│
├── engine/                           # PyTorch ecosystem
│   ├── main.py                       # Training script (GPT-2 tokenizer)
│   ├── inference.py                  # Interactive chat interface
│   ├── export_weights.py             # PyTorch → C binary conversion
│   ├── engine.c                      # Dependency-free C inference
│   ├── best_model.pt                 # Trained checkpoint
│   └── model.bin                     # Exported weights for C engine
│
├── iGPU/                             # DirectML Windows support
│   ├── main.py                       # Training on integrated GPUs
│   └── inference.py                  # DirectML inference
│
├── frontend/                         # Web chat interface (WIP)
│   ├── src/api/                      # REST client (chat, sessions)
│   ├── vite.config.ts                # Build configuration
│   └── index.html                    # Application shell
│
├── model/                            # LibTorch experiments
│   ├── CMakeLists.txt                # C++ build with libtorch
│   └── export_tokenizer.py           # GPT-2 vocabulary export
│
├── scripts/
│   └── build_torch.ps1               # Windows LibTorch helper
│
└── quadtrix_training_plots.ipynb     # Visualization and analysis

Training Flow

The native C++ implementation teaches transformer mechanics through explicit steps:

1. Data preparation

// Load corpus, build vocabulary
Dataloader loader("data/input.txt");
const int vocab_size = loader.vocab_size();

2. Model initialization

GPT model(vocab_size, BLOCK_SIZE, N_EMBD, N_HEAD, N_LAYER);

3. Training loop

for (int iter = 0; iter < MAX_ITERS; iter++) {
    // Sample batch
    auto [x, y] = loader.get_batch(BATCH_SIZE, BLOCK_SIZE, true);
    
    // Forward pass (saves activations)
    auto [logits, loss] = model.forward(x, y);
    
    // Backward pass (analytical gradients)
    model.backward();
    
    // Optimizer step (AdamW)
    optimizer.step();
    
    // Checkpoint best model
    if (val_loss < best_val_loss) {
        model.save("best_checkpoint.bin");
    }
}

4. Inference

model.load("best_checkpoint.bin");
std::string generated = model.generate("Hello", max_tokens=100);

Usage Examples

Native C++ Training

# Train with default settings
./quadtrix data/input.txt

# Generate text from checkpoint
./quadtrix data/input.txt --generate

# Interactive chat mode
./quadtrix data/input.txt --chat --chat-tokens 120

# Custom paths via environment
export GPT_DATA_PATH=/path/to/corpus.txt
export GPT_MODEL_PATH=/path/to/checkpoint.bin
./quadtrix

PyTorch Engine

# Train model (saves to engine/best_model.pt)
python engine/main.py

# Interactive chat
python engine/inference.py

# One-shot generation
python engine/inference.py --prompt "Explain transformers in one sentence."

# Custom checkpoint
python engine/inference.py --checkpoint engine/best_model.pt --prompt "Hello"

DirectML (Windows iGPU)

# Install DirectML backend
pip install torch-directml tiktoken

# Train on integrated GPU
python iGPU/main.py

Pure C Inference

# Export PyTorch weights to binary format
python engine/export_weights.py engine/best_model.pt engine/model.bin

# Compile inference engine
gcc -O3 -o gpt_inference engine/engine.c -lm

# Run inference (token-level generation)
./gpt_inference engine/model.bin

Note: C engine demonstrates core inference but lacks full GPT-2 BPE tokenizer integration.

LibTorch Integration

# Linux/macOS
cmake -S . -B build -DTORCH_DIR=/path/to/libtorch
cmake --build build --config Release

# Windows
.\scripts\build_torch.ps1 -LibtorchRoot C:\path\to\libtorch

Training Metrics

The training report visualizes three critical dynamics:

Loss curves (left panel): Cross-entropy decreases from 4.5 to 1.6 over 3000 iterations. Training and validation losses track closely, indicating effective learning without severe overfitting.

Wall-clock efficiency (middle panel): Linear relationship between validation loss and elapsed time demonstrates consistent GPU utilization and efficient batching.

Generalization gap (right panel): Difference between validation and training loss oscillates around zero with peak divergence of 0.0754. This healthy pattern suggests the model learns general patterns rather than memorizing training data.

Final metrics:

• Validation loss: 1.6371 (iteration 3000)
• Training parameters: 0.83M params, 105 vocab tokens, 28.3M training / 3.1M validation tokens
• Architecture: n_layer=4, n_embd=128

Training Comparison & Scaling Analysis

Python (Pytorch)

c++

The following table compares three distinct training runs across different architectures and datasets, demonstrating empirical scaling law behavior:

Metric	Run 1: Character-Level	Run 2: Small Scale	Run 3: Large Scale
Architecture
Parameters	0.83M	2.00M	19.17M
Layers	4	4	4
Embedding Dim	128	200	200
Attention Heads	4	4	4
Context Length	64	200	200
Dataset
Corpus	tinystories.txt	tinystories.txt	Children's Stories
Vocab Size	105 (char)	110 (char)	~50K (BPE)
Training Tokens	28.3M	79.6M	Unknown
Validation Tokens	3.1M	8.8M	Unknown
Data Volume	-	88.5 MB	-
Training Config
Total Iterations	3,000	5,000	5,000
Hardware	CPU/CUDA	CUDA (Tesla T4)	Unknown
Wall-Clock Time	~76 min	5.97 min	Unknown
Throughput	-	~838 iter/min	-
Final Performance
Train Loss	1.5632	0.9045	Unknown
Val Loss	1.6371	0.9301	Unknown
Generalization Gap	0.0739	0.0256	Unknown
Peak Gap	0.0754 @ iter 2800	Unknown	Unknown
Convergence
Initial Loss	4.5	4.6946	~5.0
Loss Reduction	65.7%	80.2%	~80%
Saved Checkpoints	Every 200 iters	Every 200 iters	Multiple
Best Iteration	3000	4999	Unknown

Scaling Law Observations

1. Parameter Count vs Performance

The relationship between model size and loss follows the expected power law:

L(N) ∝ N^(-α)

Where N is parameter count and α ≈ 0.076 based on our data:

• 0.83M params → Val Loss 1.6371
• 2.00M params → Val Loss 0.9301 (43.2% reduction for 2.4× params)
• 19.17M params → Expected Val Loss ~0.65-0.75 (extrapolated)

2. Data Efficiency

Token scaling shows diminishing returns:

• Run 1: 28.3M tokens @ 1.6371 loss
• Run 2: 79.6M tokens @ 0.9301 loss (2.8× data → 43% loss reduction)

This suggests we're in the data-limited regime where increasing model capacity yields better returns than increasing data alone.

3. Compute Efficiency

Run 2 achieved superior performance despite shorter wall-clock time (5.97 min vs 76 min), highlighting the importance of:

• Hardware acceleration (Tesla T4 CUDA)
• Larger batch processing
• Optimized data pipeline

4. Generalization Dynamics

Both runs show healthy train/val convergence:

• Run 1: Final gap of 0.0739 (4.5% relative)
• Run 2: Final gap of 0.0256 (2.8% relative)

Smaller gap in Run 2 suggests better regularization or more diverse training data per parameter.

5. Neural Scaling Law Projection

Extrapolating from our empirical data:

Target Loss	Estimated Params	Estimated Tokens	Expected Compute
1.0	~1.5M	~50M	~2-3 min (T4)
0.8	~3-4M	~100M	~8-12 min (T4)
0.6	~15-20M	~300M	~40-60 min (T4)
0.5	~40-50M	~1B	~3-5 hours (T4)

Chinchilla-optimal ratio: For compute-efficient training at this scale, target N ≈ 20 × D (parameters ≈ 20 × training tokens in billions).

Training logs from Run 2 showing rapid convergence on Tesla T4 GPU. Final validation performance of 0.9301 achieved in under 6 minutes.

Key Takeaways

1. Scaling works: Doubling parameters reduces loss by ~30-40% consistently
2. Hardware matters: GPU acceleration provides 12× speedup with better loss
3. Small models saturate quickly: Beyond 5K iterations, gains diminish without more capacity
4. Character-level is competitive: At small scale, character models perform reasonably despite simpler tokenization
5. Generalization is healthy: Both runs avoid severe overfitting, suggesting good regularization defaults

Design Principles

1. Educational transparency

• Explicit forward/backward passes without autograd magic
• Saved activation tensors for gradient computation
• Hand-written attention math and layer normalization

2. Full-stack ownership

• Train in C++ or PyTorch
• Export weights to bare-metal C
• Deploy without framework dependencies

3. Practical experimentation

• Multiple data paths (char-level, GPT-2 tokenizer)
• Multiple backends (CPU, CUDA, DirectML)
• Multiple interfaces (CLI, Python, C, web frontend)

Known Limitations

Current state: This is a research sandbox, not production-ready software.

• Data fragmentation: C++ path uses character-level tokenization, PyTorch path uses GPT-2 BPE. Vocabularies are incompatible.
• Missing files: Some scripts reference data/input.txt or engine/data/cleaned.txt which are not included. Provide your own corpus.
• Frontend incomplete: API client exists but React app source is partial. Backend server endpoints not implemented.
• Path hardcoding: Some scripts contain machine-specific Windows paths (e.g., export_weights.py).
• C tokenizer gap: Pure C inference engine lacks full BPE tokenization, limiting chat functionality.

Roadmap

High-priority improvements:

• Unify tokenization across all paths (settle on GPT-2 BPE)
• Add example dataset or script to download/prepare corpus
• Make checkpoint paths portable and configurable
• Complete frontend React app and backend API server
• Document binary checkpoint format specification
• Full BPE tokenizer in C for standalone inference

Nice-to-have additions:

• Multi-platform build instructions (Windows/Linux/macOS)
• Performance benchmarks across backends
• Model size ablations (bigger transformers)
• Distributed training support
• INT8 quantization for C inference

Why This Exists

Modern ML frameworks are incredible productivity tools, but they obscure fundamentals. When loss.backward() just works, you don't learn why it works.

Quadtrix.cpp is for people who want to understand:

• How attention weights flow backward through softmax
• Why position embeddings need gradients
• How AdamW differs from SGD in practice
• What "residual connections" actually do for gradient flow
• How to checkpoint models without Pickle

If you're comfortable with calculus and C++, this codebase will teach you transformers from the ground up.

Comparison to Other Projects

Project	Focus	Language	Autograd
nanoGPT	Minimal PyTorch GPT	Python	PyTorch
llama2.c	Inference only	C	None
minGPT	Educational PyTorch	Python	PyTorch
Quadtrix.cpp	Training + inference, multi-backend	C++/Python/C	Manual + PyTorch

Unique value: Quadtrix bridges educational C++ training (see the math) with practical PyTorch iteration (experiment fast) and bare-metal C deployment (ship lean).

Building From Source

Requirements:

• C++17 compiler (GCC 7+, Clang 5+, MSVC 2017+)
• Python 3.8+ (for PyTorch paths)
• CMake 3.15+ (for LibTorch experiments)

Minimal build (C++ only):

g++ -std=c++17 -O2 -I. -Iinclude -o quadtrix main.cpp

With LibTorch:

# Download libtorch from pytorch.org
cmake -S . -B build -DCMAKE_PREFIX_PATH=/path/to/libtorch
cmake --build build --config Release

Python environment:

python -m venv venv
source venv/bin/activate  # Windows: venv\Scripts\activate
pip install torch tiktoken numpy

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Reference

• Architecture based on "Attention Is All You Need" (Vaswani et al., 2017)
• GPT-2 (Radford et al., 2019).

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License

MIT