Introduction
Deep learning frameworks such as PyTorch and TensorFlow have become ubiquitous, yet their abstractions can sometimes obscure the mechanics that make neural networks tick. Tinygrad, a deliberately minimalistic deep‑learning library written in a single Python file, offers a unique window into the low‑level operations that underpin modern architectures. By stripping away layers of convenience, Tinygrad forces the developer to confront the core ideas of tensor manipulation, automatic differentiation, and the attention mechanism that powers transformers.
In this tutorial we will walk through the entire process of building a transformer‑based language model from the ground up using Tinygrad. We will start with the most basic building blocks—tensors and the autograd engine—then progressively layer on more sophisticated components such as multi‑head attention, feed‑forward networks, and positional encodings. Finally, we will assemble these pieces into a compact GPT‑style model capable of generating coherent text on a toy dataset. Throughout the journey, we will not only write code but also dissect the mathematics behind each operation, providing a deeper understanding that goes beyond the black‑box usage of high‑level APIs.
The goal of this post is twofold: first, to give readers a hands‑on, code‑driven introduction to transformer internals; second, to illustrate how a tiny framework can be a powerful teaching tool. By the end, you should be able to modify the architecture, experiment with different hyperparameters, and even extend Tinygrad to support new operations—all while keeping the implementation readable and well‑documented.
Main Content
Tinygrad Basics
Tinygrad’s core is a lightweight Tensor class that stores data as a NumPy array and keeps a reference to its computational graph. The graph is built lazily: every operation creates a new Tensor whose grad_fn points to the function that produced it. This design mirrors the autograd systems of larger frameworks but with far less boilerplate. The backward method traverses the graph in reverse topological order, applying the chain rule to accumulate gradients. Understanding this mechanism is essential, because every subsequent component—whether a matrix multiplication or a softmax—relies on correct gradient propagation.
When writing custom operations, one must provide both a forward pass that returns a new Tensor and a backward pass that supplies the gradient with respect to each input. Tinygrad’s API encourages this pattern by exposing a Function base class; developers subclass it, implement forward and backward, and then register the function. This approach keeps the code modular and makes it straightforward to debug or replace individual operations.
Implementing Tensors and Autograd
The first practical step is to implement the elementary tensor operations that will later compose the transformer. Matrix multiplication (matmul) is the backbone of linear layers, while element‑wise operations such as addition, multiplication, and exponentiation are needed for activation functions. For each operation, we write a forward method that performs the NumPy computation and a backward method that calculates the gradient using the derivative formulas.
For example, the backward pass of a matrix multiplication C = A @ B requires computing dA = dC @ B.T and dB = A.T @ dC. By encapsulating these formulas in a MatMul function, we guarantee that gradients flow correctly through any network that uses this operation. Similarly, the softmax function, which is central to attention, has a more involved Jacobian; implementing its backward pass correctly is a valuable exercise in matrix calculus.
Once the primitives are in place, we can test them on simple problems such as linear regression or a small feed‑forward network. These sanity checks confirm that the autograd engine is functioning before we tackle the more complex transformer components.
Building Multi‑Head Attention
Attention is the engine that lets transformers weigh the relevance of different tokens in a sequence. The multi‑head attention mechanism splits the input embeddings into several sub‑spaces, applies scaled dot‑product attention independently in each, and then concatenates the results. Implementing this from scratch requires careful handling of tensor shapes and broadcasting.
We start by defining the query, key, and value projections as linear layers. Each projection is a simple matrix multiplication followed by a bias addition. The scaled dot‑product attention itself consists of a matrix multiplication between queries and transposed keys, scaling by the square root of the head dimension, applying a softmax, and finally multiplying by the values. Tinygrad’s softmax implementation, coupled with the autograd engine, ensures that gradients can flow through the attention weights back to the input embeddings.
A subtle but important detail is the masking mechanism used during training to prevent a token from attending to future positions. We implement a causal mask by setting the upper‑triangular part of the attention score matrix to a large negative constant before the softmax. This simple trick enforces the autoregressive property of GPT‑style models.
Constructing Transformer Blocks
With multi‑head attention in place, we can assemble a full transformer block. Each block contains a residual connection around the attention sub‑module, followed by layer normalization, another residual connection around a position‑wise feed‑forward network, and a final layer normalization. Layer normalization is implemented as a custom function that normalizes across the embedding dimension and learns a scaling and bias parameter.
The feed‑forward network is a two‑layer MLP with a ReLU activation in between. Its role is to introduce non‑linearity and increase the model’s capacity. By stacking several transformer blocks, we build depth into the network, allowing it to capture increasingly abstract patterns in the data.
Positional encoding is another essential component. Since transformers lack recurrence, they rely on positional information to understand token order. We implement the sinusoidal positional encoding described in the original GPT paper, adding it to the input embeddings before the first transformer block. This addition is straightforward but crucial for the model to learn sequence structure.
Training a Mini‑GPT
Having constructed the architecture, we turn to training. We use a small text corpus—such as a subset of Shakespeare or a collection of code snippets—to keep training time reasonable. The loss function is the cross‑entropy between the predicted token distribution and the ground truth next token. Tinygrad’s autograd engine automatically computes the gradient of this loss with respect to all model parameters.
Optimization is performed with stochastic gradient descent or Adam, both of which we implement manually using Tinygrad’s tensor operations. We monitor training loss and perplexity to gauge progress. After a few epochs, the model begins to generate plausible continuations of the input text, demonstrating that even a toy transformer can learn meaningful language patterns.
Throughout training, we experiment with hyperparameters such as learning rate, batch size, and the number of attention heads. These experiments reveal how sensitive transformer performance is to architectural choices, providing valuable intuition for scaling up to larger models.
Conclusion
Building a transformer and a mini‑GPT model from scratch with Tinygrad is more than an academic exercise; it is a practical laboratory for demystifying the inner workings of modern deep‑learning systems. By writing every operation by hand, we gain a granular understanding of tensor algebra, automatic differentiation, and the attention mechanism that underlies state‑of‑the‑art language models. This knowledge equips practitioners to debug complex models, design custom architectures, and appreciate the trade‑offs involved in scaling up.
Moreover, Tinygrad’s minimal footprint makes it an ideal teaching tool. Students and hobbyists can experiment with the code without the overhead of installing large frameworks, and researchers can prototype novel ideas quickly. The principles learned here transfer directly to any deep‑learning library, ensuring that developers are not merely users of black‑box tools but informed engineers capable of pushing the boundaries of AI.
Call to Action
If you found this deep dive into transformer internals enlightening, consider taking the next step by experimenting with Tinygrad on your own datasets. Try adding new attention variants, exploring different normalization schemes, or even porting the model to run on a GPU with minimal changes. Share your findings on GitHub or in a blog post—contributing back to the community not only reinforces your own learning but also helps others navigate the complexities of deep learning. Happy coding, and may your models generate ever more compelling text!