Embeddings in CUDA: A Practical How-To Guide

This guide provides a hands-on approach to implementing embedding layers using CUDA, making it easy to understand the underlying principles, master CUDA constructs, and apply them effectively in your own Micro-LLM (small-scale Large Language Model).

Step 1: Understanding Embeddings

What is an Embedding?

Embeddings represent words or tokens as dense vectors of numbers. Words that share meanings or contexts have vectors close to each other in a high-dimensional space.

Examples:

• "France" and "Paris" are geographically related, hence closer in vector space.
• "Dog" and "Cat" are similar because they’re both animals.

Why Use Embeddings?

• They capture semantic relationships effectively.
• Allow mathematical operations such as similarity calculations and analogies.

Step 2: How Are Embeddings Learned?

Embeddings are trained using Gradient Descent, an optimization method.

Simplified Gradient Descent Explanation

Imagine searching for the lowest valley in hilly terrain (optimal solution):

• Loss Function: Measures prediction errors.
• Gradient: Indicates adjustment directions.
• Learning Rate: Controls step sizes in updates.

Basic Training Steps:

1. Initialize embeddings randomly.
2. Predict outputs.
3. Compute loss.
4. Adjust embeddings to reduce loss.
5. Iterate through dataset (epochs).

Step 3: Implementing Embeddings with CUDA

CUDA efficiently manages embedding lookups and updates through parallel GPU computation.

Key CUDA Concepts:

• Threads: Individual computation units.
• Blocks: Groups of threads.
• Grids: Groups of blocks.

CUDA Kernel for Embedding Lookup:

1__global__ void embedding_lookup(float *embedding_matrix, int *token_ids, float *output,
2                                 int vocab_size, int embedding_dim, int seq_length) {
3    int token_idx = blockIdx.x * blockDim.x + threadIdx.x;
4
5    if (token_idx < seq_length) {
6        int token_id = token_ids[token_idx];
7        for (int dim = 0; dim < embedding_dim; dim++) {
8            output[token_idx * embedding_dim + dim] =
9                embedding_matrix[token_id * embedding_dim + dim];
10        }
11    }
12}

Step 4: Project Structure & CMake Setup

Your CUDA embedding project should look like this:

tiny_llm/
├── CMakeLists.txt
├── main.cpp
├── embedding.cu
└── tokenizer.h

Simple CMake Configuration:

1cmake_minimum_required(VERSION 3.15)
2project(tiny_llm CUDA CXX)
3
4set(CMAKE_CUDA_STANDARD 20)
5set(CMAKE_CXX_STANDARD 17)
6
7set(SOURCES main.cpp embedding.cu)
8
9add_executable(tiny_llm ${SOURCES})
10target_include_directories(tiny_llm PRIVATE ${CMAKE_CURRENT_SOURCE_DIR})
11
12set_target_properties(tiny_llm PROPERTIES CUDA_SEPARABLE_COMPILATION ON)

Step 5: Tokenizer Implementation

A Tokenizer maps text to numerical token IDs based on a fixed vocabulary.

Basic Tokenizer Example:

This is ultra simplified just to get us started.

1std::unordered_map<std::string, int> vocab = { {"Hello", 1}, {"World", 2}, {"<UNK>", 0} };
2
3int tokenize_word(const std::string &word) {
4    return vocab.count(word) ? vocab[word] : vocab["<UNK>"];
5}

Step 6: CUDA Gradient Descent for Embeddings

Embedding updates using Gradient Descent:

CUDA Kernel for Embedding Updates:

1__global__ void update_embeddings(float *embedding_matrix, int *token_ids, float *gradients,
2                                  float learning_rate, int seq_length, int embedding_dim) {
3    int idx = blockIdx.x * blockDim.x + threadIdx.x;
4    int total_elements = seq_length * embedding_dim;
5
6    if (idx < total_elements) {
7        int token_idx = idx / embedding_dim;
8        int dim = idx % embedding_dim;
9
10        int token_id = token_ids[token_idx];
11        int emb_idx = token_id * embedding_dim + dim;
12        embedding_matrix[emb_idx] -= learning_rate * gradients[idx];
13    }
14}

Step 7: Optimal CUDA Threading

Why Use 256 Threads per Block?

• Matches CUDA’s warp size (32 threads per warp).
• Optimal balance between efficiency and resource utilization.

Thread Index Calculation:

1int idx = blockIdx.x * blockDim.x + threadIdx.x;

Step 8: Explaining Embeddings Simply

To explain embeddings simply:

Imagine words as cities on a map. Similar words like "Paris" and "London" are close. Embeddings are coordinates on this map, adjusted as the model learns from sentences.

Step 9: Testing & Next Steps

Recommended next actions:

• Implement tests in main.cpp.
• Optimize CUDA kernels (using cuBLAS/cuDNN).
• Add Attention layers for a full Micro-LLM.

FAQs

• Why update only used embeddings?

  • Conserves computational resources.

• Why smaller vocabulary and dimensions?

  • Suits limited GPU memory on laptops.

• Optimal threads per block?

  • Typically 128-512; experiment based on GPU specifics.

Practical Recommendations

You're now equipped to build powerful and efficient embedding layers using CUDA. With these foundational skills, you're ready to take the next steps toward developing your own sophisticated Micro-LLM.