2024-05-07 07:04:35 -05:00

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{
"cells": [
{
"cell_type": "markdown",
"id": "c024bfa4-1a7a-4751-b5a1-827225a3478b",
"metadata": {
"id": "c024bfa4-1a7a-4751-b5a1-827225a3478b"
},
"source": [
"<font size=\"1\">\n",
"Supplementary code for \"Build a Large Language Model From Scratch\": <a href=\"https://www.manning.com/books/build-a-large-language-model-from-scratch\">https://www.manning.com/books/build-a-large-language-model-from-scratch</a> by <a href=\"https://sebastianraschka.com\">Sebastian Raschka</a><br>\n",
"Code repository: <a href=\"https://github.com/rasbt/LLMs-from-scratch\">https://github.com/rasbt/LLMs-from-scratch</a>\n",
"</font>"
]
},
{
"cell_type": "markdown",
"id": "58b8c870-fb72-490e-8916-d8129bd5d1ff",
"metadata": {},
"source": [
"# Appendix E: Parameter-efficient Finetuning with LoRA"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "5b7e01c2-1c84-4f2a-bb51-2e0b74abda90",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "5b7e01c2-1c84-4f2a-bb51-2e0b74abda90",
"outputId": "9495f150-9d79-4910-d6e7-6c0d9aae4a41"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"matplotlib version: 3.7.2\n",
"numpy version: 1.25.2\n",
"tiktoken version: 0.5.1\n",
"torch version: 2.2.2\n",
"tensorflow version: 2.15.0\n",
"pandas version: 2.0.3\n"
]
}
],
"source": [
"from importlib.metadata import version\n",
"\n",
"pkgs = [\"matplotlib\",\n",
" \"numpy\",\n",
" \"tiktoken\",\n",
" \"torch\",\n",
" \"tensorflow\", # For OpenAI's pretrained weights\n",
" \"pandas\" # Dataset loading\n",
" ]\n",
"for p in pkgs:\n",
" print(f\"{p} version: {version(p)}\")"
]
},
{
"cell_type": "markdown",
"id": "21532056-0ef4-4c98-82c7-e91f61c6485e",
"metadata": {},
"source": [
"## E.1 Introduction to LoRA"
]
},
{
"cell_type": "markdown",
"id": "66edc999-3d91-4a1c-a157-9d056392e8d8",
"metadata": {},
"source": [
"- No code in this section\n",
"- Low-rank adaptation (LoRA) is a machine learning technique that modifies a pretrained model to better suit a specific, often smaller, dataset by adjusting only a small, low-rank subset of the model's parameters\n",
"- This approach is important because it allows for efficient finetuning of large models on task-specific data, significantly reducing the computational cost and time required for finetuning"
]
},
{
"cell_type": "markdown",
"id": "5bb75b5d-d59c-4948-821a-1594a5883dc1",
"metadata": {},
"source": [
"- Suppose we have a large weight matrix $W$ for a given layer\n",
"- During backpropagation, we learn a $\\Delta W$ matrix, which contains information on how much we want to update the original weights to minimize the loss function during training\n",
"- In regular training and finetuning, the weight update is defined as follows:\n",
"\n",
"$$W_{\\text{updated}} = W + \\Delta W$$\n",
"\n",
"- The LoRA method proposed by [Hu et al.](https://arxiv.org/abs/2106.09685) offers a more efficient alternative to computing the weight updates $\\Delta W$ by learning an approximation of it, $\\Delta W \\approx AB$.\n",
"- In other words, in LoRA, we have the following, where $A$ and $B$ are two small weight matrices:\n",
"\n",
"$$W_{\\text{updated}} = W + AB$$\n",
"\n",
"- The figure below illustrates these formulas for full finetuning and LoRA side by side"
]
},
{
"cell_type": "markdown",
"id": "a8a7419d-cae9-4525-bb44-1641f6ef4f3b",
"metadata": {},
"source": [
"<img src=\"https://sebastianraschka.com/images/LLMs-from-scratch-images/appendix-e_compressed/lora-1.webp\" width=\"500px\">"
]
},
{
"cell_type": "markdown",
"id": "4edd43c9-8ec5-48e6-b3fc-5fb3c16037cc",
"metadata": {},
"source": [
"- If you paid close attention, the full finetuning and LoRA depictions in the figure above look slightly different from the formulas I have shown earlier\n",
"- That's due to the distributive law of matrix multiplication: we don't have to add the weights with the updated weights but can keep them separate\n",
"- For instance, if $x$ is the input data, then we can write the following for regular finetuning:\n",
"\n",
"$$x (W+\\Delta W) = x W + x \\Delta W$$\n",
"\n",
"- Similarly, we can write the following for LoRA:\n",
"\n",
"$$x (W+A B) = x W + x A B$$\n",
"\n",
"- The fact that we can keep the LoRA weight matrices separate makes LoRA especially attractive\n",
"- In practice, this means that we don't have to modify the weights of the pretrained model at all, as we can apply the LoRA matrices on the fly\n",
"- After setting up the dataset and loading the model, we will implement LoRA in the code to make these concepts less abstract"
]
},
{
"cell_type": "markdown",
"id": "8c7017a2-32aa-4002-a2f3-12aac293ccdf",
"metadata": {
"id": "8c7017a2-32aa-4002-a2f3-12aac293ccdf"
},
"source": [
"## E.2 Preparing the dataset"
]
},
{
"cell_type": "markdown",
"id": "669c64df-4431-4d27-834d-2bb38a01fc02",
"metadata": {},
"source": [
"- This section repeats the code from chapter 6 to load and prepare the dataset\n",
"- Instead of repeating this code, one could open and run the chapter 6 notebook and then insert the LoRA code from section E.4 there\n",
"- (The LoRA code was originally the last section of chapter 6 but was moved to the appendix due to the length of chapter 6)\n",
"- In a similar fashion, we could also apply LoRA to the models in chapter 7 for instruction finetuning"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "def7c09b-af9c-4216-90ce-5e67aed1065c",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "def7c09b-af9c-4216-90ce-5e67aed1065c",
"outputId": "424e4423-f623-443c-ab9e-656f9e867559"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"sms_spam_collection/SMSSpamCollection.tsv already exists. Skipping download and extraction.\n"
]
}
],
"source": [
"from pathlib import Path\n",
"import pandas as pd\n",
"from previous_chapters import (\n",
" download_and_unzip,\n",
" create_balanced_dataset,\n",
" random_split\n",
")\n",
"\n",
"\n",
"url = \"https://archive.ics.uci.edu/static/public/228/sms+spam+collection.zip\"\n",
"zip_path = \"sms_spam_collection.zip\"\n",
"extracted_path = \"sms_spam_collection\"\n",
"data_file_path = Path(extracted_path) / \"SMSSpamCollection.tsv\"\n",
"\n",
"download_and_unzip(url, zip_path, extracted_path, data_file_path)\n",
"\n",
"df = pd.read_csv(data_file_path, sep=\"\\t\", header=None, names=[\"Label\", \"Text\"])\n",
"balanced_df = create_balanced_dataset(df)\n",
"balanced_df[\"Label\"] = balanced_df[\"Label\"].map({\"ham\": 0, \"spam\": 1})\n",
"\n",
"train_df, validation_df, test_df = random_split(balanced_df, 0.7, 0.1)\n",
"train_df.to_csv(\"train.csv\", index=None)\n",
"validation_df.to_csv(\"validation.csv\", index=None)\n",
"test_df.to_csv(\"test.csv\", index=None)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "74c3c463-8763-4cc0-9320-41c7eaad8ab7",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "74c3c463-8763-4cc0-9320-41c7eaad8ab7",
"outputId": "b5b48439-32c8-4b37-cca2-c9dc8fa86563"
},
"outputs": [],
"source": [
"import torch\n",
"from torch.utils.data import Dataset\n",
"import tiktoken\n",
"from previous_chapters import SpamDataset\n",
"\n",
"\n",
"tokenizer = tiktoken.get_encoding(\"gpt2\")\n",
"train_dataset = SpamDataset(\"train.csv\", max_length=None, tokenizer=tokenizer)\n",
"val_dataset = SpamDataset(\"validation.csv\", max_length=train_dataset.max_length, tokenizer=tokenizer)\n",
"test_dataset = SpamDataset(\"test.csv\", max_length=train_dataset.max_length, tokenizer=tokenizer)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "8681adc0-6f02-4e75-b01a-a6ab75d05542",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "8681adc0-6f02-4e75-b01a-a6ab75d05542",
"outputId": "3266c410-4fdb-4a8c-a142-7f707e2525ab"
},
"outputs": [],
"source": [
"from torch.utils.data import DataLoader\n",
"\n",
"num_workers = 0\n",
"batch_size = 8\n",
"\n",
"torch.manual_seed(123)\n",
"\n",
"train_loader = DataLoader(\n",
" dataset=train_dataset,\n",
" batch_size=batch_size,\n",
" shuffle=True,\n",
" num_workers=num_workers,\n",
" drop_last=True,\n",
")\n",
"\n",
"val_loader = DataLoader(\n",
" dataset=val_dataset,\n",
" batch_size=batch_size,\n",
" num_workers=num_workers,\n",
" drop_last=False,\n",
")\n",
"\n",
"test_loader = DataLoader(\n",
" dataset=test_dataset,\n",
" batch_size=batch_size,\n",
" num_workers=num_workers,\n",
" drop_last=False,\n",
")"
]
},
{
"cell_type": "markdown",
"id": "ab7335db-e0bb-4e27-80c5-eea11e593a57",
"metadata": {},
"source": [
"- As a verification step, we iterate through the data loaders and check that the batches contain 8 training examples each, where each training example consists of 120 tokens"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "4dee6882-4c3a-4964-af15-fa31f86ad047",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Train loader:\n",
"Input batch dimensions: torch.Size([8, 120])\n",
"Label batch dimensions torch.Size([8])\n"
]
}
],
"source": [
"print(\"Train loader:\")\n",
"for input_batch, target_batch in train_loader:\n",
" pass\n",
"\n",
"print(\"Input batch dimensions:\", input_batch.shape)\n",
"print(\"Label batch dimensions\", target_batch.shape)"
]
},
{
"cell_type": "markdown",
"id": "5cdd7947-7039-49bf-8a5e-c0a2f4281ca1",
"metadata": {},
"source": [
"- Lastly, let's print the total number of batches in each dataset"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "IZfw-TYD2zTj",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "IZfw-TYD2zTj",
"outputId": "6934bbf2-9797-4fbe-d26b-1a246e18c2fb"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"130 training batches\n",
"19 validation batches\n",
"38 test batches\n"
]
}
],
"source": [
"print(f\"{len(train_loader)} training batches\")\n",
"print(f\"{len(val_loader)} validation batches\")\n",
"print(f\"{len(test_loader)} test batches\")"
]
},
{
"cell_type": "markdown",
"id": "dec9aa4a-ffd2-4d9f-a835-cce1059fe604",
"metadata": {},
"source": [
"## E.3 Initializing the model"
]
},
{
"cell_type": "markdown",
"id": "f36ebdaf-810e-46a2-9ad9-e017a04051b1",
"metadata": {},
"source": [
"- This section repeats the code from chapter 6 to load and prepare the model"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "02b3a506-3879-4258-82b5-93a5b6bafa74",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"File already exists and is up-to-date: gpt2/124M/checkpoint\n",
"File already exists and is up-to-date: gpt2/124M/encoder.json\n",
"File already exists and is up-to-date: gpt2/124M/hparams.json\n",
"File already exists and is up-to-date: gpt2/124M/model.ckpt.data-00000-of-00001\n",
"File already exists and is up-to-date: gpt2/124M/model.ckpt.index\n",
"File already exists and is up-to-date: gpt2/124M/model.ckpt.meta\n",
"File already exists and is up-to-date: gpt2/124M/vocab.bpe\n"
]
}
],
"source": [
"from gpt_download import download_and_load_gpt2\n",
"from previous_chapters import GPTModel, load_weights_into_gpt\n",
"\n",
"\n",
"CHOOSE_MODEL = \"gpt2-small (124M)\"\n",
"INPUT_PROMPT = \"Every effort moves\"\n",
"\n",
"BASE_CONFIG = {\n",
" \"vocab_size\": 50257, # Vocabulary size\n",
" \"context_length\": 1024, # Context length\n",
" \"drop_rate\": 0.0, # Dropout rate\n",
" \"qkv_bias\": True # Query-key-value bias\n",
"}\n",
"\n",
"model_configs = {\n",
" \"gpt2-small (124M)\": {\"emb_dim\": 768, \"n_layers\": 12, \"n_heads\": 12},\n",
" \"gpt2-medium (355M)\": {\"emb_dim\": 1024, \"n_layers\": 24, \"n_heads\": 16},\n",
" \"gpt2-large (774M)\": {\"emb_dim\": 1280, \"n_layers\": 36, \"n_heads\": 20},\n",
" \"gpt2-xl (1558M)\": {\"emb_dim\": 1600, \"n_layers\": 48, \"n_heads\": 25},\n",
"}\n",
"\n",
"BASE_CONFIG.update(model_configs[CHOOSE_MODEL])\n",
"\n",
"model_size = CHOOSE_MODEL.split(\" \")[-1].lstrip(\"(\").rstrip(\")\")\n",
"settings, params = download_and_load_gpt2(model_size=model_size, models_dir=\"gpt2\")\n",
"\n",
"model = GPTModel(BASE_CONFIG)\n",
"load_weights_into_gpt(model, params)\n",
"model.eval();"
]
},
{
"cell_type": "markdown",
"id": "252614cd-7ce6-4908-83e6-3761f519904e",
"metadata": {},
"source": [
"- To ensure that the model was loaded corrected, let's double-check that it generates coherent text"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "8b6ce20c-0700-4783-8be0-4cf17c200a7f",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Every effort moves you forward.\n",
"\n",
"The first step is to understand the importance of your work\n"
]
}
],
"source": [
"from previous_chapters import (\n",
" generate_text_simple,\n",
" text_to_token_ids,\n",
" token_ids_to_text\n",
")\n",
"\n",
"\n",
"text_1 = \"Every effort moves you\"\n",
"\n",
"token_ids = generate_text_simple(\n",
" model=model,\n",
" idx=text_to_token_ids(text_1, tokenizer),\n",
" max_new_tokens=15,\n",
" context_size=BASE_CONFIG[\"context_length\"]\n",
")\n",
"\n",
"print(token_ids_to_text(token_ids, tokenizer))"
]
},
{
"cell_type": "markdown",
"id": "8174b31b-1ab5-4115-b01c-245369da5af3",
"metadata": {},
"source": [
"- Then, we prepare the model for classification finetuning similar to chapter 6, where we replace the output layer"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "e255ce91-d73a-4854-90a4-95804928eb16",
"metadata": {},
"outputs": [],
"source": [
"torch.manual_seed(123)\n",
"\n",
"num_classes = 2\n",
"model.out_head = torch.nn.Linear(in_features=768, out_features=num_classes)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "02e6f057-1383-4ece-8444-0a88e71ac75d",
"metadata": {},
"outputs": [],
"source": [
"device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
"model.to(device); # no assignment model = model.to(device) necessary for nn.Module classes"
]
},
{
"cell_type": "markdown",
"id": "8e951cd6-5e42-44d2-b21f-895cb61004fe",
"metadata": {},
"source": [
"- Lastly, let's calculate the initial classification accuracy of the non-finetuned model (we expect this to be around 50%, which means that the model is not able to distinguish between spam and non-spam messages yet reliably)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "fc7dd72c-73a2-4881-ade0-0a9605f1ab8c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Training accuracy: 46.25%\n",
"Validation accuracy: 45.00%\n",
"Test accuracy: 48.75%\n"
]
}
],
"source": [
"from previous_chapters import calc_accuracy_loader\n",
"\n",
"\n",
"torch.manual_seed(123)\n",
"train_accuracy = calc_accuracy_loader(train_loader, model, device, num_batches=10)\n",
"val_accuracy = calc_accuracy_loader(val_loader, model, device, num_batches=10)\n",
"test_accuracy = calc_accuracy_loader(test_loader, model, device, num_batches=10)\n",
"\n",
"print(f\"Training accuracy: {train_accuracy*100:.2f}%\")\n",
"print(f\"Validation accuracy: {val_accuracy*100:.2f}%\")\n",
"print(f\"Test accuracy: {test_accuracy*100:.2f}%\")"
]
},
{
"cell_type": "markdown",
"id": "398a1ec9-e2a1-43d6-bf9f-12ee54b46a7b",
"metadata": {
"id": "398a1ec9-e2a1-43d6-bf9f-12ee54b46a7b"
},
"source": [
"## E.4 Parameter-efficient finetuning with LoRA"
]
},
{
"cell_type": "markdown",
"id": "652a4a82-61ef-4d0a-9858-8988e844f12c",
"metadata": {},
"source": [
"- We begin by initializing a LoRALayer that creates the matrices $A$ and $B$, along with the `alpha` scaling hyperparameter and the `rank` ($r$) hyperparameters\n",
"- This layer can accept an input and compute the corresponding output, as illustrated in the figure below\n",
"\n",
"<img src=\"https://sebastianraschka.com/images/LLMs-from-scratch-images/appendix-e_compressed/lora-2.webp\" width=\"200px\">\n",
"\n",
"In code, this LoRA layer depicted in the figure above looks like as follows"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "2ds9ywjMwvIW",
"metadata": {
"id": "2ds9ywjMwvIW"
},
"outputs": [],
"source": [
"class LoRALayer(torch.nn.Module):\n",
" def __init__(self, in_dim, out_dim, rank, alpha):\n",
" super().__init__()\n",
" std_dev = 1 / torch.sqrt(torch.tensor(rank).float())\n",
" self.A = torch.nn.Parameter(torch.randn(in_dim, rank) * std_dev)\n",
" self.B = torch.nn.Parameter(torch.zeros(rank, out_dim))\n",
" self.alpha = alpha\n",
"\n",
" def forward(self, x):\n",
" x = self.alpha * (x @ self.A @ self.B)\n",
" return x"
]
},
{
"cell_type": "markdown",
"id": "ad21faa8-0614-4257-93cd-68952193e14a",
"metadata": {},
"source": [
"- In the code above, `rank` is a hyperparameter that controls the inner dimension of the matrices $A$ and $B$\n",
"- In other words, this parameter controls the number of additional parameters introduced by LoRA and is a key factor in determining the balance between model adaptability and parameter efficiency\n",
"- The second hyperparameter, alpha, is a scaling hyperparameter applied to the output of the low-rank adaptation\n",
"- It essentially controls the extent to which the adapted layer's output is allowed to influence the original output of the layer being adapted\n",
"- This can be seen as a way to regulate the impact of the low-rank adaptation on the layer's output\n",
"- So far, the `LoRALayer` class we implemented above allows us to transform the layer inputs $x$\n",
"- However, in LoRA, we are usually interested in replacing existing `Linear` layers so that the weight update is applied to the existing pretrained weights, as shown in the figure below\n",
"\n",
"<img src=\"https://sebastianraschka.com/images/LLMs-from-scratch-images/appendix-e_compressed/lora-3.webp\" width=\"200px\">"
]
},
{
"cell_type": "markdown",
"id": "3e6d5da0-dfce-4808-b89b-29ff333f563f",
"metadata": {},
"source": [
"- To incorporate the original `Linear` layer weights as shown in the figure above, we implement a `LinearWithLoRA` layer below that uses the previously implemented LoRALayer and can be used to replace existing `Linear` layers in a neural network, for example, the self-attention module or feed forward modules in an LLM"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "127d3a64-8359-4b21-b056-78d58cc75fe8",
"metadata": {},
"outputs": [],
"source": [
"class LinearWithLoRA(torch.nn.Module):\n",
" def __init__(self, linear, rank, alpha):\n",
" super().__init__()\n",
" self.linear = linear\n",
" self.lora = LoRALayer(\n",
" linear.in_features, linear.out_features, rank, alpha\n",
" )\n",
"\n",
" def forward(self, x):\n",
" return self.linear(x) + self.lora(x)"
]
},
{
"cell_type": "markdown",
"id": "e1145a90-35ff-462c-820b-15483fa5b051",
"metadata": {},
"source": [
"- Note that since we initialize the weight matrix $B$ (`self.B` in `LoraLayer`) with zero values in the LoRA layer, the matrix multiplication between $A$ and $B$ results in a matrix consisting of 0's and doesn't affect the original weights (since adding 0 to the original weights does not modify them)"
]
},
{
"cell_type": "markdown",
"id": "e98a6d36-7bc9-434c-a7f1-533f26aff06d",
"metadata": {
"id": "4D21Jk7Vw3nG"
},
"source": [
"- To try LoRA on the GPT model we defined earlier, we define a `replace_linear_with_lora` function to replace all `Linear` layers in the model with the new `LinearWithLoRA` layers\n",
"\n",
"<img src=\"https://sebastianraschka.com/images/LLMs-from-scratch-images/appendix-e_compressed/lora-4.webp\" width=\"400px\">"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "WlQZ8ygqzN_g",
"metadata": {
"id": "WlQZ8ygqzN_g"
},
"outputs": [],
"source": [
"def replace_linear_with_lora(model, rank, alpha):\n",
" for name, module in model.named_children():\n",
" if isinstance(module, torch.nn.Linear):\n",
" # Replace the Linear layer with LinearWithLoRA\n",
" setattr(model, name, LinearWithLoRA(module, rank, alpha))\n",
" else:\n",
" # Recursively apply the same function to child modules\n",
" replace_linear_with_lora(module, rank, alpha)"
]
},
{
"cell_type": "markdown",
"id": "8c172164-cdde-4489-b7d7-aaed9cc2f5f2",
"metadata": {},
"source": [
"- We then freeze the original model parameter and use the `replace_linear_with_lora` to replace the said `Linear` layers using the code below\n",
"- This will replace the `Linear` layers in the "
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "dbe15350-4da9-4829-9d23-98bbd3d0b1a1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total trainable parameters before: 124,441,346\n",
"Total trainable parameters after: 0\n"
]
}
],
"source": [
"total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
"print(f\"Total trainable parameters before: {total_params:,}\")\n",
"\n",
"for param in model.parameters():\n",
" param.requires_grad = False\n",
"\n",
"total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
"print(f\"Total trainable parameters after: {total_params:,}\")"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "mLk_fPq0yz_u",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "mLk_fPq0yz_u",
"outputId": "7ba89607-ca75-4718-e8dc-9cdc44c3e410"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Total trainable LoRA parameters: 1,333,264\n"
]
}
],
"source": [
"replace_linear_with_lora(model, rank=8, alpha=8)\n",
"\n",
"total_params = sum(p.numel() for p in model.parameters() if p.requires_grad)\n",
"print(f\"Total trainable LoRA parameters: {total_params:,}\")"
]
},
{
"cell_type": "markdown",
"id": "b8b6819e-ef7a-4f0d-841a-1b467496bef9",
"metadata": {},
"source": [
"- As we can see, we reduced the number of trainable parameters by almost 100x when using LoRA\n",
"- Let's now double-check whether the layers have been modified as intended by printing the model architecture"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "1711be61-bb2c-466f-9b5b-24f4aa5ccd9c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"GPTModel(\n",
" (tok_emb): Embedding(50257, 768)\n",
" (pos_emb): Embedding(1024, 768)\n",
" (drop_emb): Dropout(p=0.0, inplace=False)\n",
" (trf_blocks): Sequential(\n",
" (0): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (1): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (2): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (3): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (4): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (5): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (6): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (7): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (8): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (9): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (10): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (11): TransformerBlock(\n",
" (att): MultiHeadAttention(\n",
" (W_query): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_key): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (W_value): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (out_proj): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (dropout): Dropout(p=0.0, inplace=False)\n",
" )\n",
" (ff): FeedForward(\n",
" (layers): Sequential(\n",
" (0): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=3072, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" (1): GELU()\n",
" (2): LinearWithLoRA(\n",
" (linear): Linear(in_features=3072, out_features=768, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
" )\n",
" )\n",
" (norm1): LayerNorm()\n",
" (norm2): LayerNorm()\n",
" (drop_resid): Dropout(p=0.0, inplace=False)\n",
" )\n",
" )\n",
" (final_norm): LayerNorm()\n",
" (out_head): LinearWithLoRA(\n",
" (linear): Linear(in_features=768, out_features=2, bias=True)\n",
" (lora): LoRALayer()\n",
" )\n",
")\n"
]
}
],
"source": [
"device = torch.device(\"cuda\" if torch.cuda.is_available() else \"cpu\")\n",
"model.to(device)\n",
"\n",
"print(model)"
]
},
{
"cell_type": "markdown",
"id": "c4bbc9d7-65ec-4675-bab8-2e56eb0cfb55",
"metadata": {},
"source": [
"- Based on the model architecture above, we can see that the model now contains our new `LinearWithLoRA` layers\n",
"- Also, since we initialized matrix $B$ with 0's, we expect the initial model performance to be unchanged compared to before"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "DAlrb_I00VEU",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "DAlrb_I00VEU",
"outputId": "3dae5ff0-316d-408e-c8dc-2b8c60f9b994"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Training accuracy: 46.25%\n",
"Validation accuracy: 45.00%\n",
"Test accuracy: 48.75%\n"
]
}
],
"source": [
"torch.manual_seed(123)\n",
"train_accuracy = calc_accuracy_loader(train_loader, model, device, num_batches=10)\n",
"val_accuracy = calc_accuracy_loader(val_loader, model, device, num_batches=10)\n",
"test_accuracy = calc_accuracy_loader(test_loader, model, device, num_batches=10)\n",
"\n",
"print(f\"Training accuracy: {train_accuracy*100:.2f}%\")\n",
"print(f\"Validation accuracy: {val_accuracy*100:.2f}%\")\n",
"print(f\"Test accuracy: {test_accuracy*100:.2f}%\")"
]
},
{
"cell_type": "markdown",
"id": "13735b3e-f0c3-4dba-ae3d-4141b2878101",
"metadata": {},
"source": [
"- Let's now get to the interesting part and finetune the model by reusing the training function from chapter 6\n",
"- The training takes about 15 minutes on a M3 MacBook Air laptop computer and less than half a minute on a V100 or A100 GPU"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "wCParRvr0eff",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "wCParRvr0eff",
"outputId": "b86fd5f4-1527-4549-e0b0-9dff37836f0a"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ep 1 (Step 000000): Train loss 2.849, Val loss 2.565\n",
"Ep 1 (Step 000050): Train loss 0.515, Val loss 0.465\n",
"Ep 1 (Step 000100): Train loss 0.191, Val loss 0.423\n",
"Training accuracy: 97.50% | Validation accuracy: 97.50%\n",
"Ep 2 (Step 000150): Train loss 0.170, Val loss 0.072\n",
"Ep 2 (Step 000200): Train loss 0.014, Val loss 0.087\n",
"Ep 2 (Step 000250): Train loss 0.027, Val loss 0.197\n",
"Training accuracy: 100.00% | Validation accuracy: 92.50%\n",
"Ep 3 (Step 000300): Train loss 0.014, Val loss 0.321\n",
"Ep 3 (Step 000350): Train loss 0.015, Val loss 0.146\n",
"Training accuracy: 100.00% | Validation accuracy: 97.50%\n",
"Ep 4 (Step 000400): Train loss 0.008, Val loss 0.103\n",
"Ep 4 (Step 000450): Train loss 0.010, Val loss 0.178\n",
"Ep 4 (Step 000500): Train loss 0.097, Val loss 0.056\n",
"Training accuracy: 100.00% | Validation accuracy: 97.50%\n",
"Ep 5 (Step 000550): Train loss 0.032, Val loss 0.091\n",
"Ep 5 (Step 000600): Train loss 0.002, Val loss 0.058\n",
"Training accuracy: 100.00% | Validation accuracy: 100.00%\n",
"Ep 6 (Step 000650): Train loss 0.001, Val loss 0.009\n",
"Ep 6 (Step 000700): Train loss 0.001, Val loss 0.039\n",
"Ep 6 (Step 000750): Train loss 0.000, Val loss 0.038\n",
"Training accuracy: 100.00% | Validation accuracy: 95.00%\n",
"Training completed in 13.70 minutes.\n"
]
}
],
"source": [
"import time\n",
"from previous_chapters import train_classifier_simple\n",
"\n",
"\n",
"start_time = time.time()\n",
"\n",
"torch.manual_seed(123)\n",
"\n",
"optimizer = torch.optim.AdamW(model.parameters(), lr=5e-5, weight_decay=0.1)\n",
"\n",
"num_epochs = 6\n",
"train_losses, val_losses, train_accs, val_accs, examples_seen = train_classifier_simple(\n",
" model, train_loader, val_loader, optimizer, device,\n",
" num_epochs=num_epochs, eval_freq=50, eval_iter=5,\n",
" tokenizer=tokenizer\n",
")\n",
"\n",
"end_time = time.time()\n",
"execution_time_minutes = (end_time - start_time) / 60\n",
"print(f\"Training completed in {execution_time_minutes:.2f} minutes.\")"
]
},
{
"cell_type": "markdown",
"id": "d0c89e82-3aa8-44c6-b046-0b16200b8e6c",
"metadata": {},
"source": [
"- Finally, let's evaluate the model"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "bawWGijA0iF3",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 307
},
"id": "bawWGijA0iF3",
"outputId": "4b05b245-ffac-4d36-881b-8306a4da6b75"
},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 500x300 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"from previous_chapters import plot_values\n",
"\n",
"epochs_tensor = torch.linspace(0, num_epochs, len(train_losses))\n",
"examples_seen_tensor = torch.linspace(0, examples_seen, len(train_losses))\n",
"\n",
"plot_values(epochs_tensor, examples_seen_tensor, train_losses, val_losses, label=\"loss\")"
]
},
{
"cell_type": "markdown",
"id": "aa074723-e3f7-4f7e-a267-855531a037dc",
"metadata": {},
"source": [
"- Note that we previously calculated the accuracy values on 10 batches only; below, we calculate the accuracies on the full dataset"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "1D2awlEq0gZi",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "1D2awlEq0gZi",
"outputId": "b482af19-5ebd-45b9-a9f0-99f621203ef9"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Training accuracy: 100.00%\n",
"Validation accuracy: 96.64%\n",
"Test accuracy: 98.00%\n"
]
}
],
"source": [
"from previous_chapters import calc_accuracy_loader\n",
"\n",
"train_accuracy = calc_accuracy_loader(train_loader, model, device)\n",
"val_accuracy = calc_accuracy_loader(val_loader, model, device)\n",
"test_accuracy = calc_accuracy_loader(test_loader, model, device)\n",
"\n",
"print(f\"Training accuracy: {train_accuracy*100:.2f}%\")\n",
"print(f\"Validation accuracy: {val_accuracy*100:.2f}%\")\n",
"print(f\"Test accuracy: {test_accuracy*100:.2f}%\")"
]
},
{
"cell_type": "markdown",
"id": "1f87f5e6-339e-4fcf-900b-6d845d3c713d",
"metadata": {},
"source": [
"- As we can based on the relatively high accuracy values above, the LoRA finetuning was successful"
]
}
],
"metadata": {
"accelerator": "GPU",
"colab": {
"gpuType": "V100",
"provenance": []
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.10.12"
}
},
"nbformat": 4,
"nbformat_minor": 5
}