本笔记本演示了一种自定义 OpenAI 嵌入以适应特定任务的方法。

输入是形式为 [text_1, text_2, label] 的训练数据，其中如果配对相似，则标签为 +1，如果配对不相似，则标签为 -1。

输出是一个矩阵，您可以将其用于乘以您的嵌入。此乘法的乘积是“自定义嵌入”，它将更好地强调与您的用例相关的文本方面。在二元分类用例中，我们已将错误率降低了多达 50%。

在以下示例中，我使用了从 SNLI 语料库中挑选的 1,000 个句子对。每对句子在逻辑上都是蕴含关系（即，一个暗示另一个）。这些对是我们的正例（标签 = 1）。我们通过组合来自不同对的句子来生成合成负例，这些句子被假定为不具有逻辑蕴含关系（标签 = -1）。

对于聚类用例，您可以创建同一聚类中文本的配对来生成正例，并创建不同聚类中文本的配对来生成负例。

使用其他数据集，我们发现即使只有约 100 个训练示例也能获得不错的改进。当然，更多的示例会带来更好的性能。

0. 导入

# imports
from typing import List, Tuple  # for type hints

import numpy as np  # for manipulating arrays
import pandas as pd  # for manipulating data in dataframes
import pickle  # for saving the embeddings cache
import plotly.express as px  # for plots
import random  # for generating run IDs
from sklearn.model_selection import train_test_split  # for splitting train & test data
import torch  # for matrix optimization

from utils.embeddings_utils import get_embedding, cosine_similarity  # for embeddings

1. 输入

大多数输入都在这里。需要更改的关键是加载数据集的位置、保存嵌入缓存的位置以及您想使用的嵌入引擎。

根据您的数据格式，您可能需要重写 process_input_data 函数。

# input parameters
embedding_cache_path = "data/snli_embedding_cache.pkl"  # embeddings will be saved/loaded here
default_embedding_engine = "text-embedding-3-small"
num_pairs_to_embed = 1000  # 1000 is arbitrary
local_dataset_path = "data/snli_1.0_train_2k.csv"  # download from: https://nlp.stanford.edu/projects/snli/


def process_input_data(df: pd.DataFrame) -> pd.DataFrame:
    # you can customize this to preprocess your own dataset
    # output should be a dataframe with 3 columns: text_1, text_2, label (1 for similar, -1 for dissimilar)
    df["label"] = df["gold_label"]
    df = df[df["label"].isin(["entailment"])]
    df["label"] = df["label"].apply(lambda x: {"entailment": 1, "contradiction": -1}[x])
    df = df.rename(columns={"sentence1": "text_1", "sentence2": "text_2"})
    df = df[["text_1", "text_2", "label"]]
    df = df.head(num_pairs_to_embed)
    return df

2. 加载和处理输入数据

# load data
df = pd.read_csv(local_dataset_path)

# process input data
df = process_input_data(df)  # this demonstrates training data containing only positives

# view data
df.head()

/var/folders/r4/x3kdvs816995fnnph2gdpwp40000gn/T/ipykernel_17509/1977422881.py:13: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy
  df["label"] = df["label"].apply(lambda x: {"entailment": 1, "contradiction": -1}[x])

3. 将数据拆分为训练和测试集

请注意，在生成合成负例或正例之前，将数据拆分为训练集和测试集非常重要。您不希望训练数据中的任何文本字符串出现在测试数据中。如果存在数据污染，测试指标将看起来比实际生产中的要好。

# split data into train and test sets
test_fraction = 0.5  # 0.5 is fairly arbitrary
random_seed = 123  # random seed is arbitrary, but is helpful in reproducibility
train_df, test_df = train_test_split(
    df, test_size=test_fraction, stratify=df["label"], random_state=random_seed
)
train_df.loc[:, "dataset"] = "train"
test_df.loc[:, "dataset"] = "test"

4. 生成合成负例

这是您需要修改以匹配您的用例的另一部分代码。

如果您有包含正例和负例的数据，则可以跳过此部分。

如果您只有正例数据，则可以基本保持原样，它会生成负例。

如果您有多类数据，则需要生成正例和负例。正例可以是共享标签的文本对，负例可以是未共享标签的文本对。

最终输出应为一个包含文本对的数据框，其中每对都标记为 -1 或 1。

# generate negatives
def dataframe_of_negatives(dataframe_of_positives: pd.DataFrame) -> pd.DataFrame:
    """Return dataframe of negative pairs made by combining elements of positive pairs."""
    texts = set(dataframe_of_positives["text_1"].values) | set(
        dataframe_of_positives["text_2"].values
    )
    all_pairs = {(t1, t2) for t1 in texts for t2 in texts if t1 < t2}
    positive_pairs = set(
        tuple(text_pair)
        for text_pair in dataframe_of_positives[["text_1", "text_2"]].values
    )
    negative_pairs = all_pairs - positive_pairs
    df_of_negatives = pd.DataFrame(list(negative_pairs), columns=["text_1", "text_2"])
    df_of_negatives["label"] = -1
    return df_of_negatives

negatives_per_positive = (
    1  # it will work at higher values too, but more data will be slower
)
# generate negatives for training dataset
train_df_negatives = dataframe_of_negatives(train_df)
train_df_negatives["dataset"] = "train"
# generate negatives for test dataset
test_df_negatives = dataframe_of_negatives(test_df)
test_df_negatives["dataset"] = "test"
# sample negatives and combine with positives
train_df = pd.concat(
    [
        train_df,
        train_df_negatives.sample(
            n=len(train_df) * negatives_per_positive, random_state=random_seed
        ),
    ]
)
test_df = pd.concat(
    [
        test_df,
        test_df_negatives.sample(
            n=len(test_df) * negatives_per_positive, random_state=random_seed
        ),
    ]
)

df = pd.concat([train_df, test_df])

5. 计算嵌入和余弦相似度

在这里，我创建了一个缓存来保存嵌入。这很方便，因为如果您想再次运行代码，就不必再次付费。

# establish a cache of embeddings to avoid recomputing
# cache is a dict of tuples (text, engine) -> embedding
try:
    with open(embedding_cache_path, "rb") as f:
        embedding_cache = pickle.load(f)
except FileNotFoundError:
    precomputed_embedding_cache_path = "https://cdn.openai.com/API/examples/data/snli_embedding_cache.pkl"
    embedding_cache = pd.read_pickle(precomputed_embedding_cache_path)


# this function will get embeddings from the cache and save them there afterward
def get_embedding_with_cache(
    text: str,
    engine: str = default_embedding_engine,
    embedding_cache: dict = embedding_cache,
    embedding_cache_path: str = embedding_cache_path,
) -> list:
    if (text, engine) not in embedding_cache.keys():
        # if not in cache, call API to get embedding
        embedding_cache[(text, engine)] = get_embedding(text, engine)
        # save embeddings cache to disk after each update
        with open(embedding_cache_path, "wb") as embedding_cache_file:
            pickle.dump(embedding_cache, embedding_cache_file)
    return embedding_cache[(text, engine)]


# create column of embeddings
for column in ["text_1", "text_2"]:
    df[f"{column}_embedding"] = df[column].apply(get_embedding_with_cache)

# create column of cosine similarity between embeddings
df["cosine_similarity"] = df.apply(
    lambda row: cosine_similarity(row["text_1_embedding"], row["text_2_embedding"]),
    axis=1,
)

6. 绘制余弦相似度分布图

在这里，我们使用余弦相似度来衡量文本的相似度。根据我们的经验，大多数距离函数（L1、L2、余弦相似度）的效果都差不多。请注意，我们的嵌入长度已标准化为 1，因此余弦相似度等同于点积。

这些图显示了相似和不相似配对的余弦相似度分布之间的重叠程度。如果重叠量很大，则意味着存在一些不相似的配对，其余弦相似度大于一些相似的配对。

我计算的准确率是一个简单规则的准确率，该规则预测“相似（1）”，如果余弦相似度高于某个阈值 X，否则预测“不相似（0）”。

# calculate accuracy (and its standard error) of predicting label=1 if similarity>x
# x is optimized by sweeping from -1 to 1 in steps of 0.01
def accuracy_and_se(cosine_similarity: float, labeled_similarity: int) -> Tuple[float]:
    accuracies = []
    for threshold_thousandths in range(-1000, 1000, 1):
        threshold = threshold_thousandths / 1000
        total = 0
        correct = 0
        for cs, ls in zip(cosine_similarity, labeled_similarity):
            total += 1
            if cs > threshold:
                prediction = 1
            else:
                prediction = -1
            if prediction == ls:
                correct += 1
        accuracy = correct / total
        accuracies.append(accuracy)
    a = max(accuracies)
    n = len(cosine_similarity)
    standard_error = (a * (1 - a) / n) ** 0.5  # standard error of binomial
    return a, standard_error


# check that training and test sets are balanced
px.histogram(
    df,
    x="cosine_similarity",
    color="label",
    barmode="overlay",
    width=500,
    facet_row="dataset",
).show()

for dataset in ["train", "test"]:
    data = df[df["dataset"] == dataset]
    a, se = accuracy_and_se(data["cosine_similarity"], data["label"])
    print(f"{dataset} accuracy: {a:0.1%} ± {1.96 * se:0.1%}")

train accuracy: 89.1% ± 2.4%
test accuracy: 88.8% ± 2.4%

7. 使用提供的训练数据优化矩阵

def embedding_multiplied_by_matrix(
    embedding: List[float], matrix: torch.tensor
) -> np.array:
    embedding_tensor = torch.tensor(embedding).float()
    modified_embedding = embedding_tensor @ matrix
    modified_embedding = modified_embedding.detach().numpy()
    return modified_embedding


# compute custom embeddings and new cosine similarities
def apply_matrix_to_embeddings_dataframe(matrix: torch.tensor, df: pd.DataFrame):
    for column in ["text_1_embedding", "text_2_embedding"]:
        df[f"{column}_custom"] = df[column].apply(
            lambda x: embedding_multiplied_by_matrix(x, matrix)
        )
    df["cosine_similarity_custom"] = df.apply(
        lambda row: cosine_similarity(
            row["text_1_embedding_custom"], row["text_2_embedding_custom"]
        ),
        axis=1,
    )

def optimize_matrix(
    modified_embedding_length: int = 2048,  # in my brief experimentation, bigger was better (2048 is length of babbage encoding)
    batch_size: int = 100,
    max_epochs: int = 100,
    learning_rate: float = 100.0,  # seemed to work best when similar to batch size - feel free to try a range of values
    dropout_fraction: float = 0.0,  # in my testing, dropout helped by a couple percentage points (definitely not necessary)
    df: pd.DataFrame = df,
    print_progress: bool = True,
    save_results: bool = True,
) -> torch.tensor:
    """Return matrix optimized to minimize loss on training data."""
    run_id = random.randint(0, 2 ** 31 - 1)  # (range is arbitrary)
    # convert from dataframe to torch tensors
    # e is for embedding, s for similarity label
    def tensors_from_dataframe(
        df: pd.DataFrame,
        embedding_column_1: str,
        embedding_column_2: str,
        similarity_label_column: str,
    ) -> Tuple[torch.tensor]:
        e1 = np.stack(np.array(df[embedding_column_1].values))
        e2 = np.stack(np.array(df[embedding_column_2].values))
        s = np.stack(np.array(df[similarity_label_column].astype("float").values))

        e1 = torch.from_numpy(e1).float()
        e2 = torch.from_numpy(e2).float()
        s = torch.from_numpy(s).float()

        return e1, e2, s

    e1_train, e2_train, s_train = tensors_from_dataframe(
        df[df["dataset"] == "train"], "text_1_embedding", "text_2_embedding", "label"
    )
    e1_test, e2_test, s_test = tensors_from_dataframe(
        df[df["dataset"] == "test"], "text_1_embedding", "text_2_embedding", "label"
    )

    # create dataset and loader
    dataset = torch.utils.data.TensorDataset(e1_train, e2_train, s_train)
    train_loader = torch.utils.data.DataLoader(
        dataset, batch_size=batch_size, shuffle=True
    )

    # define model (similarity of projected embeddings)
    def model(embedding_1, embedding_2, matrix, dropout_fraction=dropout_fraction):
        e1 = torch.nn.functional.dropout(embedding_1, p=dropout_fraction)
        e2 = torch.nn.functional.dropout(embedding_2, p=dropout_fraction)
        modified_embedding_1 = e1 @ matrix  # @ is matrix multiplication
        modified_embedding_2 = e2 @ matrix
        similarity = torch.nn.functional.cosine_similarity(
            modified_embedding_1, modified_embedding_2
        )
        return similarity

    # define loss function to minimize
    def mse_loss(predictions, targets):
        difference = predictions - targets
        return torch.sum(difference * difference) / difference.numel()

    # initialize projection matrix
    embedding_length = len(df["text_1_embedding"].values[0])
    matrix = torch.randn(
        embedding_length, modified_embedding_length, requires_grad=True
    )

    epochs, types, losses, accuracies, matrices = [], [], [], [], []
    for epoch in range(1, 1 + max_epochs):
        # iterate through training dataloader
        for a, b, actual_similarity in train_loader:
            # generate prediction
            predicted_similarity = model(a, b, matrix)
            # get loss and perform backpropagation
            loss = mse_loss(predicted_similarity, actual_similarity)
            loss.backward()
            # update the weights
            with torch.no_grad():
                matrix -= matrix.grad * learning_rate
                # set gradients to zero
                matrix.grad.zero_()
        # calculate test loss
        test_predictions = model(e1_test, e2_test, matrix)
        test_loss = mse_loss(test_predictions, s_test)

        # compute custom embeddings and new cosine similarities
        apply_matrix_to_embeddings_dataframe(matrix, df)

        # calculate test accuracy
        for dataset in ["train", "test"]:
            data = df[df["dataset"] == dataset]
            a, se = accuracy_and_se(data["cosine_similarity_custom"], data["label"])

            # record results of each epoch
            epochs.append(epoch)
            types.append(dataset)
            losses.append(loss.item() if dataset == "train" else test_loss.item())
            accuracies.append(a)
            matrices.append(matrix.detach().numpy())

            # optionally print accuracies
            if print_progress is True:
                print(
                    f"Epoch {epoch}/{max_epochs}: {dataset} accuracy: {a:0.1%} ± {1.96 * se:0.1%}"
                )

    data = pd.DataFrame(
        {"epoch": epochs, "type": types, "loss": losses, "accuracy": accuracies}
    )
    data["run_id"] = run_id
    data["modified_embedding_length"] = modified_embedding_length
    data["batch_size"] = batch_size
    data["max_epochs"] = max_epochs
    data["learning_rate"] = learning_rate
    data["dropout_fraction"] = dropout_fraction
    data[
        "matrix"
    ] = matrices  # saving every single matrix can get big; feel free to delete/change
    if save_results is True:
        data.to_csv(f"{run_id}_optimization_results.csv", index=False)

    return data

# example hyperparameter search
# I recommend starting with max_epochs=10 while initially exploring
results = []
max_epochs = 30
dropout_fraction = 0.2
for batch_size, learning_rate in [(10, 10), (100, 100), (1000, 1000)]:
    result = optimize_matrix(
        batch_size=batch_size,
        learning_rate=learning_rate,
        max_epochs=max_epochs,
        dropout_fraction=dropout_fraction,
        save_results=False,
    )
    results.append(result)

Epoch 1/30: train accuracy: 89.1% ± 2.4%
Epoch 1/30: test accuracy: 88.4% ± 2.4%
Epoch 2/30: train accuracy: 89.5% ± 2.3%
Epoch 2/30: test accuracy: 88.8% ± 2.4%
Epoch 3/30: train accuracy: 90.6% ± 2.2%
Epoch 3/30: test accuracy: 89.3% ± 2.3%
Epoch 4/30: train accuracy: 91.2% ± 2.2%
Epoch 4/30: test accuracy: 89.7% ± 2.3%
Epoch 5/30: train accuracy: 91.5% ± 2.1%
Epoch 5/30: test accuracy: 90.0% ± 2.3%
Epoch 6/30: train accuracy: 91.9% ± 2.1%
Epoch 6/30: test accuracy: 90.4% ± 2.2%
Epoch 7/30: train accuracy: 92.2% ± 2.0%
Epoch 7/30: test accuracy: 90.7% ± 2.2%
Epoch 8/30: train accuracy: 92.7% ± 2.0%
Epoch 8/30: test accuracy: 90.9% ± 2.2%
Epoch 9/30: train accuracy: 92.7% ± 2.0%
Epoch 9/30: test accuracy: 91.0% ± 2.2%
Epoch 10/30: train accuracy: 93.0% ± 1.9%
Epoch 10/30: test accuracy: 91.6% ± 2.1%
Epoch 11/30: train accuracy: 93.1% ± 1.9%
Epoch 11/30: test accuracy: 91.8% ± 2.1%
Epoch 12/30: train accuracy: 93.4% ± 1.9%
Epoch 12/30: test accuracy: 92.1% ± 2.0%
Epoch 13/30: train accuracy: 93.6% ± 1.9%
Epoch 13/30: test accuracy: 92.4% ± 2.0%
Epoch 14/30: train accuracy: 93.7% ± 1.8%
Epoch 14/30: test accuracy: 92.7% ± 2.0%
Epoch 15/30: train accuracy: 93.7% ± 1.8%
Epoch 15/30: test accuracy: 92.7% ± 2.0%
Epoch 16/30: train accuracy: 94.0% ± 1.8%
Epoch 16/30: test accuracy: 93.0% ± 1.9%
Epoch 17/30: train accuracy: 94.0% ± 1.8%
Epoch 17/30: test accuracy: 93.0% ± 1.9%
Epoch 18/30: train accuracy: 94.2% ± 1.8%
Epoch 18/30: test accuracy: 93.1% ± 1.9%
Epoch 19/30: train accuracy: 94.2% ± 1.8%
Epoch 19/30: test accuracy: 93.1% ± 1.9%
Epoch 20/30: train accuracy: 94.3% ± 1.8%
Epoch 20/30: test accuracy: 93.0% ± 1.9%
Epoch 21/30: train accuracy: 94.5% ± 1.7%
Epoch 21/30: test accuracy: 93.1% ± 1.9%
Epoch 22/30: train accuracy: 94.5% ± 1.7%
Epoch 22/30: test accuracy: 93.3% ± 1.9%
Epoch 23/30: train accuracy: 94.6% ± 1.7%
Epoch 23/30: test accuracy: 93.3% ± 1.9%
Epoch 24/30: train accuracy: 94.6% ± 1.7%
Epoch 24/30: test accuracy: 93.3% ± 1.9%
Epoch 25/30: train accuracy: 94.8% ± 1.7%
Epoch 25/30: test accuracy: 93.3% ± 1.9%
Epoch 26/30: train accuracy: 94.8% ± 1.7%
Epoch 26/30: test accuracy: 93.4% ± 1.9%
Epoch 27/30: train accuracy: 94.8% ± 1.7%
Epoch 27/30: test accuracy: 93.4% ± 1.9%
Epoch 28/30: train accuracy: 94.9% ± 1.7%
Epoch 28/30: test accuracy: 93.4% ± 1.9%
Epoch 29/30: train accuracy: 94.9% ± 1.7%
Epoch 29/30: test accuracy: 93.4% ± 1.9%
Epoch 30/30: train accuracy: 94.9% ± 1.7%
Epoch 30/30: test accuracy: 93.3% ± 1.9%
Epoch 1/30: train accuracy: 89.7% ± 2.3%
Epoch 1/30: test accuracy: 89.1% ± 2.4%
Epoch 2/30: train accuracy: 89.8% ± 2.3%
Epoch 2/30: test accuracy: 89.9% ± 2.3%
Epoch 3/30: train accuracy: 90.3% ± 2.2%
Epoch 3/30: test accuracy: 90.0% ± 2.3%
Epoch 4/30: train accuracy: 91.0% ± 2.2%
Epoch 4/30: test accuracy: 90.3% ± 2.2%
Epoch 5/30: train accuracy: 91.3% ± 2.1%
Epoch 5/30: test accuracy: 90.3% ± 2.2%
Epoch 6/30: train accuracy: 91.8% ± 2.1%
Epoch 6/30: test accuracy: 90.4% ± 2.2%
Epoch 7/30: train accuracy: 92.4% ± 2.0%
Epoch 7/30: test accuracy: 91.0% ± 2.2%
Epoch 8/30: train accuracy: 92.8% ± 2.0%
Epoch 8/30: test accuracy: 91.3% ± 2.1%
Epoch 9/30: train accuracy: 93.1% ± 1.9%
Epoch 9/30: test accuracy: 91.6% ± 2.1%
Epoch 10/30: train accuracy: 93.4% ± 1.9%
Epoch 10/30: test accuracy: 91.9% ± 2.1%
Epoch 11/30: train accuracy: 93.4% ± 1.9%
Epoch 11/30: test accuracy: 91.8% ± 2.1%
Epoch 12/30: train accuracy: 93.6% ± 1.9%
Epoch 12/30: test accuracy: 92.1% ± 2.0%
Epoch 13/30: train accuracy: 93.7% ± 1.8%
Epoch 13/30: test accuracy: 92.4% ± 2.0%
Epoch 14/30: train accuracy: 93.7% ± 1.8%
Epoch 14/30: test accuracy: 92.5% ± 2.0%
Epoch 15/30: train accuracy: 93.9% ± 1.8%
Epoch 15/30: test accuracy: 92.8% ± 2.0%
Epoch 16/30: train accuracy: 94.0% ± 1.8%
Epoch 16/30: test accuracy: 92.8% ± 2.0%
Epoch 17/30: train accuracy: 94.0% ± 1.8%
Epoch 17/30: test accuracy: 92.8% ± 2.0%
Epoch 18/30: train accuracy: 94.2% ± 1.8%
Epoch 18/30: test accuracy: 92.8% ± 2.0%
Epoch 19/30: train accuracy: 94.2% ± 1.8%
Epoch 19/30: test accuracy: 92.8% ± 2.0%
Epoch 20/30: train accuracy: 94.2% ± 1.8%
Epoch 20/30: test accuracy: 93.1% ± 1.9%
Epoch 21/30: train accuracy: 94.3% ± 1.8%
Epoch 21/30: test accuracy: 93.3% ± 1.9%
Epoch 22/30: train accuracy: 94.3% ± 1.8%
Epoch 22/30: test accuracy: 93.3% ± 1.9%
Epoch 23/30: train accuracy: 94.5% ± 1.7%
Epoch 23/30: test accuracy: 93.3% ± 1.9%
Epoch 24/30: train accuracy: 94.5% ± 1.7%
Epoch 24/30: test accuracy: 93.3% ± 1.9%
Epoch 25/30: train accuracy: 94.6% ± 1.7%
Epoch 25/30: test accuracy: 93.4% ± 1.9%
Epoch 26/30: train accuracy: 94.6% ± 1.7%
Epoch 26/30: test accuracy: 93.3% ± 1.9%
Epoch 27/30: train accuracy: 94.6% ± 1.7%
Epoch 27/30: test accuracy: 93.4% ± 1.9%
Epoch 28/30: train accuracy: 94.8% ± 1.7%
Epoch 28/30: test accuracy: 93.4% ± 1.9%
Epoch 29/30: train accuracy: 94.8% ± 1.7%
Epoch 29/30: test accuracy: 93.3% ± 1.9%
Epoch 30/30: train accuracy: 94.8% ± 1.7%
Epoch 30/30: test accuracy: 93.4% ± 1.9%
Epoch 1/30: train accuracy: 90.7% ± 2.2%
Epoch 1/30: test accuracy: 89.9% ± 2.3%
Epoch 2/30: train accuracy: 90.9% ± 2.2%
Epoch 2/30: test accuracy: 90.3% ± 2.2%
Epoch 3/30: train accuracy: 91.6% ± 2.1%
Epoch 3/30: test accuracy: 90.3% ± 2.2%
Epoch 4/30: train accuracy: 92.2% ± 2.0%
Epoch 4/30: test accuracy: 90.7% ± 2.2%
Epoch 5/30: train accuracy: 92.4% ± 2.0%
Epoch 5/30: test accuracy: 91.3% ± 2.1%
Epoch 6/30: train accuracy: 92.5% ± 2.0%
Epoch 6/30: test accuracy: 91.8% ± 2.1%
Epoch 7/30: train accuracy: 93.0% ± 1.9%
Epoch 7/30: test accuracy: 92.2% ± 2.0%
Epoch 8/30: train accuracy: 93.1% ± 1.9%
Epoch 8/30: test accuracy: 92.7% ± 2.0%
Epoch 9/30: train accuracy: 93.3% ± 1.9%
Epoch 9/30: test accuracy: 92.5% ± 2.0%
Epoch 10/30: train accuracy: 93.4% ± 1.9%
Epoch 10/30: test accuracy: 92.7% ± 2.0%
Epoch 11/30: train accuracy: 93.6% ± 1.9%
Epoch 11/30: test accuracy: 92.8% ± 2.0%
Epoch 12/30: train accuracy: 93.7% ± 1.8%
Epoch 12/30: test accuracy: 92.8% ± 2.0%
Epoch 13/30: train accuracy: 94.0% ± 1.8%
Epoch 13/30: test accuracy: 93.0% ± 1.9%
Epoch 14/30: train accuracy: 93.9% ± 1.8%
Epoch 14/30: test accuracy: 93.0% ± 1.9%
Epoch 15/30: train accuracy: 94.2% ± 1.8%
Epoch 15/30: test accuracy: 93.0% ± 1.9%
Epoch 16/30: train accuracy: 94.2% ± 1.8%
Epoch 16/30: test accuracy: 93.0% ± 1.9%
Epoch 17/30: train accuracy: 94.3% ± 1.8%
Epoch 17/30: test accuracy: 93.0% ± 1.9%
Epoch 18/30: train accuracy: 94.5% ± 1.7%
Epoch 18/30: test accuracy: 93.1% ± 1.9%
Epoch 19/30: train accuracy: 94.5% ± 1.7%
Epoch 19/30: test accuracy: 93.1% ± 1.9%
Epoch 20/30: train accuracy: 94.6% ± 1.7%
Epoch 20/30: test accuracy: 93.3% ± 1.9%
Epoch 21/30: train accuracy: 94.8% ± 1.7%
Epoch 21/30: test accuracy: 93.3% ± 1.9%
Epoch 22/30: train accuracy: 94.8% ± 1.7%
Epoch 22/30: test accuracy: 93.4% ± 1.9%
Epoch 23/30: train accuracy: 94.8% ± 1.7%
Epoch 23/30: test accuracy: 93.4% ± 1.9%
Epoch 24/30: train accuracy: 94.8% ± 1.7%
Epoch 24/30: test accuracy: 93.4% ± 1.9%
Epoch 25/30: train accuracy: 94.8% ± 1.7%
Epoch 25/30: test accuracy: 93.4% ± 1.9%
Epoch 26/30: train accuracy: 94.9% ± 1.7%
Epoch 26/30: test accuracy: 93.6% ± 1.9%
Epoch 27/30: train accuracy: 94.9% ± 1.7%
Epoch 27/30: test accuracy: 93.6% ± 1.9%
Epoch 28/30: train accuracy: 94.9% ± 1.7%
Epoch 28/30: test accuracy: 93.6% ± 1.9%
Epoch 29/30: train accuracy: 95.1% ± 1.6%
Epoch 29/30: test accuracy: 93.6% ± 1.9%
Epoch 30/30: train accuracy: 95.1% ± 1.6%
Epoch 30/30: test accuracy: 93.6% ± 1.9%

runs_df = pd.concat(results)

# plot training loss and test loss over time
px.line(
    runs_df,
    line_group="run_id",
    x="epoch",
    y="loss",
    color="type",
    hover_data=["batch_size", "learning_rate", "dropout_fraction"],
    facet_row="learning_rate",
    facet_col="batch_size",
    width=500,
).show()

# plot accuracy over time
px.line(
    runs_df,
    line_group="run_id",
    x="epoch",
    y="accuracy",
    color="type",
    hover_data=["batch_size", "learning_rate", "dropout_fraction"],
    facet_row="learning_rate",
    facet_col="batch_size",
    width=500,
).show()

8. 绘制前后对比图，显示训练过程中找到的最佳矩阵的结果

矩阵越好，相似和不相似配对的分离就越清晰。

# apply result of best run to original data
best_run = runs_df.sort_values(by="accuracy", ascending=False).iloc[0]
best_matrix = best_run["matrix"]
apply_matrix_to_embeddings_dataframe(best_matrix, df)

# plot similarity distribution BEFORE customization
px.histogram(
    df,
    x="cosine_similarity",
    color="label",
    barmode="overlay",
    width=500,
    facet_row="dataset",
).show()

test_df = df[df["dataset"] == "test"]
a, se = accuracy_and_se(test_df["cosine_similarity"], test_df["label"])
print(f"Test accuracy: {a:0.1%} ± {1.96 * se:0.1%}")

# plot similarity distribution AFTER customization
px.histogram(
    df,
    x="cosine_similarity_custom",
    color="label",
    barmode="overlay",
    width=500,
    facet_row="dataset",
).show()

a, se = accuracy_and_se(test_df["cosine_similarity_custom"], test_df["label"])
print(f"Test accuracy after customization: {a:0.1%} ± {1.96 * se:0.1%}")

Test accuracy: 88.8% ± 2.4%




Test accuracy after customization: 93.6% ± 1.9%

best_matrix  # this is what you can multiply your embeddings by

array([[-1.2566795e+00, -1.5297449e+00, -1.3271648e-01, ...,
        -1.2859761e+00, -5.3254390e-01,  4.8364732e-01],
       [-1.4826347e+00,  9.2656955e-02, -4.2437232e-01, ...,
         1.1872858e+00, -1.0831847e+00, -1.0683593e+00],
       [-2.2029283e+00, -1.9703420e+00,  3.1125939e-01, ...,
         2.2947595e+00,  5.5780332e-03, -6.0171342e-01],
       ...,
       [-1.1019799e-01,  1.3599515e+00, -4.7677776e-01, ...,
         6.5626711e-01,  7.2359240e-01,  3.0733588e+00],
       [ 1.6624762e-03,  4.2648423e-01, -1.1380885e+00, ...,
         8.7202555e-01,  9.3173909e-01, -1.6760436e+00],
       [ 7.7449006e-01,  4.9213606e-01,  3.5407653e-01, ...,
         1.3460466e+00, -1.9509128e-01,  7.7514690e-01]], dtype=float32)

```