Embeddings

All first-generation models (those ending in -001) use the GPT-3 tokenizer and have a max input of 2046 tokens.

First-generation embeddings are generated by five different model families tuned for three different tasks: text search, text similarity and code search. The search models come in pairs: one for short queries and one for long documents. Each family includes up to four models on a spectrum of quality and speed:

Davinci is the most capable, but is slower and more expensive than the other models. Ada is the least capable, but is significantly faster and cheaper.

Similarity models are best at capturing semantic similarity between pieces of text.

Text search models help measure which long documents are most relevant to a short search query. Two models are used: one for embedding the search query and one for embedding the documents to be ranked. The document embeddings closest to the query embedding should be the most relevant.

Similarly to search embeddings, there are two types: one for embedding natural language search queries and one for embedding code snippets to be retrieved.

The size of the embeddings varies with the complexity of the underlying model. In order to visualize this high dimensional data we use the t-SNE algorithm to transform the data into two dimensions.

We color the individual reviews based on the star rating which the reviewer has given:

• 1-star: red
• 2-star: dark orange
• 3-star: gold
• 4-star: turquoise
• 5-star: dark green

The visualization seems to have produced roughly 3 clusters, one of which has mostly negative reviews.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
import pandas as pd
from sklearn.manifold import TSNE
import matplotlib.pyplot as plt
import matplotlib

df = pd.read_csv('output/embedded_1k_reviews.csv')
matrix = df.ada_embedding.apply(eval).to_list()

# Create a t-SNE model and transform the data
tsne = TSNE(n_components=2, perplexity=15, random_state=42, init='random', learning_rate=200)
vis_dims = tsne.fit_transform(matrix)

colors = ["red", "darkorange", "gold", "turquiose", "darkgreen"]
x = [x for x,y in vis_dims]
y = [y for x,y in vis_dims]
color_indices = df.Score.values - 1

colormap = matplotlib.colors.ListedColormap(colors)
plt.scatter(x, y, c=color_indices, cmap=colormap, alpha=0.3)
plt.title("Amazon ratings visualized in language using t-SNE")

An embedding can be used as a general free-text feature encoder within a machine learning model. Incorporating embeddings will improve the performance of any machine learning model, if some of the relevant inputs are free text. An embedding can also be used as a categorical feature encoder within a ML model. This adds most value if the names of categorical variables are meaningful and numerous, such as job titles. Similarity embeddings generally perform better than search embeddings for this task.

We observed that generally the embedding representation is very rich and information dense. For example, reducing the dimensionality of the inputs using SVD or PCA, even by 10%, generally results in worse downstream performance on specific tasks.

This code splits the data into a training set and a testing set, which will be used by the following two use cases, namely regression and classification.

1
2
3
4
5
6
7
8
from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(
    list(df.ada_embedding.values),
    df.Score,
    test_size = 0.2,
    random_state=42
)

Embeddings present an elegant way of predicting a numerical value. In this example we predict the reviewer’s star rating, based on the text of their review. Because the semantic information contained within embeddings is high, the prediction is decent even with very few reviews.

We assume the score is a continuous variable between 1 and 5, and allow the algorithm to predict any floating point value. The ML algorithm minimizes the distance of the predicted value to the true score, and achieves a mean absolute error of 0.39, which means that on average the prediction is off by less than half a star.

1
2
3
4
5
from sklearn.ensemble import RandomForestRegressor

rfr = RandomForestRegressor(n_estimators=100)
rfr.fit(X_train, y_train)
preds = rfr.predict(X_test)

This time, instead of having the algorithm predict a value anywhere between 1 and 5, we will attempt to classify the exact number of stars for a review into 5 buckets, ranging from 1 to 5 stars.

After the training, the model learns to predict 1 and 5-star reviews much better than the more nuanced reviews (2-4 stars), likely due to more extreme sentiment expression.

1
2
3
4
5
6
from sklearn.ensemble import RandomForestClassifier
from sklearn.metrics import classification_report, accuracy_score

clf = RandomForestClassifier(n_estimators=100)
clf.fit(X_train, y_train)
preds = clf.predict(X_test)

We can use embeddings for zero shot classification without any labeled training data. For each class, we embed the class name or a short description of the class. To classify some new text in a zero-shot manner, we compare its embedding to all class embeddings and predict the class with the highest similarity.

1
2
3
4
5
6
7
8
9
10
11
12
from openai.embeddings_utils import cosine_similarity, get_embedding

df= df[df.Score!=3]
df['sentiment'] = df.Score.replace({1:'negative', 2:'negative', 4:'positive', 5:'positive'})

labels = ['negative', 'positive']
label_embeddings = [get_embedding(label, model=model) for label in labels]

def label_score(review_embedding, label_embeddings):
   return cosine_similarity(review_embedding, label_embeddings[1]) - cosine_similarity(review_embedding, label_embeddings[0])

prediction = 'positive' if label_score('Sample Review', label_embeddings) > 0 else 'negative'

We can obtain a user embedding by averaging over all of their reviews. Similarly, we can obtain a product embedding by averaging over all the reviews about that product. In order to showcase the usefulness of this approach we use a subset of 50k reviews to cover more reviews per user and per product.

We evaluate the usefulness of these embeddings on a separate test set, where we plot similarity of the user and product embedding as a function of the rating. Interestingly, based on this approach, even before the user receives the product we can predict better than random whether they would like the product.

user_embeddings = df.groupby('UserId').ada_embedding.apply(np.mean)
prod_embeddings = df.groupby('ProductId').ada_embedding.apply(np.mean)

Clustering is one way of making sense of a large volume of textual data. Embeddings are useful for this task, as they provide semantically meaningful vector representations of each text. Thus, in an unsupervised way, clustering will uncover hidden groupings in our dataset.

In this example, we discover four distinct clusters: one focusing on dog food, one on negative reviews, and two on positive reviews.

1
2
3
4
5
6
7
8
9
import numpy as np
from sklearn.cluster import KMeans

matrix = np.vstack(df.ada_embedding.values)
n_clusters = 4

kmeans = KMeans(n_clusters = n_clusters, init='k-means++', random_state=42)
kmeans.fit(matrix)
df['Cluster'] = kmeans.labels_

To retrieve the most relevant documents we use the cosine similarity between the embedding vectors of the query and each document, and return the highest scored documents.

1
2
3
4
5
6
7
8
9
from openai.embeddings_utils import get_embedding, cosine_similarity

def search_reviews(df, product_description, n=3, pprint=True):
   embedding = get_embedding(product_description, model='text-embedding-ada-002')
   df['similarities'] = df.ada_embedding.apply(lambda x: cosine_similarity(x, embedding))
   res = df.sort_values('similarities', ascending=False).head(n)
   return res

res = search_reviews(df, 'delicious beans', n=3)

Code search works similarly to embedding-based text search. We provide a method to extract Python functions from all the Python files in a given repository. Each function is then indexed by the text-embedding-ada-002 model.

To perform a code search, we embed the query in natural language using the same model. Then we calculate cosine similarity between the resulting query embedding and each of the function embeddings. The highest cosine similarity results are most relevant.

1
2
3
4
5
6
7
8
9
10
11
from openai.embeddings_utils import get_embedding, cosine_similarity

df['code_embedding'] = df['code'].apply(lambda x: get_embedding(x, model='text-embedding-ada-002'))

def search_functions(df, code_query, n=3, pprint=True, n_lines=7):
   embedding = get_embedding(code_query, model='text-embedding-ada-002')
   df['similarities'] = df.code_embedding.apply(lambda x: cosine_similarity(x, embedding))

   res = df.sort_values('similarities', ascending=False).head(n)
   return res
res = search_functions(df, 'Completions API tests', n=3)

Because shorter distances between embedding vectors represent greater similarity, embeddings can be useful for recommendation.

Below, we illustrate a basic recommender. It takes in a list of strings and one 'source' string, computes their embeddings, and then returns a ranking of the strings, ranked from most similar to least similar. As a concrete example, the linked notebook below applies a version of this function to the AG news dataset (sampled down to 2,000 news article descriptions) to return the top 5 most similar articles to any given source article.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
def recommendations_from_strings(
   strings: List[str],
   index_of_source_string: int,
   model="text-embedding-ada-002",
) -> List[int]:
   """Return nearest neighbors of a given string."""

   # get embeddings for all strings
   embeddings = [embedding_from_string(string, model=model) for string in strings]

   # get the embedding of the source string
   query_embedding = embeddings[index_of_source_string]

   # get distances between the source embedding and other embeddings (function from embeddings_utils.py)
   distances = distances_from_embeddings(query_embedding, embeddings, distance_metric="cosine")

   # get indices of nearest neighbors (function from embeddings_utils.py)
   indices_of_nearest_neighbors = indices_of_nearest_neighbors_from_distances(distances)
   return indices_of_nearest_neighbors