Hey @ruby_coder @debreuil
Here is the code I wrote to do this. Hope it helps.
import numpy as np
import sklearn.decomposition
import pickle
import time
# Apply 'Algorithm 1' to the ada-002 embeddings to make them isotropic, taken from the paper:
# ALL-BUT-THE-TOP: SIMPLE AND EFFECTIVE POST- PROCESSING FOR WORD REPRESENTATIONS
# Jiaqi Mu, Pramod Viswanath
# This uses Principal Component Analysis (PCA) to 'evenly distribute' the embedding vectors (make them isotropic)
# For more information on PCA, see https://jamesmccaffrey.wordpress.com/2021/07/16/computing-pca-using-numpy-without-scikit/
# get the file pointer of the pickle containing the embeddings
fp = open('/path/to/your/data/Embedding-Latest.pkl', 'rb')
# the embedding data here is a dict consisting of key / value pairs
# the key is the hash of the message (SHA3-256), the value is the embedding from ada-002 (array of dimension 1536)
# the hash can be used to lookup the orignal text in a database
E = pickle.load(fp) # load the data into memory
# seperate the keys (hashes) and values (embeddings) into seperate vectors
K = list(E.keys()) # vector of all the hash values
X = np.array(list(E.values())) # vector of all the embeddings, converted to numpy arrays
# list the total number of embeddings
# this can be truncated if there are too many embeddings to do PCA on
print(f"Total number of embeddings: {len(X)}")
# get dimension of embeddings, used later
Dim = len(X[0])
# flash out the first few embeddings
print("First two embeddings are: ")
print(X[0])
print(f"First embedding length: {len(X[0])}")
print(X[1])
print(f"Second embedding length: {len(X[1])}")
# compute the mean of all the embeddings, and flash the result
mu = np.mean(X, axis=0) # same as mu in paper
print(f"Mean embedding vector: {mu}")
print(f"Mean embedding vector length: {len(mu)}")
# subtract the mean vector from each embedding vector ... vectorized in numpy
X_tilde = X - mu # same as v_tilde(w) in paper
# do the heavy lifting of extracting the principal components
# note that this is a function of the embeddings you currently have here, and this set may grow over time
# therefore the PCA basis vectors may change over time, and your final isotropic embeddings may drift over time
# but the drift should stabilize after you have extracted enough embedding data to characterize the nature of the embedding engine
print(f"Performing PCA on the normalized embeddings ...")
pca = sklearn.decomposition.PCA() # new object
TICK = time.time() # start timer
pca.fit(X_tilde) # do the heavy lifting!
TOCK = time.time() # end timer
DELTA = TOCK - TICK
print(f"PCA finished in {DELTA} seconds ...")
# dimensional reduction stage (the only hyperparameter)
# pick max dimension of PCA components to express embddings
# in general this is some integer less than or equal to the dimension of your embeddings
# it could be set as a high percentile, say 95th percentile of pca.explained_variance_ratio_
# but just hardcoding a constant here
D = 15 # hyperparameter on dimension (out of 1536 for ada-002), paper recommeds D = Dim/100
# form the set of v_prime(w), which is the final embedding
# this could be vectorized in numpy to speed it up, but coding it directly here in a double for-loop to avoid errors and to be transparent
E_prime = dict() # output dict of the new embeddings
N = len(X_tilde)
N10 = round(N/10)
U = pca.components_ # set of PCA basis vectors, sorted by most significant to least significant
print(f"Shape of full set of PCA componenents {U.shape}")
U = U[0:D,:] # take the top D dimensions (or take them all if D is the size of the embedding vector)
# U = U[D:,:] # take All But The Top!
print(f"Shape of downselected PCA componenents {U.shape}")
for ii in range(N):
v_tilde = X_tilde[ii]
v = X[ii]
v_projection = np.zeros(Dim) # start to build the projection
# project the original embedding onto the PCA basis vectors, use only first D dimensions
for jj in range(D):
u_jj = U[jj,:] # vector
v_jj = np.dot(u_jj,v) # scaler
v_projection += v_jj*u_jj # vector
v_prime = v_tilde - v_projection # final embedding vector
v_prime = v_prime/np.linalg.norm(v_prime) # create unit vector
E_prime[K[ii]] = v_prime
if (ii%N10 == 0) or (ii == N-1):
print(f"Finished with {ii+1} embeddings out of {N} ({round(100*ii/N)}% done)")
# save as new pickle
print("Saving new pickle ...")
embeddingName = '/path/to/your/data/Embedding-Latest-Isotropic.pkl'
with open(embeddingName, 'wb') as f: # Python 3: open(..., 'wb')
pickle.dump([E_prime,mu,U], f)
print(embeddingName)
print("Done!")
# When working with live data with a new embedding from ada-002, be sure to tranform it first with this function before comparing it
#
# def projectEmbedding(v,mu,U):
# v = np.array(v)
# v_tilde = v - mu
# v_projection = np.zeros(len(v)) # start to build the projection
# # project the original embedding onto the PCA basis vectors, use only first D dimensions
# for u in U:
# v_jj = np.dot(u,v) # scaler
# v_projection += v_jj*u # vector
# v_prime = v_tilde - v_projection # final embedding vector
# v_prime = v_prime/np.linalg.norm(v_prime) # create unit vector
# return v_prime