I'm starting out with GANs and I am training a DC-GAN on MNIST dataset. The two metrics that are used to evaluate GANs are Inception Score (IS) and Frechet Inception Distance (FID). Since Inception network is not trained to classify MNIST digits, I built a simple MNIST classifier and I'm using that. Inception score, I'm getting pretty decent values. For FID, I'm using the output of last Fully Connected Layer as feature vector. But, I'm getting values in the order of $10^6$, which doesn't look right. So, I have a few questions

  1. Does it make sense to compute FID for MNIST GAN?
  2. Is the value in the order of $10^6$ correct?
  3. How many images from real dataset should be used while computing FID
  4. Is my code below correct? I used the code provided by original authors and modified it according to my requirements.

If you can answer any of these questions, even partially, that would be of immense help to me. Thanks!

Code: FidScore.py

import warnings

import numpy
from keras.datasets import mnist
from keras.models import Model
from scipy import linalg

from DcGanBaseModel import DcGanBaseModel
from MnistClassifierModel06 import MnistClassifier06
from mnist.MnistModel02 import MnistModel02

class FrechetInceptionDistance:

    def __init__(self, real_activations: numpy.ndarray, verbose=False) -> None:
        self.real_activations = real_activations
        self.verbose = verbose

        self.real_mu = numpy.mean(real_activations, axis=0)
        self.real_sigma = numpy.cov(real_activations, rowvar=False)

    def compute_fid(self, fake_activations: numpy.ndarray):
        fake_mu = numpy.mean(fake_activations, axis=0)
        fake_sigma = numpy.cov(fake_activations, rowvar=False)
        fid = self.calculate_frechet_distance(fake_mu, fake_sigma, self.real_mu, self.real_sigma)
        return fid

    def calculate_frechet_distance(mu1, sigma1, mu2, sigma2, eps=1e-6):
        Numpy implementation of the Frechet Distance.
        The Frechet distance between two multivariate Gaussians X_1 ~ N(mu_1, C_1)
        and X_2 ~ N(mu_2, C_2) is
                d^2 = ||mu_1 - mu_2||^2 + Tr(C_1 + C_2 - 2*sqrt(C_1*C_2)).
        Stable version by Dougal J. Sutherland.
        -- mu1 : Numpy array containing the activations of the pool_3 layer of the
                 inception net ( like returned by the function 'get_predictions')
                 for generated samples.
        -- mu2   : The sample mean over activations of the pool_3 layer, precalcualted
                   on an representive data set.
        -- sigma1: The covariance matrix over activations of the pool_3 layer for
                   generated samples.
        -- sigma2: The covariance matrix over activations of the pool_3 layer,
                   precalcualted on an representive data set.
        --   : The Frechet Distance.

        mu1 = numpy.atleast_1d(mu1)
        mu2 = numpy.atleast_1d(mu2)

        sigma1 = numpy.atleast_2d(sigma1)
        sigma2 = numpy.atleast_2d(sigma2)

        assert mu1.shape == mu2.shape, "Training and test mean vectors have different lengths"
        assert sigma1.shape == sigma2.shape, "Training and test covariances have different dimensions"

        diff = mu1 - mu2

        # product might be almost singular
        covmean, _ = linalg.sqrtm(sigma1.dot(sigma2), disp=False)
        if not numpy.isfinite(covmean).all():
            msg = "fid calculation produces singular product; adding %s to diagonal of cov estimates" % eps
            offset = numpy.eye(sigma1.shape[0]) * eps
            covmean = linalg.sqrtm((sigma1 + offset).dot(sigma2 + offset))

        # numerical error might give slight imaginary component
        if numpy.iscomplexobj(covmean):
            if not numpy.allclose(numpy.diagonal(covmean).imag, 0, atol=1e-3):
                m = numpy.max(numpy.abs(covmean.imag))
                raise ValueError("Imaginary component {}".format(m))
            covmean = covmean.real

        tr_covmean = numpy.trace(covmean)

        return diff.dot(diff) + numpy.trace(sigma1) + numpy.trace(sigma2) - 2 * tr_covmean

def compute_fid_score_for_gan(gan_model: DcGanBaseModel, classifier_model, layer_name, num_classes):
    # Define Feature Extracter
    feature_layer = Model(inputs=classifier_model.model.input,

    # Compute Features for MNIST Dataset Images
    (x_train, _), _ = mnist.load_data()
    x_train = x_train.reshape(x_train.shape[0], x_train.shape[1], x_train.shape[2], 1)
    real_features = feature_layer.predict(x_train)
    fid = FrechetInceptionDistance(real_features, verbose=True)

    num_images = num_classes * 1000
    gen_images = gan_model.generate_images(num_images)
    fake_features = feature_layer.predict(gen_images)

    fid_score = fid.compute_fid(fake_features)
    return fid_score

def demo1():
    gan_model = MnistModel02(print_model_summary=False)
    classifier_model = MnistClassifier06().load_model(
    fid_score = compute_fid_score_for_gan(gan_model, classifier_model, 'dense_1', 10)

if __name__ == '__main__':


import math
import numpy
from keras import Sequential
from keras.engine.saving import load_model, model_from_json
from keras.layers import Convolution2D, Dense, Dropout, Flatten, MaxPooling2D

from MnistClassifierModelBase import MnistClassifier

class MnistClassifier06(MnistClassifier):
    def __init__(self, verbose: bool = False):
        self.model = None
        self.verbose = verbose

    def build_model(self):
        self.model = Sequential()
        self.model.add(Convolution2D(32, (3, 3), activation='relu', input_shape=(28, 28, 1)))
        self.model.add(Convolution2D(32, (3, 3), activation='relu'))
        self.model.add(MaxPooling2D(pool_size=(2, 2)))

        self.model.add(Dense(128, activation='relu'))
        self.model.add(Dense(10, activation='softmax'))


    def compile_model(self):
        self.model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])

    def fit(self, x, y, batch_size=32, epochs=30):
        history = self.model.fit(x, y, batch_size, epochs)
        return history.history['loss'], history.history['acc']

    def train_on_batch(self, x: numpy.ndarray, y: numpy.ndarray, batch_size=32):
        num_samples = x.shape[0]
        if num_samples % batch_size != 0:
            raise RuntimeWarning('Batch size does not divide number of samples exactly. '
                                 'Last set of samples will not be used for training')
        loss, accuracy = [], []
        self.verbose_log('iteration, loss, accuracy')
        for i in range(int(math.floor(num_samples / batch_size))):
            data = x[i * batch_size:(i + 1) * batch_size, :, :]
            labels = y[i * batch_size:(i + 1) * batch_size]
            batch_loss, batch_accuracy = self.model.train_on_batch(data, labels)
            self.verbose_log('{0:04},{1:2.4f},{2:0.4f}\n'.format(i + 1, batch_loss, batch_accuracy))
        return loss, accuracy

    def evaluate(self, x, y):
        score = self.model.evaluate(x, y)
        return score[0], score[1]

    def classify(self, x):
        y = self.model.predict(x)
        return y

    def save_model(self, save_path):

    def save_model_data(self, json_path, weights_path):
        with open(json_path, 'w') as json_file:

    def load_model(model_path) -> MnistClassifier:
        model = load_model(model_path)
        classifier = MnistClassifier06()
        classifier.model = model
        return classifier

    def load_model_from_data(json_path, weights_path) -> MnistClassifier:
        with open(json_path, 'r') as json_file:
            model = model_from_json(json_file.read())
        classifier = MnistClassifier06()
        classifier.model = model
        return classifier
  • $\begingroup$ Hi, I am facing same issue. For order of 10^6, I had to put L2 regularization during training the model used for regularization. After L2 regularization, the FID dropped to values of 3k however this change is not good enough for comparing results with other GAN. P.S. Did you found anything that helped after you asked this question? $\endgroup$ – saurabheights Dec 27 '19 at 16:48
  • $\begingroup$ For number of Images, 10K should do. $\endgroup$ – saurabheights Dec 27 '19 at 16:50
  • $\begingroup$ Note that I am using custom classifier to get 64 convolution maps and using average pooling to get 64-D feature vector. As of now, the only thing I can think of is resizing MNIST and passing through inception network as original FID, to get similar score. Just might work. $\endgroup$ – saurabheights Dec 27 '19 at 16:52
  • 1
    $\begingroup$ No worries and I will add info on this. Have to get this done, hope either inception or autoencoder works $\endgroup$ – saurabheights Dec 28 '19 at 13:02
  • 1
    $\begingroup$ Hi, I posted answer to your stackoverflow question, as it already had one answer there. stackoverflow.com/questions/57183647/… $\endgroup$ – saurabheights Jan 6 at 18:14

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