Neural network not converging on clear linearly seperable problem

Question

I am developing a neural network in Keras and I want to test to make sure it works. The feature set is obviously linearly seperable ('A' and 'N' in the below figure) but for some reason when I run my neural network using heart rate variability (HRV in the figure) as the sole feature, it doesn't think the positive training examples ('A' training examples) are unique:

My neural network architecture is a simple one:

model = Sequential()

model.add(Dense(10, input_shape=(None, X_train.shape[1]),
           activation='sigmoid'))

model.add(Dense(10, activation='sigmoid'))

model.add(Dense(1, activation='sigmoid'))

opt = tf.keras.optimizers.Adam(lr=learning_rate, decay=decay_rate)

model.compile(loss=loss_fn, optimizer=opt, metrics=['acc'])

model.fit(X_train, y_train, epochs=n_epochs, validation_data=(X_test, y_test))

When I test the accuracy using a confusion matrix, the NN overfits to the negative training examples:

          precision    recall  f1-score   support

     0.0       0.72      1.00      0.84     20774
     1.0       0.00      0.00      0.00      8126

accuracy                           0.72     28900
macro avg       0.36      0.50      0.42     28900
weighted avg       0.52      0.72      0.60     28900

Any suggestions?

Edit: Additional hyperparamters

Training vector shape:(67432, 1, 1)
Example of first element:[[72.710655]

loss_fn = 'binary_crossentropy'
learning_rate = 1e-2
decay_rate = 1e-8
n_epochs = 10 (have varied this but still converges to negative training example)

Edit: Additional information

I wanted to include how I formatting my arrays in case the issue is with that:

X_train = np.asarray(X_train).reshape(
    X_train.shape[0], 1, X_train.shape[1])

X_test = np.asarray(X_test).reshape(
    X_test.shape[0], 1, X_test.shape[1])

Answer 1

Since you have imbalanced data you may want to use class_weight in model.fit

model.fit(X_train, y_train, epochs=n_epochs, validation_data=(X_test, y_test), class_weight=class_weight)

Here class_weight is a dictionary. One option you can try is to set the class weight inversely proportional to the class size, ie the number of data points of each class.