You should try setting the seed of the randomness generator in Tensorflow to a fixed, arbitrary value at the beginning of your experiment. This way, running the initialization will generate the same results all the time:
tf.set_random_seed(42)
# Initialize weights the standard way! (just define tf.keras layers or similar)
Optionally (if you're defining layers at a lower level) you could set individual seeds for each weight generation
W = tf.Variable(tf.truncated_normal(((10,10)), stddev=0.1, seed=42))
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