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Training accuracy and validation accuracy gives nearly 0.87, but in testing part using evaluate() function gives fluctuated results according to different batch_size parameter values. Testing accuracy varies from 0.5 to 0.66. Is the optimum batch_size value for evaluate has to be same as in fit()?

0x01h
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I don't see how the batch size parameter of the evaluate function can change the accuracy of your model. Only the batch size used during the training can modify the performances of your model (see this). Are you testing the same trained model for your different tests? If you're testing newly trained models every time, it explains the variation of accuracy you observe (because of the random initialization of the weights for example).