def _createDense(self, dtype=core.DataType.FLOAT):
        perfect_model = np.array([2, 6, 5, 0, 1]).astype(np.float32)
        np.random.seed(123)  # make test deterministic
        numpy_dtype = np.float32 if dtype == core.DataType.FLOAT else np.float16
        initializer = Initializer if dtype == core.DataType.FLOAT else pFP16Initializer
        data = np.random.randint(2,
                                 size=(20,
                                       perfect_model.size)).astype(numpy_dtype)
        label = np.dot(data, perfect_model)[:, np.newaxis]

        model = ModelHelper(name="test", arg_scope={'order': 'NCHW'})
        out = brew.fc(model,
                      'data',
                      'fc',
                      perfect_model.size,
                      1, ('ConstantFill', {}), ('ConstantFill', {}),
                      axis=0,
                      WeightInitializer=initializer,
                      BiasInitializer=initializer)
        if dtype == core.DataType.FLOAT16:
            out = model.HalfToFloat(out, out + "_fp32")
        sq = model.SquaredL2Distance([out, 'label'])
        loss = model.AveragedLoss(sq, "avg_loss")
        grad_map = model.AddGradientOperators([loss])
        self.assertIsInstance(grad_map['fc_w'], core.BlobReference)
        return (model, perfect_model, data, label)