redundancy in TT-rank

[ShHsLin]

I might be wrong here. But isn't it the case that the tt-rank do not need to grow more than the smaller dimension of the matrixization dimension?

But as in the implementation of ultimate tensorization,

    layers.append(tensornet.layers.tt(tf.reshape(layers[-1], [-1, sz]),
                                      np.array([8, 8, 8, 16], dtype=np.int32),
                                      np.array([4, 6, 8, 8], dtype=np.int32),
                                      np.array([1, 40, 40, 40, 1], dtype=np.int32),
                                      biases_initializer=None,
                                      cpu_variables=cpu_variables, scope='tt4.1'))

I think it is actually enough to have tt_rank as [1,32,40,40,1] instead?
It is also the case in the conv layer, for example,

    layers.append(tensornet.layers.tt_conv_full(layers[-1],
                                                [3, 3],
                                                np.array([4,8,4],dtype=np.int32),
                                                np.array([4,8,4],dtype=np.int32),
                                                np.array([16,16,16,1],dtype=np.int32),
                                                [1, 1],
                                                cpu_variables=cpu_variables,
                                                biases_initializer=None, scope='tt_conv3.2'))

since the window size is 3x3, the tt-rank [9,16,16,1] would be enough.

As a result, the compression ratio could be a little bit better, if this were the original implementation for the paper?