BayesianTN

Bayesian tensor network (see https://arxiv.org/abs/1912.12923)

The code has been published on Code Ocean:
Shi-Ju Ran (2020) Bayesian Tensor Network [Source Code]. https://doi.org/10.24433/CO.2518845.v1
DOI: 10.24433/CO.2518845.v1

To use this code, you may need to install: numpy, torch, termcolor, open-cv, matplotlib, and etc. The code (in the subfolder "pytorch_gpu_memory") to watch the status of GPU was downloaded from https://github.com/darr/pytorch_gpu_memory.

The raw data of the curves shown in the arXiv was put in the subfolder "raw_data". Please open it by Origin.

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Update log:

• 2020-01-17: Scripts to run BTN1 and BTN2 to reproduce the results in the paper added;
• 2020-01-04: new layers (2xto1, 2yto1) added;
• 2020-01-04: New BTN added (see BTN2 in the arXiv paper)

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At the beginning:

Bayesian tensor network (BTN) is to efficiently represent the conditional probabilities of multiple sets of events with polynomial complexity. I have only used it for image classification. BTN should be more powerful when the number of events or sets of events is large, where the traditional Bayesian networks cannot efficiently work. It would be nice to hear any discussions and ideas :)

How to build a Bayesian TN (BTN)?

You may find an example of a BTN in the file "BayesTN.py".

In the class "VL_Bayes_sum1_Vsoftmax_TN_BP", you can find the BTN with a simple tree structure (same as the arXiv paper) for MNIST and fashion-MNIST datasets.

I will explain some more details later below.

How to use a BTN?

Note: to reproduce the results of BTN1 and BTN2 in the paper, run "RunBTN1.py" and "RunBTN2.py" respectively. To try Adam, run "RunBTN1adam.py"

The optimization algorithm can be found as the function "tn_multi_classifier_bp_mnist" in "TNN algorithms.py".

You may refer to "RunTTN.py" to see how to use a built BTN.Let me explain this file in some details.

import CollectedTNN as ctnn
from TNNalgorithms import tn_multi_classifier_bp_mnist as mps_bp

# import the default parameters of BTN
from BayesTN import Paras_VL_Bayes_sum1_Vsoftmax_TN
# Set all default parameters
para = Paras_VL_Bayes_sum1_Vsoftmax_TN()

# Change the parameters as you want
para['d'] = 2  # dimension of the root sets
para['chi'] = 2  # dimension of the hidden sets
para['dataset'] = 'fashion-mnist'  # 'mnist' or 'fashion-mnist'
para['batch_size'] = 2000  # batch size
para['lr'] = 1e-3  # learning rate

mps_bp(para)  # call the optimization algorithm

All default parameters can be found in function "parameter_tn_bp_mnist" in "TNNalgorithms.py"

Layers of BTN

All layers can be mixedly used with the layers in torch.nn.

The modules for the layers in BTN can be found in "TNNalgorithms.py", particularly the classes "TTN_Pool_2by2to1", "TTN_Pool_2xto1", "TTN_Pool_2yto1" that are used in the arXiv paper.

You may find many other kinds of layers in the file, which were not mentioned in the arXiv paper. They are for testing ideas.

The "TTN_Pool_2by2to1" layer

This layer maps the probability distributions of (Lx * Ly) sets to that of (Lx/2 * Ly/2) sets. If Lx or Ly is odd, the last row or column will be copied to make it even.

Input:

• input.shape = (num_samples, channels, sx, sy), if the ndimension of the input is 4

• input.shape = (num_samples, channels, d, sx, sy), if the ndimension of the input is 5

• Note:
  num_samples: number of samples
  channels: number of channels
  sx: number of rows of the sets (data)
  sy: number of columns of the sets (data)
  d: dimension of each set

Parameters:

• c_in: the number of input channels; int

• c_out: the number of output channels; int

• nx: the number of rows of the tensors in the layer; int

• ny: the number of columns of the tensors in the layer; int

• din: the dimension of the in-going indexes; int

• dout: the dimension of the out-going indexes; int

• device: cpu or cuda; default is to priority choose cuda (GPU) if available

• dtype: data type; default is torch.float32

• ini_way: the way to initialize the tensors

• out_dims: the ndimension of the output data

• simple_chl: whether to use simple way to deal with the channel. If simple_chl==True, one should take c_in=c_out

• if_pre_proc_T: if pre-process the tensors

• add_bias: if add bias

Output:

• if out_dims = 4, output.shape = (num_samples, c_out*d, sx, sy)

• if out_dims = 5, output.shape = (num_samples, c_out, d, sx, sy)

To realize the simple tree BTN1 in the arXiv paper, we take:

• c_in = c_out = 1

• ini_way = 'randn'

• out_dims = 5

• if_pre_proc_T = 'square' (to realize the rotation optimization proposed in the arXiv)

• add_bias = False

More instructions are to be added :)

As you can see, I am a researcher in quantum physics, and not so good at programming. Therefore, the code is a little bit chaotic. You are welcome and appreciated to modify and/or use this code. If you think this code helps, please kindly cite the arXiv paper. Thanks a lot for your interest.

Cheers,

Shi-Ju Ran

sjran@cnu.edu.cn
Associate professor
Department of Physics
Capital Normal University
Beijing, 100048 China