Framework description and usage

The code was developed with the help of Andrey Zhitnikov and is under the responsibility of Gregory Naisat. Please send all questions, inqueries and bug reports to me at: [email protected]

Anonymized version

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Requirements

Python 3.5, Tensorflow, Julia 0.64, Eirene topological data analysis package

(once Julia and Eirene are installed, update ./julia_include/include_eirene_run.jl with the path to local Eirene installation, and update ./transformers/excel_to_betti_feeder_parallel.py with the path to Julia executable)

Training a model

• Use compute.py running train_2_excel_2D pipeline for two dimensional data sets and train_2_excel_3D for three dimensional data sets.
• Specify which data set to use (D-I circles_type_8, D-II rings_9, D-III spheres_9) and what architecture to train (i.e. size of the network and the activation type e.g. 10u_by_15, Relu)
• Set the number of training epochs and learning rate
• Set the overall number of trials and frequency of log reports

For each successful training attempt (perfect classification of the data set) log file (/data/<dataset-type>/<architecture>/good_results.txt) is updated and the resulting model and output of each layer are saved in a new folder whose name is the current date and time (/data/<dataset-type>/<architecture>/<activation-type>/<current-data-time>) and whose location reflects the selected data set and the selected architecture. Betti numbers calculation pipeline will use good_results.txt log file to accesse stored models to run betti numbers calculation on their outputs.

Example:

Train on D-II data set. Using network of size 10 (layers) by 25 (neurons each), and LeakyRelu activation. Set 0.2 learning rate and run 12000 training epochs, with 80 trials, report progress every 1000 epochs:

computer.py --pipeline_name train_2_excel_3D --output ./data/rings_9/ --input-tf-dataset ./data/rings_9/rings_9.tfrecords --model 10_by_25 --activation_type LeakyRelu --trials 80 --learning_rate 0.02 --training_epochs 12000 --summary_freq 1000

Calculate Betti numbers

• Once a few well trained neural networks have been accumulated use compute.py running texcel_2_betti pipeline to compute Betti numbers

• Calculated Betti numbers for successfully trained neural networks with given architecture and activation type. Split the calculation in parallel on 10 cores. Each core limited to 10 Gb memory.

• Run computer.py with appropriately set parameters: number of neighbors for nearest neighbor graph construction ( the scale at wich to build Vietoris-Rips complex is fixed in Eirene call at ./julia_include/julia_aux2.

Example:

Calculate Betti numbers for networks trained on D-II dataset of size 10 (layers) by 25 (neurons each) with Leaky Relu activation. The calculations proceed on a subsample of the data set, which is one fouth of the original data set size. Compute Betti numbers zero and one for class A (cat2):

computer.py --pipeline_name excel_2_betti --output ./data/rings_9/ --input-tf-dataset ./data/rings_9/rings_9.tfrecords --model 10_by_25 --activation_type LeakyRelu --trials 80 --cat2 --divisor 4 --neighbors 35 --betti_max 1 --read_excel_from LeakyRelu

Visualize Data set

• Run computer.py with appropriate pipeline (currently there one basic pipeline to run all the visualisation visualize_tfrecords_dataset.py, the pipeline draw 2d projection of the dataset. Example of a call:

computer.py --pipeline
visualize_tfrecords_dataset
--input-tf-dataset
./data/spheres_9/spheres_9.tfrecords
--output-plots-folder
./data/plots/

)

• Check generated .html file with plotly data set plot.

Trials (updated July 21, 2020):

Simulation results are gradually uploaded into google drive