Unsupervised End-to-End Training with a Self-defined Target

In this work, we introduce a 'self-defined target' at the network's last layer to realize unsupervised end-to-end training. This target is defined by Winner-Take-All (WTA) selectivity combined with homeostasis mechanism. We calculate the unsupervised global mean square error (MSE) loss, which is the difference between the network's output and our unsupervisedly defined target, and update the weight with the gradient-descent based algorithms.

This approach, framework-agnostic and compatible with both global and local learning rules, in our case, Backpropation (BP) and Equilibrium propagation (EP) seperately, achieves a 97.6% test accuracy on the MNIST dataset. We also train a CNN using our unsupervised method (with BP only), achieving test accuracies of 99.2% on MNIST, 90.3% on Fashion-MNIST, and 81.5% on the SVHN dataset. Extending to semi-supervised learning, our method dynamically adjusts the target according to data availability, reaching a 96.6% accuracy with just 600 labeled MNIST samples.

In unsupervised training:

• We train two distinct network architectures using our unsupervised learning framework: a one-layer network (784-2000) and two-layer network (784-2000-2000);
• We train a convolutional network (32f5-128f3-3000) using our unsupervised target, with weight updates performed using backpropagation.
• The final accuracy of the trained network is obtained through two different classification method: direct association and linear classifier.

In semi-supervised training:

• We keep the same architecture used by Lee, 2013, which is a 784-5000-10 muti-layer perceptron;
• We test the performance in five scenarios with different amounts of available labeled data: 100, 300, 600, 1000, 3000 randomly selected labelled mnist samples.

Getting Started

Prerequisites

python >= 3.8
pytorch version 2.2.1
cuda 12.1 (if you use GPU to accelerate)

Installing

Clone the repository:
git clone https://github.com/yourusername/projectname.git

Packages for training:

skit-learn: pip install -U scikit-learn
Image: pip install image
Optuna: pip install optuna
pandas: pip install pandas

Packages for plotting:

jupyter notebook: pip install notebook
matplotlib: pip install matplotlib
seaborn: pip install seaborn
For plotting the Fig.3, brokenaxes package should be installed:
pip install brokenaxes

For plotting the Fig.8, UMAP package should be installed:
pip install umap-learn

File organization

• bp/: code of the backpropagation training.
• ep/: code of the equilibrium propagation training.
• funcs/: common functions shared by bp and ep training.
• configFile/: config files.
• simuResults/: our trained simulation result files.
• figuresPlot/: plotted figures in the article.
• reproduce_figures.ipynb: jupyter file to reproduce the figures.

The following two folders will be generated after the training :

• data/: data used for training.
• DATA-0/: training results.

Training

Parameters explanation

Parameters defined in config.json.

Name	Description	Examples
device	Execution device: CPU (-1) or GPU (device number).	-1, 0, 1
dataset	Dataset for training.	"mnist", "fashionMnist", "cifar10"
n_class	Number of dataset classes.	10
action	Training type: BP or EP, supporting various modes.	BP: "bp", "unsupervised_bp", "semi_supervised_bp"; EP: "ep", "unsupervised_ep", "semi_supervised_ep"
epochs	Total training epochs.	200
batchSize	Mini batch size for training; set to 1 for unsupervised sequential mode.	256
test_batchSize	Mini batch size for testing.	512
cnn	Whether use a convolutional network.	false, true
fcLayers	Architecture of fully connected layers (input, hidden, output).	[784, 2000, 2000]
lr	Layer-specific learning rates.	[0.5, 0.3]
activation_function	Layer-specific activation in BP; identical across all EP layers.	BP: ["x", "relu", "hardsigm"]; EP: "hardsigm"
optimizer	Optimizer for training, specifying the unsupervised optimizer in semi-supervised setups.	"Adam", "SGD"
loss	Loss function.	"MSE", "Cross-entropy"
eta	Exponential moving average parameter for unsupervised stochastic mode.	0.6
gamma	Coefficient for homeostasis in unsupervised training.	0.5
nudge	Number of winners in unsupervised target (k-WTA).	3
smooth	Enable label smoothing.	true, false
dropProb	Dropout probability per layer; 0 disables dropout.	[0.2, 0.2, 0.2]
semi_seed	Method to separate labeled/unlabeled data in semi-supervised learning (-1 for random, positive for seed number).	-1, 13
train_label_number	Labeled data count in semi-supervised learning.	100, 300, 600, 1000, 3000
pre_epochs	Pre-training epochs (N1) for semi-supervised learning.	80
pre_batchSize	Mini batch size for pre-training in semi-supervised learning.	32
pre_lr	Learning rate for pre-training in semi-supervised learning.	[0.001, 0.003]
class_label_percentage	Label percentage for class association in unsupervised training.	0.01
class_activation	Activation function for added linear classifier.	"x"
class_lr	Learning rate for linear classifier.	[0.1]
class_epoch	Training epochs for linear classifier.	50
class_optimizer	Optimizer for linear classifier training.	"Adam"
class_dropProb	Dropout probability at classifier input; 0 disables dropout.	0.4
class smooth	Enable label smoothing for classifier training.	true, false

Some parameters especially used in EP training:

Name	Description	Examples
dt	Discretization time interval.	0.2
T	Free phase duration, measured in time steps.	60
Kmax	Nudging phase duration, in time steps.	10
beta	Nudging coefficient, within the range [0, 1].	0.5
clamped	Restrict neuron values to the range [0, 1].	true, false
error_estimate	Error estimation strategy: either single-phase or symmetric two-phase.	one-sided, symmetric
dropout	Enable dropout regularization.	true, false

Commands

The commands should be executed at the same level as the README file in bash script.

Unsupervised BP

Train a one-layer network:
python -m bp.main --json_path "./configFile/unsupervised_bp/1layer"
Train a two-layer network:
python -m bp.main --json_path "./configFile/unsupervised_bp/2layer"
Train a CNN for MNIST dataset:
python -m bp.main --json_path "./configFile/unsupervised_bp/cnn/mnist"
Train a CNN for Fashion-MNIST dataset:
python -m bp.main --json_path "./configFile/unsupervised_bp/cnn/fashionMnist"
Train a CNN for SVHN dataset:
python -m bp.main --json_path "./configFile/unsupervised_bp/cnn/svhn"
Train a CNN for CIFAR-10 dataset:
python -m bp.main --json_path "./configFile/unsupervised_bp/cnn/cifar10"

Unsupervised EP

Train a one-layer network:
python -m ep.main --json_path "./configFile/unsupervised_ep/1layer"
Train a two-layer network:
python -m ep.main --json_path "./configFile/unsupervised_ep/2layer"

Semi-supervised BP

Different configuration files are used for various labeled number scenarios.
python -m bp.main --json_path "./configFile/semi_bp/100"
python -m bp.main --json_path "./configFile/semi_bp/300"
python -m bp.main --json_path "./configFile/semi_bp/600"
python -m bp.main --json_path "./configFile/semi_bp/1000"
python -m bp.main --json_path "./configFile/semi_bp/3000"

Semi-supervised EP

Different configuration files are used for various labeled number scenarios.
python -m ep.main --json_path "./configFile/semi_ep/100"
python -m ep.main --json_path "./configFile/semi_ep/300"
python -m ep.main --json_path "./configFile/semi_ep/600"
python -m ep.main --json_path "./configFile/semi_ep/1000"
python -m ep.main --json_path "./configFile/semi_ep/3000"

Supervised BP

Train a perceptron with 2000 output neurons:
python -m bp.main --json_path "./configFile/supervised_bp/1layer"
Train a MLP with 2000 output neurons:
python -m bp.main --json_path "./configFile/supervised_bp/2layer"

Supervised EP

Train a perceptron with 10 output neurons:
python -m ep.main --json_path './configFile/supervised_ep/1layer"
Train a MLP with 10 output neurons:
python -m ep.main --json_path './configFile/supervised_ep/2layer"

Hyperparameters research

We use the random research offer by optuna to do the hyper-parameters optimization.

Parameters explanation

We list here the parameters defined in optuna_config.json that differ from those in the config.json file.

Name	Description	Examples
mode	Defines how the neural average activity is calculated: in batch or sequentially.	batch, sequential
nudge_max	Sets the upper limit for the number of winners that can be selected.	10

Commands

We take the two-layer network as an example. For alternative network structures, simply modify the network architecture in the pre_config.file.

BP hyperparameters

Supervised learning with a MLP:
python -m bp.optuna_optim --json_path "./configFile/hyper_bp/supervised"
Unsupervised learning with a two-layer network:
python -m bp.optuna_optim --json_path "./configFile/hyper_bp/unsupervised"
Unsupervised learning with a CNN:
python -m bp.optuna_optim --json_path "./configFile/hyper_bp/unsupervised_cnn"
Semi-supervised learning with a MLP (change the train_label_number in pre_config file):
python -m bp.optuna_optim --json_path "./configFile/hyper_bp/semi"
Train the linear classifier on top of a trained unsupervised network:
python -m bp.optuna_optim --json_path "./configFile/hyper_bp/classifier' --trained_path './simuResults/unsupervised_bp_2layer/model"

EP hyperparameters

Supervised learning with a MLP:
python -m ep.optuna_optim --json_path "./configFile/hyper_ep/supervised"
Unsupervised learning with a two-layer network:
python -m ep.optuna_optim --json_path "./configFile/hyper_ep/unsupervised"
Semi-supervised learning with a MLP (change the train_label_number in pre_config file):
python -m ep.optuna_optim --json_path "./configFile/hyper_ep/semi"
Train the linear classifier on top of a trained unsupervised network:
python -m ep.optuna_optim --json_path "./configFile/hyper_ep/classifier' --trained_path './simuResults/unsupervised_ep_2layer/model"

Plotting the figures

We use the reproduce_figures.ipynb to plot all the figures used in the article.