Training an Ising Machine with Equilibrium Propagation

This repository contains the code to reproduce the results of the paper "Training an Ising Machine with Equilibrium Propagation".

The project contains the following folder:

• MLP/QA-SA: contain the code to train the fully-connected neural network with an Ising machine (the D-Wave Ising machine or with Simulated annealing - /!\ the D-Wave Ising machine requires the user to have acces to the machine)

• MLP/Deterministic: contain the code to train the fully-connected neural network with a deterministic dynamics (with binary neurons and real-value weights)

• Conv/QA-SA: contain the code to train the small convolutional neural network with an Ising machine (the D-Wave Ising machine or with Simulated annealing - /!\ the D-Wave Ising machine requires the user to have acces to the machine)

Training the fully-connected architecture with an Ising machine (D-Wave, Simulated annealing)

The code for training the convolutional architecture can be found in the folder ./MLP/QA-SA.

Details about main.py

The parser accepts the following arguments:

• Hardware settings:

Arguments	Description	Example
simulated	0 if the D-Wave Ising machine is used (need access to the D-Wave Ising machine) - 1 if the Simulated annealing sampler is used	--simulated 0

• Architecture settings:

Arguments	Description	Example
layersList	Number of neurons in the output layer	--layerList 784 120 40
expand_output	How much we duplicate the output neurons (required for nudging a binary system)	--expand_output 2

• EqProp settings:

Arguments	Description	Example
mode	Type of Ising problem to be submitted to the Ising machine - ising= {+/- 1 spins}, qubo: {0/1 spins}	--mode ising
beta	Nudging parameter	-beta 5
n_iter_free	Number of iterations for the free phase on a single data point	--n_iter_free 10
n_iter_nudge	Number of iterations for the nudge phase on a single data point	--n_iter_nudge 10
frac_anneal_nudge	Fraction of system non-annealed during the second phase	--frac_anneal_nudge 0.25

• Training settings:

Arguments	Description	Example
dataset	Dataset used to train the network	--dataset mnist
N_data	Number of training images (for MNIST dataset)	--N_data mnist
N_data_test	Number of testing images (for MNIST dataset)	--N_data_test mnist
lrW0	Learning rate for the weights of the fully-connected layer between the input and the hidden layer	--lrW0 0.01
gain_weight0	Multiplicative gain for initializing the weights of the fully-connected layer between the input and the hidden layer	--gain_weight0 0.5
lrW1	Learning rate for the weights of the fully-connected layer between the hidden and the output layer	--lrW1 0.01
gain_weight1	Multiplicative gain for initializing the weights of the fully-connected layer between the hidden and output layer	--gain_weight1 0.25
lrB0	Learning rate for the biases of the hidden layer	--lrB0 0.001
lrB1	Learning rate for the biases of the output layer	--lrB1 0.001
bias_lim	Maximal absolute value for the biases	--bias_lim 4
batchSize	Batch size (train and test)	--batchSize 1
epochs	Number of epochs	--epochs 20
chain_strength	Value of the coupling in the chain of identical spins	--chain_strength 1
auto_scale	Enable (1) or disable (0) the auto-scale feature	--auto_scale 0
load_model	Create a new model (0) or load (>0) a model already or partially trained to continue the training	--load-model 0

Details about Network.py:

Each file contains a class of a network. Each class inherits from a nn.Module.

Each network has the following built-in functions:

• init: specifies the parameter and the architecture of the network.

• computeLossAcc: compute the loss and if the network predict the good class for the input (accuracy)

• computeGrads: compute the instantaneous gradient for each parameter

• updateParams: update all parameters in the network according to the gradient computed in computeGradient - vanilla SGD

Details about Tools.py:

Each file contains the same functions but adapted for each architecture.

• generate_digits: generate the digits dataset from sklearn.

• generate_mnist: generate the MNIST/X dataset given the number of training and testing images specified in the parser.

• createBQM: translates the neural network architecture into a Ising problem (ie convert the weights into couplings between nodes and biases into individual bias fields)

• train: trains the network over the whole training dataset once. Run the free and nudge phase and update the weights. Track the number of changes in the weights.

• test: tests the network over the whole testing dataset once.

• initDataframe: inits the dataframe where we store the training data.

• updateDataframe: updates the same dataframe after each epoch: update train error, test error, number of changes of weights for each layer.

• createPath: creates the path and the folder where the training data will be stored. Copy the plotFunction.py file in the same folder. Create a folder specific to the training 'S-X' in this general folder.

• saveHyperparameters: creates a .txt file with all hyperparameters in the parser in the folder 'S-X'.

Commands to be run in the terminal to reproduce the results of the paper:

python MLP/QA-SA/main.py --load_model 0 --simulated 1 --dataset mnist -- N_data 1000 --N_data_test 100 --layersList 784 120 40 --expand_output 4 --mode ising --beta 5 --n_iter_free 10 --n_iter_nudge 10 --frac_anneal_nudge 0.25 --lrW0 0.01 --gain_weight0 0.5 --lrW1 0.01 --gain_weight0 0.25 --lrB0 0.001 --lrB1 0.001 --batchSize 1 --epochs 50 --chain_strenght 1 --auto_scale 0

Training the fully-connected architecture with a deterministic dynamics

The code for training the convolutional architecture can be found in the folder ./MLP/Deterministic.

Details about main.py

The parser accepts the following arguments:

• Hardware settings:

Arguments	Description	Example
device	ID (0, 1, ...) of the GPU if provided - -1 for CPU	--device 0

• Architecture settings:

Arguments	Description	Example
layersList	List of fully connected layers in the network	--layerList 784 120 40
expand_output	How much we duplicate the output neurons (required for nudging a binary system)	--expand_output 4

• EqProp settings:

Arguments	Description	Example
activationFun	Activation function used in the network	--activationFun heaviside
T	Number of time steps for the free phase	--T 20
Kmax	Number of time steps for the nudge phase	--Kmax 10
beta	Nudging parameter	--beta 2
gamma_neur	Time step	--gamma_neur 0.5
clamped	Clamp the neurons states (1) or not (0)	--clamped 1
rho_threshold	Offset for the jump of the heaviside function	--rho_threshold 0.5

• Training settings:

Arguments	Description	Example
dataset	Selects which dataset to select to train the network on (mnist or digits)	--dataset mnist
N_data	Number of training images (for MNIST dataset)	--N_data mnist
N_data_test	Number of testing images (for MNIST dataset)	--N_data_test mnist
lrW	List of the learning for the biases	--lrBias 1e-2 1e-2
weightClip	Clamp the weights to an absolute given value	--weightClip 1
lrB	List of the learning for the biases	--lrBias 1e-2 1e-2
biasClip	Clamp the biases to an absolute given value	--biasClip 1
batchSize	Size of training mini-batches	--batchSize 1
test_batchSize	Size of testing mini-batches	--test_batchSize 128
epochs	Number of epochs to train the network	--epochs 50

Details about Network.py:

Each file contains a class of a network. Each class inherits from a nn.Module.

Each network has the following built-in functions:

• init: specifies the parameter and the architecture of the network.

• get_bin_state: return the binary state of a layer given the internal state at each time step

• stepper: compute the update for the neurons state at a specific time step (Euler scheme)

• forward: solve the dynamics of the system for a specific number of time steps (free or nudge phase)

• computeGrads: compute the gradient of the parameters given the two equilibrium states

• updateWeight: update all parameters in the network according to the gradient computed in computeGradient - vanilla SGD

• initHidden: initialize the state of network before each free phase.

Details about Tools.py:

Each file contains the same functions but adapted for each architecture.

• train_bin: trains the network over the whole training dataset once. Run the free and nudge phase and update the weights. Track the number of changes in the weights.

• test_bin: tests the network over the whole testing dataset once.

• initDataframe: inits the dataframe where we store the training data.

• updateDataframe: updates the same dataframe after each epoch: update train error, test error, number of changes of weights for each layer.

• createPath: creates the path and the folder where the training data will be stored. Copy the plotFunction.py file in the same folder. Create a folder specific to the training 'S-X' in this general folder.

• saveHyperparameters: creates a .txt file with all hyperparameters in the parser in the folder 'S-X'.

• generate_digits: generate the digits dataset from sklearn.

• generate_mnist: generate the MNIST/X dataset given the number of training and testing images specified in the parser.

Commands to be run in the terminal to reproduce the results of the paper:

python MLP/Determnistic/main.py --dataset mnist --N_data 1000 --N_data_test 100 --layersList 784 120 40 --expand_output 4 --lrW 0.1 0.1 --weightClip 1 -- --lrB 0.1 0.1 --biasClip 1 --batchSize 1 --test_batchSize 128 --epochs 50 --T 20 --Kmax 10 --beta 2  --activationFun heaviside --gamma_neur 0.5 --clamped 1 --rho_threshold 0.5 --device -1 --

Training the convolutional architecture

The code for training the convolutional architecture can be found in the folder ./Conv/QA-SA.

Details about main.py

The parser accepts the following arguments:

• Hardware settings:

Arguments	Description	Example
simulated	0 if the D-Wave Ising machine is used - 1 if the Simulated annealing sampler is used	--simulated 0

• Architecture settings:

Arguments	Description	Example
layersList	Number of neurons in the output layer	--layerList 4
expand_output	How much we duplicate the output neurons (required for nudging a binary system)	--expand_output 2
convList	List of the conv layers with the numbers of channels specified - the number of channels of the input (1 for the patterns) has to be specified	--convList 4 1
padding	Padding applied for all the convolutions	--padding 0
kernelSize	Size of the kernel used for all the convolutions	--kernelSize 2
Fpool	Size of the pooling kernel	--Fpool 2
pool_coef	Coefficient used for the averaged pooling operation	--pool_coef 0.25

• EqProp settings:

Arguments	Description	Example
mode	Type of Ising problem to be submitted to the Ising machine - ising= {+/- 1 spins}, qubo: {0/1 spins}	--mode ising
beta	Nudging parameter	-beta 5
n_iter_free	Number of iterations for the free phase on a single data point	--n_iter_free 10
n_iter_nudge	Number of iterations for the nudge phase on a single data point	--n_iter_nudge 10
frac_anneal_nudge	Fraction of system non-annealed during the second phase	--frac_anneal_nudge 0.25

• Training settings:

Arguments	Description	Example
dataset	Dataset used to train the network	--dataset patterns
lrWeightsFC	Learning rate for the weights of the fully-connected classifier	-lrWeightsFC 0.1
lrWeightsCONV	Learning rate for the weights of the convolutional layer	--lrWeightsCONV 0.1
lrBiasFC	Learning rate for the biases of the fully-connected classifier	-lrBiasFC 0.1
lrBiasCONV	Learning rate for the biases of the convolutional layer	--lrBiasCONV 0.1
batchSize	Batch size	--batchSize 1
epochs	Number of epochs	--epochs 20
chain_strength	Value of the coupling in the chain of identical spins	--chain_strength 2
auto_scale	Enable (1) or disable (0) the auto-scale feature	--auto_scale 0

Details about Network.py:

Each file contains a class of a network. Each class inherits from a nn.Module.

Each network has the following built-in functions:

• init: specifies the parameter and the architecture of the network.

• sample_to_s: convert the sample obtained with the D-Wave Ising machine or the Simulated annealing sampler to tensors that match the dimension of each layer

• computeLossAcc: compute the loss and if the network predict the good class for the input (accuracy)

• computeGradients: compute the instantaneous gradient for each parameter

• updateParams: update all parameters in the network according to the gradient computed in computeGradient - vanilla SGD

Details about Tools.py:

Each file contains the same functions but adapted for each architecture.

• train: trains the network over the whole training dataset once. Run the free and nudge phase and update the weights. Track the number of changes in the weights.

• test: tests the network over the whole testing dataset once.

• initDataframe: inits the dataframe where we store the training data.

• updateDataframe: updates the same dataframe after each epoch: update train error, test error, number of changes of weights for each layer.

• createPath: creates the path and the folder where the training data will be stored. Copy the plotFunction.py file in the same folder. Create a folder specific to the training 'S-X' in this general folder.

• saveHyperparameters: creates a .txt file with all hyperparameters in the parser in the folder 'S-X'.

Commands to be run in the terminal to reproduce the results of the paper:

python Conv/QA-SA/main.py --simulated 1 --dataset pattern --layersList 4 --expand_output 2 --convList 4 1 --padding 0 --kernelSize 2 --stride 1 --Fpool 2 --pool_coef 0.25 --lrWeightsFC 0.1 --lrWeightsCONV 0.1 --lrBiasFC 0.1 --lrBiasCONV 0.1 --batchSize 1 --epochs 20 --chain_strenght 2 --auto_scale 0