| Version: | 1.0 |
| Date: | 2025-07-23 |
| Title: | Hopfield Artificial Neural Networks |
| Description: | Builds and optimizes Hopfield artificial neural networks (Hopfield, 1982, <doi:10.1073/pnas.79.8.2554>). One-layer and three-layer models are implemented. The energy of the Hopfield network is minimized with formula from Krotov and Hopfield (2016, <doi:10.48550/ARXIV.1606.01164>). Optimization (supervised learning) is done through a gradient-based method. Classification is done with S3 methods predict(). Parallelization with 'OpenMP' is used if available during compilation. |
| URL: | https://github.com/emmanuelparadis/hann |
| BugReports: | https://github.com/emmanuelparadis/hann/issues |
| License: | GPL-3 |
| NeedsCompilation: | yes |
| Packaged: | 2025-07-23 22:43:06 UTC; paradis |
| Author: | Emmanuel Paradis 
[aut, cre, cph] |
| Maintainer: | Emmanuel Paradis <Emmanuel.Paradis@ird.fr> |
| Repository: | CRAN |
| Date/Publication: | 2025-07-25 15:40:07 UTC |
Hopfield Artificial Neural Networks
Description
hann provides tools to build Hopfield-based artificial neural networks. Two types of networks can be built: one-layer Hopfield network, and three-layer network with a hidden (convoluted) layer.
The complete list of functions can be displayed with
library(help = hann). See the vignette
“IntroductionHopfieldNetworks” for several examples.
More information on hann can be found at https://github.com/emmanuelparadis/hann.
Author(s)
Emmanuel Paradis
Maintainer: Emmanuel Paradis <Emmanuel.Paradis@ird.fr>
Hopfield Network Energy
Description
Minimize the energy of the Hopfield network.
Usage
buildSigma(xi, n = 20, nrep = 100, quiet = FALSE)
Arguments
xi |
a matrix of patterns coded with 1 and -1. |
n |
the parameter of the energy function (integer). |
nrep |
the number of attempts. |
quiet |
a logical value indicating whether to print the details for each attempt. |
Details
The number of columns in xi is equal to the size of the
Hopfield network (i.e., the number of input neurons denoted as N),
whereas the number of columns is the number of memories denoted as K
(Krotov and Hopfield, 2016).
A random vector ‘sigma’ is first generated and then updated in order to minimize the energy level of the Hopfield network. The convergence to a low energy level depends on the initial values in ‘sigma’, so the procedure is repeated several times. The vector with the lowest energy level is returned.
Value
a vector of integers (-1/1). The length of this vector (N) is equal to
the number of columns in xi.
Author(s)
Emmanuel Paradis
References
Krotov, D. and Hopfield, J. J. (2016) Dense associative memory for pattern recognition. doi:10.48550/ARXIV.1606.01164.
See Also
Examples
xi <- matrix(NA, K <- 1000, N <- 60)
xi[] <- sample(c(1L, -1L), K * N, TRUE)
(sigma <- buildSigma(xi))
Parameters for Neural Network Optimization
Description
Set the parameters for the Hopfield artificial neural network optimization.
Usage
control.hann(...)
Arguments
... |
named arguments to be modified (see examples). |
Details
When the user modifies one or several parameters by giving them as named arguments, if some names are incorrect they are ignored with a warning.
The parameters with their default values are:
-
iterlim = 100: an integer giving the number of iterations. -
quiet = FALSE: a logical controlling whether to print the value of the objective (loss) function at each iteration. -
quasinewton = FALSE: a logical. IfTRUE, quasi-Newton steps are performed (not recommended unless for networks with few parameters and/or for a small number of iterations). -
fullhessian = FALSE: (ignored ifquasinewton = FALSE) a logical, by default only some blocks of the Hessian matrix are computed. IfTRUE, the full Hessian matrix is computed (very time consuming). -
trace.error = FALSE: a logical. IfTRUE, the error rate is printed at each iteration of the optimization process. -
wolfe = FALSE: a logical. IfTRUE, Wolfe's conditions are tested and printed at each iteration. -
target = 0.001: the target value of the loss function to stop the optimization. -
beta = 0.2: the hyperparameter of the activation function. -
mc.cores = 1: an integer. The number of cores used when computing the loss function.
If mc.cores is greater than one, the optimization process calls
a multithreaded code using OMP. So, do not do this together
with functions from the package parallel. On the other hand, if
you leave this parameter to its default value, you should be able to
run several optimizations in parallel, for instance with
mclapply.
See the vignette for applications.
Value
a list with named elements as detailed above.
Note
For the moment, the parameter mc.cores is accepted only by
hann1.
Author(s)
Emmanuel Paradis
References
https://en.wikipedia.org/wiki/Wolfe_conditions
See Also
Examples
control.hann() # default values
ctrl <- control.hann(iterlim = 1000)
ctrl
## verbose is not a parameter:
ctrl <- control.hann(iterlim = 1000, verbose = TRUE)
One-layer Hopfield ANN
Description
This optimizes a one-layer Hopfield-based artificial neural
network. The structure of the network is quite simple: a Hopfield
network with N input neurons all connected to C output neurons. The
number of parameters (N and C) is determined by the input data:
xi has N columns (which is also the length of sigma) and
the number of unique values of classes is equal to C.
See the vignette of this package for an example and some background.
Usage
hann1(xi, sigma, classes, net = NULL, control = control.hann())
## S3 method for class 'hann1'
print(x, details = FALSE, ...)
Arguments
xi |
a matrix of patterns with K rows. |
sigma |
a vector coding the Hopfield network. |
classes |
the classes of the patterns (vector of length K). |
net, x |
an object of class |
control |
the control parameters. |
details |
a logical value (whether to print the parameter values of the network). |
... |
further arguments passed to |
Details
By default, the parameters of the neural network are initialized with random values from a uniform distribution between -1 and 1 (except the biases which are initialized to zero).
If an object of "hann1" is given to the argument net,
then its parameter values are used to initialize the parameters of the
network.
The main control parameters are given as a list to the control
argument. They are detailed in the page of the function
control.hann().
Value
an object of class "hann1" with the following elements:
parameters |
a list with one matrix, |
sigma |
the Hopfield network. |
beta |
the hyperparameter of the activation function. |
call |
the function call. |
Author(s)
Emmanuel Paradis
References
Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, USA, 79, 2554–2558. doi:10.1073/pnas.79.8.2554.
Krotov, D. and Hopfield, J. J. (2016) Dense associative memory for pattern recognition. doi:10.48550/ARXIV.1606.01164.
See Also
Three-layer Hopfield ANN
Description
This optimizes a three-layer Hopfield-based artificial neural
network. The network is made of a Hopfield network with N input
neurons all connected to H hidden neurons. The latter are all
connected together (convoluation) which is equivalent to defining two
hidden layers. Each hidden neuron is connected to C output
neurons. The values of the parameters N and C are determined by the
input data: xi has N columns (which is also the length of
sigma) and the number of unique values of classes is
equal to C. The value of H must be given by the user (a default of
half the number of input neurons is defined).
See the vignette of this package for an example.
Usage
hann3(xi, sigma, classes, H = 0.5 * length(sigma),
net = NULL, control = control.hann())
## S3 method for class 'hann3'
print(x, details = FALSE, ...)
Arguments
xi |
a matrix of patterns with K rows. |
sigma |
a vector coding the Hopfield network. |
classes |
the classes of the patterns (vector of length K). |
H |
the number of numbers in the hidden layer; by default half the number of input neurons (rounded to the lowest integer if the latter is odd). |
net, x |
an object of class |
control |
the control parameters. |
details |
a logical value (whether to print the parameter values of the network). |
... |
further arguments passed to |
Details
By default, the parameters of the neural network are initialized with random values from a uniform distribution between -1 and 1 (expect the biases which are initialized to zero).
If an object of "hann3" is given to the argument net,
then its parameter values are used to initialize the parameters of the
network.
The main control parameters are given as a list to the control
argument. They are detaild in the page of the function
control.hann().
Value
an object of class "hann3" with the following elements:
parameters |
a list with three matrices, |
sigma |
the Hopfield network. |
beta |
the hyperparameter of the activation function. |
call |
the function call. |
Author(s)
Emmanuel Paradis
References
Hopfield, J. J. (1982) Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences, USA, 79, 2554–2558. doi:10.1073/pnas.79.8.2554.
Krotov, D. and Hopfield, J. J. (2016) Dense associative memory for pattern recognition. doi:10.48550/ARXIV.1606.01164.
See Also
buildSigma, control.hann,
predict.hann3
Prediction
Description
Classification of patterns with Hopfield-based artificial neural networks.
Usage
## S3 method for class 'hann1'
predict(object, patterns, rawsignal = TRUE, ...)
## S3 method for class 'hann3'
predict(object, patterns, rawsignal = TRUE, ...)
Arguments
object |
an object of class |
patterns |
the patterns to be classified. |
rawsignal |
a logical value (see details). |
... |
(ignored). |
Details
The patterns have to be coded in the same way than the matrix
xi used to train the networks.
If rawsignal = TRUE, the raw signal of each neuron is output
for each pattern. Otherwise, a classification of each pattern is done
by finding the neuron with the largest signal.
Value
If rawsignal = TRUE a matrix; if rawsignal = FALSE a vector.
Author(s)
Emmanuel Paradis