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Title: Kolmogorov-Arnold Fourier Networks in R
Version: 0.1.0
Description: Provides an R implementation of Kolmogorov-Arnold Fourier Networks using the torch backend. The package supports regression, binary classification, multiclass classification, formula and matrix interfaces, mini-batch training, validation splits, early stopping, standardization, best-model restoration, and KAF-specific diagnostics.
License: MIT + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.3.3
Depends: R (≥ 4.1.0)
Imports: stats, graphics, torch
Suggests: testthat (≥ 3.0.0), knitr, rmarkdown, pkgdown
Config/testthat/edition: 3
URL: https://github.com/gsidoine/rkaf, https://gsidoine.github.io/rkaf/
BugReports: https://github.com/gsidoine/rkaf/issues
VignetteBuilder: knitr
NeedsCompilation: no
Packaged: 2026-04-26 17:46:14 UTC; gjhsi
Author: Guillaume Sidoine [aut, cre]
Maintainer: Guillaume Sidoine <gjh.sidoine@gmail.com>
Repository: CRAN
Date/Publication: 2026-04-28 19:40:02 UTC

rkaf: Kolmogorov-Arnold Fourier Networks in R

Description

rkaf provides an R implementation of Kolmogorov-Arnold Fourier Networks using the torch backend.

Details

The package supports:

Author(s)

Maintainer: Guillaume Sidoine gjh.sidoine@gmail.com

See Also

Useful links:

Extract KAF Fourier parameters

Description

Extracts the trainable Random Fourier Feature weights and biases from a KAF model.

Usage

extract_fourier_params(object, layer = NULL)

Arguments

object

A fitted object returned by kaf_fit(), or a raw nn_kaf torch module.

layer

Optional integer. If supplied, only extract parameters from this layer.

Value

A data frame with Fourier weights and biases.

Extract KAF branch scales

Description

Extracts the learned GELU/base and Fourier branch scales from each KAF layer.

Usage

extract_kaf_scales(object)

Arguments

object

A fitted object returned by kaf_fit(), or a raw nn_kaf torch module.

Value

A data frame with one row per layer-feature pair.

Create a Kolmogorov-Arnold Fourier Network

Description

Convenience wrapper around nn_kaf() using a more user-facing API.

Usage

kaf(
  input_dim,
  output_dim = 1,
  hidden = c(64, 64),
  num_grids = 16,
  dropout = 0,
  use_layernorm = TRUE,
  activation_expectation = 1.64,
  fourier_init_scale = 0.01
)

Arguments

input_dim

Integer. Number of input features.

output_dim

Integer. Number of output dimensions.

hidden

Integer vector. Hidden layer sizes.

num_grids

Integer. Number of Fourier frequencies per KAF layer.

dropout

Numeric. Dropout probability.

use_layernorm

Logical. Whether to apply layer normalization.

activation_expectation

Numeric. Scaling constant for Fourier initialization.

fourier_init_scale

Numeric. Initial scale of the Fourier branch.

Value

A torch KAF network.

Fit a Kolmogorov-Arnold Fourier Network

Description

Fits a KAF model for regression using mean squared error loss.

Usage

kaf_fit(
  x,
  y,
  task = c("auto", "regression", "binary", "multiclass"),
  hidden = c(64, 64),
  num_grids = 16,
  dropout = 0,
  use_layernorm = TRUE,
  fourier_init_scale = 0.01,
  epochs = 1000,
  lr = 0.001,
  batch_size = NULL,
  shuffle = TRUE,
  validation_split = 0,
  x_val = NULL,
  y_val = NULL,
  weight_decay = 0,
  standardize_x = TRUE,
  standardize_y = NULL,
  patience = NULL,
  verbose = TRUE,
  print_every = 100,
  seed = NULL,
  restore_best = TRUE,
  min_delta = 0
)

Arguments

x

Matrix, data frame, vector, or 2D torch tensor of predictors.

y

Vector, matrix, data frame, or torch tensor of targets.

task

Character. One of "auto", "regression", "binary", or "multiclass". With "auto", factor, character, and logical targets are treated as classification; numeric targets are treated as regression.

hidden

Integer vector. Hidden layer sizes.

num_grids

Integer. Number of Fourier frequencies per KAF layer.

dropout

Numeric. Dropout probability.

use_layernorm

Logical. Whether to apply layer normalization.

fourier_init_scale

Numeric. Initial scale of the Fourier branch.

epochs

Integer. Maximum number of training epochs.

lr

Numeric. Learning rate.

batch_size

Optional integer. Mini-batch size. If NULL, full-batch training is used.

shuffle

Logical. Whether to shuffle training rows each epoch.

validation_split

Numeric in ⁠[0, 1)⁠. Fraction of rows to reserve for validation. Ignored if x_val and y_val are supplied.

x_val

Optional validation predictors.

y_val

Optional validation targets.

weight_decay

Numeric. Adam weight decay.

standardize_x

Logical. Whether to standardize predictors using the training-set mean and standard deviation.

standardize_y

Logical or NULL. Whether to standardize regression targets using the training-set mean and standard deviation. If NULL, targets are standardized for regression and not standardized for classification. Predictions are automatically transformed back to the original target scale.

patience

Optional integer. Number of epochs without improvement before early stopping.

verbose

Logical. Whether to print progress.

print_every

Integer. Print frequency.

seed

Optional integer random seed.

restore_best

Logical. Whether to restore the best observed model state after training.

min_delta

Numeric. Minimum loss improvement required to update the best model state.

Value

An object of class "kaf_fit".

Fit a KAF model using an R formula

Description

Fits a Kolmogorov-Arnold Fourier Network using a formula and data frame. This is a convenience wrapper around kaf_fit() for regression tasks.

Usage

kaf_fit_formula(
  formula,
  data,
  include_intercept = FALSE,
  na.action = stats::na.omit,
  ...
)

Arguments

formula

A model formula, such as y ~ x1 + x2.

data

A data frame.

include_intercept

Logical. Whether to keep the model-matrix intercept column. Defaults to FALSE.

na.action

Missing-value handling function passed to model.frame().

...

Additional arguments passed to kaf_fit().

Value

An object of class "kaf_fit".

Kolmogorov-Arnold Fourier Network

Description

Torch module implementing a stacked Kolmogorov-Arnold Fourier Network.

Usage

nn_kaf(
  layers,
  num_grids = 8,
  dropout = 0,
  use_layernorm = TRUE,
  activation_expectation = 1.64,
  fourier_init_scale = 0.01
)

Arguments

layers

Integer vector. Network architecture, including input and output dimensions. For example, c(10, 64, 64, 1).

num_grids

Integer. Number of Fourier frequencies per KAF layer.

dropout

Numeric. Dropout probability.

use_layernorm

Logical. Whether to apply layer normalization before the Fourier feature block.

activation_expectation

Numeric. Scaling constant for Fourier initialization.

fourier_init_scale

Numeric. Initial scale of the Fourier component.

Value

A torch nn_module.

Kolmogorov-Arnold Fourier Layer

Description

Torch module implementing one KAF layer using a hybrid GELU and trainable Random Fourier Features activation.

Usage

nn_kaf_layer(
  input_dim,
  output_dim,
  num_grids = 8,
  dropout = 0,
  use_layernorm = TRUE,
  activation_expectation = 1.64,
  fourier_init_scale = 0.01
)

Arguments

input_dim

Integer. Input dimension.

output_dim

Integer. Output dimension.

num_grids

Integer. Number of Fourier frequencies.

dropout

Numeric. Dropout probability.

use_layernorm

Logical. Whether to apply layer normalization before the Fourier feature block.

activation_expectation

Numeric. Scaling constant for Fourier initialization.

fourier_init_scale

Numeric. Initial scale of the Fourier component.

Details

The layer computes a feature-wise hybrid activation of the form:

z = \alpha \odot GELU(x) + \beta \odot RFF(x)

followed by a linear projection to the output dimension.

Value

A torch nn_module.

Random Fourier Features Layer

Description

Torch module implementing trainable random Fourier features for Kolmogorov-Arnold Fourier Networks.

Usage

nn_random_fourier_features(
  input_dim,
  num_grids = 8,
  dropout = 0,
  activation_expectation = 1.64
)

Arguments

input_dim

Integer. Input dimension.

num_grids

Integer. Number of Fourier frequencies.

dropout

Numeric. Dropout probability.

activation_expectation

Numeric. Scaling constant for initialization.

Value

A torch nn_module.

Plot a fitted KAF model

Description

Plot a fitted KAF model

Usage

## S3 method for class 'kaf_fit'
plot(x, type = c("loss", "fit"), newdata = NULL, y = NULL, ...)

Arguments

x

A fitted object returned by kaf_fit().

type

Character. Either "loss" or "fit".

newdata

Optional predictors used when type = "fit".

y

Optional observed target values used when type = "fit".

...

Additional arguments passed to base plotting functions.

Value

Invisibly returns x.

Plot KAF branch scales

Description

Visualizes the learned base/GELU and Fourier branch scales for a selected KAF layer.

Usage

plot_kaf_scales(object, layer = 1, type = c("ratio", "branch"), ...)

Arguments

object

A fitted object returned by kaf_fit(), or a raw nn_kaf torch module.

layer

Integer. Layer to inspect.

type

Character. Either "ratio" or "branch".

...

Additional arguments passed to base plotting functions.

Value

Invisibly returns the extracted scale data.

Predict from a fitted KAF model

Description

Predict from a fitted KAF model

Usage

## S3 method for class 'kaf_fit'
predict(
  object,
  newdata,
  type = c("response", "prob", "class", "link"),
  threshold = 0.5,
  as_tensor = FALSE,
  ...
)

Arguments

object

A fitted object returned by kaf_fit().

newdata

Matrix, data frame, vector, or 2D torch tensor.

type

Character. Prediction type. "response" returns regression predictions for regression, probabilities for classification. "prob" returns probabilities for classification. "class" returns predicted classes. "link" returns raw model logits/outputs.

threshold

Numeric. Classification threshold used for binary class predictions.

as_tensor

Logical. If TRUE, return a torch tensor where supported.

...

Unused.

Value

Predictions as a vector, matrix, factor, or torch tensor.

Print a fitted KAF model

Description

Print a fitted KAF model

Usage

## S3 method for class 'kaf_fit'
print(x, ...)

Arguments

x

A fitted object returned by kaf_fit().

...

Unused.

Value

Invisibly returns x.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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