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Getting started with rkaf

Overview

rkaf provides Kolmogorov-Arnold Fourier Networks for R users through the torch backend.

The package supports:

regression
binary classification
multiclass classification
formula and matrix interfaces
mini-batch training
validation splits
early stopping
automatic standardization
best-model restoration
KAF-specific diagnostics

This vignette gives a quick tour of the main workflow.

library(rkaf)

set.seed(123)
torch::torch_manual_seed(123)

Regression with the matrix interface

We first fit a KAF model to a synthetic one-dimensional function with both low-frequency and high-frequency structure.

x <- as.matrix(seq(-1, 1, length.out = 128))

y <- sin(8 * pi * x) +
  0.35 * cos(3 * pi * x) +
  0.15 * x^2

fit <- kaf_fit(
  x = x,
  y = y,
  hidden = c(256, 256),
  num_grids = 32,
  use_layernorm = FALSE,
  epochs = 1000,
  lr = 1e-3,
  standardize_x = FALSE,
  standardize_y = TRUE,
  fourier_init_scale = 5e-2,
  restore_best = TRUE,
  verbose = FALSE,
  seed = 123
)

fit
#> <kaf_fit>
#> Task:         regression
#> Architecture: 1 -> 256 -> 256 -> 1
#> Fourier grids: 32 
#> Epochs:       1000
#> Batch size:   128
#> Validation:   no
#> Standardize x: no 
#> Standardize y: yes 
#> Final train loss: 0.0227977
#> Best train loss:  0.0198582 at epoch 945

pred <- predict(fit, x)

head(data.frame(
  observed = round(as.numeric(y), 3),
  predicted = round(pred, 3)
))
#>   observed predicted
#> 1   -0.200     0.195
#> 2    0.185     0.356
#> 3    0.517     0.474
#> 4    0.748     0.540
#> 5    0.842     0.545
#> 6    0.787     0.486

plot(
  x,
  y,
  type = "l",
  lwd = 2,
  xlab = "x",
  ylab = "f(x)",
  main = "KAF regression fit"
)

lines(x, pred, lwd = 2, lty = 2)

legend(
  "topright",
  legend = c("Observed", "Predicted"),
  lty = c(1, 2),
  lwd = 2,
  bty = "n"
)

Regression with the formula interface

For tabular data, rkaf also supports a formula interface.

fit_mtcars <- kaf_fit_formula(
  mpg ~ wt + hp + cyl,
  data = mtcars,
  hidden = c(32, 32),
  num_grids = 16,
  epochs = 200,
  verbose = FALSE,
  seed = 123
)

fit_mtcars
#> <kaf_fit>
#> Task:         regression
#> Formula:      mpg ~ wt + hp + cyl
#> Architecture: 3 -> 32 -> 32 -> 1
#> Fourier grids: 16 
#> Epochs:       200
#> Batch size:   32
#> Validation:   no
#> Standardize x: yes 
#> Standardize y: yes 
#> Final train loss: 0.0542788
#> Best train loss:  0.0542788 at epoch 200

mtcars_pred <- predict(fit_mtcars, mtcars)

head(data.frame(
  observed = mtcars$mpg,
  predicted = round(mtcars_pred, 2)
))
#>   observed predicted
#> 1     21.0     21.16
#> 2     21.0     21.15
#> 3     22.8     21.86
#> 4     21.4     20.03
#> 5     18.7     16.58
#> 6     18.1     18.30

Binary classification

If the response is a factor with two classes, rkaf automatically treats the problem as binary classification.

df <- mtcars

df$high_mpg <- factor(
  ifelse(df$mpg > median(df$mpg), "yes", "no"),
  levels = c("no", "yes")
)

fit_binary <- kaf_fit_formula(
  high_mpg ~ wt + hp + cyl,
  data = df,
  hidden = c(32, 32),
  num_grids = 16,
  epochs = 200,
  verbose = FALSE,
  seed = 123
)

fit_binary
#> <kaf_fit>
#> Task:         binary
#> Classes:      no, yes
#> Formula:      high_mpg ~ wt + hp + cyl
#> Architecture: 3 -> 32 -> 32 -> 1
#> Fourier grids: 16 
#> Epochs:       200
#> Batch size:   32
#> Validation:   no
#> Standardize x: yes 
#> Standardize y: no 
#> Final train loss: 0.00163561
#> Best train loss:  0.00163561 at epoch 200

Predicted probabilities and classes:

prob_binary <- predict(fit_binary, df, type = "prob")
class_binary <- predict(fit_binary, df, type = "class")

head(data.frame(
  observed = df$high_mpg,
  prob_yes = round(prob_binary, 3),
  predicted = class_binary
))
#>   observed prob_yes predicted
#> 1      yes    0.999       yes
#> 2      yes    0.999       yes
#> 3      yes    1.000       yes
#> 4      yes    0.983       yes
#> 5       no    0.000        no
#> 6       no    0.008        no

Confusion matrix

table(
  observed = df$high_mpg,
  predicted = class_binary
)
#>         predicted
#> observed no yes
#>      no  17   0
#>      yes  0  15

Raw logits:

head(predict(fit_binary, df, type = "link"))
#> [1]  7.551862  6.966256  7.803174  4.073124 -8.898857 -4.818394

Multiclass classification

If the response is a factor with more than two classes, rkaf fits a multiclass classifier.

fit_iris <- kaf_fit_formula(
  Species ~ .,
  data = iris,
  hidden = c(32, 32),
  num_grids = 16,
  epochs = 300,
  verbose = FALSE,
  seed = 123
)

fit_iris
#> <kaf_fit>
#> Task:         multiclass
#> Classes:      setosa, versicolor, virginica
#> Formula:      Species ~ .
#> Architecture: 4 -> 32 -> 32 -> 3
#> Fourier grids: 16 
#> Epochs:       300
#> Batch size:   150
#> Validation:   no
#> Standardize x: yes 
#> Standardize y: no 
#> Final train loss: 0.00819381
#> Best train loss:  0.00819381 at epoch 300

Confusion matrix

class_iris <- predict(fit_iris, iris, type = "class")

table(
  observed = iris$Species,
  predicted = class_iris
)
#>             predicted
#> observed     setosa versicolor virginica
#>   setosa         50          0         0
#>   versicolor      0         50         0
#>   virginica       0          0        50

Class probabilities:

head(round(predict(fit_iris, iris, type = "prob"), 3))
#>      setosa versicolor virginica
#> [1,]  0.999      0.001     0.000
#> [2,]  0.995      0.003     0.002
#> [3,]  0.997      0.001     0.001
#> [4,]  0.997      0.001     0.001
#> [5,]  0.999      0.000     0.000
#> [6,]  1.000      0.000     0.000

Validation and early stopping

kaf_fit() supports validation splits, mini-batches, and early stopping.

fit_val <- kaf_fit(
  x = x,
  y = y,
  hidden = c(64, 64),
  num_grids = 16,
  use_layernorm = FALSE,
  epochs = 300,
  lr = 5e-4,
  batch_size = 64,
  validation_split = 0.2,
  patience = 100,
  restore_best = TRUE,
  verbose = FALSE,
  seed = 123
)

plot(fit_val)

The fitted object stores both train_loss_history and validation_loss_history, so users can inspect training and validation behavior directly.

KAF diagnostics

The KAF architecture contains a base/GELU branch and a Fourier branch. The package exposes helper functions to inspect the learned branch scales and Fourier parameters.

scales <- extract_kaf_scales(fit)

head(scales)
#>   layer feature base_scale fourier_scale fourier_to_base_ratio
#> 1     1       1  1.0369691    0.11137812            0.10740737
#> 2     2       1  0.9652719    0.15750510            0.16317174
#> 3     2       2  0.9738784    0.39944243            0.41015638
#> 4     2       3  0.9945174    0.12360517            0.12428658
#> 5     2       4  0.9936960    0.08714252            0.08769535
#> 6     2       5  1.0083405    0.08873361            0.08799965

fourier_params <- extract_fourier_params(fit, layer = 1)

head(fourier_params)
#>   layer input_feature grid     weight      bias
#> 1     1             1    1  0.1379520 4.5462580
#> 2     1             1    2 -0.1811931 4.3979001
#> 3     1             1    3 -0.1297648 5.7381864
#> 4     1             1    4 -0.4164377 2.7132401
#> 5     1             1    5  0.3679259 0.4899397
#> 6     1             1    6  0.3606938 2.3420620

Low-level torch interface

Advanced users can use the low-level torch modules directly.

model <- nn_kaf(
  layers = c(4, 16, 16, 1),
  num_grids = 8
)

x_tensor <- torch::torch_randn(10, 4)
y_tensor <- model(x_tensor)

y_tensor$shape
#> [1] 10  1

Summary

The standard workflow is:

fit <- kaf_fit_formula(
  y ~ .,
  data = df,
  hidden = c(64, 64),
  num_grids = 16,
  validation_split = 0.2,
  patience = 30
)

predict(fit, newdata)
plot(fit)
extract_kaf_scales(fit)

For classification, use:

predict(fit, newdata, type = "prob")
predict(fit, newdata, type = "class")

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.
Health stats visible at Monitor.