Struct NeuralTangentKernel 

pub struct NeuralTangentKernel<State = Untrained> { /* private fields */ }

Neural Tangent Kernel (NTK) Approximation

The Neural Tangent Kernel describes the evolution of an infinitely-wide neural network during gradient descent. This implementation provides both exact infinite-width computation and finite-width approximations.

Mathematical Background

For a fully-connected neural network with L layers and activation σ:

• The NTK is defined as: Θ(x, x’) = E[∂f/∂θ(x) · ∂f/∂θ(x’)]
• In the infinite-width limit, the NTK remains constant during training
• The network evolution follows: df/dt = Θ(X, X) ∇f L(f)

Examples

use sklears_kernel_approximation::deep_learning_kernels::{NeuralTangentKernel, NTKConfig, Activation};
use scirs2_core::ndarray::array;
use sklears_core::traits::{Fit, Transform};

let config = NTKConfig {
    n_layers: 3,
    activation: Activation::ReLU,
    infinite_width: true,
    ..Default::default()
 };

let ntk = NeuralTangentKernel::new(config);
let X = array![[1.0, 2.0], [3.0, 4.0]];
let fitted = ntk.fit(&X, &()).unwrap();
let features = fitted.transform(&X).unwrap();
assert_eq!(features.shape()[0], 2);

Implementations

impl NeuralTangentKernel<Untrained>

pub fn new(config: NTKConfig) -> Self

Create a new Neural Tangent Kernel with the given configuration

pub fn with_layers(n_layers: usize) -> Self

Create a new NTK with default configuration

pub fn activation(self, activation: Activation) -> Self

Set activation function

pub fn infinite_width(self, infinite: bool) -> Self

Set whether to use infinite-width limit

pub fn n_components(self, n: usize) -> Self

Set number of components

impl NeuralTangentKernel<Trained>

pub fn x_train(&self) -> &Array2<Float>

Get the training data

pub fn eigenvectors(&self) -> Option<&Array2<Float>>

Get the eigenvectors

Trait Implementations

impl<State: Clone> Clone for NeuralTangentKernel<State>

fn clone(&self) -> NeuralTangentKernel<State>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<State: Debug> Debug for NeuralTangentKernel<State>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Estimator for NeuralTangentKernel<Untrained>

type Config = NTKConfig

Configuration type for the estimator

type Error = SklearsError

Error type for the estimator

type Float = f64

The numeric type used by this estimator

fn config(&self) -> &Self::Config

Get estimator configuration

fn validate_config(&self) -> Result<(), SklearsError>

Validate estimator configuration with detailed error context

fn check_compatibility( &self, n_samples: usize, n_features: usize, ) -> Result<(), SklearsError>

Check if estimator is compatible with given data dimensions

fn metadata(&self) -> EstimatorMetadata

Get estimator metadata

impl Fit<ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>, ()> for NeuralTangentKernel<Untrained>

type Fitted = NeuralTangentKernel<Trained>

The fitted model type

fn fit(self, x: &Array2<Float>, _y: &()) -> Result<Self::Fitted>

Fit the model to the provided data with validation

fn fit_with_validation( self, x: &X, y: &Y, _x_val: Option<&X>, _y_val: Option<&Y>, ) -> Result<(Self::Fitted, FitMetrics), SklearsError>

where Self: Sized,

Fit with custom validation and early stopping

impl Transform<ArrayBase<OwnedRepr<f64>, Dim<[usize; 2]>>> for NeuralTangentKernel<Trained>

fn transform(&self, x: &Array2<Float>) -> Result<Array2<Float>>

Transform the input data