Struct TropicalNeuralAnalysis 

pub struct TropicalNeuralAnalysis { /* private fields */ }

Analyzes ReLU neural networks using tropical geometry

Implementations

impl TropicalNeuralAnalysis

pub fn new( architecture: Vec<usize>, weights: Vec<Vec<Vec<f64>>>, biases: Vec<Vec<f64>>, ) -> Self

Create analyzer for a ReLU network

pub fn random(architecture: Vec<usize>, seed: u64) -> Self

Create a random network for testing

pub fn forward(&self, input: &[f64]) -> Vec<f64>

Forward pass of the ReLU network

pub fn linear_region_upper_bound(&self) -> u128

Upper bound on number of linear regions

For a network with widths n_0, n_1, …, n_L where n_0 is input dimension: Upper bound = prod_{i=1}^{L-1} sum_{j=0}^{min(n_0, n_i)} C(n_i, j)

This follows from tropical geometry considerations.

pub fn estimate_linear_regions(&self, num_samples: usize, seed: u64) -> usize

Estimate actual linear regions by sampling

Samples random points and counts how many distinct activation patterns occur.

pub fn as_tropical_polynomial_1d(&self) -> Option<TropicalPolynomial>

Compute the tropical polynomial representation for 1D input Returns the piecewise linear function f(x)

pub fn decision_boundary_complexity(&self, num_samples: usize, seed: u64) -> f64

Compute decision boundary complexity for binary classification

Trait Implementations

impl Clone for TropicalNeuralAnalysis

fn clone(&self) -> TropicalNeuralAnalysis

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for TropicalNeuralAnalysis

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

Formats the value using the given formatter.