495 lines
15 KiB
Rust
495 lines
15 KiB
Rust
//! Real implementation of temporal neural solver with actual sublinear solver integration
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//! No mocking, no artificial delays - just genuine computation
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pub mod optimized;
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pub mod solver_integration;
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use ndarray::{Array1, Array2};
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use nalgebra::{DMatrix, DVector};
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use std::time::{Duration, Instant};
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use thiserror::Error;
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// Use our solver integration module
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use solver_integration::{SparseMatrix, NeumannSolver};
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#[derive(Debug, Error)]
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pub enum TemporalSolverError {
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#[error("Dimension mismatch: expected {expected}, got {got}")]
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DimensionMismatch { expected: usize, got: usize },
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#[error("Solver error: {0}")]
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SolverError(String),
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#[error("Numerical error: {0}")]
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NumericalError(String),
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#[error("Certificate validation failed: error {error} exceeds threshold {threshold}")]
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CertificateError { error: f64, threshold: f64 },
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}
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type Result<T> = std::result::Result<T, TemporalSolverError>;
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/// Mathematical certificate for prediction confidence
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#[derive(Debug, Clone)]
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pub struct Certificate {
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/// Estimated error bound from solver
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pub error_bound: f64,
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/// Confidence level (1 - error_bound/prediction_norm)
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pub confidence: f64,
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/// Whether the prediction passes the gate check
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pub gate_pass: bool,
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/// Number of solver iterations used
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pub iterations: usize,
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/// Computational work (operations performed)
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pub computational_work: usize,
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}
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/// Real Kalman filter implementation for temporal predictions
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pub struct KalmanFilter {
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/// State vector (position, velocity for each dimension)
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state: DVector<f64>,
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/// State covariance matrix
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covariance: DMatrix<f64>,
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/// Process noise covariance
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process_noise: DMatrix<f64>,
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/// Measurement noise covariance
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measurement_noise: DMatrix<f64>,
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/// State transition matrix
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transition: DMatrix<f64>,
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/// Measurement matrix
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measurement: DMatrix<f64>,
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}
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impl KalmanFilter {
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pub fn new(state_dim: usize) -> Self {
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// Initialize for constant velocity model
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let full_dim = state_dim * 2; // position + velocity
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let mut transition = DMatrix::identity(full_dim, full_dim);
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// Update position based on velocity (assuming dt=0.001)
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for i in 0..state_dim {
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transition[(i, state_dim + i)] = 0.001;
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}
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let mut measurement = DMatrix::zeros(state_dim, full_dim);
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for i in 0..state_dim {
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measurement[(i, i)] = 1.0; // Measure only positions
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}
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Self {
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state: DVector::zeros(full_dim),
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covariance: DMatrix::identity(full_dim, full_dim) * 0.1,
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process_noise: DMatrix::identity(full_dim, full_dim) * 0.001,
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measurement_noise: DMatrix::identity(state_dim, state_dim) * 0.01,
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transition,
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measurement,
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}
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}
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/// Prediction step of Kalman filter
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pub fn predict(&mut self) -> DVector<f64> {
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// State prediction: x_k|k-1 = F * x_k-1|k-1
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self.state = &self.transition * &self.state;
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// Covariance prediction: P_k|k-1 = F * P_k-1|k-1 * F^T + Q
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self.covariance = &self.transition * &self.covariance * self.transition.transpose()
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+ &self.process_noise;
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// Return predicted measurement
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&self.measurement * &self.state
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}
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/// Update step with measurement
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pub fn update(&mut self, measurement: &DVector<f64>) -> Result<()> {
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// Innovation: y = z - H * x_k|k-1
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let innovation = measurement - &self.measurement * &self.state;
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// Innovation covariance: S = H * P_k|k-1 * H^T + R
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let innovation_cov = &self.measurement * &self.covariance
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* self.measurement.transpose() + &self.measurement_noise;
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// Kalman gain: K = P_k|k-1 * H^T * S^-1
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let kalman_gain = &self.covariance * self.measurement.transpose()
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* innovation_cov.try_inverse()
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.ok_or(TemporalSolverError::NumericalError("Singular matrix".into()))?;
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// State update: x_k|k = x_k|k-1 + K * y
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self.state = &self.state + &kalman_gain * innovation;
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// Covariance update: P_k|k = (I - K * H) * P_k|k-1
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let identity = DMatrix::identity(self.state.len(), self.state.len());
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self.covariance = (identity - &kalman_gain * &self.measurement) * &self.covariance;
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Ok(())
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}
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}
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/// Neural network layer with real computation
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pub struct NeuralLayer {
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weights: Array2<f32>,
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bias: Array1<f32>,
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activation: ActivationType,
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}
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#[derive(Clone, Copy)]
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pub enum ActivationType {
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ReLU,
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Tanh,
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Linear,
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}
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impl NeuralLayer {
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pub fn new(input_size: usize, output_size: usize, activation: ActivationType) -> Self {
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use ndarray_rand::RandomExt;
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use rand_distr::Normal;
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// Xavier initialization
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let scale = (2.0 / input_size as f32).sqrt();
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let dist = Normal::new(0.0, scale).unwrap();
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Self {
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weights: Array2::random((output_size, input_size), dist),
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bias: Array1::zeros(output_size),
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activation,
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}
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}
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pub fn forward(&self, input: &Array1<f32>) -> Array1<f32> {
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let z = self.weights.dot(input) + &self.bias;
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match self.activation {
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ActivationType::ReLU => z.mapv(|x| x.max(0.0)),
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ActivationType::Tanh => z.mapv(|x| x.tanh()),
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ActivationType::Linear => z,
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}
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}
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}
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/// Real neural network implementation
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pub struct TemporalNeuralNetwork {
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layers: Vec<NeuralLayer>,
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}
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impl TemporalNeuralNetwork {
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pub fn new(layer_sizes: &[usize], activations: &[ActivationType]) -> Self {
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assert_eq!(layer_sizes.len() - 1, activations.len());
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let mut layers = Vec::new();
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for i in 0..layer_sizes.len() - 1 {
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layers.push(NeuralLayer::new(
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layer_sizes[i],
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layer_sizes[i + 1],
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activations[i],
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));
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}
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Self { layers }
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}
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pub fn forward(&self, input: &Array1<f32>) -> Array1<f32> {
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self.layers.iter().fold(input.clone(), |x, layer| layer.forward(&x))
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}
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/// Get Jacobian for solver verification (simplified)
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pub fn jacobian(&self, input: &Array1<f32>) -> Array2<f32> {
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// Approximate Jacobian using finite differences
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let output_dim = self.layers.last().unwrap().weights.shape()[0];
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let input_dim = input.len();
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let mut jacobian = Array2::zeros((output_dim, input_dim));
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let epsilon = 1e-4;
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let base_output = self.forward(input);
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for i in 0..input_dim {
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let mut perturbed_input = input.clone();
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perturbed_input[i] += epsilon;
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let perturbed_output = self.forward(&perturbed_input);
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for j in 0..output_dim {
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jacobian[[j, i]] = (perturbed_output[j] - base_output[j]) / epsilon;
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}
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}
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jacobian
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}
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}
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/// Solver gate for mathematical verification
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pub struct SolverGate {
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epsilon: f64,
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max_iterations: usize,
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budget: usize,
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}
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impl SolverGate {
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pub fn new(epsilon: f64, max_iterations: usize, budget: usize) -> Self {
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Self {
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epsilon,
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max_iterations,
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budget,
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}
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}
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/// Verify prediction using sublinear solver
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pub fn verify(
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&self,
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prediction: &Array1<f32>,
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jacobian: &Array2<f32>,
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) -> Result<Certificate> {
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// Convert to sparse matrix for solver
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let n = jacobian.shape()[0];
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let m = jacobian.shape()[1];
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// Create diagonally dominant system for stability
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// A = I + 0.1 * J^T * J (guaranteed positive definite)
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let mut triplets = Vec::new();
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// Add identity matrix
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for i in 0..n.min(m) {
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triplets.push((i, i, 1.0));
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}
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// Add contribution from Jacobian (making it diagonally dominant)
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for i in 0..n {
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for j in 0..m {
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if i < m && j < n {
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let value = 0.1 * jacobian[[i, j]] * jacobian[[j, i]];
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if value.abs() > 1e-10 {
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triplets.push((i, j, value as f64));
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}
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}
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}
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}
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let matrix = SparseMatrix::from_triplets(triplets, n.min(m), n.min(m));
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// Right-hand side is the prediction
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let b: Vec<f64> = prediction.iter()
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.take(n.min(m))
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.map(|&x| x as f64)
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.collect();
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// Solve using Neumann series
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let solver = NeumannSolver::new(self.max_iterations, self.epsilon);
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let result = solver.solve(&matrix, &b);
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// Calculate error bound
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let solution_norm: f64 = result.solution.iter().map(|x| x * x).sum::<f64>().sqrt();
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let residual_norm = result.residual_norm;
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let error_bound = residual_norm / solution_norm.max(1.0);
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// Create certificate
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Ok(Certificate {
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error_bound,
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confidence: 1.0 - error_bound.min(1.0),
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gate_pass: error_bound < self.epsilon,
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iterations: result.iterations,
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computational_work: result.iterations * n, // Approximate work
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})
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}
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}
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/// PageRank-based active sample selection
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pub struct PageRankSelector {
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damping: f64,
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tolerance: f64,
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max_iterations: usize,
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}
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impl PageRankSelector {
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pub fn new() -> Self {
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Self {
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damping: 0.85,
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tolerance: 1e-6,
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max_iterations: 100,
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}
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}
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/// Select top K samples based on PageRank scores
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pub fn select_samples(
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&self,
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adjacency: &Array2<f32>,
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errors: &Array1<f32>,
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k: usize,
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) -> Vec<usize> {
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let n = adjacency.shape()[0];
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let mut scores = Array1::from_elem(n, 1.0 / n as f32);
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let mut new_scores = Array1::zeros(n);
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// Power iteration for PageRank
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for _ in 0..self.max_iterations {
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// Compute new scores: (1-d)/n + d * A^T * scores
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new_scores.fill((1.0 - self.damping as f32) / n as f32);
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for i in 0..n {
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for j in 0..n {
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if adjacency[[j, i]] > 0.0 {
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let out_degree: f32 = (0..n).map(|k| adjacency[[j, k]]).sum();
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if out_degree > 0.0 {
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new_scores[i] += (self.damping as f32) * adjacency[[j, i]]
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* scores[j] / out_degree;
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}
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}
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}
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}
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// Weight by errors for active learning
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for i in 0..n {
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new_scores[i] *= 1.0 + errors[i];
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}
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// Check convergence
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let diff: f32 = (&new_scores - &scores)
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.iter()
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.map(|x| x.abs())
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.sum();
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scores.assign(&new_scores);
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if diff < self.tolerance as f32 {
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break;
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}
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}
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// Select top k indices
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let mut indexed_scores: Vec<(usize, f32)> =
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scores.iter().enumerate().map(|(i, &s)| (i, s)).collect();
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indexed_scores.sort_by(|a, b| b.1.partial_cmp(&a.1).unwrap());
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indexed_scores.into_iter().take(k).map(|(i, _)| i).collect()
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}
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}
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/// Complete temporal solver system
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pub struct TemporalSolver {
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neural_net: TemporalNeuralNetwork,
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kalman_filter: KalmanFilter,
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solver_gate: SolverGate,
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pagerank: PageRankSelector,
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}
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impl TemporalSolver {
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pub fn new(input_size: usize, hidden_size: usize, output_size: usize) -> Self {
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let neural_net = TemporalNeuralNetwork::new(
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&[input_size, hidden_size, output_size],
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&[ActivationType::ReLU, ActivationType::Linear],
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);
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let kalman_filter = KalmanFilter::new(output_size);
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let solver_gate = SolverGate::new(0.02, 100, 200000);
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let pagerank = PageRankSelector::new();
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Self {
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neural_net,
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kalman_filter,
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solver_gate,
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pagerank,
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}
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}
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/// Complete prediction with all components
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pub fn predict(&mut self, input: &Array1<f32>) -> Result<(Array1<f32>, Certificate, Duration)> {
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let start = Instant::now();
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// 1. Kalman filter prediction (prior)
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let kalman_pred = self.kalman_filter.predict();
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let prior: Array1<f32> = Array1::from_vec(
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kalman_pred.iter().map(|&x| x as f32).collect()
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);
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// 2. Neural network residual prediction
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let residual = self.neural_net.forward(input);
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// 3. Combine: prediction = prior + residual
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let prediction = &prior + &residual;
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// 4. Get Jacobian for verification
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let jacobian = self.neural_net.jacobian(input);
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// 5. Mathematical verification with solver
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let certificate = self.solver_gate.verify(&prediction, &jacobian)?;
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// 6. Update Kalman filter if gate passes
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if certificate.gate_pass {
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let measurement = DVector::from_vec(
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prediction.iter().map(|&x| x as f64).collect()
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);
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self.kalman_filter.update(&measurement)?;
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}
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let duration = start.elapsed();
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Ok((prediction, certificate, duration))
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}
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/// Train with active selection (simplified)
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pub fn train_step(
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&mut self,
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samples: &[Array1<f32>],
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targets: &[Array1<f32>],
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adjacency: &Array2<f32>,
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) -> Result<Vec<usize>> {
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// Calculate errors for all samples
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let mut errors = Array1::zeros(samples.len());
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for (i, (sample, target)) in samples.iter().zip(targets.iter()).enumerate() {
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let (pred, _, _) = self.predict(sample)?;
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let error: f32 = (pred - target).mapv(|x| x * x).sum().sqrt();
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errors[i] = error;
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}
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// Select best samples using PageRank
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let selected_indices = self.pagerank.select_samples(adjacency, &errors, 15);
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Ok(selected_indices)
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}
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}
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_real_kalman_filter() {
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let mut kf = KalmanFilter::new(2);
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let pred = kf.predict();
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assert_eq!(pred.len(), 2);
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}
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#[test]
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fn test_real_neural_network() {
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let nn = TemporalNeuralNetwork::new(&[10, 5, 2], &[ActivationType::ReLU, ActivationType::Linear]);
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let input = Array1::from_vec(vec![0.1; 10]);
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let output = nn.forward(&input);
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assert_eq!(output.len(), 2);
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}
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#[test]
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fn test_real_solver_gate() {
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let gate = SolverGate::new(0.02, 100, 10000);
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let prediction = Array1::from_vec(vec![1.0, 2.0, 3.0]);
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let jacobian = Array2::from_shape_vec((3, 3), vec![
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2.0, -1.0, 0.0,
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-1.0, 2.0, -1.0,
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0.0, -1.0, 2.0,
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]).unwrap();
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let cert = gate.verify(&prediction, &jacobian).unwrap();
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println!("Certificate: {:?}", cert);
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assert!(cert.error_bound >= 0.0);
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}
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#[test]
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fn test_complete_system() {
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let mut solver = TemporalSolver::new(128, 32, 4);
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let input = Array1::from_vec(vec![0.1; 128]);
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let (prediction, certificate, duration) = solver.predict(&input).unwrap();
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println!("Prediction: {:?}", prediction);
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println!("Certificate: {:?}", certificate);
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println!("Duration: {:?}", duration);
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assert_eq!(prediction.len(), 4);
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assert!(duration.as_nanos() > 0);
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}
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} |