Latent Space Interpolation - Entrenar - Training & Optimization Library
Description: A comprehensive guide to building neural network training systems with autograd, optimizers, LoRA/QLoRA, and quantization using EXTREME TDD methodology

# Latent Space Interpolation

Explore the code generation space through latent vector manipulation.

## LatentCode Type

    #![allow(unused)]
    fn main() {
    use entrenar::generative::LatentCode;

    // Sample from standard normal
    let z = LatentCode::sample(&mut rng, 128);

    // Create from vector
    let z = LatentCode::new(vec![0.0; 128]);

    // Properties
    println!("Dimension: {}", z.dim());
    println!("Norm: {}", z.norm());
    }

## Linear Interpolation (LERP)

Simple straight-line interpolation:

    #![allow(unused)]
    fn main() {
    let z1 = LatentCode::new(vec![0.0; 128]);
    let z2 = LatentCode::new(vec![1.0; 128]);

    // t=0 gives z1, t=1 gives z2
    let z_mid = z1.lerp(&z2, 0.5);
    }

## Spherical Linear Interpolation (SLERP)

Interpolate along the surface of a hypersphere:

    #![allow(unused)]
    fn main() {
    let z1 = LatentCode::sample(&mut rng, 128).normalize();
    let z2 = LatentCode::sample(&mut rng, 128).normalize();

    // SLERP maintains constant norm
    let z_mid = z1.slerp(&z2, 0.5);
    assert!((z_mid.norm() - 1.0).abs() < 0.1);
    }

### When to Use SLERP

- Latent vectors are typically sampled from unit sphere
- SLERP avoids "dead zones" in latent space
- Smoother visual transitions for image GANs
- Better semantic interpolation for code GANs

## Interpolation for Code Generation

    #![allow(unused)]
    fn main() {
    let mut gan = CodeGan::new(config);

    // Generate two random codes
    let z1 = gan.sample_latent(1)[0].clone();
    let z2 = gan.sample_latent(1)[0].clone();

    // Generate 11 intermediate samples
    let samples = gan.interpolate(&z1, &z2, 10);

    for (i, code) in samples.iter().enumerate() {
        println!("Step {}: {:?}", i, code);
    }
    }

## Latent Space Arithmetic

Discover semantic directions:

    #![allow(unused)]
    fn main() {
    // Vector arithmetic in latent space
    // e.g., "loop" - "if" + "match" might give switch-like patterns
    let z_loop = encode_code("for i in 0..n { }");
    let z_if = encode_code("if cond { }");
    let z_match = encode_code("match x { }");

    let z_result = z_loop.subtract(&z_if).add(&z_match);
    let code = generator.generate(&z_result);
    }