Machine Learning Fundamentals

Overview

Linea is designed from the ground up for machine learning. It provides native support for tensors, matrices, neural networks, and GPU acceleration—no external ML frameworks needed.

Tensors and Matrices

Creating Matrices

var mat @ Matrix = [
    [1.0, 2.0, 3.0],
    [4.0, 5.0, 6.0],
    [7.0, 8.0, 9.0]
]

Matrix Operations

var a @ Matrix = [[1.0, 2.0], [3.0, 4.0]]
var b @ Matrix = [[5.0, 6.0], [7.0, 8.0]]

// Matrix multiplication
var result @ Matrix = matmul(a, b)

Tensor Operations

var tensor @ Tensor = [
    [[1.0, 2.0], [3.0, 4.0]],
    [[5.0, 6.0], [7.0, 8.0]]
]

// Broadcasting and element-wise operations
var scaled @ Tensor = tensor * 2.0

Common ML Operations

Vector Dot Product

var v1 @ [float] = [1.0, 2.0, 3.0]
var v2 @ [float] = [4.0, 5.0, 6.0]
var dot @ float = dot_product(v1, v2)  // 32.0

Activation Functions

var x @ float = 2.5

var relu_out @ float = relu(x)                 // ReLU activation
var sigmoid_out @ float = sigmoid(x)         // Sigmoid
var tanh_out @ float = tanh(x)             // Tanh

Softmax

var logits @ [float] = [1.0, 2.0, 3.0]
var probs @ [float] = softmax(logits)

Loss Functions

Mean Squared Error (MSE)

var predicted @ [float] = [1.2, 2.1, 2.9]
var actual @ [float] = [1.0, 2.0, 3.0]
var loss @ float = mse(predicted, actual)

Cross Entropy

var predictions @ [float] = [0.1, 0.7, 0.2]
var targets @ [float]  [0.0, 1.0, 0.0]
var loss @ float = cross_entropy(predictions, targets)

GPU Acceleration

Mark functions for GPU execution with the @gpu decorator:

func matrix_multiply(a: any, b: any) -> any {
    return matmul(a, b)
}

Common Patterns

var data @ [float] = [1.0, 2.0, 3.0, 4.0, 5.0]
var mean @ float = mean(data)
var std @ float = std(data)

var normalized @ [float] = (data - mean) / std

Best Practices

• Use matrices for batch operations: Faster than element-wise loops
• Mark GPU functions: Use: gpu for acceleration
• Normalize inputs: Better convergence during training
• Use appropriate dtypes: float32 for most ML, float64 for precision
• Profile your code: Find bottlenecks before optimizing