Deep Learning & Neural Networks

1. Neural Networks as Function Sculptors

At heart, a neural network is a differentiable function with tuneable parameters. Given enough layers and neurons, it can approximate astonishingly complex mappings: from raw pixels to labels, from words to embeddings, from audio to intent.

2. Layers, Activations, and Representations

• Input Layer: Raw data—pixels, tokens, sensor values.
• Hidden Layers: Stacked linear transformations plus non-linear activations that progressively build richer representations.
• Output Layer: Task-specific mapping, such as class probabilities or numeric predictions.

3. Backpropagation and Gradient Descent

Training a neural network means adjusting its parameters to reduce a loss function—usually the gap between predictions and ground truth. Backpropagation efficiently computes how much each parameter contributed to that loss, so gradient descent can nudge them in the right direction.

# Extremely simplified gradient descent step (conceptual)
params = initialize_params()
learning_rate = 1e-3

for x, y in data_loader:
    y_pred = model(x, params)
    loss = loss_fn(y_pred, y)

    grads = compute_gradients(loss, params)  # via backprop
    for p in params:
        p -= learning_rate * grads[p]

4. Architectures as Inductive Biases

Different architectures bake in different assumptions about the world. Convolutional networks assume locality and translation invariance in images. Recurrent networks and Transformers encode sequence structure in text or time series.

5. Deep Learning Meets Evolution and Agents

Genetic algorithms can evolve neural network architectures or hyperparameters. Deep networks can power perception and decision-making inside agentic AI systems. Together, they form hybrid systems that both learn from gradients and explore via evolutionary search.