Deep Learning Algorithms
Explore the core algorithms that power deep learning systems. Learn through interactive visualizations that bring complex concepts to life.
Algorithms
Coming Soon
- •Stochastic Gradient Descent
- •Momentum Optimization
- •Dropout Regularization
- •Batch Normalization
Gradient Descent
The fundamental optimization algorithm that powers neural network training. Learn how networks find the optimal weights to minimize error.
Key Concepts
- 1Loss Function:
A measure of how well the model's predictions match the actual data.
- 2Gradient:
The direction and magnitude of the steepest increase in the loss function.
- 3Learning Rate:
Controls how large of a step to take in the direction of the negative gradient.
Interactive Visualization
Mathematical Representation
θ = θ - α ∇J(θ)
When To Use
Use for small to medium-sized datasets when you want to understand the optimization process clearly. The foundation for most optimization methods.
Implementation Example
# Basic gradient descent implementation
def gradient_descent(X, y, theta, alpha, num_iters):
m = len(y)
J_history = []
for i in range(num_iters):
# Compute predictions
h = X.dot(theta)
# Compute error
error = h - y
# Compute gradient
gradient = X.T.dot(error) / m
# Update parameters
theta = theta - alpha * gradient
# Calculate cost
J = np.sum(error ** 2) / (2 * m)
J_history.append(J)
return theta, J_historyBackpropagation
Understand how neural networks learn by propagating errors backward through the network to update weights efficiently.
Key Concepts
- 1Chain Rule:
The mathematical principle that allows gradients to flow backward through the network.
- 2Forward Pass:
Computing the output of the network given an input.
- 3Backward Pass:
Computing the gradient with respect to each weight by propagating the error backward.
Interactive Visualization
Mathematical Representation
δⁿ = (Wⁿ⁺¹)ᵀ δⁿ⁺¹ ⊙ σ'(zⁿ)
When To Use
Always used in neural network training. It's not a standalone algorithm but rather the method for computing gradients in the network.
Implementation Example
# Backpropagation in a simple neural network
def backpropagation(X, y, weights, learning_rate):
# Forward pass
a1 = X
z2 = np.dot(a1, weights[0])
a2 = sigmoid(z2)
z3 = np.dot(a2, weights[1])
a3 = sigmoid(z3)
# Compute error
error = a3 - y
# Backward pass
delta3 = error * sigmoid_derivative(z3)
dW2 = np.dot(a2.T, delta3)
delta2 = np.dot(delta3, weights[1].T) * sigmoid_derivative(z2)
dW1 = np.dot(a1.T, delta2)
# Update weights
weights[0] -= learning_rate * dW1
weights[1] -= learning_rate * dW2
return weightsAdam Optimizer
A powerful adaptive optimization algorithm that combines the benefits of momentum and RMSProp for faster convergence.
Key Concepts
- 1Adaptive Learning Rates:
Different learning rates for different parameters based on historical gradients.
- 2Momentum:
Accelerates training by considering the "velocity" of parameter updates.
- 3Bias Correction:
Counteracts the bias in moment estimates during the initial iterations.
Interactive Visualization
Mathematical Representation
θₜ = θₜ₋₁ - α · m̂ₜ / (√v̂ₜ + ε)
When To Use
Ideal for most deep learning tasks, especially those with noisy or sparse gradients. Often the default choice for modern neural networks.
Implementation Example
# Adam optimizer implementation
def adam_update(params, grads, m, v, t, learning_rate=0.001,
beta1=0.9, beta2=0.999, epsilon=1e-8):
"""
Adam update rule
"""
# Updated biased first moment estimate
m = [beta1 * m_param + (1 - beta1) * g for m_param, g in zip(m, grads)]
# Updated biased second raw moment estimate
v = [beta2 * v_param + (1 - beta2) * (g ** 2) for v_param, g in zip(v, grads)]
# Compute bias-corrected first moment estimate
m_corrected = [m_param / (1 - beta1 ** t) for m_param in m]
# Compute bias-corrected second raw moment estimate
v_corrected = [v_param / (1 - beta2 ** t) for v_param in v]
# Update parameters
params = [param - learning_rate * m_c / (np.sqrt(v_c) + epsilon)
for param, m_c, v_c in zip(params, m_corrected, v_corrected)]
return params, m, vFurther Learning Resources
Books & Papers
- • "Deep Learning" by Ian Goodfellow et al.
- • "Pattern Recognition and Machine Learning" by Christopher Bishop
- • "Adam: A Method for Stochastic Optimization" by Kingma & Ba (2015)
Online Courses
- • Andrew Ng's Deep Learning Specialization on Coursera
- • Fast.ai Practical Deep Learning for Coders
- • Stanford CS231n: Convolutional Neural Networks for Visual Recognition
Research Areas
- • Optimization for Deep Learning
- • Generative Models & Diffusion Models
- • Transformer Architecture & Attention Mechanisms