"Where exactly is calculus used in neural networks?"
When people first hear about neural networks, they often picture complex architectures and advanced computations and code.
But at the heart of this powerful AI tool lies something fundamental: Calculus.
Calculus, particularly differentiation, is the backbone of how neural networks learn.
Let me explain:
Optimizing the Model: Neural networks adjust their internal parameters (weights and biases) to minimize errors during training. This process relies on gradient descent, which is essentially a calculus-driven optimization algorithm. Gradients, computed using derivatives, tell the model in which direction (and how much) to adjust the parameters to reduce the loss function.
Understanding Backpropagation: Backpropagation is the method used to efficiently compute these gradients. It applies the chain rule from calculus to propagate error signals backward through the layers of the network. Without this elegant application of calculus, training deep networks would be computationally infeasible.
Activation Functions and Learning: Many activation functions, like sigmoid, tanh, and ReLU, require derivatives during backpropagation. Calculus helps in understanding how these functions influence the learning process and how to tweak them for better performance.
Interpreting Models: Beyond training, calculus also plays a role in understanding how inputs affect outputs. For example, techniques like gradient-based feature attribution rely on derivatives to explain model predictions.
The next time you see a neural network predicting the weather, detecting a disease, or generating human-like text, remember that the principles of calculus are quietly working behind the scenes, enabling these breakthroughs.
On Vizuara's YouTube channel, I have released a new lecture on "Introduction to Calculus for ML". Completely beginner-friendly. Check this out: [ Ссылка ]
Here's a simple breakdown of the math!
z=W∗X
y=1/(1+exp(−z))
Loss=1−y
Step-by-Step Derivation:
1️⃣ Apply the Chain Rule:
dLoss/dW=(dLoss/dy)∗(dy/dz)∗(dz/dW)
2️⃣ Compute each term:
dLoss/dy=−1
dy/dz=y∗(1−y)
dz/dW=X
3️⃣ Combine them:
dLoss/dW=−1∗(y∗(1−y))∗X
W changes to W - alpha * dLoss/dW
The gradient dLoss/dW depends on:
1️⃣ The prediction y,
2️⃣ The sigmoid slope y∗(1−y)
3️⃣ The input X.
This drives how weights W are updated during training!
