Neural networks train by constructing a computational graph in the forward pass, chaining basic operations such as x × y × z into composite functions of the inputs.
Derivatives of the output with respect to every input are then obtained in the backward pass by applying the chain rule at each node, where local gradients multiply: ∂f/∂y = ∂f/∂(x × y) × ∂(x × y)/∂y and ∇ₓz = ∇ₓy · ∇ᵧz, with intermediate values stored along the graph.
This process updates the parameters of convolutional networks that classify medical scans to flag early-stage tumors in hospital imaging systems.
Four equations link electric charges, currents and fields into classical electromagnetism.
∯𝐄·𝐧̂ dS = q/ε₀
∯𝐁·𝐧̂ dS = 0
∮𝐁·dl = μ₀(i + ε₀ dΦ_E/dt)
∮𝐄·dl = −dΦ_B/dt
∇·𝐄 = ρ/ε₀ ∇·𝐁 = 0
∇×𝐁 = μ₀(𝐉 + ε₀ ∂𝐄/∂t) ∇×𝐄 = −∂𝐁/∂t
Transformers step voltage up or down across power grids by inducing emf from changing magnetic flux.
Introduction to Machine Learning (Tübingen)
Introduction to Machine Learning The course serves as a basic introduction to machine learning and covers key concepts /Untitled.png)