Convolutional Neural Networks (CNNs): Convolution as a local, weight-sharing linear operator; pooling and receptive fields
ResNets and skip connections, UNets.
Training Dynamics: Loss functions (MSE, Cross-Entropy), Gradient Descent, SGD and Adam. Practical training considerations: dropout, batch normalisation, weight decay, and learning rate scheduling.
The Chain Rule of Calculus: Mathematical derivation of Backpropagation.
Generalisation of Backpropagation to operators stemming from optimisation problems, fixed-point problems, or continuous limits of network architectures.
13:00 – 14:00: Lunch
14:00 – 16:00: Introduction to the Coding Challenge (Practice)
Problem Statement: Recovering a sharp image from noisy, degraded measurements using a known forward operator.
Software Stack: PyTorch, DeepInverse.
Baseline Implementation: A total-variation based reconstruction method.
Competition: You will compete with your peers in groups of two/three to achieve the highest PSNR and SSIM on a hidden test set. Model weights ≤ 100 MB, inference on CPU within 20 minutes.
Bilevel Optimisation: Formulating hyper-parameter learning as a nested upper/lower-level problem.
A brief inntroduction to convex and non-convex optimisation and algorithms
Differentiating Through the Lower Level: The Implicit Function Theorem (IFT) and sensitivity analysis; handling non-smooth functions via smoothing (Huber loss).
The Unrolling Principle: Truncating iterative algorithms to a fixed number of layers with learnable weights trained end-to-end.
Unrolled Architectures: LISTA for sparse coding; Learned Primal-Dual (LPD) network as an unrolled PDHG.
13:00 – 14:00: Lunch
14:00 – 16:00: Coding Challenge (continued)
Learning the regularisation parameter of a variational deblurring model via bilevel optimisation, differentiating through the lower-level reconstruction, or using unrolled architectures via Deep Inverse.
11:00 – 13:00: Generative Models, Continuous Dynamics, and Deep Equilibrium Models (Lecture)
Autoencoders and Variational Autoencoders (VAEs): Encoder–decoder structure; the reparameterisation trick; the ELBO objective; VAEs as learned latent-space priors.
Score-Based and Diffusion Models: Denoising score matching; the forward diffusion process and reverse-time SDE; diffusion models as priors for inverse problems.
Deep Learning as Dynamical Systems: ResNets as forward Euler discretisations of an ODE; training as an optimal control problem and the adjoint state equation.
Deep Equilibrium Models (DEQ): Replacing finite depth with a single fixed-point condition; memory-efficient training via implicit differentiation.
13:00 – 14:00: Lunch
14:00 – 16:00: Guest Lecture and Q&A
Topic: Real-world deployment of deep learning in Medical Imaging.