Monash University · S2 2026 · FACULTY OF COMPUTER SCIENCE

ECE5179 Neural networks and deep learning

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The Complete Exam Bible · S2 2026

ECE5179 Overview

Neural networks and deep learning
— derive the gradient, size the layer, explain the design
  • Monash University
  • S2 2026
  • 12 chapters
  • Computer Science

ECE5179 Neural networks and deep learning is a postgraduate Monash University unit that builds deep learning from first principles.

  • Assessed by Weekly quizzes, two homeworks, a mid-semester test, an assignment and a final examination
  • Hardest step Pushing gradients backwards through a network by hand
  • How to prepare Rework studio problems from a blank page, then check against the solutions
  • Pass rule An overall mark of at least half the available marks
ECE5179 · Monash University
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Assessment

How ECE5179 is assessed

ComponentWeightFormat
Engagement Quizzes5%Ten weekly online quizzes worth 0.5% each, one in each of Weeks 1 to 5 and 7 to 11; missed quizzes cannot be retaken
Homework 15%Coding and written questions: completed Jupyter notebooks plus Moodle questions; released Week 1, due end of Week 2
Homework 210%Coding and written questions: completed Jupyter notebooks plus Moodle questions; released Week 3, due end of Week 4
Mid-Semester Test15%In person during the Week 6 workshop; 40 minutes; multiple-choice, numerical and handwritten questions with no coding; closed book apart from up to five A4 sheets of personal notes written on both sides, the provided cheat sheet, a dictionary and a calculator
Assignment15%Individual; theoretical concepts and coding problems; released Week 7, due end of Week 9
Final Examination50%Held in the official examination period and covering the unit learning outcomes; date, time and venue appear on your official examination timetable

Weights are from the unit's Assessment Summary and agree with the Monash Handbook entry for ECE5179 in 2026 (quizzes 5%, test 15%, written work 30%, examination 50%). The unit materials state a pass requirement of an overall mark of at least 50%. The final examination's duration, question format and permitted materials are not given in the unit pages available here; check the examination notice on Moodle and your official timetable.

Current dates · verify in LMS

Current ECE5179 dates

DateItemControl
Mon 5 Oct 2026, 11:55 pmAssignment dueLate homework and assignment submissions lose 5% of the available mark per day
Mon 19 Oct 2026Week 12 beginsFinal workshop and studio week, used for consolidation and exam preparation
Examination periodFinal ExaminationDate, time and venue on your official examination timetable

Dates are as published in the ECE5179 Moodle schedule and assessment pages for Semester 2 2026. Confirm exact deadlines and submission settings in the live LMS.

Contents · every chapter, one map

What ECE5179 covers

Follow the unit from linear models and gradient descent through multilayer perceptrons, convolutional, residual, generative and recurrent networks to attention, language models and vision transformers.

01

Learning Types and Linear Regression

Week 1. Supervised, unsupervised and self-supervised learning, the McCulloch-Pitts neuron, least squares in closed form, normal equations and bias augmentation.

Week 1 sets out the kinds of learning problem, from supervised to self-supervised, traces the artificial neuron back to the McCulloch-Pitts model, and then develops linear regression as the first trainable model.

  • Supervised, unsupervised, semi-supervised and self-supervised learning
  • Regression versus classification targets
  • The McCulloch-Pitts neuron and the modern artificial neuron
  • Residuals and the mean squared error
  • Closed-form slope and intercept from covariance and variance
  • Normal equations, the pseudoinverse and bias augmentation
02

Logistic Regression and the Softmax Classifier

Week 2. The sigmoid and log-odds, binary cross-entropy and its gradient, softmax probabilities, shift invariance and numerical stability.

Week 2 replaces the straight-line fit with models that output probabilities. Logistic regression passes a linear score through the sigmoid and is trained with binary cross-entropy, whose gradient takes the simple error-times-input form.

  • Why least squares fails on class labels
  • Hyperplanes, signed distance and the decision boundary
  • The sigmoid, odds and the logit
  • Binary cross-entropy and its gradient
  • One-hot labels and the softmax classifier
  • Shift invariance and the log-sum-exp trick
03

Gradient Descent and Optimisation Geometry

Week 3. Gradients and level sets, the update rule, stopping criteria, convexity, learning-rate diagnosis and momentum.

Week 3 explains how large models are trained when no closed-form solution exists. The gradient points uphill and is orthogonal to the level sets, so stepping against it decreases the loss for a small enough learning rate.

  • Why grid search fails in high dimensions
  • The gradient as the direction of steepest ascent
  • Level sets and why paths zigzag in narrow valleys
  • The gradient-descent update and stopping criteria
  • Critical points, convexity and global minima
  • Sublinear and linear convergence
04

Multilayer Perceptrons and Backpropagation

Week 4. Activation functions, MLP anatomy and parameter counts, representational power, the chain rule on a computation graph and a full backward pass.

Week 4 builds the first deep networks. A multilayer perceptron alternates affine maps with non-linear activations; without the activations, any stack of layers collapses to a single linear map.

  • Why stacked linear layers collapse
  • Sigmoid, tanh, ReLU and smoother activations
  • MLP anatomy and parameter counts
  • Universal approximation and the role of depth
  • The chain rule on a computation graph
  • Local gradient rules for linear, ReLU and sigmoid nodes
05

Convolutional Neural Networks

Weeks 5 and 6. Why convolution, output size with padding, stride and dilation, parameters and multiplications, pooling, LeNet and AlexNet.

Weeks 5 and 6 introduce convolutional networks for images. A small kernel slides over the input with shared weights, so the layer detects local patterns anywhere while using far fewer parameters than a dense layer.

  • Why convolution suits images: locality and shared weights
  • Output size with padding, stride and dilation
  • Parameter and multiplication counts
  • Pooling and receptive fields
  • LeNet-5 and AlexNet
  • Transposed and depthwise-separable convolutions
06

Overfitting and Regularisation

Validation and early stopping, dropout and its scaling, weight decay and penalties, augmentation, transfer learning and evaluation metrics.

This chapter gathers the unit's tools for models that fit their training data too well.

  • Training, validation and test sets; k-fold cross-validation
  • Early stopping from validation loss
  • Dropout and inverted dropout scaling
  • Weight decay, ridge and LASSO penalties
  • Augmentation, transfer learning and linear probes
  • Accuracy, precision, recall and F1
07

Residual Networks and Batch Normalisation

Week 7. The degradation problem, residual and bottleneck blocks, ResNet stages, batch normalisation in training and evaluation, and group and layer normalisation.

Week 7 revisits convolutional design with two ideas that made very deep networks trainable. Residual connections let a block output F(x) + x, so extra depth can default to the identity and gradients flow through the shortcut.

  • The degradation problem in deep plain networks
  • Residual blocks and identity shortcuts
  • Downsampling shortcuts and bottleneck blocks
  • ResNet-18 to ResNet-152 stage designs
  • Batch normalisation for fully connected and convolutional layers
  • Training mode versus evaluation mode
08

Generative Adversarial Networks

Week 8. Generator and discriminator, the discriminator loss, minimax and non-saturating generator losses, the optimal discriminator and mode collapse.

Week 8 moves from prediction to generation. A generative adversarial network trains a generator to turn random noise into realistic samples and a discriminator to tell real from generated, in alternating steps.

  • Generator, discriminator and the two-player game
  • Alternating training and the equilibrium D = ½
  • The discriminator loss as binary cross-entropy
  • Minimax versus non-saturating generator losses
  • The optimal discriminator for a fixed generator
  • Mode collapse, DCGAN and conditional GANs
09

Recurrent Neural Networks and LSTMs

Week 9. Hidden states and weight sharing, unrolling through time, exploding and vanishing gradients, LSTM gates, GRUs and parameter counts.

Week 9 turns to sequences such as text and signals, where inputs vary in length and order matters. A recurrent network carries a hidden state, updated by one shared cell at every step, so it can be unrolled into a deep network with tied weights.

  • Why fixed-size feedforward networks struggle with sequences
  • The vanilla RNN cell and weight sharing across time
  • Unrolling a recurrence by hand
  • Exploding and vanishing gradients through time
  • Gradient clipping and gated recurrent cells
  • LSTM forget, write and output gates
10

Attention and the Transformer Block

Weeks 10 and 11. Queries, keys and values, scaled dot-product attention, multi-head attention, the transformer block and its computational cost.

Weeks 10 and 11 introduce attention, the operation that lets each token build its own vector from all the others.

  • Why one word needs context-dependent vectors
  • Queries, keys and values as learned projections
  • Scaled dot-product attention and the √d_k divisor
  • Attention weights as convex combinations
  • Multi-head attention and per-head width
  • The transformer block: attention, MLP, residuals and Layer Norm
11

Tokenisation, Positional Encoding and BERT

Week 11. Character, word and subword tokens, byte-pair encoding, sinusoidal and learned positional encodings, masked language modelling and fine-tuning heads.

Week 11 builds the pieces that turn the transformer into a language model. Tokenisation cuts text into units, with subword schemes such as byte-pair encoding balancing vocabulary size against sequence length.

  • Character, word and subword tokens
  • Byte-pair encoding merge by merge
  • Permutation equivariance and the need for position
  • Properties of an ideal positional encoding
  • Sinusoidal, learned and rotary encodings
  • BERT pre-training by masked language modelling
12

Vision Transformers, Evaluation and Decoding

Week 12. Patch tokens and the classification token, ViT against ResNet, perplexity, BLEU, temperature, top-k, top-p and beam search.

Week 12 applies transformers to images and asks how language models are measured and used.

  • Patch tokens, the classification token and learned positions
  • ViT variants and the data-scale comparison with ResNet
  • Linear probing and imageGPT
  • Perplexity as exponentiated cross-entropy
  • BLEU: clipped n-gram precision and brevity penalty
  • Greedy decoding, temperature, top-k and top-p

The unit synopsis describes neural networks first, then how they are trained with backpropagation, then the main families of deep networks: multilayer perceptrons, convolutional networks and recurrent networks, followed by modern transformers and large language models, and how such models are deployed and fine-tuned.

Optimisation and generalisation theory explains why these networks behave as they do, and Python with PyTorch is the programming environment.

The teaching runs over twelve weeks of workshops and studios. Weeks 1 to 3 cover regression and classification models and gradient descent.

Week 4 introduces multilayer perceptrons and the backpropagation algorithm, Week 5 convolutional networks, and Week 6 PyTorch alongside the mid-semester test.

Week 7 revisits convolutional design with residual networks and batch normalisation, Week 8 turns to generative adversarial networks, and Week 9 to recurrent networks and LSTMs. The final three weeks cover the attention mechanism, large language models and transformers for text and images.

Assessment combines continuous work worth half the unit with a final examination worth the other half.

The in-semester tasks are ten engagement quizzes, two homeworks that mix coding with written questions, an in-person mid-semester test and an individual assignment. To pass, a student needs an overall mark of at least 50%.

Studio worksheets carry no marks but come with released solutions, and they are the best rehearsal for the hand calculations the tests reward: gradients, layer sizes, attention weights and losses worked step by step.

Worked example · free

Gradient descent zigzags on an elongated bowl

Q [5 marks]. Minimise f(w1, w2) = w1² + 6w2² by gradient descent from (−4, 1.5) with learning rate 0.15. Take two steps and explain why the path zigzags in w2 while w1 shrinks steadily. The marks shown are our own practice weighting and do not come from the University.
Gradient descent on an elongated bowl.Gradient descent on an elongated bowl. Ellipses are level sets of w1² + 6w2²; the orange path starts at the left and zigzags along the steep axis while creeping along the shallow one.minimumstartlevel setssteep w2 direction zigzags
Gradient descent on an elongated bowl. Ellipses are level sets of w1² + 6w2²; the orange path starts at the left and zigzags along the steep axis while creeping along the shallow one.
  • 1Gradient: ∇f = (2w1, 12w2), so at the start ∇f = (−8, 18).
  • 1First step: w = (−4, 1.5) − 0.15(−8, 18) = (−2.8, −1.2).
  • 1Second step: ∇f = (−5.6, −14.4), so w = (−2.8, −1.2) − 0.15(−5.6, −14.4) = (−1.96, 0.96).
  • 1Per step, w1 is multiplied by 1 − 0.15 × 2 = 0.7, a steady shrink towards zero.
  • 1Per step, w2 is multiplied by 1 − 0.15 × 12 = −0.8, so it flips sign each time while shrinking: the zigzag across the steep direction.
After two steps the iterate is (−1.96, 0.96). The shallow coordinate contracts by 0.7 per step, while the steep coordinate overshoots and contracts by a factor of −0.8, so the path zigzags across the narrow axis of the bowl; both still converge because each factor has magnitude below one.
Sia tip — Write the per-coordinate factor 1 − η × curvature before iterating; a negative factor predicts a zigzag and a magnitude above one predicts divergence.
Glossary

Key terms

Mean squared error
Mean squared error is the average of the squared differences between predictions and targets, the loss minimised by least-squares regression.
Sigmoid function
The sigmoid function σ(z) = 1/(1 + e^(−z)) maps any real score to a probability between 0 and 1.
Cross-entropy loss
Cross-entropy loss is the negative log-probability a model assigns to the true class, averaged over the training samples.
Softmax
Softmax converts a vector of logits into probabilities by exponentiating each entry and dividing by the sum of the exponentials.
Learning rate
The learning rate is the step size that scales the negative gradient in each gradient-descent update.
Backpropagation
Backpropagation is the algorithm that applies the chain rule backwards through a computation graph to find how the loss changes with each parameter.
Receptive field
A receptive field is the region of the input image that influences one value in a convolutional feature map.
Dropout
Dropout is a regulariser that sets each hidden unit to zero with probability p during training and rescales the survivors.
Residual connection
A residual connection adds a block's input to its output, so the block computes F(x) + x and can represent the identity easily.
Batch normalisation
Batch normalisation standardises each feature using mini-batch statistics and then applies a learned scale and shift.
Mode collapse
Mode collapse is a GAN failure in which the generator produces realistic samples that cover only part of the real data distribution.
LSTM cell
An LSTM cell is a gated recurrent unit with a separate cell state controlled by forget, write and output gates.
Scaled dot-product attention
Scaled dot-product attention weights value vectors by a softmax of query-key dot products divided by the square root of the key dimension.
FAQ

ECE5179 FAQ

How is the unit assessed?

Half the unit is continuous assessment: ten engagement quizzes worth 0.5% each, Homework 1 at 5%, Homework 2 at 10%, the Mid-Semester Test at 15% and an individual Assignment at 15%. The other half is a final examination worth 50% in the official examination period. You need an overall mark of at least 50% to pass the unit.

What do we know about the final exam?

The unit pages give its weight, 50%, place it in the official examination period and say it covers the unit learning outcomes. They do not state the duration, the question types or which materials you may bring. Check the examination notice on Moodle and your personal timetable, and prepare for both calculation and explanation questions.

What was the format of the mid-semester test?

It was a 40-minute invigilated test in the Week 6 workshop, worth 15% and focused on the early weeks. Questions mixed multiple choice, numerical answers entered in Moodle and handwritten working on paper. No coding was required. Students could bring up to five double-sided A4 sheets of notes, the provided cheat sheet, a dictionary and a calculator.

Do I need to code in the exams, or calculate by hand?

The mid-semester test explicitly required no coding and could be finished with Moodle, pen, paper and a calculator. Coding is assessed through the homeworks and the assignment, which use Jupyter notebooks and PyTorch. For timed tests, practise hand derivations: gradients, backpropagation through small graphs, layer output sizes and parameter counts.

How much mathematics does the unit use?

Expect calculus and linear algebra throughout. Studio 1 revises matrices, norms and angles, and the formula sheet lists derivatives, the chain rule, norms and the regression, logistic and softmax formulas. Later weeks add probability for cross-entropy, GAN objectives and divergences. The algebra is rarely long, but each step must be exact.

Which topics do students find hardest?

Backpropagation by hand is the usual sticking point, because one sign or missed factor spoils every later gradient. Convolution arithmetic with padding, stride and dilation is a close second. The later weeks add new ideas quickly, so attention shapes, GAN losses and LSTM gates reward careful revision rather than last-minute reading.

Is there a textbook for the unit?

The unit names Dive into Deep Learning by Zhang and colleagues as the main textbook, freely available online, and suggests Deep Learning by Goodfellow and colleagues, also free, for further study. Weekly lecture notes, slides, workshop notebooks and studio worksheets carry the examinable detail, so use the books to clarify rather than replace them.

Chapter questions

Questions students ask in each ECE5179 chapter

Why does the least-squares line pass through the mean point?
Setting the derivative of the mean squared error with respect to the intercept to zero forces the residuals to average zero. That condition gives b = ȳ − w x̄, and substituting x̄ into the line returns ȳ exactly. Checking this property is a quick way to catch an arithmetic slip in a hand-fitted line. Chapter 01 · Learning Types and Linear Regression
Why use cross-entropy instead of squared error for classification?
With a sigmoid output, squared error keeps a factor ŷ(1 − ŷ) in its gradient, so a confidently wrong prediction learns about a thousand times more slowly than under cross-entropy. Cross-entropy is also convex in the weights, so gradient descent has no poor local minima to fall into for this model. Chapter 02 · Logistic Regression and the Softmax Classifier
How do I tell from a loss curve whether the learning rate is too big?
A rate that is too large makes the loss oscillate, rise or diverge, while a rate that is too small gives a slow, steady decline. A good rate falls quickly and then levels off. If two curves start from the same loss, they share an initialisation, so differences come from the step size. Chapter 03 · Gradient Descent and Optimisation Geometry
Why do neural networks need activation functions?
Without them, each layer is an affine map and a composition of affine maps is still affine, so the whole network can only draw flat decision boundaries. The non-linearity between layers is what lets hidden layers bend the input space and build features that a final linear layer can separate. Chapter 04 · Multilayer Perceptrons and Backpropagation
What formula gives the output size of a convolution?
With input size H, padding p on each side, kernel size k, dilation d and stride s, the output size is the floor of (H + 2p − d(k − 1) − 1)/s, plus one. With no dilation this becomes the floor of (H + 2p − k)/s plus one, which covers most studio questions. Chapter 05 · Convolutional Neural Networks
Why must survivors be rescaled in dropout?
If units are zeroed with probability p during training but all fire at test time, the next layer receives more input at test time than it learned to expect. Inverted dropout divides the surviving activations by 1 − p during training, so the expected input is the same in both modes and the test network needs no change. Chapter 06 · Overfitting and Regularisation
Why do residual connections help very deep networks?
A residual block outputs F(x) + x, so learning the identity only requires F to be zero, which is easy. The derivative of the block includes an identity term, so gradients pass through the shortcut undiminished. The lectures show that plain deep networks underfit rather than overfit, so this is an optimisation fix. Chapter 07 · Residual Networks and Batch Normalisation
Why is the non-saturating generator loss preferred?
Early in training the discriminator rejects fakes confidently, so D(G(z)) is near zero and the minimax loss log(1 − D(G(z))) is almost flat. Measured against the discriminator's logit, its gradient is −D, which is tiny, while the non-saturating loss −log D(G(z)) gives −(1 − D), close to −1 in the same direction. Chapter 08 · Generative Adversarial Networks
Why do vanilla RNNs forget long-range information?
Backpropagating across k steps multiplies k factors, each the recurrent weight times a tanh derivative of at most one. When those factors are below one the product shrinks geometrically, so early inputs barely affect the gradient. Factors above one make it explode instead, which clipping can control but vanishing cannot be fixed that way. Chapter 09 · Recurrent Neural Networks and LSTMs
Why divide the attention scores by the square root of d_k?
If query and key entries are roughly independent with unit variance, their dot product has variance close to d_k. Large scores push softmax towards a one-hot output whose gradients nearly vanish. Dividing by √d_k restores unit scale, which the lectures describe as scaling the softmax for stability. Chapter 10 · Attention and the Transformer Block
Why do transformers need positional encodings?
Dot-product attention is permutation equivariant: shuffling the input tokens simply shuffles the outputs in the same way. Two sentences with the same words in a different order would therefore look identical. Adding a position vector to each token makes order part of the input, so attention can use it. Chapter 11 · Tokenisation, Positional Encoding and BERT
How many tokens does a Vision Transformer read?
For an H by W image and patch size P there are (H/P) times (W/P) patch tokens, plus one classification token. A 224 by 224 image with 16 by 16 patches gives 196 patches and 197 tokens. Halving the patch size quadruples the patches and multiplies the attention table roughly sixteen-fold. Chapter 12 · Vision Transformers, Evaluation and Decoding
Study strategy

How to study for the exam

Work through the unit in its own order, because every later week reuses an earlier one: least squares and cross-entropy become output layers, gradient descent becomes the training loop, and backpropagation is the same chain rule on a larger graph. For each week, rebuild the key derivation on a blank page before reading the notes again, then redo one studio problem without the solution and compare line by line.

Keep a single sheet of size rules, covering parameter counts for dense, convolutional and recurrent layers, convolution output size, multiplication counts and attention shapes, and test yourself on new numbers until each takes under a minute. When a calculation goes wrong, record whether the cause was a sign, a shape, a missed factor or a calculator mode, since the same slip tends to recur.

In the final fortnight, mix questions from different weeks so the topic name no longer tells you the method, and practise explaining a design choice in two or three sentences after every calculation.

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