M6 · Lesson 4 — Writing Research Papers

Writing the
Method Section

The method section is where you prove the claim you made in the introduction.
Formalism and intuition must work together.

01

M6 · L4 — Structure

Standard structure

Four subsections in
every method section

3.1

Problem Formulation

Formal definitions. Inputs, outputs, objective. This is where M5 skills apply.

3.2

Overview

A figure + 1 paragraph. High-level picture before the details. Most papers skip this — don't.

3.3

Detailed Components

Each equation explained. Each design choice justified. This is the heart of the section.

3.4

Training Objective

Loss function. Optimisation algorithm. Complexity analysis if relevant.

"The overview figure is the most underused tool in methods writing. A single diagram can replace three paragraphs of architecture description."

Common mistake: Diving into equations without telling the reader what you're trying to achieve. Always provide the intuition before the formalism — not after.

02

M6 · L4 — Problem Formulation

The foundation of everything

Problem formulation:
be precise before being clever

A good problem formulation defines:

Entities — users 𝒰, items ℐ, interactions 𝒪
Input — what the model receives at inference time
Output — what the model returns
Objective — what you're optimising for and why

Test: Could a reader implement your model's input/output interface from the formulation alone, before reading your architecture? If not — formalise further.

          Definition 1. Let 𝒰 = {u₁,...,uₙ} and ℐ = {i₁,...,iₘ}.

          Observed interactions: 𝒪 ⊆ 𝒰 × ℐ where (u,i) ∈ 𝒪 indicates u interacted with i.

          Task. Given user u and 𝒪, learn f: 𝒰 × ℐ → ℝ such that

          ∀i ∈ ℐ⁺_u, ∀j ∉ ℐ⁺_u: f(u,i) > f(u,j).

          # Inputs, outputs, and objective — all explicit.

03

M6 · L4 — Balancing Formalism and Intuition

The hardest writing balance

When to use equations,
when to use words

Use equations when:

The exact operation matters for reproducibility
A diagram alone is ambiguous
You're making a claim about optimality or convergence

Use words when:

Explaining why a design choice was made
Connecting the formal definition to the intuition
Describing something whose exact form is not critical

❌ Formalism without intuition

"z^(l)_u = σ(W^(l) · AGG({z^(l-1)_i : i ∈ 𝒩_u}) + b^(l))"

What is this doing? Why this aggregation? Why σ here? Silence.

✅ Equation + intuition

"We aggregate each user's neighbours (Eq. 3) to capture collaborative signals. A non-linear activation σ is applied to model higher-order interactions that linear aggregation misses."

04

M6 · L4 — Key Takeaways

What to remember

01

Four subsections

Problem formulation → Overview → Components → Training. Use this order every time.

02

Intuition before formalism

Tell the reader what you're trying to achieve before showing the equation. Never the reverse.

03

Justify design choices

For every non-obvious decision: "We use X instead of Y because Z." Silence on design choices invites reviewer speculation.

Next: M6 · L5 — Novelty and Impact Statements

05

Writing theMethod Section