1.1. Fundamentals of Representation Learning
🪄 Step 1: Intuition & Motivation
- Core Idea: Imagine you’re teaching a computer to understand the world. You show it a cat, a dog, and a banana — and you want it to somehow feel the difference between them. But to a computer, everything is just numbers. So, how do we turn “cat,” “dog,” and “banana” into numbers that actually mean something?
That’s what representation learning does — it helps a model learn useful ways to represent data automatically, rather than forcing humans to hand-design every feature.
- Simple Analogy: Think of representation learning like learning to describe a city by exploring it — instead of reading a list of landmarks. After wandering for a while, you intuitively know where everything is and how close two places are — that’s what embeddings do in data-space.
🌱 Step 2: Core Concept
Representation learning is the art of turning raw, messy data (like words, images, or sounds) into meaningful vectors of numbers — numbers that capture essence, not noise.
What’s Happening Under the Hood?
In the early days of Machine Learning, humans used to handcraft features. For example, to detect spam emails, you might count the number of words like “discount” or “offer.”
But this approach is limited — what if the spammer writes “disc0unt” instead?
Deep learning changed everything. Now, instead of manually telling the model what matters, we let the model learn what’s important by itself — by adjusting internal parameters (weights) to build internal representations of the data.
These internal representations (or “features”) are learned automatically as the model sees more data and minimizes its loss function.
Why It Works This Way
Humans don’t consciously think about features either. When you look at a dog, you don’t count its legs or measure its tail. You just “know” it’s a dog.
Similarly, a neural network starts with raw data and learns useful intermediate features — shapes, edges, textures (for images), or relationships between words (for text).
These learned features become embeddings — compact numerical descriptions that preserve meaningful relationships.
How It Fits in ML Thinking
Representation learning lies at the core of deep learning. Every powerful model — CNNs, RNNs, and especially Transformers — thrives because they learn internal representations that make complex patterns easier to capture.
In Transformers, the entire mechanism of attention depends on comparing learned representations — the queries, keys, and values are just different forms of learned embeddings.
📐 Step 3: Mathematical Foundation
Vector Representations (Embeddings)
Each input item $x_i$ (say, a word or token) is mapped to a vector $\mathbf{v}_i$ of dimension $d$.
- $x_i$ → the original symbol (like “cat”).
- $\mathbf{v}_i$ → its learned numerical representation.
- $d$ → embedding size (e.g., 100 or 768 in Transformers).
The model learns these vectors so that similar meanings produce similar vectors (low distance between them).
Distance and Similarity
This formula measures how aligned two vectors are — a way of saying, “How similar are these two ideas?” A higher cosine similarity (closer to 1) means the meanings are close.
🧠 Step 4: Key Ideas
- Representation learning reduces complexity — instead of memorizing raw inputs, models learn patterns.
- Embeddings capture relationships — distance between vectors represents semantic closeness.
- Higher dimensions ≠ better always — more dimensions add expressive power, but too many can lead to overfitting or inefficiency. This is called the curse of dimensionality.
⚖️ Step 5: Strengths, Limitations & Trade-offs
- Learns features automatically from data.
- Captures complex patterns (semantic meaning, relationships).
- Enables transfer learning — once learned, embeddings can be reused across tasks.
- Needs large, diverse datasets to learn meaningful representations.
- Hard to interpret directly — embeddings are not human-readable.
- Sensitive to biases in data — learned patterns reflect what the data contains.
- The trade-off lies between expressivity (capturing meaning) and efficiency (keeping embeddings compact). Think of it as balancing a “zoomed-in map” vs. a “global map” — one gives detail, the other gives context.
🚧 Step 6: Common Misunderstandings
🚨 Common Misunderstandings (Click to Expand)
“Embeddings are just word IDs.” No — one-hot vectors are IDs. Embeddings are dense, continuous, and learned.
“Bigger embeddings mean better performance.” Not necessarily. Bigger vectors can overfit; meaningful structure matters more than size.
“Embeddings capture grammar or logic explicitly.” They don’t. They capture patterns of usage, not grammatical rules directly.
🧩 Step 7: Mini Summary
🧠 What You Learned: Representation learning turns raw data into meaningful numeric representations — embeddings.
⚙️ How It Works: The model learns these embeddings automatically by minimizing loss and adjusting internal weights.
🎯 Why It Matters: Embeddings are the foundation of modern architectures like Transformers — every attention score, context vector, or token interaction starts here.