Deep Learning and Representation Learning

Manual: General · Subject: Artificial Intelligence

Explores neural networks, optimization, scaling laws, architectural inductive bias, and representation learning.

Neural Networks as Function Approximators

Why deep models matter

Deep learning learns layered representations that can capture hierarchical structure in images, language, audio, and other modalities. Its success stems from a combination of expressive power, optimization advances, and data scale.

Optimization objective

Training typically minimizes $\min_\theta \frac{1}{n}\sum_{i=1}^n \ell(f_\theta(x_i), y_i) + \lambda \Omega(\theta)$ , where the regularizer $\Omega$ imposes inductive bias.

Architectural families

MLP

General-purpose feedforward network.

CNN

Exploits local spatial structure and translation invariance.

RNN/LSTM

Models sequences with recurrence.

Transformer

Uses attention for long-range dependencies.

Representative capabilities and limitations

Architecture	Strength	Limitation
CNN	Strong inductive bias for vision	Less natural for long-range context
Transformer	Parallelizable sequence modeling	Quadratic attention cost in standard form
RNN	Online sequence processing	Optimization and long-context issues
MLP	Conceptual simplicity	Weak structural bias

What is the most distinctive feature of transformers compared with recurrent models?

Use of attention over sequence positions Need for labeled graphs Inability to process language No parameters are trained

Why are representation learning methods important in modern AI?

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Optimization is not the whole story

Architecture, data curation, optimization dynamics, and alignment with downstream objectives all affect performance; better training loss alone does not guarantee useful representations.

Studying a new neural architecture

1

Step 1: Identify the inductive bias encoded by the architecture.
2

Step 2: Compare optimization behavior against strong baselines.
3

Step 3: Measure scaling with data, model size, and compute.
4

Step 4: Analyze representational geometry and feature reuse.
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Step 5: Test robustness, calibration, and transfer.

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Concept Constellation

Deep Learning and Representation Learning

Neural Networks as Function Approximators

Why deep models matter

Optimization objective

Studying a new neural architecture