Real World: Transformer Architecture

Linear Algebra for Machine Learning · Axiom Academy

Transformers Through Linear Algebra Modern NLP and Vision models deconstructed into matrix operations Overview: What Is a Transformer? Transformers (BERT, GPT, Vision Transformer) are built entirely from: Matrix multiplications (linear layers) Softmax (element-wise exponential + normalization) Element-wise operations (activations, layer norms) No recurrence, no convolution—pure matrix algebra and attention. Transformer Block Architecture Applying Transformers to Images The Training Loop (Pseudocode) Why Transformers Work (Linear Algebra Perspective) Self-attention: Q @ K^T / √d_k allows every position to dynamically attend to relevant positions Multi-head: Different heads learn different attention patterns (syntax, semantics, long-range) Residual connections: Help gradients flow through deep networks Layer normalization: Keeps activations stable, enables higher learning rates Positional encodings: Inject order information without implicit recurrence Massive scale: With 175B parameters and self-supervised pretraining, emergence of remarkable capabilities NLP: BERT, GPT (text generation, QA, summarization) Vision: Vision Transformer, CLIP (image classification, image-text matching) Multimodal: DALL-E, Flamingo (combining image and text) Science: AlphaFold (protein structure using transformer-like architecture) All built on the linear algebra foundations we've studied in this unit! Unit 8: Linear Algebra in Neural Networks | Module 15: Transformers

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