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Computer Science
Artificial Intelligence
Deep Learning
Transformer deep learning architecture
1. Foundational Concepts and Predecessors
2. The Original Transformer Architecture
3. Transformer Encoder
4. Transformer Decoder
5. Output Generation and Decoding
6. Training Methodology
7. Mathematical Foundations
8. Architectural Analysis
9. Interpretability and Analysis
10. Transformer Variants and Evolution
11. Advanced Attention Mechanisms
12. Applications and Adaptations
13. Implementation Considerations
7.
Mathematical Foundations
7.1.
Linear Algebra Concepts
7.1.1.
Matrix Operations
7.1.1.1.
Matrix Multiplication
7.1.1.2.
Transpose Operations
7.1.1.3.
Batch Matrix Operations
7.1.2.
Vector Spaces
7.1.2.1.
Embedding Spaces
7.1.2.2.
Attention Score Spaces
7.1.3.
Dimensionality Considerations
7.2.
Probability and Information Theory
7.2.1.
Probability Distributions
7.2.1.1.
Softmax Distribution
7.2.1.2.
Categorical Distribution
7.2.2.
Information Measures
7.2.2.1.
Entropy
7.2.2.2.
Cross-Entropy
7.2.2.3.
KL Divergence
7.3.
Optimization Theory
7.3.1.
Gradient-based Optimization
7.3.2.
Convexity and Non-convexity
7.3.3.
Local vs Global Optima
7.4.
Computational Complexity
7.4.1.
Time Complexity Analysis
7.4.1.1.
Self-Attention Complexity
7.4.1.2.
Feed-Forward Complexity
7.4.2.
Space Complexity
7.4.2.1.
Memory Requirements
7.4.2.2.
Attention Matrix Storage
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6. Training Methodology
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8. Architectural Analysis