Lecture Notes: Tensors for Neural Networks

Introduction

• Presenter: Josh Starmer
• Topic: Tensors in neural networks
• Sponsored by: Lightning and Grid.ai
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Understanding Tensors

• Confusion: Different definitions in math/physics vs. machine learning
• Focus: Machine learning perspective
• Relation to Neural Networks: Tensors are integral to neural networks

Neural Networks Overview

• Basic Function: Neural networks can predict outcomes from inputs
• Example 1: Simple network predicting drug efficacy from dosage
  • Challenge: Involves complex math for fitting data
• Example 2: Neural network predicting iris species from flower measurements
  • Complexity: More inputs and outputs
• Example 3: Image classification with convolutional neural networks
  • Challenge: Large amount of math for predictions

Practical Application

• Real-world Networks:
  • Larger inputs (e.g., 256x256 pixel color images)
  • Increased complexity with multiple color channels
  • High computational demand with video input

Role of Tensors

• Data Storage: Tensors store inputs, weights, biases
• Terminology:
  • Scalar = 0D Tensor
  • Array = 1D Tensor
  • Matrix = 2D Tensor
  • Multi-dimensional array = N-dimensional Tensor
• Hardware Acceleration:
  • Utilize GPUs and TPUs for processing
  • Faster computation for neural networks

Automatic Differentiation

• Back Propagation: Tensors facilitate automatic differentiation
• Benefit: Simplifies creation of complex networks by handling calculus

Conclusion

• Two Types of Tensors:
  • Math/Physics tensors (not covered)
  • Neural network tensors (focus of lecture)
• Advantages:
  • Designed for hardware acceleration
  • Simplifies back propagation with automatic differentiation

Additional Resources

• StatQuest Study Guides: Available for offline review
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• Final Note: Tensors are crucial in efficiently managing the computational demands of neural networks.