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Algorithms for calculating gradients
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Classroom Contents
Differentiable Functional Programming
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- 1 Intro
- 2 Parametrised functions Supervised learning Gradient descent
- 3 Choose parameters to fit data
- 4 Algorithmically choose parameters
- 5 Calculate the derivative of the loss function with respect to the parameters
- 6 Calculate gradient for current parameters
- 7 Deep learning is supervised learning of parameterised functions by gradient descent
- 8 Tensor multiplication and non-linearity
- 9 Tensors: multidimensional arrays
- 10 Conditionals and loops
- 11 Algorithms for calculating gradients
- 12 Composition of Derivatives
- 13 Symbolic differentiation
- 14 No loops or conditionals
- 15 Inexact. Choosing e is hard
- 16 Two main algorithms: forward and reverse
- 17 Calculate with dual numbers
- 18 There is a monad for Dual
- 19 Forward-mode scales in the size of the input dimension
- 20 Chain rule doesn't care about order
- 21 Use a monad (or continuations)
- 22 flatMap is the chain rule
- 23 Reverse-mode scales in the size of the output dimension
- 24 Tensor dimensions must agree
- 25 Solution: expressive type systems
- 26 Linear logic and differential A-calculus
- 27 Need compilation (to GPU) for performance
- 28 Scala is well positioned for the next generation of DL systems
