Make Ruby Differentiable

Apr 21, 20190 likes2,311 views

The document discusses making Ruby differentiable by introducing automatic differentiation capabilities. It presents a differentiation gem that allows making Ruby methods, procs, numbers and matrices differentiable. This allows defining and computing gradients of functions. It demonstrates this on a multilayer perceptron neural network model solving XOR. The goal is to make Ruby differentiable in order to apply automatic differentiation to Ruby programs.

Make Ruby Differentiable
(Automatic Differentiation for Ruby)
@nagachika
2019-04-19 RubyKaigi 2019

Make Ruby Differentiable
This LT is homage for the episode #206 of Rebuild.fm

Make Ruby Differentiable
There are two LT talks for ‘Automatic Differentiation’!!

Swift for TensorFlow
https://github.com/tensor?ow/swift/blob/master/docs/AutomaticDi?erentiation.md

Automatic Differentiation
Berland at English Wikipedia [Public domain],?
via Wikimedia Commons

Differentiation Gem
https://rubygems.org/gems/differentiation
https://github.com/nagachika/differentiation

differential def func(x, y)
(x + 1.0) * (y - 2.0)
end
result = func(1.0, 2.0)
result
=> 0.0
result.gradients
=> { x: 0.0, y: 2.0 }
result.gradients(:x, :y)
=> [ 0.0, 2.0 ]
Make method differentiable

$l = ->(x, y){ (x + 1.0) * (y - 2.0) } differentiable_l = differential l result = differentiable_l.call(1.0, 2.0) result => 0.0 result.gradients => { x: 0.0, y: 2.0 } result.gradients(:x, :y) => [ 0.0, 2.0 ] Make Proc differentiable$

x = 1.0.to_dual_number
y = 2.0.to_dual_number
result = (x + 1.0) * (y - 2.0)
result
=> 0.0
result.gradients(x, y)
=> [ 0.0, 2.0 ]
Make Numeric Differentiable

mat = Matrix[
[ 0.0, 1.0],
[ 2.0, 3.0]
]
differential def matmul_reduce(m)
(m * m).sum
end
result = matmul_reduce(mat)
=> 22.0
result.gradients(:m)
=> [Matrix[[3.0, 7.0], [5.0, 9.0]]]
Make Matrix Differentiable

class DualNumber
…
def coerce(other)
if Differentiation.differentiable?(other)
[ Differentiation.convert_to_dual_number(other), self]
else
super
end
end
end
Numeric#coerce

Differentiable DEMO
Multiple Layered Perceptron solving XOR
x1 x2 y
0 0 0
0 1 1
1 0 1
1 1 0
x1
x2
y

Differentiable DEMO
Multiple Layered Perceptron solving XOR?
with Matrix and differentiation.gem

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Make Ruby Differentiable

1. Make Ruby Differentiable (Automatic Differentiation for Ruby) @nagachika 2019-04-19 RubyKaigi 2019

2. Make Ruby Differentiable This LT is homage for the episode #206 of Rebuild.fm

3. Make Ruby Differentiable There are two LT talks for ‘Automatic Differentiation’!!

4. Swift for TensorFlow https://github.com/tensor?ow/swift/blob/master/docs/AutomaticDi?erentiation.md

5. Automatic Differentiation Berland at English Wikipedia [Public domain],? via Wikimedia Commons

6. Differentiation Gem https://rubygems.org/gems/differentiation https://github.com/nagachika/differentiation

7. differential def func(x, y) (x + 1.0) * (y - 2.0) end result = func(1.0, 2.0) result => 0.0 result.gradients => { x: 0.0, y: 2.0 } result.gradients(:x, :y) => [ 0.0, 2.0 ] Make method differentiable

8. l = ->(x, y){ (x + 1.0) * (y - 2.0) } differentiable_l = differential l result = differentiable_l.call(1.0, 2.0) result => 0.0 result.gradients => { x: 0.0, y: 2.0 } result.gradients(:x, :y) => [ 0.0, 2.0 ] Make Proc differentiable

9. x = 1.0.to_dual_number y = 2.0.to_dual_number result = (x + 1.0) * (y - 2.0) result => 0.0 result.gradients(x, y) => [ 0.0, 2.0 ] Make Numeric Differentiable

10. mat = Matrix[ [ 0.0, 1.0], [ 2.0, 3.0] ] differential def matmul_reduce(m) (m * m).sum end result = matmul_reduce(mat) => 22.0 result.gradients(:m) => [Matrix[[3.0, 7.0], [5.0, 9.0]]] Make Matrix Differentiable

11. class DualNumber … def coerce(other) if Differentiation.differentiable?(other) [ Differentiation.convert_to_dual_number(other), self] else super end end end Numeric#coerce

12. Differentiable DEMO Multiple Layered Perceptron solving XOR x1 x2 y 0 0 0 0 1 1 1 0 1 1 1 0 x1 x2 y

13. Differentiable DEMO Multiple Layered Perceptron solving XOR? with Matrix and differentiation.gem

14. Let’s Make Ruby Differentiable

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Make Ruby Differentiable

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