Pseudo-Random Number Generators Functional Programming and - - PowerPoint PPT Presentation

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Pseudo-Random Number Generators Functional Programming and - - PowerPoint PPT Presentation

Aug 17, 2023 353 likes •596 views

Pseudo-Random Number Generators Functional Programming and Intelligent Algorithms Prof Hans Georg Schaathun Hgskolen i lesund 14th February 2017 1 Randomness 1. What is randomness? 2 Randomness 1. What is randomness? 2. How do we

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Pseudo-Random Number Generators

Functional Programming and Intelligent Algorithms Prof Hans Georg Schaathun Høgskolen i Ålesund 14th February 2017

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Randomness

  • 1. What is randomness?

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Randomness

  • 1. What is randomness?
  • 2. How do we create probabilistic computer programs?

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Randomness

  • 1. What is randomness?
  • 2. How do we create probabilistic computer programs?
  • 3. I.e. how do we make the computer act at random?

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Two options

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Two options

True randomness uses physical sources of entropy

  • 1. /dev/random on many systems
  • 2. random-fu in Haskell

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Two options

True randomness uses physical sources of entropy

  • 1. /dev/random on many systems
  • 2. random-fu in Haskell

Pseudo-random number generators (PRNG) are deterministic but random-looking — random, standard package in Haskell — random-tf, more recent Haskell package

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Linear Congruential Generators

xi = a + cxi−1 mod m, x0 is a given seed — Pseudo-random sequence [x0, x1, x2, . . .] — Aka. Lehmer’s algorithm

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Ciphers in counter mode

Alice Bob Eve ek(m) xi = ek(i) x0 is a given seed Pseudo-random sequence [x0, x1, x2, . . .]

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The PRNG is a state machine

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n e x t next n e x t n e x t next next

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The PRNG is a state machine

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n e x t next n e x t n e x t next next

x1 x2 x3 x4 x5 x6

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The PRNG is a state machine

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n e x t next n e x t n e x t next next

x1 x2 x3 x4 x5 x6 — next :: State -> (State,Int)

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The PRNG is a state machine

s1 s2 s3 s4 s5 s6 s7

n e x t next n e x t n e x t next next

x1 x2 x3 x4 x5 x6 — next :: State -> (State,Int) — Lehmer: next s = (s’,s’) where s’ = (a + x*s) ‘mod‘ m

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The PRNG is a state machine

s1 s2 s3 s4 s5 s6 s7

n e x t next n e x t n e x t next next

x1 x2 x3 x4 x5 x6 — next :: State -> (State,Int) — Lehmer: next s = (s’,s’) where s’ = (a + x*s) ‘mod‘ m — Cipher: next s = (s + 1 ‘mod‘ m, encrypt k s)

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random-tf package

  • 1. next ::

TFGen -> (TFGen,Word32)

Exercise

Given a TFGen object, how do you generate an random, infinite list

  • f Word32 objects?

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Splitting a PRNG

  • 1. split ::

TFGen -> (TFGen,TFGen)

  • 2. (g’,newstate) = split g
  • 3. Use g’ to generate the list
  • 4. newstate is your new state

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Where do you get the initial state?

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Where do you get the initial state?

  • 1. Hardcode an arbitrary seed
  • 2. Use initialisation functions in the library

2.1 initTFGen

  • 3. Use a library which provides true random values
  • random-fu

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Tuning parameters

  • 1. Distribution of random initial weights?
  • 2. β in the sigmoid function?
  • 3. Number of iterations?

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Some guidelines

— Weights: −1/√n ≤ w ≤ 1/√n

  • where n is the number of inputs to the layer

— The weights should have similar magnitude — Small β — β ≤ 3

  • 1. β = 1 is a good starting point

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Number of epochs

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Exercise

— Random starting weights

  • 1. initNeuron
  • 2. initNetwork

— Test your network — Experiment by varying

  • 1. magnitude of initial weights
  • 2. β
  • 3. number of epochs

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