Intrinsic
Dimension

PyTorch & Deep Learning SG

Martin Andrews @ redcatlabs.com
Martin Andrews @ reddragon.ai

15 May 2018

About Me

  • Machine Intelligence / Startups / Finance
    • Moved from NYC to Singapore in Sep-2013
  • 2014 = 'fun' :
    • Machine Learning, Deep Learning, NLP
    • Robots, drones
  • Since 2015 = 'serious' :: NLP + deep learning
    • & Papers...
    • & Dev Course...

About Red Dragon AI

  • Deep Learning Consulting & Prototyping
  • Education / Training
  • Products :
    • Conversational Computing
    • Natural Voice Generation - multiple languages
    • Knowledgebase interaction & reasoning

Uber Research

Bonus Video

Uber Video link

Clickable Link

Overall Goal

  • Want to quantify :
    • Data 'difficulty'
    • Model 'relative effectiveness'
    • ... value of model structure
  • Ideally : How many parameters are required for data?

Big idea

  • Today's models have many parameters : 'D' dimensional
  • Probably, there are many free parameters :
    • Many of these parameters are redundant
    • So the 'solution(s)' are a space, not a point
    • Restrict search to lower dimension 'd'
    • Build 'D' parameters by random projection
  • Intrinsic Dimension = lowest 'd' that 'solves' problem

Parameter Search

Parameter Search

Implementation

  • Create a model
  • Start with regular random initialisation
  • Search along lower dimensional 'ray'
  • Can use backprop as normal
  • If performance is >90% of optimal : Accept

Intrisic Dimension

Intrinsic Dimension Search graph

Hunt for the critical value (idealised)

Random Projections

Underlying Details

  • Known to be ~ distance-preserving
  • Unlikely to be co-linear
  • Matrix can be :
    • Dense, and stored
    • Sparse (still likely to be non-colinear)
    • Other, easily computed forms
    • Possibly created on-the-fly

Code



https://github.com/
mdda/deep-learning-workshop/
notebooks/work-in-progress/
IntrinsicDimension.ipynb


Load Directly into Colab

MNIST

Fully Connected vs CNN

MNIST : FC vs CNN

Shows that 'visual invariance' is a win

Shuffled MNIST

Fully Connected vs CNN

Shuffled MNIST : FC vs CNN

FC is identical, CNN is of negative value

CIFAR-10

Fully Connected vs CNN

CIFAR-10 : FC vs CNN

CIFAR-10 is about '10 times harder' than MNIST

Reinforcement Learning

RL Games

Can measure different problem spaces

Toy RL Problem

RL Toy problem

Surprisingly easy...

Wrap-up

  • This is a very simple idea
  • Real research still possible with MNIST
  • Having a free GPU is VERY helpful
GitHub - mdda

* Please add a star... *

Deep Learning
MeetUp Group

Deep Learning : Jump-Start Workshop

  • Dates + Cost : End-June, S$600
    • Full day (week-end)
    • Play with real models
    • Get inspired!
    • Pick-a-Project to do at home
    • 1-on-1 support online
    • Regroup on subsequent week-nights

Deep Learning
Developer Course

  • Plan : Advanced modules in September/October
  • JumpStart module is ~ prerequisite
  • Each 'module' will include :
    • Instruction
    • Individual Projects
    • Support by SG govt (planned)
  • Location : SGInnovate
  • Status : TBA

- QUESTIONS -


Martin @
RedDragon.ai


My blog : http://mdda.net/

GitHub : mdda