Intrinsic
Dimension
PyTorch & Deep Learning SG
15 May 2018
About Me
- Machine Intelligence / Startups / Finance
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- Moved from NYC to Singapore in Sep-2013
- 2014 = 'fun' :
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- Machine Learning, Deep Learning, NLP
- Robots, drones
- Since 2015 = 'serious' :: NLP + deep learning
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- & Papers...
- & Dev Course...
About Red Dragon AI
- Deep Learning Consulting & Prototyping
- Education / Training
- Products :
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- Conversational Computing
- Natural Voice Generation - multiple languages
- Knowledgebase interaction & reasoning
Uber Research
- Lots of explanatory material :
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Overall Goal
- Want to quantify :
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- 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 :
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- 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
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
Hunt for the critical value (idealised)
Random Projections
Underlying Details
- Known to be ~ distance-preserving
- Unlikely to be co-linear
- Matrix can be :
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- Dense, and stored
- Sparse (still likely to be non-colinear)
- Other, easily computed forms
- Possibly created on-the-fly
MNIST
Fully Connected vs CNN
Shows that 'visual invariance' is a win
Shuffled MNIST
Fully Connected vs CNN
FC is identical, CNN is of negative value
CIFAR-10
Fully Connected vs CNN
CIFAR-10 is about '10 times harder' than MNIST
Reinforcement Learning
Can measure different problem spaces
Toy RL Problem
Surprisingly easy...
Wrap-up
- This is a very simple idea
- Real research still possible with MNIST
- Having a free GPU is VERY helpful
* Please add a star... *
Deep Learning
MeetUp Group
Deep Learning : Jump-Start Workshop
- Dates + Cost : End-June, S$600
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- 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 :
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- Instruction
- Individual Projects
- Support by SG govt (planned)
- Location : SGInnovate
- Status : TBA