Neural networks and Chinese character recognition...Deep learning examples Neural networks...
19
Deep learning examples Neural networks Handwriting recognition Signatures Neural networks and Chinese character recognition Jeremy Reizenstein May 2016 Reizenstein NeuralNets and Chinese
Transcript of Neural networks and Chinese character recognition...Deep learning examples Neural networks...
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Neural networks and Chinese character recognition
Jeremy Reizenstein
May 2016
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Table of Contents
1 Deep learning examples
2 Neural networks
3 Handwriting recognition
4 Signatures
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Example: Mnist
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Example: Imagenet
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Example: EEG
1
1Multi-channel EEG recordings during 3,936 grasp and lift trials, Luciw,Jarocka and Edin, Scientific Data 1, 2014; kaggle 2014
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Neural Networks
H = σ(W1I + b1)
O = σ(W2H + b2)
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Typical approach to supervised machine learning
input Rk labelsrepresentation classification
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Timeseries and paths
Data which varies in time doesn’t live in a fixed Rk .Time-structure of the data matters
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Recurrent Neural Networks
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Recurrent Neural Networks
http://karpathy.github.io/2015/05/21/rnn-effectiveness/
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Convolutional Neural Networks
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Chinese - the Casia online dataset
http://www.nlpr.ia.ac.cn/databases/handwriting/Home.htmlReizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Online handwriting
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Typical approaches
input Rk labels
input×t Rk×t labels
representation classification
representation RNN
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Signatures
The signature of a path is a set of iterated integrals.Consider a path in R3 parameterised by the variable t ranging from0 to 1, given by
t 7→ (f1(t), f2(t), f3(t))
Then, for example, the element 2,3 of the signature is∫ 1
0
[∫ t
0f ′2(s) ds
]f ′3(t) dt =
∫ 1
0
∫ t
0df2(s) df3(t)
and element 2,1,2 of the signature is∫ 1
0
∫ t
0
∫ s
0df2(r) df1(s) df2(t).
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Signatures
The mth level of the signature of a path in Rd is the dm values ofthe elements with m integrated integrals. It takes values in(Rd)⊗m. Given a piecewise linear path, it is easy to compute thefirst m levels of its signature using a theorem called Chen’s identity.
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Log-Signature demonstration
There is redundancy in the signature. The log signature is atransformation of the same information as the signature which isnot redundant. For example, in R2, the first four levels of thesignature look like this
(· ·)
+
((· ·)(· ·)
)+
(((· ·)(· ·)
)((· ·)(· ·)
))+
((
(· ·)(· ·)
)((· ·)(· ·)
))((
(· ·)(· ·)
)((· ·)(· ·)
))
- that is 2 + 4 + 8 + 16 = 30 numbers while the log signature isonly 2 + 1 + 2 + 3 = 8 numbers.
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Questions
A signature is a nice representation of a path of arbitrary length.When is it good enough? What properties of a complicated pathcan be derived from some levels of its signature? How to balance arepresentation using more levels of the signature versus choppingthe path up and looking at signatures of the chunks?
Reizenstein NeuralNets and Chinese
Deep learning examplesNeural networks
Handwriting recognitionSignatures
Thanks!
centre for
complexityscience
Dr Ben Graham
Reizenstein NeuralNets and Chinese
