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Lecture 3 – Neural Networks
1. Course plan: coming up
Homeworks
A note on your experience!
Lecture Plan
2. Classification setup and notation
Classification intuition
Details of the softmax classifier
Training with softmax and cross-entropy loss
Background: What is “cross entropy” loss/error?
Classification over a full dataset
Traditional ML optimization
3. Neural Network Classifiers
Neural Nets for the Win!
Classification difference with word vectors
Neural computation
An artificial neuron
A neuron can be a binary logistic regression unit
A neural network = running several logistic regressions at the same time
Matrix notation for a layer
Non-linearities (aka “f ”): Why they’re needed
4. Named Entity Recognition (NER)
Named Entity Recognition on word sequences
Why might NER be hard?
5. Binary word window classification
Window classification
Window classification: Softmax
Simplest window classifier: Softmax
Binary classification with unnormalized scores
Binary classification for NER Location
Neural Network Feed-forward Computation
Main intuition for extra layer
The max-margin loss
Simple net for score
Remember: Stochastic Gradient Descent
Computing Gradients by Hand
Gradients
Jacobian Matrix: Generalization of the Gradient
Chain Rule
Example Jacobian: Elementwise activation Function
Other Jacobians
Back to our Neural Net!
1. Break up equations into simple pieces
2. Apply the chain rule
3. Write out the Jacobians
Re-using Computation
Derivative with respect to Matrix: Output shape
Derivative with respect to Matrix
Why the Transposes?
What shape should derivatives be?
Next time: Backpropagation
