Show Menu

Neural Network Theory Cheat Sheet by

theory

Formal Systems

Cognition, cognitive theory are formal systems, we use mathem­atics to study them
Abstract concepts can be reasoned about precisely when situated in formal systems
Neural networks are continuous systems

Constr­ucting the continum

Axioma­tiz­ation
Describe the basic properties and declare them to be true by definition
Constr­uction
Use simpler objects and operations to explicitly define more complex models
Equiva­lence classes
Partitions a set based on some rules

Dynamic Systems

Recurrent ,learning, and biological neural networks
Motor control is the effector of a dynamic system
The mind is an abstract dynamical system with continuous state variables that are not activation values of units or repres­ent­ations

NNs as Probab­ilistic Models

Used for
stocha­sti­cally searching for global optima
 
repres­enting and rationally coping with uncert­ainty
 
measuring inform­ation
Deployed in
neural network models
 
symbolic modes with non-de­ter­minism and uncert­ainty (e.g. inferring knowledge from experi­ence, using knowledge to infer outputs given inputs)
 

Optimi­zation

Processing
Activation dynamics. Maximizes well-f­orm­edness (harmony) of the activation patter (depends on the connection weight). Spreading activation dynamics is an optimi­zation algorithm for the repres­ent­ation.
Learning
Weight dynamics. Minimizes error. Weight­-ad­jus­tment dynamics is an optimi­zation algorithm for the knownledge in the weights: learning algorithm
Probab­ilistic modelling
Parameters of the statis­tical model change as more data is received. Optimized based of likelihood according to data or Bayesian posterior probab­ility of the data

Fourier analysis

f(x) = \sum_k c_k e^{ikx} employs a basis of imaginary powers of x, {e^{i­kx}}_{k \in \Z}
Also a basis of cos(kx) and sin(kx)
Fourier coeffi­cient states how strongly an oscill­ation of frequency 1/k is present in f
{f(t)}_t describe f in the time / spatial domain
{c_k}_k describe f in the frequency / spatia­l-f­req­uency domain

Support Vector Machines

Use supervised learning to learn a region of activation space for each concept
Classi­fic­ation driven only by training near the region boundary
Wide margin: error function favors a large margin between the training samples and the boundary it posits for separating the categories
Slack variable: minimizes a variable for each training example that "­picks up the slack" between the point and the category region it should be in
Kernel trick: implicitly maps the data into a high dimens­ional space in which classi­fic­ation concep­tually takes places (imple­mented through a kernel function)
 

Discrete structures of distri­bution patterns

vectors v in R: distri­buted repres­ent­ation
With respect to an approp­riate conceptual basis for V, components of a repres­ent­ation v indicate the strength of a set of basis concepts in v: gradient conceptual repres­ent­ation
Eigen-­basis re-scales components
Analyse the entire distri­bution within V of the repres­ent­ations {v^k} of a set of repres­ented items {x^k}
Clusters of {v^k} constitute a conceptual group and may be hierac­hically structured
Can construct is such that greater distance between v^{k} and v^{t} means greater mental distin­gui­sha­bility of x^{k} and x^\{t}

Harmony

Weight matrices, error functions, learning as optimi­zation
Activation vectors, well-f­orm­edness = harmony function, processing as optimz­ation
- Parallel, violab­le-­con­straint satisf­action
- Schema­s/p­rot­otypes in Harmony landscapes
Local optima is a determ­inistic problem, global optima require random­ize­d/s­toc­hastic algorithms

Inductive learning

Finding the best hypothesis within a hypothesis space about the word that the learning is trying to understand
Goodness of a hypothesis is determined jointly by how well H fits the data that the learning has received about the world and how simple H is
A hypothesis is a probab­ilistic data-g­ene­rator
Maximum Likelihood Principle
Maximum A Posteriori Principle: Bayesian principle that says pick the hypothesis that has highest a posteriori probab­ility, balancing the likelihood of the data against the a priori probab­ility of H. Best not pick a H, maintain a degree of belief for every H in the H space
Maximum Entropy Principle: Maxent. Pick the H with the max missing inform­ation, among those H that are consistent with the known data
Minimum Descri­ption Length Principle: shorter is better

Download the Neural Network Theory Cheat Sheet

2 Pages
//media.cheatography.com/storage/thumb/goldmist_neural-network-theory.750.jpg

PDF (recommended)

Alternative Downloads

Share This Cheat Sheet!

 

Comments

No comments yet. Add yours below!

Add a Comment

Your Comment

Please enter your name.

    Please enter your email address

      Please enter your Comment.

          Related Cheat Sheets

          Motivation Theory Cheat Sheet
          EECS 203 Final Exam Cheat Sheet Cheat Sheet