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| '''Sparse distributed memory''' is a mathematical model of human long-term memory introduced by [[Pentti Kanerva]] in 1988. It is used for storing and retrieving large amounts (<math>2^{1000}</math> [[bit]]s) of information without focusing on the accuracy of the information. It uses patterns to serve as [[memory address]]es, where information is retrieved based on similarities between addresses. Memory addresses are all in a list even if they are not related, and are retrieved based on similar content.<ref name=book>{{cite book|last=Kanerva|first=Pentti|title=Sparse Distributed Memory|year=1988|publisher=The MIT Press|isbn=978-0-262-11132-4}}</ref>
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| ==Formula==
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| The general formula is <math>2^n</math> where ''n'' is the number of dimensions of the space, and <math>2^n</math> is the number of feasible memory items.<ref name=book />
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| ===Critical Distance===
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| The critical distance of a Sparse Distributed Memory can be approximately evaluated minimizing the following equation with the restriction <math>d \in N </math> and <math>d \leqslant n</math>. The proof can be found in <ref name="msbrogli"/>
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| <math>
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| \tilde{f}(d) = \left\{ \frac{1}{2} \cdot \left[ 1 - N \left( z < \frac{w \cdot shared(d)}{\sqrt{\theta}} \right) + N \left( z < \frac{- w \cdot shared(d)}{\sqrt{\theta}} \right) \right] - \frac{d}{n} \right\}^2
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| </math>
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| Where:
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| * <math>d</math>: be the distance to the target;
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| * <math>h</math>: be the number of hard-locations activated during read and write operations (this value depends on access radius values);
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| * <math>s</math>: be the number of total stored bitstrings in memory;
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| * <math>H</math>: be the number of hard-locations in memory;
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| * <math>w</math>: be the number of times the target bitstring was written in memory;
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| * <math>\theta</math>: be the total of random bitstrings in all <math>h</math> hard-locations activated by a read operation;
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| * <math>shared(d)</math>: be the mean number of shared hard-locations activated by two bitstrings <math>d</math> bits away from each other. One can find some values for a 1000-dimensional SDM in Kanerva's book, Table 7.1, p. 63, or the equations to calculate to any SDM in Appendix B, p. 125 of the same book.
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| ==Definition==
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| ===Principle===
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| Sparse distributed memory is a mathematical representation of human memory, and uses [[Clustering high-dimensional data|high-dimensional space]] to help model the large amounts of memory that mimics that of the human neural network.<ref name=psu>{{cite web|title=Sparse Distributed Memory and Related Models|id = {{citeseerx|10.1.1.2.8403}}|publisher=Pennsylvania State University|accessdate=3 November 2011|author=Pentti Kanerva|year=1993}}</ref> It utilizes the [[Hamming distance]] to measure mismatched bits and read back data between the original write address and one near it.<ref name=stanford>{{cite web|title=Sparse Distributed Memory: Principles and Operation|url=ftp://reports.stanford.edu/pub/cstr/reports/csl/tr/89/400/CSL-TR-89-400.pdf|publisher=Stanford University|accessdate=1 November 2011|author=M. J. Flynn, P. Kanerva, and N. Bhadkamkar|date=December 1989}}</ref> Human memory has a tendency to congregate memories based on similarities between them(although they may not be related), such as "firetrucks are red and apples are red".<ref name=ship>{{cite web|title=General Psychology|url=http://webspace.ship.edu/cgboer/memory.html|publisher=Shippensburg University|author=C. George Boeree|year=2002}}</ref>
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| ===Neurons===
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| [[Neuron]]s are [[electrically]] excitable cells that transmit information to and from the brain. They are used as models for sending and retrieving data in a sparse distributed memory system. Neurons are the cells that recall and send information in a memory system.<ref name=mastin>{{cite web|title=NEURONS & SYNAPSES|last=Mastin|first=Luke|url=http://www.human-memory.net/brain_neurons.html|accessdate=10 November 2011}}</ref>
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| ===Computers===
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| Memory inside of a computer is [[random-access memory]](RAM), contrary to [[sequential access memory]]. All of the items in a single list, or [[Array data structure|array]], are stored in RAM. The computer has address decoders, similar to the way neurons work in the brain, and return items from the array that match or are similar. Each address in an array points to an individual line in the memory. That line is then returned if it is similar to other lines.
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| ==Example==
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| Sparse distributed memory is based on pulling in patterns between different addresses.
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| Imagine each line as a different memory address, an example from Kanerva's book:
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| :"Why are fire engines painted red?
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| :Firemen's suspenders are red, too.
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| :Two and two are four.
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| :Four times three is twelve.
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| :Twelve inches in a foot.
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| :A foot is a ruler.
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| :Queen Mary is a ruler.
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| :Queen Mary sailed the sea.
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| :The sea has sharks.
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| :Sharks have fins.
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| :The Russians conquered the Finns.
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| :The Russians' color is red.
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| :Fire engines are always rushin'.
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| :So that's why they're painted red!"<ref name=book />
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| As a result, all of these addresses are [[Return statement|returned]] to the user, although these may not be the only addresses in that list.
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| ==Uses==
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| ==="Realizing forgetting"===
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| {| border="1" cellpadding="5" cellspacing="0" align="right"
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| |+ '''Decay Functions'''
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| |-
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| | colspan="3" align="center" |
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| {| border="0"
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| | [[Image:Exponential Decay Function.png|thumb|320px|center|The exponential decay function]]
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| |-
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| | [[Image:Negated sigmoid function.png|thumb|320px|center|The negated-translated sigmoid function]]
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| |}
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| |-
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| | style="background-color:#EDEDED; border-bottom: 3px solid grey;" | ''x''
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| | style="border-bottom: 3px solid grey;" | Independent variable
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| |-
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| | style="background-color:#EDEDED; border-bottom: 3px solid grey;" | ''a''
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| | style="border-bottom: 3px solid grey;" | Constant
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| |-
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| | style="background-color:#EDEDED; border-bottom: 3px solid grey;" | ''c''
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| | style="border-bottom: 3px solid grey;" | Counter
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| |-
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| |}
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| At the University of Memphis, Uma Ramamurthy, Sidney K. D’Mello, and Stan Franklin created a modified version of the sparse distributed memory system that represents "realizing forgetting." It uses a decay equation to better show interference in data. The sparse distributed memory system distributes each pattern into approximately one hundredth of the locations,{{Clarify|date=March 2013}} so interference can have detrimental results.<ref name=memphis>{{cite web|title=Realizing Forgetting in a Modified Sparse Distributed Memory System|url=http://csjarchive.cogsci.rpi.edu/proceedings/2006/docs/p1992.pdf|work=Computer Science Department and The Institute for Intelligent Systems|publisher=The University of Memphis|accessdate=1 November 2011|author=Uma Ramamurthy, Sidney K. D’Mello, Stan Franklin|archiveurl=http://csjarchive.cogsci.rpi.edu/proceedings/2006/|archivedate=2006|pages=1992–1997}}</ref>
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| Two possible examples of decay from this modified sparse distributed memory are presented
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| '''Exponential decay mechanism''': <math>\!f(x)=1+e^{-ax}</math>
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| '''Negated-translated sigmoid decay mechanism''': <math>f(x)=1-[\frac{1}{1+e^{-a(x-c)}}]</math>
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| In the exponential decay function, it approaches zero more quickly as ''x'' increases, and ''a'' is a constant(usually between 3-9) and ''c'' is a counter. For the negated-[[Translation (geometry)|translated]] [[sigmoid function]], the decay is similar to the exponential decay function when ''a'' is greater than 4.<ref name=memphis />
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| As the graph approaches 0, it represents how the memory is being forgotten using decay mechanisms.
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| ===Genetic memory===
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| [[Genetic memory (computer science)|Genetic memory]] uses genetic algorithm and sparse distributed memory as an artificial neural network. It has been considered for use in creating artificial life.<ref name="Rocha">{{cite journal |author=Rocha LM, Hordijk W |title=Material representations: From the genetic code to the evolution of cellular automata |journal=Artificial Life |volume=11 |issue= 1-2|pages=189–214 |year=2005 |pmid= 15811227|doi=10.1162/1064546053278964|url=http://informatics.indiana.edu/rocha/caalife04.html }}</ref>
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| ===LIDA===
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| [[LIDA (cognitive architecture)|LIDA]] uses sparse distributed memory to help model [[cognition]] in biological systems. The sparse distributed memory places space is recalling or recognizing the object that it has in relation to other objects. It was developed by Stan Franklin, the creator of the "realizing forgetting" modified sparse distributed memory system.<ref name=psdm>Rao, R. P. N., & Fuentes, O. (1998). [http://www.cs.utep.edu/ofuentes/raoML98.pdf Hierarchical Learning of Navigational Behaviors in an Autonomous Robot using a Predictive Sparse Distributed Memory]. Machine Learning, 31, 87-113</ref>
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| ==Implementations==
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| * [https://github.com/msbrogli/sdm Implementation of Sparse Distributed Memory in Github]: This implementation has been used for research in [[Fundação Getúlio Vargas]] headed by Ph.D. Alexandre Linhares. It was first developed to study Critical Distance and it was tested checking with Kanerva's book theoretical results.<ref name="msbrogli">{{Cite thesis |author=Brogliato, Marcelo Salhab |title=Understanding Critical Distance in Sparse Distributed Memory |year=2012 }}</ref>
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| ==References==
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| {{Reflist}}
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| [[Category:Memory]]
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