<p>If you have a physics background, you may be particularly interested in <a href="https://en.wikipedia.org/wiki/Sparse_distributed_memory" rel="nofollow">Sparse Distributed Memory</a>, a model that provides a number of psychologically plausible characteristics, and is also neuroscientifically plausible.  </p>

<p>The model and some of its characteristics are summarized in <a href="http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00222/full" rel="nofollow">this paper</a>.  </p>

<p>Many great references have been provided by Nick Stauner, but this model is, in my view, one of the most promising and comprehensive ones in Cognitive Science.  </p>

CC BY-SA 3.0
2014-07-14T05:12:02.593Z
2015-04-11T15:43:01.020Z
2015-04-11T15:43:01.020Z
linhares
<p>Memory is a big word. Usually, neuroscientists and psychologists will try to model a specific cognitive process: for example, long-term recognition memory (the ability to distinguish between previously learned items and new items). Here is a link to a very good introductory text in computational neuroscience (which includes a section about memory and learning): <a href="http://grey.colorado.edu/CompCogNeuro/index.php?title=CCNBook/Main" rel="nofollow">http://grey.colorado.edu/CompCogNeuro/index.php?title=CCNBook/Main</a></p>

<p>Here is a link to a bible of neural networks: <a href="http://www.ru.lv/~peter/zinatne/ebooks/The%20MIT%20Press%20-%202003%20-%20The%20Handbook%20of%20Brain%20Theory%20and%20Neural%20Networks%20-%202nd%20Edition%20-%20ISBN%200262011972%20-%201309s%20-%20TLFeBOOK.pdf" rel="nofollow">http://www.ru.lv/~peter/zinatne/ebooks/The%20MIT%20Press%20-%202003%20-%20The%20Handbook%20of%20Brain%20Theory%20and%20Neural%20Networks%20-%202nd%20Edition%20-%20ISBN%200262011972%20-%201309s%20-%20TLFeBOOK.pdf</a></p>

CC BY-SA 3.0
2014-07-10T18:41:10.463Z
2014-07-10T18:41:10.463Z
summer_rain
<p>My lab uses the Semantic Pointer Architecture (where vectors are used as pointers between different dimensions, for more information check out "How to Build a Brain" by Chris Eliasmith) which is a Vector Symbolic Architecture (where sparse vectors represent symbols) to model working memory in a biologically plausible manner. So far this has been used in <a href="http://compneuro.uwaterloo.ca/files/publications/eliasmith.2012.pdf" rel="nofollow">Spaun</a> in it's model of serial memorization, as well as various other cognitive tasks such as the n-back task (soon to be published).</p>

CC BY-SA 3.0
2015-04-11T15:51:15.533Z
2015-04-11T15:51:15.533Z
Seanny123
<p>Very many references may easily be found with <a href="https://www.google.com/search?q=mathematical+model+memory" rel="nofollow noreferrer">a Google search for "mathematical model memory"</a>. Probably the most classic and iconic reference is <a href="http://www.rca.ucsd.edu/selected_papers/IMSSS_79.pdf" rel="nofollow noreferrer">Atkinson and Shiffrin <sup><sub>(1965)</sub></sup></a>, which is also <a href="http://en.wikipedia.org/wiki/Atkinson%E2%80%93Shiffrin_memory_model" rel="nofollow noreferrer">described on Wikipedia</a>. Its three components and their relationships are nicely encapsulated in this figure:</p>

<p><a href="http://en.wikipedia.org/wiki/File:Multistore_model.png" rel="nofollow noreferrer"><img src="https://upload.wikimedia.org/wikipedia/commons/b/bf/Multistore_model.png" alt=""></a></p>

<p>Many other, lesser-known mathematical models of memory exist, including but not limited to these:</p>

<ul>
<li>A model of recognition memory <sup><sub>(Atkinson &amp; Juola, 1974)</sub></sup></li>
<li>A model of the circular process in short-term memory <sup><sub>(Min'ko &amp; Petunin, 1981)</sup></sub></li>
<li>An application of interference theory to memory retention failures <sup><sub>(Anninos, 1972)</sup></sub></li>
<li>A model of <a href="http://en.wikipedia.org/wiki/Hippocampus#Role_in_memory" rel="nofollow noreferrer">hippocampus</a> activity involving affine and chaotic rules <sup><sub>(Yamaguti, Kuroda, Fukushima, Tsukada, &amp; Tsuda, 2011; see also Tsuda, Yamaguti, Kuroda, Fukushima, &amp; Tsukada, 2008; Fukushima, Tsukada, Tsuda, Yamaguti, &amp; Kuroda, 2009)</sub></sup></li>
<li>A computer simulation model of short-term learning <sup><sub>(Anderson, 1983; see also a simpler model proposed by Hicklin, 1976, cited in <a href="http://onlinelibrary.wiley.com/doi/10.1002/tea.3660210910/pdf" rel="nofollow noreferrer">a review of Anderson's article by Preece &amp; Anderson, 1984</a>)</sub></sup></li>
<li>A computer simulation model of <a href="http://en.wikipedia.org/wiki/Operant_conditioning" rel="nofollow noreferrer">operant conditioning</a> <sup><sub>(Bower, 1967; Mandler, 1967)</sup></sub></li>
<li>The Hopfield <sup><sub>(<a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC346238/pdf/pnas00447-0135.pdf" rel="nofollow noreferrer">1982</a>, <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC345226/pdf/pnas00611-0151.pdf" rel="nofollow noreferrer">1984</a>, <a href="http://arxiv.org/ftp/q-bio/papers/0609/0609006.pdf" rel="nofollow noreferrer">2006</a>)</sub></sup> <a href="http://www.scholarpedia.org/article/Hopfield_network#Associative_memory" rel="nofollow noreferrer">neural network model of associative memory</a> <sup><sub>(<a href="http://page.mi.fu-berlin.de/rojas/neural/chapter/K13.pdf" rel="nofollow noreferrer">Rojas, 1996</a>; see also <a href="http://en.wikipedia.org/wiki/Hopfield_network#Human_memory" rel="nofollow noreferrer">Wikipedia</a>; thanks @Memming!)</sup></sub> describes neural activity as binary, the attributes of memories as <a href="http://en.wikipedia.org/wiki/State_space" rel="nofollow noreferrer">state space</a> locations, and the system as governed by a <a href="http://www.scholarpedia.org/article/Lyapunov_function" rel="nofollow noreferrer">Lyupanov function</a>. Much more could be said about <a href="http://en.wikipedia.org/wiki/Artificial_neural_network#Types_of_models" rel="nofollow noreferrer">artificial neural network models of memory</a> in general (e.g., <a href="http://en.wikipedia.org/wiki/Long_short_term_memory" rel="nofollow noreferrer">LSTM</a>, <sup><sub><a href="http://web.eecs.utk.edu/~itamar/courses/ECE-692/Bobby_paper1.pdf" rel="nofollow noreferrer">Hochreiter &amp; Schmidhuber, 1997</a>;</sup></sub> <a href="http://www.learnartificialneuralnetworks.com/art.html" rel="nofollow noreferrer">ART</a>, <sup><sub>Carpenter &amp; Grossberg, <a href="http://www.opticsinfobase.org/ao/fulltext.cfm?uri=ao-26-23-4919&amp;id=30891" rel="nofollow noreferrer">1987a</a>, <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.9588&amp;rep=rep1&amp;type=pdf" rel="nofollow noreferrer">1987b</a>).</sup></sub></li>
</ul>

<p>You may also be interested in the following references:</p>

<ul>
<li>A book chapter, "Mathematical models of human memory" <sup><sub>(Raaijmakers, 2008)</sup></sub></li>
<li>A book, <em>Mathematical Models in Psychology</em> <sup><sub>(Restle, 1971)</sup></sub></li>
<li><a href="http://page.mi.fu-berlin.de/rojas/neural/neuron.pdf" rel="nofollow noreferrer">Rojas' <sup><sub>(1996)</sub></sup> entire book, <em>Neural Networks: A Systematic Introduction</em></a> seems pertinent. (And free!)</li>
</ul>

<p>And a related question here, in which "memory" comes up twice:</p>

<ul>
<li><a href="https://cogsci.stackexchange.com/q/1391/4086">https://cogsci.stackexchange.com/q/1391/4086</a></li>
</ul>

<hr>

<p><sup><strong>References</strong><br>
<strong>&middot;</strong> Anderson, O. R. (1983). A neuromathematical model of human information processing and its application to science content acquisition. <em>Journal of Research in Science Teaching, 20</em>(7), 603–620.<br>
<strong>&middot;</strong> Anninos, P. A. (1972). Mathematical model of memory trace and forgetfulness. <em>Kybernetik, 10</em>(3), 165–167.<br>
<strong>&middot;</strong> Atkinson, R. C., &amp; Juola, J. F. (1974). Search and decision processes in recognition memory. In D. H. Krantz, R. C. Atkinson, R. D. Luce, &amp; P. Suppes (Eds.), <em>Contemporary developments in mathematical psychology: I. Learning, memory and thinking</em>. Oxford, England: W. H. Freeman.<br>
<strong>&middot;</strong> Atkinson, R. C., &amp; Shiffrin, R. M. (1965). Mathematical models for memory and learning. <em>Technical Report No. 79: Psychological Series.</em> Institute for Mathematical Studies in the Social Sciences, Stanford University. Retrieved from <a href="http://www.rca.ucsd.edu/selected_papers/IMSSS_79.pdf" rel="nofollow noreferrer">http://www.rca.ucsd.edu/selected_papers/IMSSS_79.pdf</a>.<br>
<strong>&middot;</strong> Bower, G. (1967). A multicomponent theory of the memory trace. In K. W. Spence &amp; J. T. Spence (Eds.), <em>The psychology of learning and motivation: I</em>. Oxford, England: Academic Press.<br>
<strong>&middot;</strong> Carpenter, G. A., &amp; Grossberg, S. (1987). ART 2: Self-organization of stable category recognition codes for analog input patterns. <em>Applied Optics, 26</em>(23), 4919–4930. Retrieved from <a href="http://www.opticsinfobase.org/ao/fulltext.cfm?uri=ao-26-23-4919&amp;id=30891" rel="nofollow noreferrer">http://www.opticsinfobase.org/ao/fulltext.cfm?uri=ao-26-23-4919&amp;id=30891</a>.<br>
<strong>&middot;</strong> Carpenter, G. A., &amp; Grossberg, S. (1987). A massively parallel architecture for a self-organizing neural pattern recognition machine. <em>Computer Vision, Graphics, and Image Processing, 37</em>(1), 54–115. Retrieved from <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.9588&amp;rep=rep1&amp;type=pdf" rel="nofollow noreferrer">http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.9588&amp;rep=rep1&amp;type=pdf</a>.<br>
<strong>&middot;</strong> Fukushima, Y., Tsukada, M., Tsuda, I., Yamaguti, Y., &amp; Kuroda, S. (2009). Coding mechanisms in hippocampal networks for learning and memory. In <em>Advances in Neuro-Information Processing</em> (pp. 72–79). Springer: Berlin Heidelberg.<br>
<strong>&middot;</strong> Hicklin, W. J. (1976). A model for mastery learning based on dynamic equilibrium theory. <em>Journal of Mathematical Psychology, 13</em>(1), 79–88.<br>
<strong>&middot;</strong> Hochreiter, S., &amp; Schmidhuber, J. (1997). Long short-term memory. <em>Neural Computation, 9</em>(8), 1735–1780. Retrieved from <a href="http://web.eecs.utk.edu/~itamar/courses/ECE-692/Bobby_paper1.pdf" rel="nofollow noreferrer">http://web.eecs.utk.edu/~itamar/courses/ECE-692/Bobby_paper1.pdf</a>.<br>
<strong>&middot;</strong> Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. <em>Proceedings of the National Academy of Sciences, 79</em>(8), 2554–2558. Retrieved from <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC346238/pdf/pnas00447-0135.pdf" rel="nofollow noreferrer">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC346238/pdf/pnas00447-0135.pdf</a>.<br>
<strong>&middot;</strong> Hopfield, J. J. (1984). Neurons with graded response have collective computational properties like those of two-state neurons. <em>Proceedings of the National Academy of Sciences, 81</em>(10), 3088–3092. Retrieved from <a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC345226/pdf/pnas00611-0151.pdf" rel="nofollow noreferrer">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC345226/pdf/pnas00611-0151.pdf</a>.<br>
<strong>&middot;</strong> Hopfield, J. J. (2008). Searching for memories, Sudoku, implicit check bits, and the iterative use of not-always-correct rapid neural computation. <em>Neural Computation, 20</em>(5), 1119–1164. Retrieved from <a href="http://arxiv.org/ftp/q-bio/papers/0609/0609006.pdf" rel="nofollow noreferrer">http://arxiv.org/ftp/q-bio/papers/0609/0609006.pdf</a>.<br>
<strong>&middot;</strong> Mandler, G. (1967). Organization and memory. In K. W. Spence &amp; J. T. Spence (Eds.), <em>The psychology of learning and motivation: I</em>. Oxford, England: Academic Press.<br>
<strong>&middot;</strong> Min'ko, A. A., &amp; Petunin, Y. I. (1981). Mathematical modeling of short-term memory. <em>Cybernetics, 17</em>(2), 287–298.<br>
<strong>&middot;</strong> Preece, P. F., &amp; Anderson, O. R. (1984). Mathematical modeling of learning. <em>Journal of Research in Science Teaching, 21</em>(9), 953–955. Retrieved from <a href="http://onlinelibrary.wiley.com/doi/10.1002/tea.3660210910/pdf" rel="nofollow noreferrer">http://onlinelibrary.wiley.com/doi/10.1002/tea.3660210910/pdf</a>.<br>
<strong>&middot;</strong> Raaijmakers, J. G. W. (2008). Mathematical models of human memory. In <em>Learning and Memory: A Comprehensive Reference, Vol. 2: Cognitive Psychology of Memory</em> (pp. 445–466). Elsevier.<br>
<strong>&middot;</strong> Restle, F. (1971). <em>Mathematical models in psychology</em>. Harmondsworth: Penguin.<br>
<strong>&middot;</strong> Rojas, R. (1996). <em>Neutral networks: A systematic introduction</em>. Springer. Retrieved from <a href="http://page.mi.fu-berlin.de/rojas/neural/neuron.pdf" rel="nofollow noreferrer">http://page.mi.fu-berlin.de/rojas/neural/neuron.pdf</a>.<br>
<strong>&middot;</strong> Tsuda, I., Yamaguti, Y., Kuroda, S., Fukushima, Y., &amp; Tsukada, M. (2008). A mathematical model for the hippocampus: Towards the understanding of episodic memory and imagination. <em>Progress of Theoretical Physics Supplement, 173</em>, 99–108.<br>
<strong>&middot;</strong> Yamaguti, Y., Kuroda, S., Fukushima, Y., Tsukada, M., &amp; Tsuda, I. (2011). A mathematical model for Cantor coding in the hippocampus. <em>Neural Networks, 24</em>(1), 43–53.
</sup></p>

CC BY-SA 3.0
2014-02-26T22:19:29.817Z
I'll try to keep tacking on other examples and references as I come across them, but I'd welcome others' edits (or upvote their separate answers) too.
Nick Stauner
CC BY-SA 3.0
2014-03-08T03:36:43.160Z
@potpie also mentioned: "One lab [[Computational Memory Lab](http://memory.psych.upenn.edu/Main_Page)] that comes to mind right now working on topics related to the modeling of memory" Thanks for that!
Nick Stauner
CC BY-SA 4.0
2014-02-18T22:48:39.300Z
2018-09-29T10:15:39.800Z
2018-09-29T10:15:39.800Z
Nick Stauner
<p>Are there mathematical models of memory in humans or animals?</p>

<p>I want to know how neuroscientists use mathematics to describe memory in living creatures. <strong>How do neuroscientists model memory and show how it works by mathematics?</strong></p>

<p>I am a theoretical physics PhD student, and interested in neuroscience too. The only tool which I have and I could use to study neuroscience is mathematics and programing. That's why I want to know how neuroscientists address the memory by mathematics. I know how math works to describe neurons oscillations and action potential, but I don't know how it works for memory.</p>

<p>Any reference or review article is welcome too.</p>

CC BY-SA 3.0
2014-07-14T05:19:16.847Z
A user (who deleted the post) mentioned [the homepage for the University of Pennsylvania's Computational Memory Lab](http://memory.psych.upenn.edu/Main_Page).
Nick Stauner
CC BY-SA 3.0
2014-07-15T18:15:48.187Z
@Memming Hopfield network lacks too many properties in human memory. That model was only well-known in Computer Science, not Cognitive Science.
InformedA
CC BY-SA 3.0
2014-02-18T19:07:38.570Z
The cellular models of memory involve plenty of math but those models are only half the story. At the psychological level, we know a lot more about memory as a phenomenon but that knowledge is not encapsulated by any grand formal model. In any case, here are the mathematical models of plasticity which is thought to be a mechanism underlying memory formation. http://www.scholarpedia.org/article/Models_of_synaptic_plasticity
jerad
CC BY-SA 3.0
2014-02-26T08:09:57.230Z
Surprised that nobody mentioned Hopfield network.
Memming
CC BY-SA 4.0
2022-07-20T10:10:07.810Z
Our small contribution to the topic https://aip.scitation.org/doi/10.1063/5.0088823
mkatkov
<memory><theoretical-neuroscience><computational-modeling><mathematical-psychology>
What are the mathematical models of memory?
MOON
# What are the mathematical models of memory?

(Asked by: username_0 on 2014-02-18)

Are there mathematical models of memory in humans or animals?

I want to know how neuroscientists use mathematics to describe memory in living creatures. **How do neuroscientists model memory and show how it works by mathematics?**

I am a theoretical physics PhD student, and interested in neuroscience too. The only tool which I have and I could use to study neuroscience is mathematics and programing. That's why I want to know how neuroscientists address the memory by mathematics. I know how math works to describe neurons oscillations and action potential, but I don't know how it works for memory.

Any reference or review article is welcome too.

**Tags:** memory, theoretical-neuroscience, computational-modeling, mathematical-psychology

> **Comments:**
> **username_3**: The cellular models of memory involve plenty of math but those models are only half the story. At the psychological level, we know a lot more about memory as a phenomenon but that knowledge is not encapsulated by any grand formal model. In any case, here are the mathematical models of plasticity which is thought to be a mechanism underlying memory formation. http://www.scholarpedia.org/article/Models_of_synaptic_plasticity  
> **username_4**: Surprised that nobody mentioned Hopfield network.  
> **username_1**: A user (who deleted the post) mentioned [the homepage for the University of Pennsylvania's Computational Memory Lab](http://memory.psych.upenn.edu/Main_Page).  
> **username_2**: @username_4 Hopfield network lacks too many properties in human memory. That model was only well-known in Computer Science, not Cognitive Science.  
> **username_5**: Our small contribution to the topic https://aip.scitation.org/doi/10.1063/5.0088823  

---

## 4 answers

### Answer by username_1 on 2014-02-18. Score: 12 | Accepted answer

Very many references may easily be found with [a Google search for "mathematical model memory"](https://www.google.com/search?q=mathematical+model+memory). Probably the most classic and iconic reference is [Atkinson and Shiffrin (1965)](http://www.rca.ucsd.edu/selected_papers/IMSSS_79.pdf), which is also [described on Wikipedia](http://en.wikipedia.org/wiki/Atkinson%E2%80%93Shiffrin_memory_model). Its three components and their relationships are nicely encapsulated in this figure:

[![](https://upload.wikimedia.org/wikipedia/commons/b/bf/Multistore_model.png)](http://en.wikipedia.org/wiki/File:Multistore_model.png)

Many other, lesser-known mathematical models of memory exist, including but not limited to these:

* A model of recognition memory (Atkinson & Juola, 1974)
* A model of the circular process in short-term memory (Min'ko & Petunin, 1981)
* An application of interference theory to memory retention failures (Anninos, 1972)
* A model of [hippocampus](http://en.wikipedia.org/wiki/Hippocampus#Role_in_memory) activity involving affine and chaotic rules (Yamaguti, Kuroda, Fukushima, Tsukada, & Tsuda, 2011; see also Tsuda, Yamaguti, Kuroda, Fukushima, & Tsukada, 2008; Fukushima, Tsukada, Tsuda, Yamaguti, & Kuroda, 2009)
* A computer simulation model of short-term learning (Anderson, 1983; see also a simpler model proposed by Hicklin, 1976, cited in [a review of Anderson's article by Preece & Anderson, 1984](http://onlinelibrary.wiley.com/doi/10.1002/tea.3660210910/pdf))
* A computer simulation model of [operant conditioning](http://en.wikipedia.org/wiki/Operant_conditioning) (Bower, 1967; Mandler, 1967)
* The Hopfield ([1982](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC346238/pdf/pnas00447-0135.pdf), [1984](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC345226/pdf/pnas00611-0151.pdf), [2006](http://arxiv.org/ftp/q-bio/papers/0609/0609006.pdf)) [neural network model of associative memory](http://www.scholarpedia.org/article/Hopfield_network#Associative_memory) ([Rojas, 1996](http://page.mi.fu-berlin.de/rojas/neural/chapter/K13.pdf); see also [Wikipedia](http://en.wikipedia.org/wiki/Hopfield_network#Human_memory); thanks @username_4!) describes neural activity as binary, the attributes of memories as [state space](http://en.wikipedia.org/wiki/State_space) locations, and the system as governed by a [Lyupanov function](http://www.scholarpedia.org/article/Lyapunov_function). Much more could be said about [artificial neural network models of memory](http://en.wikipedia.org/wiki/Artificial_neural_network#Types_of_models) in general (e.g., [LSTM](http://en.wikipedia.org/wiki/Long_short_term_memory), [Hochreiter & Schmidhuber, 1997](http://web.eecs.utk.edu/~itamar/courses/ECE-692/Bobby_paper1.pdf); [ART](http://www.learnartificialneuralnetworks.com/art.html), Carpenter & Grossberg, [1987a](http://www.opticsinfobase.org/ao/fulltext.cfm?uri=ao-26-23-4919&id=30891), [1987b](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.9588&rep=rep1&type=pdf)).

You may also be interested in the following references:

* A book chapter, "Mathematical models of human memory" (Raaijmakers, 2008)
* A book, *Mathematical Models in Psychology* (Restle, 1971)
* [Rojas' (1996) entire book, *Neural Networks: A Systematic Introduction*](http://page.mi.fu-berlin.de/rojas/neural/neuron.pdf) seems pertinent. (And free!)

And a related question here, in which "memory" comes up twice:

* <https://cogsci.stackexchange.com/q/1391/4086>

---

**References**  
**·** Anderson, O. R. (1983). A neuromathematical model of human information processing and its application to science content acquisition. *Journal of Research in Science Teaching, 20*(7), 603–620.  
**·** Anninos, P. A. (1972). Mathematical model of memory trace and forgetfulness. *Kybernetik, 10*(3), 165–167.  
**·** Atkinson, R. C., & Juola, J. F. (1974). Search and decision processes in recognition memory. In D. H. Krantz, R. C. Atkinson, R. D. Luce, & P. Suppes (Eds.), *Contemporary developments in mathematical psychology: I. Learning, memory and thinking*. Oxford, England: W. H. Freeman.  
**·** Atkinson, R. C., & Shiffrin, R. M. (1965). Mathematical models for memory and learning. *Technical Report No. 79: Psychological Series.* Institute for Mathematical Studies in the Social Sciences, Stanford University. Retrieved from <http://www.rca.ucsd.edu/selected_papers/IMSSS_79.pdf>.  
**·** Bower, G. (1967). A multicomponent theory of the memory trace. In K. W. Spence & J. T. Spence (Eds.), *The psychology of learning and motivation: I*. Oxford, England: Academic Press.  
**·** Carpenter, G. A., & Grossberg, S. (1987). ART 2: Self-organization of stable category recognition codes for analog input patterns. *Applied Optics, 26*(23), 4919–4930. Retrieved from <http://www.opticsinfobase.org/ao/fulltext.cfm?uri=ao-26-23-4919&id=30891>.  
**·** Carpenter, G. A., & Grossberg, S. (1987). A massively parallel architecture for a self-organizing neural pattern recognition machine. *Computer Vision, Graphics, and Image Processing, 37*(1), 54–115. Retrieved from <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.70.9588&rep=rep1&type=pdf>.  
**·** Fukushima, Y., Tsukada, M., Tsuda, I., Yamaguti, Y., & Kuroda, S. (2009). Coding mechanisms in hippocampal networks for learning and memory. In *Advances in Neuro-Information Processing* (pp. 72–79). Springer: Berlin Heidelberg.  
**·** Hicklin, W. J. (1976). A model for mastery learning based on dynamic equilibrium theory. *Journal of Mathematical Psychology, 13*(1), 79–88.  
**·** Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. *Neural Computation, 9*(8), 1735–1780. Retrieved from <http://web.eecs.utk.edu/~itamar/courses/ECE-692/Bobby_paper1.pdf>.  
**·** Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. *Proceedings of the National Academy of Sciences, 79*(8), 2554–2558. Retrieved from <http://www.ncbi.nlm.nih.gov/pmc/articles/PMC346238/pdf/pnas00447-0135.pdf>.  
**·** Hopfield, J. J. (1984). Neurons with graded response have collective computational properties like those of two-state neurons. *Proceedings of the National Academy of Sciences, 81*(10), 3088–3092. Retrieved from <http://www.ncbi.nlm.nih.gov/pmc/articles/PMC345226/pdf/pnas00611-0151.pdf>.  
**·** Hopfield, J. J. (2008). Searching for memories, Sudoku, implicit check bits, and the iterative use of not-always-correct rapid neural computation. *Neural Computation, 20*(5), 1119–1164. Retrieved from <http://arxiv.org/ftp/q-bio/papers/0609/0609006.pdf>.  
**·** Mandler, G. (1967). Organization and memory. In K. W. Spence & J. T. Spence (Eds.), *The psychology of learning and motivation: I*. Oxford, England: Academic Press.  
**·** Min'ko, A. A., & Petunin, Y. I. (1981). Mathematical modeling of short-term memory. *Cybernetics, 17*(2), 287–298.  
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> **Comments:**
> **username_1**: I'll try to keep tacking on other examples and references as I come across them, but I'd welcome others' edits (or upvote their separate answers) too.  
> **username_1**: @potpie also mentioned: "One lab [[Computational Memory Lab](http://memory.psych.upenn.edu/Main_Page)] that comes to mind right now working on topics related to the modeling of memory" Thanks for that!  

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### Answer by username_6 on 2014-07-14. Score: 4

If you have a physics background, you may be particularly interested in [Sparse Distributed Memory](https://en.wikipedia.org/wiki/Sparse_distributed_memory), a model that provides a number of psychologically plausible characteristics, and is also neuroscientifically plausible.

The model and some of its characteristics are summarized in [this paper](http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00222/full).

Many great references have been provided by username_1, but this model is, in my view, one of the most promising and comprehensive ones in Cognitive Science.


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### Answer by username_8 on 2015-04-11. Score: 1

My lab uses the Semantic Pointer Architecture (where vectors are used as pointers between different dimensions, for more information check out "How to Build a Brain" by Chris Eliasmith) which is a Vector Symbolic Architecture (where sparse vectors represent symbols) to model working memory in a biologically plausible manner. So far this has been used in [Spaun](http://compneuro.uwaterloo.ca/files/publications/eliasmith.2012.pdf) in it's model of serial memorization, as well as various other cognitive tasks such as the n-back task (soon to be published).


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### Answer by username_7 on 2014-07-10. Score: 0

Memory is a big word. Usually, neuroscientists and psychologists will try to model a specific cognitive process: for example, long-term recognition memory (the ability to distinguish between previously learned items and new items). Here is a link to a very good introductory text in computational neuroscience (which includes a section about memory and learning): <http://grey.colorado.edu/CompCogNeuro/index.php?title=CCNBook/Main>

Here is a link to a bible of neural networks: <http://www.ru.lv/~peter/zinatne/ebooks/The%20MIT%20Press%20-%202003%20-%20The%20Handbook%20of%20Brain%20Theory%20and%20Neural%20Networks%20-%202nd%20Edition%20-%20ISBN%200262011972%20-%201309s%20-%20TLFeBOOK.pdf>


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