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<h1 class="title">Computational Modeling for Psychology Students</h1>
<div id="table-of-contents" role="doc-toc">
<h2>Table of Contents</h2>
<div id="text-table-of-contents" role="doc-toc">
<ul>
<li><a href="#org9d965f0">1. Welcome to Psych 420</a></li>
<li><a href="#org9ed41a2">2. Introductions  <span class="tag"><span class="assignment">assignment</span></span></a></li>
<li><a href="#org3256435">3. Learning Objectives</a>
<ul>
<li><a href="#org14bee7b">3.1. From the Course Outline:</a></li>
<li><a href="#org44862f4">3.2. General</a></li>
<li><a href="#orgc4dff85">3.3. Some recommendations.</a>
<ul>
<li><a href="#orge3a2a79">3.3.1. Things to help you early on</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org800cadf">4. What is a cognitive model</a>
<ul>
<li><a href="#orga1837bb">4.1. Divide class into teams of four or five each.</a></li>
<li><a href="#orga02d30a">4.2. Assign to each team a label:</a></li>
<li><a href="#orgdc2c942">4.3. Consider the following question from the point of view of your assigned role:</a></li>
<li><a href="#org9d38a79">4.4. Give time for developing an answer.</a></li>
<li><a href="#orgc34a9bb">4.5. Review the suggestions.</a></li>
<li><a href="#orgdd5a17f">4.6. Now consider the following.</a></li>
<li><a href="#orgdf5ac4b">4.7. Reorganize the groups</a>
<ul>
<li><a href="#org65fce4c">4.7.1. Two sets of groups</a></li>
</ul>
</li>
<li><a href="#orgc8aed23">4.8. Rescorla Wagner Equation</a></li>
<li><a href="#orgcab7a00">4.9. What are Marr's Levels?</a></li>
<li><a href="#org112b675">4.10. LLMs</a>
<ul>
<li><a href="#org6c0b1d8">4.10.1. Are they a good model system for the mind? That is, does an LLM think like you do?</a></li>
<li><a href="#org127d0ff">4.10.2. Are they a good tool for studying the mind?</a></li>
<li><a href="#orgee736a8">4.10.3. How do we best use LLMs as a tool for our learning? How should we change our classroom experience?</a></li>
</ul>
</li>
<li><a href="#org4cd6969">4.11. Reminder</a></li>
</ul>
</li>
<li><a href="#orga1d7f4d">5. Where will your grade come from?</a>
<ul>
<li><a href="#orgfb2033f">5.1. Why incentivize classroom time?</a></li>
<li><a href="#org10d6cb0">5.2. Why is "doing" so important for this course?</a></li>
<li><a href="#orgaec2916">5.3. I find this stuff hard and am worrying about failing</a></li>
<li><a href="#orgd8bbeb1">5.4. Why have a final project?</a></li>
<li><a href="#org7831aa6">5.5. A look ahead – what we will code</a></li>
<li><a href="#orgc22f2cd">5.6. A look ahead – what we talk about</a></li>
</ul>
</li>
<li><a href="#org9e04697">6. Computational Neuroscience</a>
<ul>
<li><a href="#org63a791b">6.1. Slime assignment</a></li>
<li><a href="#org6e5b29d">6.2. What are examples of research combining cognitive, computational, and neuroscience methods?</a>
<ul>
<li><a href="#orge269e16">6.2.1. Evaluating Academic Work  <span class="tag"><span class="exercise">exercise</span></span></a></li>
</ul>
</li>
<li><a href="#org6cfc325">6.3. Is a mathematical formula a model?</a>
<ul>
<li><a href="#org6ae072a">6.3.1. Forgetting Curve — Ebbinghaus</a></li>
<li><a href="#orgb800eb0">6.3.2. A Mathematical Function</a></li>
<li><a href="#orgaac2e84">6.3.3. More on the fitting curves to Ebbinghaus Data</a></li>
</ul>
</li>
<li><a href="#org23ccfad">6.4. Reprise</a></li>
</ul>
</li>
<li><a href="#org6d828e0">7. Neurally Inspired Models 1: The cellular level</a>
<ul>
<li><a href="#org6cb4347">7.1. That which you cannot code, you do not understand.</a></li>
<li><a href="#orgea71c01">7.2. What is an action potential?</a></li>
<li><a href="#org52605ec">7.3. Notation</a>
<ul>
<li><a href="#org86dc735">7.3.1. Notation Scavenger Hunt  <span class="tag"><span class="exercise">exercise</span></span></a></li>
</ul>
</li>
<li><a href="#orga9246cb">7.4. Differential Equations  <span class="tag"><span class="exercise">exercise</span></span></a></li>
<li><a href="#org5419248">7.5. Using a DE</a></li>
<li><a href="#org88d417d">7.6. Using DEs to compute a cube root</a>
<ul>
<li><a href="#org9c414ab">7.6.1. Your turn  <span class="tag"><span class="assignment">assignment</span></span></a></li>
</ul>
</li>
<li><a href="#orga829d72">7.7. Using DEs - Practicing with Springs  <span class="tag"><span class="homework">homework</span></span></a>
<ul>
<li><a href="#orga2991a3">7.7.1. Try with a <b>Damped Oscillator</b>  <span class="tag"><span class="homework">homework</span></span></a></li>
</ul>
</li>
<li><a href="#org41f99cf">7.8. Solving DEs</a></li>
<li><a href="#org55d65dd">7.9. Integrate and Fire Neuron</a>
<ul>
<li><a href="#org09502c7">7.9.1. Historical Notes</a></li>
<li><a href="#org7f27bad">7.9.2. Formula I and F</a></li>
<li><a href="#org0009522">7.9.3. Coding up the Integrate and Fire Neuron</a></li>
</ul>
</li>
<li><a href="#org855850c">7.10. Integrate and Fire Homework</a></li>
<li><a href="#org0ee4346">7.11. Hodgkin and Huxley Model</a>
<ul>
<li><a href="#org8fb314a">7.11.1. Who were Hodgkin and Huxley</a></li>
<li><a href="#orgfec152d">7.11.2. Biographical Sources</a></li>
<li><a href="#org512f981">7.11.3. Methodology</a></li>
<li><a href="#org9299461">7.11.4. Model Description</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org813fc2f">8. What is computation and what is its role in cognitive science?</a>
<ul>
<li><a href="#org3f332d8">8.1. What do you think?</a></li>
<li><a href="#orgc57ae82">8.2. Computing in Minds and Computers</a></li>
<li><a href="#org2d9e9c1">8.3. What is a Turing machine? Some Background and Details</a>
<ul>
<li><a href="#org0934105">8.3.1. Classroom Activity</a></li>
</ul>
</li>
<li><a href="#orgdf8b107">8.4. Programming a Turing Machine: the Busy Beaver</a>
<ul>
<li><a href="#orgfa4ca8e">8.4.1. A Busy Beaver Warm-Up</a></li>
<li><a href="#orgc35c1d5">8.4.2. Busy Beaver Problem Demo Code</a></li>
</ul>
</li>
<li><a href="#orgb684d4f">8.5. The Lambda Calculus</a>
<ul>
<li><a href="#orged25fef">8.5.1. Why should a psychology student care?</a></li>
<li><a href="#orgd329a55">8.5.2. Lambda Notation Basics</a></li>
</ul>
</li>
<li><a href="#org27d3376">8.6. The Church-Turing Thesis</a>
<ul>
<li><a href="#org752ed01">8.6.1. Church Numerals</a></li>
<li><a href="#org7af3ac6">8.6.2. Computing with the Lambda Calculus</a></li>
<li><a href="#orgdf287c4">8.6.3. Lambda Calculas Homework</a></li>
</ul>
</li>
<li><a href="#orgf54be24">8.7. Two Completely Different Models</a></li>
<li><a href="#org2d4459a">8.8. Implications</a></li>
</ul>
</li>
<li><a href="#org29914c2">9. Neurally Inspired Models 2: The network effect</a>
<ul>
<li><a href="#org4eda532">9.1. Neural Networks</a>
<ul>
<li><a href="#orgbb34529">9.1.1. Cellular Automata</a></li>
<li><a href="#orgebcede4">9.1.2. More Lessons from Cellular Automata</a></li>
<li><a href="#org728afca">9.1.3. John Hopfield</a></li>
<li><a href="#orgc3d48f9">9.1.4. Linear Algebra</a></li>
<li><a href="#org946eb42">9.1.5. Neural Networks Redux</a></li>
<li><a href="#orge09f87b">9.1.6. What is a Neural Network?</a></li>
<li><a href="#org1190d48">9.1.7. Our First Neural Network: The Perceptron</a></li>
<li><a href="#org678a5bb">9.1.8. The Delta Rule - Homework</a></li>
<li><a href="#orgd268a46">9.1.9. Not all Networks are the Same: Hopfield</a></li>
<li><a href="#org63102d3">9.1.10. Hopfield Homework Description: Robustness to Noise (this might take awhile).</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org003a478">10. Theory Creation in the Cognitive and Psychological Sciences</a>
<ul>
<li><a href="#org5741e8b">10.1. What is a scientific theory?</a>
<ul>
<li><a href="#org19c4857">10.1.1. What is prediction?</a></li>
<li><a href="#org4b4ff51">10.1.2. What is explanation?</a></li>
</ul>
</li>
<li><a href="#org1ea585a">10.2. Classroom Activity</a></li>
<li><a href="#org7b530e3">10.3. Do we have a theory crisis in Psychology?</a></li>
<li><a href="#orgaea3bde">10.4. Classroom Activity</a></li>
<li><a href="#orga4375cc">10.5. What are scientific theories good for? Or, in other words, why should we care?</a></li>
<li><a href="#orgfb156f5">10.6. What makes a theory a good theory?</a></li>
<li><a href="#orgb1f0c55">10.7. What are the first steps towards building a theory?</a></li>
<li><a href="#org1d8c175">10.8. What should you do next if you think you have a theory?</a>
<ul>
<li><a href="#org5a3e481">10.8.1. What role should a model play?</a></li>
</ul>
</li>
<li><a href="#org14f48af">10.9. Formal Modeling (Advocacy)</a>
<ul>
<li><a href="#org7b6e242">10.9.1. Advantages</a></li>
</ul>
</li>
<li><a href="#orgc3caf4c">10.10. Steps to Formalizing a Model</a></li>
<li><a href="#org85dd465">10.11. Can you now provide a good example of a psychological theory?</a></li>
<li><a href="#org9e051db">10.12. Some Interesting Reading on this Topic</a></li>
<li><a href="#orgf9f3522">10.13. Theory Homework</a></li>
</ul>
</li>
<li><a href="#org45723ab">11. Algebraic Psychology</a>
<ul>
<li><a href="#orgc5b9acf">11.1. Opening Questions</a>
<ul>
<li><a href="#org8040da4">11.1.1. What is a theory?</a></li>
<li><a href="#orgb5c45b2">11.1.2. Name a psychological theory.</a></li>
</ul>
</li>
<li><a href="#orgdad5bfc">11.2. I demand a satisfactory explanation</a>
<ul>
<li><a href="#orge999581">11.2.1. A celestial example and a Planetary Context</a></li>
</ul>
</li>
<li><a href="#orgbc7c981">11.3. Thagard's Principles of Explanatory Coherence</a></li>
<li><a href="#org2bcbc3e">11.4. Taking up all the oxygen in the room</a></li>
<li><a href="#orgea6eecb">11.5. And the network said ..</a></li>
<li><a href="#orga80e012">11.6. From Lisp to R</a></li>
<li><a href="#org152a367">11.7. And the network said … (ECHO, Echo, echo …)</a></li>
<li><a href="#orgcb2a87c">11.8. Formal CONTEXTS</a></li>
<li><a href="#org842c690">11.9. Formal CONCEPTS</a></li>
<li><a href="#org4dc1919">11.10. A Romantic Connection</a></li>
<li><a href="#org2ea11fa">11.11. A celestial example</a></li>
<li><a href="#org9b86036">11.12. Jacob's Ladder</a>
<ul>
<li><a href="#org42451f4">11.12.1. A Planetary Lattice</a></li>
<li><a href="#org838fb3f">11.12.2. The Context</a></li>
</ul>
</li>
<li><a href="#orgd6f3552">11.13. From ECHO to FCA: The Lavoisier Context</a></li>
<li><a href="#org9592cd8">11.14. Sample Formal Concepts</a></li>
<li><a href="#org880047b">11.15. Implications in the Lavoisier Context</a></li>
<li><a href="#orgf608651">11.16. The Lavoisier Concept Lattice</a></li>
</ul>
</li>
<li><a href="#org501b201">12. Reasons to Prefer FCA</a>
<ul>
<li><a href="#org3212e9d">12.1. Data Processing Inequality</a></li>
<li><a href="#org64d0acf">12.2. Formal Contexts are Chu Spaces</a></li>
<li><a href="#org5fd83a9">12.3. Chu Spaces are *-autonomous categories</a></li>
<li><a href="#orgbbb1b59">12.4. Unifying Logic, Geometry, and Computation</a></li>
</ul>
</li>
<li><a href="#org774f1a2">13. But wait! There's more!</a>
<ul>
<li><a href="#org834653e">13.1. I probably ran out of time so come talk to me</a>
<ul>
<li><a href="#org7c945ba">13.1.1. Bibliography and Other Readings</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#org7c5b9a6">14. Final Projects</a>
<ul>
<li><a href="#org708f630">14.1. Overview</a></li>
<li><a href="#org205d78c">14.2. Evaluation</a></li>
<li><a href="#org4506cfe">14.3. Project Topics</a>
<ul>
<li><a href="#org9cf102c">14.3.1. Reinforcement Learning</a></li>
<li><a href="#orge7da6d5">14.3.2. Self-organizing Maps (Kohonen Neural Networks)</a></li>
<li><a href="#orgda24895">14.3.3. Morris-Lecar Networks</a></li>
<li><a href="#orgde1ad09">14.3.4. Backpropagation</a></li>
<li><a href="#org59d0ac7">14.3.5. Agent Based Models</a></li>
<li><a href="#org0027f6d">14.3.6. Linear Ballistic Accumulators</a></li>
</ul>
</li>
<li><a href="#orgee3d4f3">14.4. Project Deliverables Summarized</a>
<ul>
<li><a href="#org0621904">14.4.1. Presentation</a></li>
<li><a href="#org784b141">14.4.2. Report</a></li>
</ul>
</li>
<li><a href="#org0237142">14.5. General Suggestions</a></li>
<li><a href="#orge5d8b95">14.6. Some Examples from Last Year</a></li>
</ul>
</li>
<li><a href="#org06f8525">15. Some references</a></li>
</ul>
</div>
</div>
<div id="outline-container-org9d965f0" class="outline-2">
<h2 id="org9d965f0"><span class="section-number-2">1.</span> Welcome to Psych 420</h2>
</div>
<div id="outline-container-org9ed41a2" class="outline-2">
<h2 id="org9ed41a2"><span class="section-number-2">2.</span> Introductions  <span class="tag"><span class="assignment">assignment</span></span></h2>
<div class="outline-text-2" id="text-2">
<ol class="org-ol">
<li>Who am I?</li>
<li>Who are you?
Circulate cards and review as an ice breaker.
<ol class="org-ol">
<li>Your name (and any pronounciation tips).</li>
<li>Area of concentration,</li>
<li>Year of study,</li>
<li>Programming language you are most capable in (and your level of competency),</li>
<li>Reason you took this course.</li>
</ol></li>
<li>What you will need: A functioning computer that you know how to use.
What to do now:
<ul class="org-ul">
<li>Update your operating system.</li>
<li>Verify you know how to find a file on your computer (e.g. do you know the name of your home directory)?</li>
<li>Confirm you know how to install software on your computer.</li>
<li>You know (or will know by next week) what <code>git</code> is and how to use it, and that you will have an <code>IDE</code> installed.</li>
</ul></li>
</ol>
</div>
</div>
<div id="outline-container-org3256435" class="outline-2">
<h2 id="org3256435"><span class="section-number-2">3.</span> Learning Objectives</h2>
<div class="outline-text-2" id="text-3">
</div>
<div id="outline-container-org14bee7b" class="outline-3">
<h3 id="org14bee7b"><span class="section-number-3">3.1.</span> From the Course Outline:</h3>
<div class="outline-text-3" id="text-3-1">
<ol class="org-ol">
<li>You will understand the scope of subjects and tools that comprise computational neuroscience and computational cognitive modeling.</li>
<li>You will program a few different versions of a spiking neuron. This will introduce us to how differential equations may be used in computational modeling We will also look at how some of the tools developed for studying differential equations can be brought to bear on neural models.</li>
<li>You will program a few simple examples of a few different types of neural networks. We will use these to introduce us to some of the ways that linear algebra is used in computational modeling, and how some of the tools of analyzing linear systems can be brought to bear on neural and cognitive models.</li>
<li>Have an informed opinion on what is it meant by a "computational model" whether it is correct to consider the mind as such. You will program a simple Turing machine.</li>
<li>You will compare the symbolic and computational approaches to brain and mind modeling by implementing a simple logic in code.</li>
<li>Interleaved throughout all these exercises you will develop an informed perspective on what is meant by a theory and a model, and what might be the benefits from a computational characterization.</li>
</ol>
</div>
</div>
<div id="outline-container-org44862f4" class="outline-3">
<h3 id="org44862f4"><span class="section-number-3">3.2.</span> General</h3>
<div class="outline-text-3" id="text-3-2">
<ol class="org-ol">
<li>The specific domain content will change quickly in the years to come. Thus, I target general approaches for,
<ol class="org-ol">
<li>acquiring computational knowledge,</li>
<li>evaluating claims that rely on it,</li>
<li>developing intuition about whether a claim is sensible,</li>
<li>how to test it,</li>
<li>learn how to learn new tools you will need in the future to extend your knowledge and conduct (or even just read about) this sort of material in the future.</li>
</ol></li>
<li>Gain experience in reading the computational neuroscience literature.</li>
<li>Practice writing in a technical and academic style your evaluation of computational cognitive science material.</li>
<li>Become proficient in the basics and fundamentals of a programming language like python or R.</li>
<li>Learn to use LLMs as an adjunct to learning and not a substitute.</li>
</ol>
</div>
</div>
<div id="outline-container-orgc4dff85" class="outline-3">
<h3 id="orgc4dff85"><span class="section-number-3">3.3.</span> Some recommendations.</h3>
<div class="outline-text-3" id="text-3-3">
</div>
<div id="outline-container-orge3a2a79" class="outline-4">
<h4 id="orge3a2a79"><span class="section-number-4">3.3.1.</span> Things to help you early on</h4>
<div class="outline-text-4" id="text-3-3-1">
<p>
Take a look at <a href="https://github.com/brittAnderson/uwlooP390">https://github.com/brittAnderson/uwlooP390</a> and <a href="https://brittanderson.github.io/uwlooP390/">https://brittanderson.github.io/uwlooP390/</a>
Things you absolutely should be able to do.
</p>
<ol class="org-ol">
<li>Verify our laptop's operating system is up to date.</li>
<li>Know what a directory is and how to find files on your computer.</li>
<li>Know how to install software.</li>
<li>Have at least beginner level programming experience in one course.</li>
<li>Know what git/github are.
Git Clone and Github Acct :assignment:
An early home work will be a screen shot of your github homepage showing you forked or cloned the course repository. And the screen shot should be done using a program and not your phone. <a href="https://github.com/brittAnderson/compNeuroIntro420">Course Webpage</a> . That is the course content. If you want to view a web viewable form you can go to this link: <a href="https://brittanderson.github.io/compNeuroIntro420/">course notes</a>.</li>
<li>You will want an IDE. I personally use emacs. Experience has taught me that only about 3 in a 100 of you will share my opinion. Thus, I recommend VS Code if you have no other preference. It is becoming a sort of de facto standard.</li>
</ol>
</div>
</div>
</div>
</div>
<div id="outline-container-org800cadf" class="outline-2">
<h2 id="org800cadf"><span class="section-number-2">4.</span> What is a cognitive model</h2>
<div class="outline-text-2" id="text-4">
</div>
<div id="outline-container-orga1837bb" class="outline-3">
<h3 id="orga1837bb"><span class="section-number-3">4.1.</span> Divide class into teams of four or five each.</h3>
</div>
<div id="outline-container-orga02d30a" class="outline-3">
<h3 id="orga02d30a"><span class="section-number-3">4.2.</span> Assign to each team a label:</h3>
<div class="outline-text-3" id="text-4-2">
<ul class="org-ul">
<li>cognitive psychologist</li>
<li>experimental neuroscientist</li>
<li>computational neuroscientist</li>
<li>philosopher of mind</li>
</ul>
</div>
</div>
<div id="outline-container-orgdc2c942" class="outline-3">
<h3 id="orgdc2c942"><span class="section-number-3">4.3.</span> Consider the following question from the point of view of your assigned role:</h3>
<div class="outline-text-3" id="text-4-3">
<p>
An X learns that a cue Y predicts a reward Z. What evidence would you want to see to support this claim? What would constitute an "explanation" for such a relation?
</p>
</div>
</div>
<div id="outline-container-org9d38a79" class="outline-3">
<h3 id="org9d38a79"><span class="section-number-3">4.4.</span> Give time for developing an answer.</h3>
</div>
<div id="outline-container-orgc34a9bb" class="outline-3">
<h3 id="orgc34a9bb"><span class="section-number-3">4.5.</span> Review the suggestions.</h3>
</div>
<div id="outline-container-orgdd5a17f" class="outline-3">
<h3 id="orgdd5a17f"><span class="section-number-3">4.6.</span> Now consider the following.</h3>
<div class="outline-text-3" id="text-4-6">
<p>
Give each scenario in turn.
</p>
<ul class="org-ul">
<li>X = Dog; Y = Bell; Z = food.</li>
<li>X = Sunflower; Y = sun ; Z = sugar</li>
<li>X = Pea Plant ; Y = air puff ; Z = light <a href="https://www.nature.com/articles/srep38427">link</a></li>
</ul>
</div>
</div>
<div id="outline-container-orgdf5ac4b" class="outline-3">
<h3 id="orgdf5ac4b"><span class="section-number-3">4.7.</span> Reorganize the groups</h3>
<div class="outline-text-3" id="text-4-7">
</div>
<div id="outline-container-org65fce4c" class="outline-4">
<h4 id="org65fce4c"><span class="section-number-4">4.7.1.</span> Two sets of groups</h4>
<div class="outline-text-4" id="text-4-7-1">
<p>
Half of people in teams of 4. Half the people solo. Teams of four, please don't use LLMs or even an internet search. Library books are okay. Just talk it through with your group and each of you submit an answer. The other "solo" half. Please don't discuss your answer or ideas with anyone other than an llm. Answer the same questions, but in addition you will need to provide info on which LLM you used and the prompts (or even the entire chat if you want).
</p>
<p>
We want to help decide ourselves how to make the most constructive use of these tools.
</p>
<p>
What you will be submitting – 1/2 to one page (max) essay addressing:
</p>
<ol class="org-ol">
<li>For which of our examples is the Rescorla-Wagner Model a good fit?</li>
<li>RW belongs to which of Marr's levels?</li>
<li>What is the level that we should be working at?</li>
</ol>
<p>
To help let's take a quick look at both Rescorla-Wagner and Marr's Levels.
</p>
</div>
</div>
</div>
<div id="outline-container-orgc8aed23" class="outline-3">
<h3 id="orgc8aed23"><span class="section-number-3">4.8.</span> <a href="https://en.wikipedia.org/wiki/Rescorla%E2%80%93Wagner_model">Rescorla Wagner Equation</a></h3>
<div class="outline-text-3" id="text-4-8">
<p>
<a href="rw.pdf">rw.pdf</a>
</p>
<ul class="org-ul">
<li>Is this an explanation? Is this a theory? What do we learn by changing our perspective to include equations?</li>
</ul>
</div>
</div>
<div id="outline-container-orgcab7a00" class="outline-3">
<h3 id="orgcab7a00"><span class="section-number-3">4.9.</span> What are Marr's Levels?</h3>
<div class="outline-text-3" id="text-4-9">
<ul class="org-ul">
<li>Computational</li>
<li>Algorithmic</li>
<li>Implementational</li>
</ul>
</div>
</div>
<div id="outline-container-org112b675" class="outline-3">
<h3 id="org112b675"><span class="section-number-3">4.10.</span> LLMs</h3>
<div class="outline-text-3" id="text-4-10">
<p>
A little prime for why I divided the assignment groups this way?
</p>
</div>
<div id="outline-container-org6c0b1d8" class="outline-4">
<h4 id="org6c0b1d8"><span class="section-number-4">4.10.1.</span> Are they a good model system for the mind? That is, does an LLM think like you do?</h4>
</div>
<div id="outline-container-org127d0ff" class="outline-4">
<h4 id="org127d0ff"><span class="section-number-4">4.10.2.</span> Are they a good tool for studying the mind?</h4>
</div>
<div id="outline-container-orgee736a8" class="outline-4">
<h4 id="orgee736a8"><span class="section-number-4">4.10.3.</span> How do we best use LLMs as a tool for our learning? How should we change our classroom experience?</h4>
</div>
</div>
<div id="outline-container-org4cd6969" class="outline-3">
<h3 id="org4cd6969"><span class="section-number-3">4.11.</span> Reminder</h3>
<div class="outline-text-3" id="text-4-11">
<p>
Bring pencil/pen and paper to the next class. There will be some writing that you have to turn in.
</p>
</div>
</div>
</div>
<div id="outline-container-orga1d7f4d" class="outline-2">
<h2 id="orga1d7f4d"><span class="section-number-2">5.</span> Where will your grade come from?</h2>
<div class="outline-text-2" id="text-5">
<table border="2" cellspacing="0" cellpadding="6" rules="groups" frame="hsides">
<colgroup>
<col class="org-left" />
<col class="org-right" />
</colgroup>
<thead>
<tr>
<th scope="col" class="org-left">Category</th>
<th scope="col" class="org-right">Contribution</th>
</tr>
</thead>
<tbody>
<tr>
<td class="org-left">Participation</td>
<td class="org-right">12%.</td>
</tr>
<tr>
<td class="org-left">Final Project</td>
<td class="org-right">20%.</td>
</tr>
<tr>
<td class="org-left">Homeworks</td>
<td class="org-right">68%</td>
</tr>
</tbody>
</table>
</div>
<div id="outline-container-orgfb2033f" class="outline-3">
<h3 id="orgfb2033f"><span class="section-number-3">5.1.</span> Why incentivize classroom time?</h3>
<div class="outline-text-3" id="text-5-1">
<p>
The classroom is for doing and clarifying.
You have no way of knowing if your understanding developed from online material is complete or accurate unless you match it off against others.
We will therefore emphasize doing, discussing, and collaborate.
</p>
</div>
</div>
<div id="outline-container-org10d6cb0" class="outline-3">
<h3 id="org10d6cb0"><span class="section-number-3">5.2.</span> Why is "doing" so important for this course?</h3>
<div class="outline-text-3" id="text-5-2">
<p>
Learning math and computing, and how to use them, is not something that can be learned through observation.
Like playing piano, or improving your golf swing, improvement comes from practice, practice, practice.
It is not enough to merely state the principles.
You must demonstrate that they have been internalized.
We will therefore do small exercises in class.
And since one of the best ways to learn is to teach, we will frequently do these exercises in small groups.
You might find your peers description of a problematic fact more useful than mine since they are at a more similar learning level.
You may find your own understanding grows as you have to reframe my teachings in your own words to help a fellow student grasp a difficult concept.
</p>
<p>
This emphasizes again why class participation is important.
It is where we will test our comprehension of important points, I will learn if a concept is not well appreciated, and you will have the chance to practice the skills you later may wish to use in your own way on your own problems.
Each week's attendance is worth 1% of the final grade.
</p>
</div>
</div>
<div id="outline-container-orgaec2916" class="outline-3">
<h3 id="orgaec2916"><span class="section-number-3">5.3.</span> I find this stuff hard and am worrying about failing</h3>
<div class="outline-text-3" id="text-5-3">
<p>
I like to give lots of small homeworks.
That takes the pressure of any one assignment, and means you get both frequent feedback on your performance, and you are coerced into not falling behind.
</p>
</div>
</div>
<div id="outline-container-orgd8bbeb1" class="outline-3">
<h3 id="orgd8bbeb1"><span class="section-number-3">5.4.</span> Why have a final project?</h3>
<div class="outline-text-3" id="text-5-4">
<p>
The final project is meant to give you an opportunity to showcase your learning and to use the general and specific skills that you will use in the future, whether in academics or industry, for sharing complex technical material with others.
</p>
</div>
</div>
<div id="outline-container-org7831aa6" class="outline-3">
<h3 id="org7831aa6"><span class="section-number-3">5.5.</span> A look ahead – what we will code</h3>
<div class="outline-text-3" id="text-5-5">
<ol class="org-ol">
<li>Turing Machine</li>
<li>Integrate and Fire Neuron</li>
<li>Hodgkin-Huxley Neuron</li>
<li>Perceptron</li>
<li>Hopfield Net</li>
<li>Agent Based Model</li>
<li>And possibly more</li>
</ol>
</div>
</div>
<div id="outline-container-orgc22f2cd" class="outline-3">
<h3 id="orgc22f2cd"><span class="section-number-3">5.6.</span> A look ahead – what we talk about</h3>
<div class="outline-text-3" id="text-5-6">
<ol class="org-ol">
<li>What is cognition?</li>
<li>What is a cognitive model?</li>
<li>What is the relationship between cognition and neuroscience?</li>
<li>All of which will benefit from better understanding what is a theory.</li>
</ol>
</div>
</div>
</div>
<div id="outline-container-org9e04697" class="outline-2">
<h2 id="org9e04697"><span class="section-number-2">6.</span> Computational Neuroscience</h2>
<div class="outline-text-2" id="text-6">
</div>
<div id="outline-container-org63a791b" class="outline-3">
<h3 id="org63a791b"><span class="section-number-3">6.1.</span> Slime assignment</h3>
</div>
<div id="outline-container-org6e5b29d" class="outline-3">
<h3 id="org6e5b29d"><span class="section-number-3">6.2.</span> What are examples of research combining cognitive, computational, and neuroscience methods?</h3>
<div class="outline-text-3" id="text-6-2">
<ol class="org-ol">
<li>Form groups of two (or three if odd number) (even numbers allowed llm use;odd numbers any resources, including on line, but <b>not</b> llm).</li>
<li>Go to the following web site: <a href="https://2026.ccneuro.org/poster-sessions/?view=all">2026 Posters Cognitive Computational Neuroscience meeting</a>.
<ol class="org-ol">
<li>Pick a poster.
Note it's label (letter-number; on the left)</li>
<li>Be ready with a two sentence summary.</li>
<li>Tell us why it is a good example of computational modeling of either mind or brain.</li>
<li>Why you chose it.</li>
</ol></li>
</ol>
</div>
<div id="outline-container-orge269e16" class="outline-4">
<h4 id="orge269e16"><span class="section-number-4">6.2.1.</span> Evaluating Academic Work  <span class="tag"><span class="exercise">exercise</span></span></h4>
</div>
</div>
<div id="outline-container-org6cfc325" class="outline-3">
<h3 id="org6cfc325"><span class="section-number-3">6.3.</span> Is a mathematical formula a model?</h3>
<div class="outline-text-3" id="text-6-3">
<p>
Yes or No? If yes, what makes it so? Are all equations models? If no, why not? What else is needed to supplement the equation?
</p>
</div>
<div id="outline-container-org6ae072a" class="outline-4">
<h4 id="org6ae072a"><span class="section-number-4">6.3.1.</span> Forgetting Curve — Ebbinghaus</h4>
<div class="outline-text-4" id="text-6-3-1">
<div id="org27a43c7" class="figure">
<p><img src="./images/Forgetting_curve_decline.svg.png" alt="Forgetting_curve_decline.svg.png" />
</p>
<p><span class="figure-number">Figure 1: </span>The original uploader was Icez at English Wikipedia.</p>
</div>
</div>
</div>
<div id="outline-container-orgb800eb0" class="outline-4">
<h4 id="orgb800eb0"><span class="section-number-4">6.3.2.</span> A Mathematical Function</h4>
<div class="outline-text-4" id="text-6-3-2">
<div class="org-src-container">
<pre class="src src-haskell"><code><span style="color: #ff6f9f;">import</span> <span style="color: #79a8ff;">Graphics.Gnuplot.Simple</span>
<span style="color: #79a8ff;">:</span>{
<span style="color: #4ae2ff;">plotFunc</span> [<span style="color: #79a8ff;">PNG</span> <span style="color: #00d3d0;">"./images/expdecay.png"</span>]
(linearScale 100 (1,6))
((<span style="color: #6ae4b9;">\</span>x <span style="color: #6ae4b9;">-></span> exp (1.0<span style="color: #6ae4b9;">/</span>x)) <span style="color: #6ae4b9;">::</span> <span style="color: #79a8ff;">Double</span> <span style="color: #6ae4b9;">-></span> <span style="color: #79a8ff;">Double</span>)
<span style="color: #79a8ff;">:</span>}
</code></pre>
</div>
<div id="orgba4e637" class="figure">
<p><img src="./images/expdecay.png" alt="expdecay.png" />
</p>
<p><span class="figure-number">Figure 2: </span>Plot of \(e^{\frac{1}{x}}\).</p>
</div>
</div>
<ol class="org-ol">
<li><a id="org926cee3"></a>A digression on code<br />
<div class="outline-text-5" id="text-6-3-2-1">
<p>
The above example is coded in <a href="https://www.haskell.org/">Haskell</a>.
</p>
<ol class="org-ol">
<li>What makes Haskell different from other programming languages?</li>
<li>When might it be a good/bad choice?</li>
<li>Do you need to learn to write code?
Why or why not?</li>
<li>Regardless of your answer, how do we get LLMs to support us? Or should we not use LLMs at all?</li>
</ol>
</div>
</li>
<li><a id="orgd4cd0f9"></a>Programming Exponential Decay  <span class="tag"><span class="exercise">exercise</span></span><br />
<div class="outline-text-5" id="text-6-3-2-2">
<p>
Compute the numbers needed for a plot of exponential decay. Plot the exponential decay. Be prepared to come to the front and show us your code; your plot; and the tools you needed to get it to run.
Groups of 2 or 3.
Programming languages:
</p>
<ol class="org-ol">
<li>Python</li>
<li>R</li>
<li>Javascript</li>
</ol>
</div>
</li>
<li><a id="org1bdea8e"></a>Same Exercise as Homework with one of these languages <i>that I will assign</i>. For this exercise you are supposed to use an LLM. See the Learn Dropbox for additional instructions.<br />
<div class="outline-text-5" id="text-6-3-2-3">
<ol class="org-ol">
<li>Racket (common lisp is okay too, but may be harder to install)</li>
<li>Go</li>
<li>Rust</li>
<li>Lean4</li>
<li>Typescript</li>
<li>Ruby</li>
<li>Ocaml</li>
<li>APL (or any variant of APL you can get to work)</li>
<li>Prolog</li>
</ol>
<p>
It is possible to fail at generating the code, and still get full credit. The purpose of this exercise is to learn about using LLMs to generate code: which one(s) should we use, how should we use them, what do we need to know to use them well, how do we know we can trust what they give us?
</p>
</div>
</li>
</ol>
</div>
<div id="outline-container-orgaac2e84" class="outline-4">
<h4 id="orgaac2e84"><span class="section-number-4">6.3.3.</span> More on the fitting curves to Ebbinghaus Data</h4>
<div class="outline-text-4" id="text-6-3-3">
<p>
What can we infer from the similarity between Figure <a href="#org27a43c7">1</a> and Figure <a href="#orgba4e637">2</a> ?
</p>
<p>
What equations did Ebbinghaus fit to his own data? And what have other suggested?
</p>
<p>
You can find the answers here: <a href="https://doi.org/10.1371/journal.pone.0120644">Replication and Analysis of Ebbinghaus' Forgetting Curve</a>.
</p>
<p>
Programming one of the alternatives and compare the plot to your exponential. See how close you can get.
</p>
<p>
What is the difference between a power function and an exponential function?
</p>
<p>
How might we reconcile the exponential and power function versions? An answer might be <a href="https://doi.org/10.3758/s13423-011-0076-y">here</a>.
</p>
<p>
Want to play with Ebbinghaus' original data? Load the <code>HistData</code> R package. Package description is <a href="https://cran.r-project.org/web/packages/HistData/HistData.pdf">here (pdf)</a>.
</p>
<p>
Once again, what is the difference between curve fitting and a mathematical (or computational) model?
</p>
</div>
</div>
</div>
<div id="outline-container-org23ccfad" class="outline-3">
<h3 id="org23ccfad"><span class="section-number-3">6.4.</span> Reprise</h3>
<div class="outline-text-3" id="text-6-4">
<ol class="org-ol">
<li>What does COMPUTATIONAL cognitive neuroscience/science/psychology mean?
<ol class="org-ol">
<li>Consider checking out <a href="https://www.sciencedirect.com/science/article/pii/S0960982219306141?via%3Dihub">Bain, What is Cognition?</a></li>
</ol></li>
<li>What are our first impressions of what research in the field looks like?</li>
<li>What are our early impressions about the use of LLM for
<ul class="org-ul">
<li>answering conceptual questions?</li>
<li>coding implementations?</li>
</ul></li>
</ol>
</div>
</div>
</div>
<div id="outline-container-org6d828e0" class="outline-2">
<h2 id="org6d828e0"><span class="section-number-2">7.</span> Neurally Inspired Models 1: The cellular level</h2>
<div class="outline-text-2" id="text-7">
<p>