AI (and Robotics) From Scratch in 2026

• 10-202 Intro to Modern AI so you can modify any open source LLM as this will take off soon with new hardware. You can easily get paid insane amounts of money doing this right now.

• 10-714 DL Algorithms & Implementation teaches how to build your own PyTorch stack from scratch and trust me you want to use types and toss out Python into the dustbin of history because right now types are making agentic coding very simple to use and for AI-assisted "lightweight formal methods" to verify the code.

To understand these courses:

• Ziko Kolter's LA crash course
  • Combine these with 3Blue1Brown Linear Algebra lectures on YouTube or NJ Wildberger's excellent LinAlg course which walks through everything at the geometric level.
• This single video Matrix Calculus from MIT's 2020 18.06 course on linear algebra which we will take here too as our first math lecture. Derivatives are covered and explained simply. There is a full Matrix calculus course but it's not needed at this applied level but we take it below.
• The notes from MIT's 6.390 Intro to ML

This is all you really need for those 2 courses as they're both mostly self-contained anyway. These are the best applied ML resources I've found anywhere in 2026 then just ask ChatGPTx/Grok/DeepSeek/Fable or whatever new agent to help you understand the rest and find more YouTube tutorials. If you want to go out into the world and sign up companies to "AI" (and get paid) or you want to hack around some LLM open source model project this is all you need.

The rest of this workshop is to understand the modern theory of AI because much of it is not available to the public anymore so I asked everyone I work with what's going on and everything below is what they came up with.

Does there exist a unified theory of modern AI yet or something close to it?

• These 30 Lectures were recently put together by MIT's leading Neuroscience researcher by that I mean he's the world's most cited Neuroscience researcher. He used the assistance of a research paper Agentic Investigator. Give it a research topic and it gives you back an entire paper on that topic.

These lectures show current AI provides a generic mean or 'smoothing' effect on everything they generate. The human user has to provide the sparse logical jumps to escape the annoying politeness and homogenizing of scientific thought that AI defaults to. They also show compositionality which means a complex thing is constructed of many small reusable basic things and these are (as described in the prologue) mathematically implied to be sparse for the simple reason that we can compute them efficiently. Genericity is another trait of modern AI and means a learning function being defined by any set of coordinates is invariant to transformations and defining it in different spaces where you 'shift' the function doesn't really matter. There will be many lectures about this in detail and we will take them. AI also can't be sentient (yet) no matter what AGI marketing these companies claim. This is another theme of these lectures.

Things we have to take to understand these lectures:

• The mathematical model of Machine Learning which hasn't changed.
  • All lectures are taught by the author of the book and there's undergrad notes (MIT).
  • This book is 'over simplified' sometimes things can seem 'incorrect' but teaches statistical learning theory
• Some optional short lectures from the perspective of theoretical neuroscience.
  • An optional book Understanding Deep Learning
  • All the Calculus/Algebra content below
  • Maybe the Zhang book on statistical learning theory but depends what I can find, what I want is Poggio's 9.520 'draft book' that isn't available anywhere but we can always watch old lectures and take our own notes then go on a hunt for new papers. I may just skip all this and go on a tangent with the deep learning lectures because that's what matters right now in research.

As per Tomaso Poggio in his 30 lectures on Deep Learning the vast majority of Real Numbers are uncomputable and undecidable so numerical approximations in the discrete world have to be done. The inputs are simply too gigantic, a tiny 3D model is 100 x 100 x 100 with 10⁶ unknowns, so almost all linear algebra learned in undergrad is not used as now you live in the world of factoring (SVD), matrices have to be randomized (jack polynomials), eigenvalues are approximated, and preconditioning is needed as gradient descent is too slow because it 'zig-zags'.

The following is very similar to CMU's Math Foundations for Robotics course as well:

• Matrix calculus
• MIT Numerical Methods and large scale linear algebra.
• Modern Regression and Data Analysis because in applied ML you often find yourself trying to interpret data. We came this far why not be "advanced" students in the art of data analysis too (think quant finance).

• 6.8200 Computational Sensorimoto Learning this guy is the leading researcher for "control learning" so we will learn the math model. There is many other math models for robotics but an AI will eventually discard them for it's own interpretation hence I chose this course just to get a taste of robotic learning. We are interested in that link to the full lecture notes.

You can use the Agentic Investigator to help you research these fields by yourself.

Modern machine learning is theoretically done with Banach spaces where you get a vector space with measurement. This is to promote sparsity (weights that are exact zeros) while classical machine learning relies on Hilbert spaces (inner product norms). Then you have to convert all this to the real world of computer hardware using numerical methods.

We should just skip all of vector calculus and proceed in a direct path to Banach spaces. There's a free book for this "TBB-Dripped" or Elementary Real Analysis by Thomson-Bruckner the dripped version or 'Dump the Riemann Integral Project' version. Many concepts here will come up in the Tomaso Poggio Deep Learning lectures and for any probability material. It looks like a large book but half way through any undergrad math text you pick up speed as the problems become too easy to solve.

There's a concept of groups and inside those are an abelian group with the ability to perform 'actions' over a ring structure that has a special case of being a field. This is the space of vectors and linear maps. A book exists to teach all this from scratch by Paolo Aluffi called Algebra: Chapter 0. There are many other great undergrad linear algebra texts but what is the point in taking them if we are only using numerical analysis (SVD) and matrix calculus thus throwing out most of their content. We may as well learn how it all works at the big picture level plus group theory structures and symmetry in ML is another emerging field right now.

I will create my own Linear Algebra course

• NJ Wilberger geometrical demonstrations of transformations
• The SVD 'compact version' to avoid block matrices and Edelman's 18.06 MIT course
• The entire field described in category theory so you understand what's going on at the overview level now everything makes sense

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