When you type a prompt into ChatGPT, the response appears instantaneously. What happens in the intervening seconds remains a black box for most users: layers, parameters, attention mechanisms, and fine-tuning. Vocabulary expands, but comprehension often stalls. Tom Yeh, an associate professor of computer science at the University of Colorado Boulder, is attempting the opposite approach. He shrinks these complex models until they fit on a single sheet of paper, picks up a pen, and performs every multiplication himself. The project is titled AI by Hand. No code, no GPUs, and no complex frameworks are required.1
At first glance, this effort seems like a stubborn protest against a world dominated by models with billions of parameters. Yeh’s argument is different: beneath the technical jargon, almost every model performs the same repetitive task. That task is matrix multiplication. When you perform the calculation by hand, the magic evaporates, leaving only the steady rhythm of addition and multiplication.
- Tom Yeh reduces AI models to single-page arithmetic tasks performed by hand.
- The series includes twenty-eight exercises covering everything from matrix multiplication to backpropagation, attention mechanisms, and RLHF.
- The goal is not to train a GPT model at home, but to visualize the skeletal structure beneath the jargon.
- The boundaries are clear: while you cannot run a billion-parameter model on paper, you can break the illusion of its mystery.
Can a complex AI model be reduced to a single page?
Between late 2023 and 2024, Tom Yeh authored twenty-eight computational exercises, eventually organizing them into a structured series. The journey begins with matrix multiplication, progressing through multilayer perceptrons, backpropagation, batch normalization, and dropout. It continues with recurrent networks, LSTM, self-attention, and the transformer architecture. The series also covers autoencoders, generative adversarial networks, CLIP, mixture-of-experts, BitNet, and reinforcement learning from human feedback. In each article, the model is scaled down to a manageable size, allowing a student to work through the logic from start to finish.2
The examples are intentionally kept small: a weight table of just two or three rows, a few input numbers, and an activation threshold. Once the calculation is complete, you have a result. While that output may not resemble the prose generated by a large language model, the answer to the question of what the network actually did is no longer a marketing slogan—it is the lines of math you have written yourself.
This approach moves beyond typical university coursework. Yeh’s lab focuses on human-centered artificial intelligence, prioritizing the readability of models and the deconstruction of the black box. AI by Hand translates academic research into a public exercise, expanding AI literacy through the accessible medium of pen and paper.1
Why abandon the code?
Today, the standard path to learning AI usually involves watching a video, opening a notebook, and calling a software library. The training command executes, the loss decreases, and a graph appears on the screen. It is functional, but the arithmetic occurring between the lines is often overlooked. Yeh’s method reverses this: you produce the number yourself, then verify that the machine produces the same result. A similar discipline exists in the Soroban open-course repository, which requires students to perform small training runs on paper before verifying them with code. The pedagogical challenge arises when the machine and the paper disagree, forcing the student to identify where the error occurred.3 The common premise is that true understanding requires working through the calculations before simply observing the output.
How does AI really impact your screen?
This approach does not ask users to discard their chat interfaces. Instead, it invites them to understand what lies behind the interface. In a forward pass, inputs are multiplied by weights, summed, and passed through an activation function. An activation is a simple rule—such as ReLU—that dictates whether a number passes through, is dampened, or is discarded. During backpropagation, errors are distributed backward, and each weight provides a numerical answer to the question of its contribution to that error. The weights then shift accordingly, and training is essentially the repetition of this shifting process. In attention mechanisms, three matrices—query, key, and value—interact. The model uses these products to determine which words or components to prioritize. When a chatbot maintains the context of a long text, it is not utilizing magic; it is performing a soft ranking of these scores. Once you have written this by hand, the claim that a model is paying attention becomes more than a hollow metaphor. As the number of parameters increases, the logic remains the same, only the scale grows. Yeh’s recurring finding is that beneath the jargon, almost everything is a chain of matrix multiplications.2
What is possible and what is not?
The boundary of this method is clear: manual calculation cannot digest a massive training set. You cannot run a production-scale transformer on paper. Yeh provides Excel workbooks and live seminars to accelerate the logic, yet the examples remain intentionally small. This is not an engineering shortcut, but a tool for reading and comprehension. It makes no promise that this method will allow you to build your own large language model, but it makes a more modest and robust claim: that you can break the spell of AI magic. As the discourse surrounding artificial intelligence inflates, the feeling of genuine understanding often becomes cheap. The pen serves to disrupt that convenience. If your calculation is incorrect, the paper catches you—unlike a library that silently passes the error along. The twenty-eight exercises in Yeh’s 2026 collection serve as a guide to this transparency, covering the entire spectrum from matrix multiplication to reinforcement learning.2
Notes and Sources
- Tom Yeh, Associate Professor of Computer Science, University of Colorado Boulder. Human-centered AI, interpretability, and AI by Hand education: colorado.edu/cs/tom-yeh. ↩
- Yeh, T. (updated 2026). "Calculating AI by Hand": 28 hand-calculation exercises (matrix multiplication, MLP, backpropagation, self-attention, transformer, MoE, BitNet, RLHF, etc.). byhand.ai. ↩
- Soroban (open course): Paper arithmetic and training runs verified with assertions. github.com/tamnd/soroban. ↩
- By Hand Research / AI by Hand: Research publication on model interpretability through mathematics and algorithms. byhand.ai/about. ↩
This article is for educational and informational purposes only; it is not a guide for training or safety auditing models in production.
