AlphaFold by hand✍️ Excel ~ I designed this exercise... to show (1) MSA multi-head attention, (2) Pair triangular update, two key components of the EvoFormer architecture.👇Join the AI Math community. Download xlsx.show more

Transformer by hand✍️ Excel ~ I designed this exercise... to show the core math of a Transformer model is to combine columns (attention), combine rows (feed forward), and repeat.👇Join the 'AI Math' community. 👇Download xlsx.show more

LSTM by hand✍️Excel ~ I designed this exercise to... show it is possible to calculate a simple LSTM by hand. Green🟩: Short Term. Blue🟦: Long Term. +equations. +medium.👇Join the 'AI Math' community. Download xlsx.show more

Autoencoder by hand✍️Excel~ I designed this exercise to show... how an Encoder-Decoder network convert input to code and reconstruct input from code. It is annotated with equations, PyTorch, and graphs. 👇Join the 'AI Math' community. Download xlsx.show more

ResNet by hand✍️Excel~ I designed this exercise to compare... a ResNet to an MLP and show skip-connections are simply identity matrices next to weights and biases. I also made a medium version to show how it scales. 👇Join the 'AI Math' community. Download xlsx.show more

Autoencoder by hand✍️Excel~ I designed this exercise to show... how an Encoder-Decoder network convert input to code and reconstruct input from code. It is annotated with equations, PyTorch, and graphs. I also made a medium version.👇Join the 'AI Math' community. Download xlsx.show more

Backpropagation by hand✍️ ~ spreadsheet. I designed this exercise... to show it is possible to calculate backpropagation for a non-trivial, three-layer network by hand. p.s. I just started this community to share useful resources on AI math. 👇 Join the community.show more

Transformer: Multi-Head Attention ~ Math vs Code 🔢💻 ~... I made this visualization to show you how to implement the multi-head attention math in PyTorch within 50 LoC. Multi-Head Attention is what makes the Transformer's performance outstanding. It captures and represents more diverse linguistic relationships and patterns, and attends to different learned input embedding spaces. The parallel computing design also makes the model more efficient.show more

At MIT, the only course I ever dropped was... signal processing. The DFT math was too intimidating. It’s so easy to just type fft() in MATLAB and move on. Years later, I finally did DFT by hand. ✍️ If you are also afraid of DFT, I hope this helps! ⬇️ Download:show more

At MIT, I learned about RNNs in my NLP... class with Prof. Michael Collins. He built a model from my keystrokes to predict who I was. To me, it felt like a magic box. Years later, when I had to teach RNNs, I forced myself to go inside the box. ⬇️ Download: First, with a tiny example on paper by hand ✍️. Then, a slightly larger one in Excel. That’s when it finally clicked: 👉 The weights are reused (weight matrices on the left side) 👉 The hidden states are passed down (H's) When I built it by hand and saw everything visually, it clicked, just math you can actually trace. Now I try to give others the same “aha!” moment I had. ⬇️ Download Excel:show more

Single vs Multi-hand Attention by hand ✍️ Resize matrices... yourself 👉 The most important fact about multi-head attention: it has the same parameter count as single-head attention. The difference is purely structural — same total Wqkv weights, partitioned into smaller q–k–v triples. Look at the two diagrams below. Both Wqkv matrices have the same height — same number of weight rows, same number of parameters. What changes is how that single tall block is sliced. • Left. One head. The full Wqkv produces one big QKV: a tall Q (36 rows), a tall K, a tall V. One scoring computation runs over those full-width tensors. • Right. 3 heads. The same-height Wqkv is sliced into 3 smaller q–k–v triples — each 12 rows tall. 3 scoring computations run in parallel, each a thinner version of the left. The compute trade-off — kind of. Same Wqkv weights. Multi-head runs the attention scoring S = Kᵀ × Q once per head, so the dot-product count multiplies by H. • Single-head: seq × seq = 40² = 1600 dot products • Multi-head: seq × seq × H = 40² × 3 = 4800 dot products (3×) But each multi-head dot product is narrower — its inner dimension is head_dim instead of H × head_dim. So when you count actual scalar multiplications, the totals are equal: • Single-head: seq² × (H × head_dim) = 40² × 36 = 57600 • Multi-head: seq² × H × head_dim = 40² × 3 × 12 = 57600 Same FLOPs. Multi-head buys you H independent attention patterns at no extra weight cost and no extra arithmetic cost — it's the same total compute, sliced into H finer-grained heads.show more

I designed these worksheets to turn Agentic AI concepts... into simple math problems you can do by hand. ✍️ Download PDF: Problems 1 to 5: 1. Count the tokens: split on spaces, one word per box 2. Subword splitting: when one word is three tokens 3. Punctuation counts: the marks are tokens too 4. Tokens per word: the ratio that turns words into a bill 5. Will it fit? A document against a context window Why am I making these worksheets? AI is making people (including me) think less. It's just too easy to ask AI a few questions about a new AI concept and start to believe I get it. Until recently, we could use a coding problem to practice a new AI concept. But now it has become too easy to ask AI to write the code, and we start to think we must know the concept, since we technically solved a coding problem. Thus, my approach is to recast AI concepts as simple math problems we must solve with pen and paper. Using our hands is one way to motivate ourselves to start thinking again. ✍️ ~ Prof. Tom Yehshow more

Transformer by hand ✍️ ~ 6 steps walkthrough below... Open the hood of a transformer and the parts list is overwhelming: embeddings, positional encoding, attention weighting, self-attention, cross-attention, multi-head attention, layer norm, skip connections, softmax, linear, Nx, shifted right, query, key, value, masking. Which of those actually make the car run? Two of them. Attention weighting and the feed-forward network. Everything else is an enhancement to make it run faster and longer, which is how we got from a car to a truck, and to the word "large" in large language model. So I drew and calculated those two parts entirely by hand. Goal: push five features through one transformer block, filling in every cell yourself. 1. Given Five positions of input features, arriving from the previous block. 2. Attention matrix Let us feed all five features to a query-key module (QK) and read back an attention weight matrix, A. The details of that module are a post of their own. 3. Attention weighting We multiply the input features by A to get the attention weighted features, Z. Still five positions. The effect is to combine features *across positions*, horizontally: X1 becomes X1 + X2, X2 becomes X2 + X3, and so on. 4. First layer Let us feed all five weighted features into the first layer of the FFN. Multiply by the weights and biases. This time the combining happens *across feature dimensions*, vertically, and each feature grows from 3 numbers to 4. Note that every position goes through the same weight matrix. That is what "position-wise" means. 5. ReLU We cross out the negatives. They become zeros. 6. Second layer Let us bring it back down: 4 dimensions to 3. The output feeds the next block, which has a completely separate set of parameters, and the whole thing runs again. You have just calculated a transformer block by hand. ✍️ The takeaway: the two parts are doing two different jobs, and neither one alone is enough. Attention mixes *across positions*, so a feature can see its neighbours. The FFN mixes *across feature dimensions*, so each position can think about itself. Horizontal, then vertical. Then that pattern repeats N times, each block with its own separate set of weights. That is the Nx from the list up top, and that is what makes the transformer run. 💾 Save this post! #AIbyHand #Transformers #DeepLearningshow more

HOLY CRAP! I can't tell you how big this... is for the medical community and drug discovery: Google Announces AlphaFold 3 AI. Details: Enhanced Molecular Prediction: AlphaFold 3 predicts the structure and interactions of all life's molecules, including proteins, DNA, RNA, ligands, and more, with unprecedented accuracy. Improved Interaction Accuracy: For protein interactions with other molecule types, AlphaFold 3 offers at least a 50% improvement over existing methods, and doubles the accuracy for some critical interactions. Transformative Potential for Science and Medicine: The model aims to deepen our understanding of biological processes and significantly advance drug discovery efforts. Accessibility for Researchers: AlphaFold 3's capabilities are largely accessible for free via the AlphaFold Server, providing an essential tool for scientific research. Drug Design Innovation: AlphaFold 3 is utilized by Isomorphic Labs in collaboration with pharmaceutical companies to accelerate drug design, potentially leading to new treatments for various diseases. Foundation in AlphaFold 2: Building on the breakthroughs of AlphaFold 2, this version extends its scope beyond proteins to a wide range of biomolecules, enhancing its utility in scientific research and application. Global Accessibility and Educational Support: The AlphaFold Server is a free platform for non-commercial research worldwide, supported by educational resources to foster wider adoption and innovation. Empowering Rapid Scientific Advancements: By making detailed molecular interactions easily accessible, AlphaFold 3 enables faster hypothesis testing and could reduce the time and cost typically associated with experimental protein-structure prediction. Responsible Development and Deployment: DeepMind has engaged with domain experts to assess the impacts and potential risks of AlphaFold, ensuring its responsible use in the scientific community. Broad Implications for Biology:AlphaFold 3 helps reveal complex cellular mechanisms and interactions, offering insights that could lead to improved agricultural crops, enhanced understanding of diseases, and novel therapeutic strategies.show more

MLP in PyTorch by hand ✍️ ~ 7 steps... walkthrough below Goal: fill in every blank in the PyTorch code to build a multi-layer perceptron. 1. Given Let us start with a code template on the left and the network it is supposed to build on the right. Every blank in the code can be worked out from the picture. 2. Linear layer We count: 3 features in, 4 features out. So the weight matrix is 4 by 3. There is an extra column for the biases, which means bias = T. 3. ReLU Let us apply the activation. ReLU crosses out the negatives, so -1 becomes 0. 4. Linear layer The input size is 4, because that is what the previous layer put out. The output size is 2. A 2 by 4 weight matrix, and this time no extra column, so bias = F. 5. ReLU We cross out the negatives again. 6. Linear layer Two features in, five out. A 5 by 2 weight matrix, with a bias column, so bias = T. 7. Sigmoid Let us finish. Sigmoid squashes the raw scores (3, 0, -2, 5, -5) into probabilities between 0 and 1. You have just implemented a three-layer deep neural network by hand. ✍️ == Story == Three years ago I gave this exercise to my students, to connect the code to the math. They found it odd. Every other AI course they were taking lived inside a Jupyter notebook, and here I was handing out paper. Three years later, my colleagues are the ones rushing to move their materials to paper. The exercise has not changed. Paper still asks the one thing a notebook lets you skip: do you actually understand what the code is doing? If you can tell me why the weight matrix is 4 by 3, and why bias is F on the second layer, you understand nn.Linear better than someone who has been copy-pasting it for a year. 💾 Save this post! #AIbyHand #PyTorch #DeepLearningshow more

Calling All AI Filmmakers💀🎃 Since I didn't have time... to make my annual AI Halloween short film this year I figured I'd enlist the help of the AI community. Help me finish ENTER THE CLOSET by posting an AI Generated Sequence in the comments of what happens next once we "enter the closet." I'll try to slice them all together for Halloween! Join in below!show more

VIDEO 1: John Ratcliffe, the Director of the Central... Intelligence Agency (CIA) in his BMW 7 Series followed by just a Chevrolet Suburban carrying his security details. Just two cars. The richest most powerful country in the world. VIDEO 2: The convoy of Nuhu Ribadu, the National Security Adviser of the Federal Republic of Nigeria. One of the poorest country in the world. A country over 60% of the citizens live in multi-dimensional poverty. You be the judge. I beg somebody show this to oga Zacch Adedeji #unmutedthepodcast #tegatalksshow more

Yet another scene that would make #AI bros cry…... This one was entirely hand drawn with key frames and main in-betweens done by me. It was my first episode as a director and I wanted to show what could be done with the show in terms of dynamic action. This episode paved the way for all of the #FairlyOddParents movies and established that we COULD, in fact, have big action sequences. It also established me as the “action guy for comedy shows.”show more

[LSTM] by Hand ✍️ LSTMs have been the most... effective architecture to process long sequences of data, until our world was taken over by the Transformers. LSTMs belong to the broader family of recurrent neural network (RNNs) that process data sequentially in a recurrent manner. Transformers, on the other hand, abandon recurrence and use self-attention instead to process data concurrently in parallel. Recently, there is renewed interest in recurrence as people realized self-attention doesn’t scale to extremely long sequences, like hundreds of thousands of tokens. Mamba is a good example to bring back recurrence. All of a sudden, it is cool to study LSTMs. How do LSTMs work? [1] Given ↳ 🟨 Input sequence X1, X2, X3 (d = 3) ↳ 🟩 Hidden state h (d = 2) ↳ 🟦 Memory C (d = 2) ↳ Weight matrices Wf, Wc, Wi, Wo Process t = 1 [2] Initialize ↳ Randomly set the previous hidden state h0 to [1, 1] and memory cells C0 to [0.3, -0.5] [3] Linear Transform ↳ Multiply the four weight matrices with the concatenation of current input (X1) and the previous hidden state (h0). ↳ The results are feature values, each is a linear combination of the current input and hidden state. [4] Non-linear Transform ↳ Apply sigmoid σ to obtain gate values (between 0 and 1). • Forget gate (f1): [-4, -6] → [0, 0] • Input gate (i1): [6, 4] → [1, 1] • Output gate (o1): [4, -5] → [1, 0] ↳ Apply tanh to obtain candidate memory values (between -1 and 1) • Candidate memory (C’1): [1, -6] → [0.8, -1] [5] Update Memory ↳ Forget (C0 .* f1): Element-wise multiply the current memory with forget gate values. ↳ Input (C’1 .* o1): Element-wise multiply the “candidate” memory with input gate values. ↳ Update the memory to C1 by adding the two terms above: C0 .* f1 + C’1 .* o1 = C1 [6] Candiate Output ↳ Apply tanh to the new memory C1 to obtain candidate output o’1. [0.8, -1] → [0.7, -0.8] [7] Update Hidden State ↳ Output (o’1 .* o1 → h1): Element-wise multiply the candidate output with the output gate. ↳ The result is updated hidden state h1 ↳ Also, it is the first output. Process t = 2 [8] Initialize ↳ Copy previous hidden state h1 and memory C1 [9] Linear Transform ↳ Repeat [3] [10] Update Memory (C2) ↳ Repeat [4] and [5] [11] Update Hidden State (h2) ↳ Repeat [6] and [7] Process t = 3 [12] Initialize ↳ Copy previous hidden state h2 and memory C2 [13] Linear Transform ↳ Repeat [3] [14] Update Memory (C3) ↳ Repeat [4] and [5] [15] Update Hidden State (h3) ↳ Repeat [6] and [7]show more

Ape Terminal IDO #23 🦍 Sharpe AI - Sharpe... AI Sharpe AI is the 1st web3 project recognized by two multi-trillion dollar firms: Google and Microsoft. Sharpe AI is among the 1st Bittensor ecosystem projects, using the AIT subnet (80x ROI) to mine $TAO. This edge fuels its rapid growth, establishing it as the fastest-growing AI super app. 🟠 Backed by Contango, main investor of Bittensor ($12.7B) 🟠 #1 on Product Hunt globally for AI and Crypto 🟠 100k+ active users With AI emerging as one of the hottest narratives this cycle, Sharpe AI positions itself at the forefront as one of the 1st AI projects with solid backing and an established user base. Sale opens NOW:show more