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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...

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Tom Yeh

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13,318 views • 26 days ago •via X (Twitter)

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Batch Normalization by hand ✍️ ~ 7 steps walkthrough below Batch normalization is common practice for improving training and achieving faster convergence. It sounds simple. But it is often misunderstood. 🤔 Does batch normalization involve trainable parameters, tunable hyper-parameters, or both? 🤔 Is batch normalization applied to inputs, features, weights, biases, or outputs? 🤔 How is batch normalization different from layer normalization? So I drew and calculated one entirely by hand. Goal: normalize a mini-batch of 4 examples to mean 0 and variance 1, then let the network scale it back. = 1. Given = A mini-batch of 4 training examples, each with 3 features. = 2. Linear layer = Let us multiply by the weights and add the biases. Batch norm sits after this, which answers the second question: what gets normalized is features, not inputs, weights or biases. = 3. ReLU = We apply the activation, and -2 becomes 0. Negative values are suppressed before any statistic is taken. = 4. Batch statistics = Let us compute the sum, mean, variance and standard deviation, one row at a time. A row is a feature and the four columns are the four examples, so every number here measures one feature against the rest of the batch. That is the "batch" in batch normalization, and it is exactly what layer normalization does not do. The statistics are rounded to whole numbers, which is what keeps the rest of the page doable in pen. = 5. Shift to mean 0 = We subtract the mean, in green. The four values in each feature now average to zero. = 6. Scale to variance 1 = Let us divide by the standard deviation, in orange. Each feature now has variance one, whatever scale it arrived at. = 7. Scale and shift = We multiply by a linear transformation and pass the result on. The diagonal and the last column are trainable, so having just forced every feature to mean 0 and variance 1, we hand the network the means to undo it. The outputs: Mean of each feature = [2, 1, 2] Std dev of each feature = [1, 1, 2] To the next layer = [2, -2, 2, 0], [-3, 3, 6, -3], [2, 0, 1, 2] The answers: 🤔 Both. The scale and shift are trainable, the statistics are not. Epsilon and the momentum on the running statistics are the hyper-parameters, and one mini-batch by hand needs neither. 🤔 Features, after the linear layer, not inputs, weights or biases. 🤔 Batch norm measures across the batch, one feature at a time. Layer norm measures across the features, one example at a time. 💾 Save this post!
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Batch Normalization by hand ✍️ ~ 7 steps walkthrough below Batch normalization is common practice for improving training and achieving faster convergence. It sounds simple. But it is often misunderstood. 🤔 Does batch normalization involve trainable parameters, tunable hyper-parameters, or both? 🤔 Is batch normalization applied to inputs, features, weights, biases, or outputs? 🤔 How is batch normalization different from layer normalization? So I drew and calculated one entirely by hand. Goal: normalize a mini-batch of 4 examples to mean 0 and variance 1, then let the network scale it back. = 1. Given = A mini-batch of 4 training examples, each with 3 features. = 2. Linear layer = Let us multiply by the weights and add the biases. Batch norm sits after this, which answers the second question: what gets normalized is features, not inputs, weights or biases. = 3. ReLU = We apply the activation, and -2 becomes 0. Negative values are suppressed before any statistic is taken. = 4. Batch statistics = Let us compute the sum, mean, variance and standard deviation, one row at a time. A row is a feature and the four columns are the four examples, so every number here measures one feature against the rest of the batch. That is the "batch" in batch normalization, and it is exactly what layer normalization does not do. The statistics are rounded to whole numbers, which is what keeps the rest of the page doable in pen. = 5. Shift to mean 0 = We subtract the mean, in green. The four values in each feature now average to zero. = 6. Scale to variance 1 = Let us divide by the standard deviation, in orange. Each feature now has variance one, whatever scale it arrived at. = 7. Scale and shift = We multiply by a linear transformation and pass the result on. The diagonal and the last column are trainable, so having just forced every feature to mean 0 and variance 1, we hand the network the means to undo it. The outputs: Mean of each feature = [2, 1, 2] Std dev of each feature = [1, 1, 2] To the next layer = [2, -2, 2, 0], [-3, 3, 6, -3], [2, 0, 1, 2] The answers: 🤔 Both. The scale and shift are trainable, the statistics are not. Epsilon and the momentum on the running statistics are the hyper-parameters, and one mini-batch by hand needs neither. 🤔 Features, after the linear layer, not inputs, weights or biases. 🤔 Batch norm measures across the batch, one feature at a time. Layer norm measures across the features, one example at a time. 💾 Save this post!

Tom Yeh

20,638 views • 19 days ago

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 #DeepLearning
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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 #DeepLearning

Tom Yeh

25,944 views • 23 days ago

[Graph Convolutional Network] by hand ✍️ Graph Convolutional Networks (GCNs), introduced by Thomas Kipf and Max Welling in 2017, have emerged as a powerful tool in the analysis and interpretation of data structured as graphs. This exercise demonstrates how GCN works in a simple application: binary classification. -- Goal -- Predict if a node in a graph is X. -- Architecture -- 🟪 Graph Convolutional Network (GCN) 1. GCN1(4,3) 2. GCN2(3,3) 🟦 Fully Connected Network (FCN) 1. Linear1(3,5) 2. ReLU 3. Linear2(5,1) 4. Sigmoid Simplications: • Adjacent matrices are not normalized. • ReLU is applied to messages directly. -- Walkthrough -- [1] Given ↳ A graph with five nodes A, B, C, D, E [2] 🟩 Adjacency Matrix: Neighbors ↳ Add 1 for each edge to neighbors ↳ Repeat in both directions (e.g., A->C, C->A) ↳ Repeat for both GCN layers [3] 🟩 Adjacency Matrix: Self ↳ Add 1's for each self loop ↳ Equivalent to adding the identity matrix ↳ Repeat for both GCN layers [4] 🟪 GCN1: Messages ↳ Multiply the node embeddings 🟨 with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is one message per node [5] 🟪 GCN1: Pooling ↳ Multiply the messages with the adjacent matrix ↳ The purpose is the pool messages from each node's neighbors as well as from the node itself. ↳ The result is a new feature per node [6] 🟪 GCN1: Visualize ↳ For node 1, visualize how messages are pooled to obtain a new feature for better understanding ↳ [3,0,1] + [1,0,0] = [4,0,1] [7] 🟪 GCN2: Messages ↳ Multiply the node features with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is one message per node [8] 🟪 GCN2: Pooling ↳ Multiply the messages with the adjacent matrix ↳ The result is a new feature per node [9] 🟪 GCN2: Visualize ↳ For node 3, visualize how messages are pooled to obtain a new feature for better understanding ↳ [1,2,4] + [1,3,5] + [0,0,1] = [2,5,10] [10] 🟦 FCN: Linear 1 + ReLU ↳ Multiply node features with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is a new feature per node ↳ Unlike in GCN layers, no messages from other nodes are included. [11] 🟦 FCN: Linear 2 ↳ Multiply node features with weights and biases [12] 🟦 FCN: Sigmoid ↳ Apply the Sigmoid activation function ↳ The purpose is to obtain a probability value for each node ↳ One way to calculate Sigmoid by hand ✍️ is to use the approximation below: • >= 3 → 1 • 0 → 0.5 • <= -3 → 0 -- Outputs -- A: 0 (Very unlikely) B: 1 (Very likely) C: 1 (Very likely) D: 1 (Very likely) E: 0.5 (Neutral)
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[Graph Convolutional Network] by hand ✍️ Graph Convolutional Networks (GCNs), introduced by Thomas Kipf and Max Welling in 2017, have emerged as a powerful tool in the analysis and interpretation of data structured as graphs. This exercise demonstrates how GCN works in a simple application: binary classification. -- Goal -- Predict if a node in a graph is X. -- Architecture -- 🟪 Graph Convolutional Network (GCN) 1. GCN1(4,3) 2. GCN2(3,3) 🟦 Fully Connected Network (FCN) 1. Linear1(3,5) 2. ReLU 3. Linear2(5,1) 4. Sigmoid Simplications: • Adjacent matrices are not normalized. • ReLU is applied to messages directly. -- Walkthrough -- [1] Given ↳ A graph with five nodes A, B, C, D, E [2] 🟩 Adjacency Matrix: Neighbors ↳ Add 1 for each edge to neighbors ↳ Repeat in both directions (e.g., A->C, C->A) ↳ Repeat for both GCN layers [3] 🟩 Adjacency Matrix: Self ↳ Add 1's for each self loop ↳ Equivalent to adding the identity matrix ↳ Repeat for both GCN layers [4] 🟪 GCN1: Messages ↳ Multiply the node embeddings 🟨 with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is one message per node [5] 🟪 GCN1: Pooling ↳ Multiply the messages with the adjacent matrix ↳ The purpose is the pool messages from each node's neighbors as well as from the node itself. ↳ The result is a new feature per node [6] 🟪 GCN1: Visualize ↳ For node 1, visualize how messages are pooled to obtain a new feature for better understanding ↳ [3,0,1] + [1,0,0] = [4,0,1] [7] 🟪 GCN2: Messages ↳ Multiply the node features with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is one message per node [8] 🟪 GCN2: Pooling ↳ Multiply the messages with the adjacent matrix ↳ The result is a new feature per node [9] 🟪 GCN2: Visualize ↳ For node 3, visualize how messages are pooled to obtain a new feature for better understanding ↳ [1,2,4] + [1,3,5] + [0,0,1] = [2,5,10] [10] 🟦 FCN: Linear 1 + ReLU ↳ Multiply node features with weights and biases ↳ Apply ReLU (negatives → 0) ↳ The result is a new feature per node ↳ Unlike in GCN layers, no messages from other nodes are included. [11] 🟦 FCN: Linear 2 ↳ Multiply node features with weights and biases [12] 🟦 FCN: Sigmoid ↳ Apply the Sigmoid activation function ↳ The purpose is to obtain a probability value for each node ↳ One way to calculate Sigmoid by hand ✍️ is to use the approximation below: • >= 3 → 1 • 0 → 0.5 • <= -3 → 0 -- Outputs -- A: 0 (Very unlikely) B: 1 (Very likely) C: 1 (Very likely) D: 1 (Very likely) E: 0.5 (Neutral)

Tom Yeh

46,779 views • 1 year ago

In my class, I teach the autoencoder by asking everyone to stand up. 🙆 Stretch your arms out wide. Imagine you are holding a heavy textbook (like Introduction to Algorithms by Prof. Cormen), the whole thing, every page. Now bring your hands slowly together until they almost touch your neck. The bottle "neck." The final exam is tomorrow and you are allowed one cheat sheet: whatever you can scribble on your palm. All nine hundred pages have to survive the squeeze. That is the encoder. Now imagine you sit in the exam. Push your arms back out to where they started. You try to rebuild the textbook from your palm notes. That is the decoder. Of course you cannot get every page back. What you get back is what mattered enough to write down, and the gap between the two is the loss the network is trying to shrink. I call it AI by Arms 🙆. It gets a laugh, and then it gets remembered. Goal: squeeze four numbers down to two, then rebuild the original four from them. 1. Given Let us start with four training examples: X1, X2, X3, X4. 2. Auto (copy to targets) We copy the training examples straight into the targets. That is the whole trick behind the name: "auto" is Greek for "self", and the data is its own label. 3. Encoder, layer 1 Let us multiply the inputs by the weights, add the biases, and apply ReLU. Negative values get crossed out and become zero. 4. Encoder, layer 2 (the bottleneck) We do it again, and now the four dimensions have become two. This layer is called the bottleneck, because everything has to fit through it. 5. Decoder, layer 1 Let us go back the other way: multiply, add, ReLU. This time there are no negatives to cross out. 6. Decoder, layer 2 We multiply once more and get the outputs Y. This is the decoder's attempt to rebuild the four original numbers from the two it was given. 7. MSE loss gradients Let us compare Y with the targets Y'. The gradient is 2 x (Y - Y'): subtract, then double. Those gradients kick off backpropagation, and the weights start to learn. Your entire education is all about encoding and decoding!
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In my class, I teach the autoencoder by asking everyone to stand up. 🙆 Stretch your arms out wide. Imagine you are holding a heavy textbook (like Introduction to Algorithms by Prof. Cormen), the whole thing, every page. Now bring your hands slowly together until they almost touch your neck. The bottle "neck." The final exam is tomorrow and you are allowed one cheat sheet: whatever you can scribble on your palm. All nine hundred pages have to survive the squeeze. That is the encoder. Now imagine you sit in the exam. Push your arms back out to where they started. You try to rebuild the textbook from your palm notes. That is the decoder. Of course you cannot get every page back. What you get back is what mattered enough to write down, and the gap between the two is the loss the network is trying to shrink. I call it AI by Arms 🙆. It gets a laugh, and then it gets remembered. Goal: squeeze four numbers down to two, then rebuild the original four from them. 1. Given Let us start with four training examples: X1, X2, X3, X4. 2. Auto (copy to targets) We copy the training examples straight into the targets. That is the whole trick behind the name: "auto" is Greek for "self", and the data is its own label. 3. Encoder, layer 1 Let us multiply the inputs by the weights, add the biases, and apply ReLU. Negative values get crossed out and become zero. 4. Encoder, layer 2 (the bottleneck) We do it again, and now the four dimensions have become two. This layer is called the bottleneck, because everything has to fit through it. 5. Decoder, layer 1 Let us go back the other way: multiply, add, ReLU. This time there are no negatives to cross out. 6. Decoder, layer 2 We multiply once more and get the outputs Y. This is the decoder's attempt to rebuild the four original numbers from the two it was given. 7. MSE loss gradients Let us compare Y with the targets Y'. The gradient is 2 x (Y - Y'): subtract, then double. Those gradients kick off backpropagation, and the weights start to learn. Your entire education is all about encoding and decoding!

Tom Yeh

22,479 views • 10 days ago

[Backpropagation] by Hand✍️ [1] Forward Pass ↳ Given a multi layer perceptron (3 levels), an input vector X, predictions Y^{Pred} = [0.5, 0.5, 0], and ground truth label Y^{Target} = [0, 1, 0]. [2] Backpropagation ↳ Insert cells to hold our calculations. [3] Layer 3 - Softmax (blue) ↳ Calculate ∂L / ∂z3 directly using the simple equation: Y^{Pred} - Y^{Target} = [0.5, -0.5, 0]. ↳ This simple equation is the benefit of using Softmax and Cross Entropy Loss together. [4] Layer 3 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W3 and ∂L / ∂b3 by multiplying ∂L / ∂z3 and [ a2 | 1 ]. [5] Layer 2 - Activations (green) ↳ Calculate ∂L / ∂a2 by multiplying ∂L / ∂z3 and W3. [6] Layer 2 - ReLU (blue) ↳ Calculate ∂L / ∂z2 by multiplying ∂L / ∂a2 with 1 for positive values and 0 otherwise. [7] Layer 2 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W2 and ∂L / ∂b2 by multiplying ∂L / ∂z2 and [ a1 | 1 ]. [8] Layer 1 - Activations (green) ↳ Calculate ∂L / ∂a1 by multiplying ∂L / ∂z2 and W2. [9] Layer 1 - ReLU (blue) ↳ Calculate ∂L / ∂z1 by multiplying ∂L / ∂a1 with 1 for positive values and 0 otherwise. [10] Layer 1 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W1 and ∂L / ∂b1 by multiplying ∂L / ∂z1 and [ x | 1 ]. [11] Gradient Descent ↳ Update weights and biases (typically a learning rate is applied here). 💡 Matrix Multiplication is All You Need: Just like in the forward pass, backpropagation is all about matrix multiplications. You can definitely do everything by hand as I demonstrated in this exercise, albeit slow and imperfect. This is why GPU's ability to multiply matrices efficiently plays such an important role in the deep learning evolution. This is why NVIDIA is now close to $1 trillion in valuation. 💡Exploding Gradients: We can already see the gradients are getting larger as we back-propagate up, even in this simple 3-layer network. This motivates using methods like skip connections to handle exploding (or diminishing) gradients as in the ResNet. I did the calculations entirely by hand. Please let me know if you spot any error or have any questions!
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[Backpropagation] by Hand✍️ [1] Forward Pass ↳ Given a multi layer perceptron (3 levels), an input vector X, predictions Y^{Pred} = [0.5, 0.5, 0], and ground truth label Y^{Target} = [0, 1, 0]. [2] Backpropagation ↳ Insert cells to hold our calculations. [3] Layer 3 - Softmax (blue) ↳ Calculate ∂L / ∂z3 directly using the simple equation: Y^{Pred} - Y^{Target} = [0.5, -0.5, 0]. ↳ This simple equation is the benefit of using Softmax and Cross Entropy Loss together. [4] Layer 3 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W3 and ∂L / ∂b3 by multiplying ∂L / ∂z3 and [ a2 | 1 ]. [5] Layer 2 - Activations (green) ↳ Calculate ∂L / ∂a2 by multiplying ∂L / ∂z3 and W3. [6] Layer 2 - ReLU (blue) ↳ Calculate ∂L / ∂z2 by multiplying ∂L / ∂a2 with 1 for positive values and 0 otherwise. [7] Layer 2 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W2 and ∂L / ∂b2 by multiplying ∂L / ∂z2 and [ a1 | 1 ]. [8] Layer 1 - Activations (green) ↳ Calculate ∂L / ∂a1 by multiplying ∂L / ∂z2 and W2. [9] Layer 1 - ReLU (blue) ↳ Calculate ∂L / ∂z1 by multiplying ∂L / ∂a1 with 1 for positive values and 0 otherwise. [10] Layer 1 - Weights (orange) & Biases (black) ↳ Calculate ∂L / ∂W1 and ∂L / ∂b1 by multiplying ∂L / ∂z1 and [ x | 1 ]. [11] Gradient Descent ↳ Update weights and biases (typically a learning rate is applied here). 💡 Matrix Multiplication is All You Need: Just like in the forward pass, backpropagation is all about matrix multiplications. You can definitely do everything by hand as I demonstrated in this exercise, albeit slow and imperfect. This is why GPU's ability to multiply matrices efficiently plays such an important role in the deep learning evolution. This is why NVIDIA is now close to $1 trillion in valuation. 💡Exploding Gradients: We can already see the gradients are getting larger as we back-propagate up, even in this simple 3-layer network. This motivates using methods like skip connections to handle exploding (or diminishing) gradients as in the ResNet. I did the calculations entirely by hand. Please let me know if you spot any error or have any questions!

Tom Yeh

64,645 views • 2 years ago

[VAE] by Hand ✍️ A Variational Auto Encoder (VAE) learns the structure (mean and variance) of hidden features and generates new data from the learned structure. In contrast, GANs only learn to generate new data to fool a discriminator; they may not necessarily know the underlying structure of the data. The International Conference on Learning Representations (ICLR) this year announced its first ever "Test of Time Award" to recognizes the VAE paper, published 10 years ago. This exercise demonstrates how to calculate a VAE by hand. [1] Given: ↳ Three training examples X1, X2, X3 ↳ Copy training examples to the bottom ↳ The purpose is to train the network to reconstruct the training examples. ↳ Since each target is a training example itself, we use the Greek word "auto" which means "self." This crucial step is what makes an autoencoder "auto." [2] Encoder: Layer 1 + ReLU ↳ Multiply inputs with weights and biases ↳ Apply ReLU, crossing out negative values (-1 -> 0) [3] Encoder: Mean and Variance ↳ Multiply features with two sets of weights and biases ↳ 🟩 The first set predicts the means (𝜇) of latent distributions ↳ 🟪 The second set predicts the standard deviation (𝜎) of latent distributions [4] Reparameterization Trick: Random Offset ↳ Sample epsilon ε from the normal distribution with mean = 0 and variance = 1. ↳ The purpose is to randomly pick a offset away from the mean. ↳ Multiply the standard deviation values with epsilon values. ↳ The purpose is to scale the offset by the standard deviation. [5] Reparameterization Trick: Mean + Offset ↳ Add the sampled offset to predicted mean ↳ The result are new parameters or features 🟨 as inputs to the Decoder. [6] Decoder: Layer 1 + ReLU ↳ Multiply input features with weights and biases ↳ Apply ReLU, crossing out negative values. Here, -4 is crossed out. [7] Decoder: Layer 2 ↳ Multiply features with weights and biases ↳ The output is Decoder's attempt to reconstruct the input data X from reparameterized distributions described by 𝜇 and 𝜎. [8]-[10] KL Divergence Loss [8] Loss Gradient: Mean 𝜇 ↳ We want 𝜇 to approach 0. ↳ A lot of math called SGVB simplifies the calculation of loss gradients to simply 𝜇 [9,10] Loss Gradient: Stdev 𝜎 ↳ We want 𝜎 to approach 1. ↳ A lot of math simplifies the calculation to 𝜎 - (1/ 𝜎) [11] Reconstruction Loss ↳ We want the reconstructed data Y (dark 🟧) to be the same as the input data X. ↳ Some math involving Mean Square Error simplifies the calculation to Y - X.
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[VAE] by Hand ✍️ A Variational Auto Encoder (VAE) learns the structure (mean and variance) of hidden features and generates new data from the learned structure. In contrast, GANs only learn to generate new data to fool a discriminator; they may not necessarily know the underlying structure of the data. The International Conference on Learning Representations (ICLR) this year announced its first ever "Test of Time Award" to recognizes the VAE paper, published 10 years ago. This exercise demonstrates how to calculate a VAE by hand. [1] Given: ↳ Three training examples X1, X2, X3 ↳ Copy training examples to the bottom ↳ The purpose is to train the network to reconstruct the training examples. ↳ Since each target is a training example itself, we use the Greek word "auto" which means "self." This crucial step is what makes an autoencoder "auto." [2] Encoder: Layer 1 + ReLU ↳ Multiply inputs with weights and biases ↳ Apply ReLU, crossing out negative values (-1 -> 0) [3] Encoder: Mean and Variance ↳ Multiply features with two sets of weights and biases ↳ 🟩 The first set predicts the means (𝜇) of latent distributions ↳ 🟪 The second set predicts the standard deviation (𝜎) of latent distributions [4] Reparameterization Trick: Random Offset ↳ Sample epsilon ε from the normal distribution with mean = 0 and variance = 1. ↳ The purpose is to randomly pick a offset away from the mean. ↳ Multiply the standard deviation values with epsilon values. ↳ The purpose is to scale the offset by the standard deviation. [5] Reparameterization Trick: Mean + Offset ↳ Add the sampled offset to predicted mean ↳ The result are new parameters or features 🟨 as inputs to the Decoder. [6] Decoder: Layer 1 + ReLU ↳ Multiply input features with weights and biases ↳ Apply ReLU, crossing out negative values. Here, -4 is crossed out. [7] Decoder: Layer 2 ↳ Multiply features with weights and biases ↳ The output is Decoder's attempt to reconstruct the input data X from reparameterized distributions described by 𝜇 and 𝜎. [8]-[10] KL Divergence Loss [8] Loss Gradient: Mean 𝜇 ↳ We want 𝜇 to approach 0. ↳ A lot of math called SGVB simplifies the calculation of loss gradients to simply 𝜇 [9,10] Loss Gradient: Stdev 𝜎 ↳ We want 𝜎 to approach 1. ↳ A lot of math simplifies the calculation to 𝜎 - (1/ 𝜎) [11] Reconstruction Loss ↳ We want the reconstructed data Y (dark 🟧) to be the same as the input data X. ↳ Some math involving Mean Square Error simplifies the calculation to Y - X.

Tom Yeh

48,432 views • 2 years ago

Full Fine-tuning vs. Freezing Layers. Interact 👉 and == Full Fine-tuning == A real network has many — three layers in this example, billions of parameters in a production model. What does fine-tuning look like when you update all of them? That’s full fine-tuning: continue training every weight in the pretrained network on your new task. Every layer’s W gets its own ΔW. Nothing is frozen — every parameter is in play. Think of an MLP as a chain of prerequisites leading to an advanced course. Layer 1 might be Linear Algebra, layer 2 Probability, layer 3 Advanced Machine Learning — each one building on what came before. Fine-tuning is what happens during graduate study: the foundations are already there from undergrad, so you’re not re-learning. Full fine-tuning is reviewing every prerequisite to see what new topics have appeared and what discoveries the field has made since the last time you sat through them. Effective — but exhausting. This diagram shows the same three-layer MLP twice, side by side. On the left, the pretrained network runs on input X: three weight matrices W₁, W₂, W₃, each followed by a ReLU activation. Full fine-tuning gives the model the most freedom to specialize. Every parameter can move — and every parameter that can move must be stored. But not every prerequisite needs revisiting. The further you go back in the chain, the less the material has changed since pretraining — the linear-algebra basics under your computer-vision course are largely the same as they ever were. The next page does exactly that: freeze the prerequisites that haven’t moved, and only refresh the advanced one closest to your specialization. == Freezing Layers == Full fine-tuning reviewed every prerequisite — Linear Algebra, Probability, Advanced ML — to refresh each subject with the latest topics. Effective, but exhausting. Then you realize something. The prerequisites haven’t actually changed that much. Linear Algebra is still Linear Algebra; the matrix decompositions you learned still hold. Probability is still Probability; the distributions and Bayes’ rule haven’t moved. Almost all the new material — the new ideas, the recent discoveries — lives in the advanced layer at the top. That’s freezing layers: keep the prerequisite layers fixed at their pretrained state, and only update the advanced one. In the diagram below, W1​ and W2​ — the foundational prerequisites — stay frozen. Only W3​ — the layer closest to your task-specific output — gets a ΔW.
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Full Fine-tuning vs. Freezing Layers. Interact 👉 and == Full Fine-tuning == A real network has many — three layers in this example, billions of parameters in a production model. What does fine-tuning look like when you update all of them? That’s full fine-tuning: continue training every weight in the pretrained network on your new task. Every layer’s W gets its own ΔW. Nothing is frozen — every parameter is in play. Think of an MLP as a chain of prerequisites leading to an advanced course. Layer 1 might be Linear Algebra, layer 2 Probability, layer 3 Advanced Machine Learning — each one building on what came before. Fine-tuning is what happens during graduate study: the foundations are already there from undergrad, so you’re not re-learning. Full fine-tuning is reviewing every prerequisite to see what new topics have appeared and what discoveries the field has made since the last time you sat through them. Effective — but exhausting. This diagram shows the same three-layer MLP twice, side by side. On the left, the pretrained network runs on input X: three weight matrices W₁, W₂, W₃, each followed by a ReLU activation. Full fine-tuning gives the model the most freedom to specialize. Every parameter can move — and every parameter that can move must be stored. But not every prerequisite needs revisiting. The further you go back in the chain, the less the material has changed since pretraining — the linear-algebra basics under your computer-vision course are largely the same as they ever were. The next page does exactly that: freeze the prerequisites that haven’t moved, and only refresh the advanced one closest to your specialization. == Freezing Layers == Full fine-tuning reviewed every prerequisite — Linear Algebra, Probability, Advanced ML — to refresh each subject with the latest topics. Effective, but exhausting. Then you realize something. The prerequisites haven’t actually changed that much. Linear Algebra is still Linear Algebra; the matrix decompositions you learned still hold. Probability is still Probability; the distributions and Bayes’ rule haven’t moved. Almost all the new material — the new ideas, the recent discoveries — lives in the advanced layer at the top. That’s freezing layers: keep the prerequisite layers fixed at their pretrained state, and only update the advanced one. In the diagram below, W1​ and W2​ — the foundational prerequisites — stay frozen. Only W3​ — the layer closest to your task-specific output — gets a ΔW.

Tom Yeh

27,587 views • 3 months ago

[Discrete Fourier Transform] by Hand ✍️ In signal processing, the Discrete Fourier Transform (DFT) is no doubt the most important method. But the math involved is extremely complex, literally, involving a summation over a complex number term e^(-iwt). I developed this exercise to demonstrate that underneath such complexity, DFT is just a series of matrix multiplications you can calculate by hand. ✍️ Once you see that, it should not surprise you that a deep neural network, which is also a series of matrix multiplications, with activation functions in-between, can learn to perform DFT to process and analyze signals so effectively. How does DFT work? [1] Given ↳ Signals A, B, and C in the 🟧 frequency domain: ◦ A = cos(w) + 2cos(2w) ◦ B = cos(w) + cos(3w) + cos(4w) ◦ C = -cos(2w) + cos(3w) ◦ Each signal is a weighed sum of four cosine waves at frequencies 1w, 2w, 3w, and 4w. ◦ We will apply Inverse DFT to convert the signals to time domain representations, and then demonstrate DFT can convert back to their original frequency domain representations. ↳ Signal X in the 🟩 time domain. X is sampled at 10 time points 1t, 2t, …, 10t: ◦ X = [-2.5, -1.8, 3, -0.7, -1.0, -0.7, 3, -1.8, -2.5, 5] ◦ Suppose X is also a weighted sum of the same four cosine waves, but we don’t already know their weights. We will apply DFT to discover them. [2] 🟧 Frequency Matrix (F) ↳ Write the coefficients of A, B, C as a matrix F. Each signal is a row. Each frequency is a column. ↳ A → [1, 2, 0, 0] ↳ B → [1, 0, 1, 1] ↳ C → [0, 1-, 1, 0] [3] Cosine → Discrete ↳ Sample from the continuous cosine waves at discrete time points 1t, 2t, 3t, to 10t. [4] Cosine Matrix (W) ↳ Write the samples as a matrix, Each frequency is a row. Each time point is a column. [5] Inverse DFT: 🟧 Frequency → 🟩 Time ↳ Multiply the frequency matrix F and the cosine matrix W. ↳ The meaning of this multiplication is to linearly combine the four cosine waves (rows in W) into time-domain signals (rows in T) using the weights specified in F. ↳ The result is matrix T, which are signals A, B, C converted to the time domain. Each signal is a row. Each time point is a column. [6] Transpose ↳ Transpose T, converting each signal’s time domain representation from a row to a column. [7] DFT: 🟩 Time → 🟧 Frequency ↳ Multiply the cosine matrix W with the transpose of matrix T. ↳ The purpose of this multiplication is to take a dot-product between each time-domain signal (columns in the transpose of T) and each cosine wave (rows in W), which has the effect of projecting the signal onto a cosine wave to determine how much they are correlated. Zero means not correlated at all. ↳ The result is an intermediate version of the “recovered” frequency matrix where each column corresponds to a signal and each row corresponds to a frequency. ↳ Compared to the original frequency matrix F, this intermediate matrix has non-zero weights in the correct places, but scaled up by a factor of 5 (n/2, n=10). For example, signal A, originally [1,2,0,0], is recovered at [5,10,0,0]. [8] Scale ↳ Multiply each value by 2/n = 1/5 to scale down the intermediate matrix to match the magnitude of the original frequency matrix F. [9] Transpose ↳ Transpose the recovered frequency matrix back to the same orientation of the original frequency matrix F. ↳ Like magic 🪄, the result is identical to the original F, which means DFT successfully recovered the frequency components of signals A, B, C. [10] Apply DFT to X: 🟩 Time → 🟧 Frequency ↳ Now that we have some confidence in DFT’s ability to recover frequency components, we apply DFT to X’s time-domain representation by multiplying W with X. ↳ The result is the an intermediate matrix. [11] Scale ↳ Similarly, we scale down by a factor of 5 to obtain the recovered frequency components of X (a column). [12] Transpose ↳ Similarly, we transpose the recovered column to row to match the orientation of the frequency matrix. ↳ Using the coefficients [0,0,3,2], we can write the equation of X as 3cos(3w) + 2cos(4w). Notes: I hope this by hand exercise helps you understand the essence of DFT. But there is more technical details, such as: • Sine: The complete DFT math also includes sine waves that follow a similar calculation process. • Phase: Here, we assume all the cosine waves are aligned at the origin, namely, phase is 0. If a phase p is added, for example, cos(w+p), we will need to calculate the sine component and use their ratio to figure out what p is. • Magnitude: If phase is not zero, the magnitude will need to be calculated by combining both cosine and sine terms.
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[Discrete Fourier Transform] by Hand ✍️ In signal processing, the Discrete Fourier Transform (DFT) is no doubt the most important method. But the math involved is extremely complex, literally, involving a summation over a complex number term e^(-iwt). I developed this exercise to demonstrate that underneath such complexity, DFT is just a series of matrix multiplications you can calculate by hand. ✍️ Once you see that, it should not surprise you that a deep neural network, which is also a series of matrix multiplications, with activation functions in-between, can learn to perform DFT to process and analyze signals so effectively. How does DFT work? [1] Given ↳ Signals A, B, and C in the 🟧 frequency domain: ◦ A = cos(w) + 2cos(2w) ◦ B = cos(w) + cos(3w) + cos(4w) ◦ C = -cos(2w) + cos(3w) ◦ Each signal is a weighed sum of four cosine waves at frequencies 1w, 2w, 3w, and 4w. ◦ We will apply Inverse DFT to convert the signals to time domain representations, and then demonstrate DFT can convert back to their original frequency domain representations. ↳ Signal X in the 🟩 time domain. X is sampled at 10 time points 1t, 2t, …, 10t: ◦ X = [-2.5, -1.8, 3, -0.7, -1.0, -0.7, 3, -1.8, -2.5, 5] ◦ Suppose X is also a weighted sum of the same four cosine waves, but we don’t already know their weights. We will apply DFT to discover them. [2] 🟧 Frequency Matrix (F) ↳ Write the coefficients of A, B, C as a matrix F. Each signal is a row. Each frequency is a column. ↳ A → [1, 2, 0, 0] ↳ B → [1, 0, 1, 1] ↳ C → [0, 1-, 1, 0] [3] Cosine → Discrete ↳ Sample from the continuous cosine waves at discrete time points 1t, 2t, 3t, to 10t. [4] Cosine Matrix (W) ↳ Write the samples as a matrix, Each frequency is a row. Each time point is a column. [5] Inverse DFT: 🟧 Frequency → 🟩 Time ↳ Multiply the frequency matrix F and the cosine matrix W. ↳ The meaning of this multiplication is to linearly combine the four cosine waves (rows in W) into time-domain signals (rows in T) using the weights specified in F. ↳ The result is matrix T, which are signals A, B, C converted to the time domain. Each signal is a row. Each time point is a column. [6] Transpose ↳ Transpose T, converting each signal’s time domain representation from a row to a column. [7] DFT: 🟩 Time → 🟧 Frequency ↳ Multiply the cosine matrix W with the transpose of matrix T. ↳ The purpose of this multiplication is to take a dot-product between each time-domain signal (columns in the transpose of T) and each cosine wave (rows in W), which has the effect of projecting the signal onto a cosine wave to determine how much they are correlated. Zero means not correlated at all. ↳ The result is an intermediate version of the “recovered” frequency matrix where each column corresponds to a signal and each row corresponds to a frequency. ↳ Compared to the original frequency matrix F, this intermediate matrix has non-zero weights in the correct places, but scaled up by a factor of 5 (n/2, n=10). For example, signal A, originally [1,2,0,0], is recovered at [5,10,0,0]. [8] Scale ↳ Multiply each value by 2/n = 1/5 to scale down the intermediate matrix to match the magnitude of the original frequency matrix F. [9] Transpose ↳ Transpose the recovered frequency matrix back to the same orientation of the original frequency matrix F. ↳ Like magic 🪄, the result is identical to the original F, which means DFT successfully recovered the frequency components of signals A, B, C. [10] Apply DFT to X: 🟩 Time → 🟧 Frequency ↳ Now that we have some confidence in DFT’s ability to recover frequency components, we apply DFT to X’s time-domain representation by multiplying W with X. ↳ The result is the an intermediate matrix. [11] Scale ↳ Similarly, we scale down by a factor of 5 to obtain the recovered frequency components of X (a column). [12] Transpose ↳ Similarly, we transpose the recovered column to row to match the orientation of the frequency matrix. ↳ Using the coefficients [0,0,3,2], we can write the equation of X as 3cos(3w) + 2cos(4w). Notes: I hope this by hand exercise helps you understand the essence of DFT. But there is more technical details, such as: • Sine: The complete DFT math also includes sine waves that follow a similar calculation process. • Phase: Here, we assume all the cosine waves are aligned at the origin, namely, phase is 0. If a phase p is added, for example, cos(w+p), we will need to calculate the sine component and use their ratio to figure out what p is. • Magnitude: If phase is not zero, the magnitude will need to be calculated by combining both cosine and sine terms.

Tom Yeh

116,622 views • 2 years ago

HOW TO DODGE EVERY SKILLSHOT IN LEAGUE OF LEGENDS SO YOU GET ACCUSED OF SCRIPTING - Script in your mind - Draw out how far, wide, fast an ability is relative to your character thats all the easy stuff that I have been preaching already you can find in my free discord for improvement however one thing that League coaches fail to explain is the human aspect of it every game you play in League of Legends, every single person in the game is constantly building their profile in a game on how they operate both sides are constantly trying to mind f*ck each other to land and dodge skillshots. I have broken it down into layers the three layers to dodging are layer 0 - no dodge (unconscious) layer 1 - dodge (conscious) layer 2 - no dodge (conscious) Notice how in the clip in a challenger game below Olaf shoots a layer 0 skillshot, but because I am playing at a layer 1, I dodge his axe. Now the Thresh hook gets a little deeper bare with me, because I built the profile that I will dodge an ability in that moment, he thinks that I won't dodge and is shooting a hook at a layer 2 thinking that I will dodge at a layer 2 also. However I know that he knows I will likely not juke and walk straight so I make the conscious choice to dodge AGAIN playing at a layer 1 resulting in me dodging the hook, of course he could be accounting for my tumble but the point still stands. There are many deeper things to consider like zoning abilities, environment etc but you generally want to always play at a layer 1 until you gain more data in a game to adapt. However one thing that always stays true throughout my 13 years of playing League is in teamfights that have gone on for awhile, human beings tend to panic and default to layer 0 of shooting abilities, so if your able to operate at layer 1 as a teamfight progresses, you will likely dodge that one final skillshot that wins you the game. study the saskio way
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HOW TO DODGE EVERY SKILLSHOT IN LEAGUE OF LEGENDS SO YOU GET ACCUSED OF SCRIPTING - Script in your mind - Draw out how far, wide, fast an ability is relative to your character thats all the easy stuff that I have been preaching already you can find in my free discord for improvement however one thing that League coaches fail to explain is the human aspect of it every game you play in League of Legends, every single person in the game is constantly building their profile in a game on how they operate both sides are constantly trying to mind f*ck each other to land and dodge skillshots. I have broken it down into layers the three layers to dodging are layer 0 - no dodge (unconscious) layer 1 - dodge (conscious) layer 2 - no dodge (conscious) Notice how in the clip in a challenger game below Olaf shoots a layer 0 skillshot, but because I am playing at a layer 1, I dodge his axe. Now the Thresh hook gets a little deeper bare with me, because I built the profile that I will dodge an ability in that moment, he thinks that I won't dodge and is shooting a hook at a layer 2 thinking that I will dodge at a layer 2 also. However I know that he knows I will likely not juke and walk straight so I make the conscious choice to dodge AGAIN playing at a layer 1 resulting in me dodging the hook, of course he could be accounting for my tumble but the point still stands. There are many deeper things to consider like zoning abilities, environment etc but you generally want to always play at a layer 1 until you gain more data in a game to adapt. However one thing that always stays true throughout my 13 years of playing League is in teamfights that have gone on for awhile, human beings tend to panic and default to layer 0 of shooting abilities, so if your able to operate at layer 1 as a teamfight progresses, you will likely dodge that one final skillshot that wins you the game. study the saskio way

Tony Chau

185,544 views • 9 months ago

ReLU vs Leaky ReLU 👉 = ReLU = ReLU is the default activation in modern deep learning — cheap to compute, and stable enough to train networks hundreds of layers deep. To see what it does, picture five boba tea shops on the same block — 𝚊, 𝚋, 𝚌, 𝚍, 𝚎 — each running their own books. Each value is a shop's monthly profit — receipts minus rent, ingredients, and wages. When profit is positive, the shop stays open and the owner pockets every dollar. When profit turns negative, the shop runs out of cash and shutters — the lights go off, the books are wiped to zero. ReLU is exactly that rule, applied one shop at a time. Read the diagram left to right. The first column is the raw value x — each shop's profit at month's end. The second column is the gate: 1 if the shop is open (x > 0), 0 if it has shuttered. The last column is the ReLU output: open shops pass their profit through untouched, while shuttered ones are zeroed out. Five rows means five parallel shops on the same block, each evaluated independently. That's why ReLU is called an element-wise activation: every neuron decides its own fate. = LeakyRelu = Plain ReLU wipes negative values to zero — clean, but a shop that shutters can never recover, since both its output and its gradient stay pinned at zero. This is the dying ReLU problem, and in deep networks it can quietly kill a meaningful fraction of the units. Leaky ReLU is the one-line fix: instead of shuttering, the shop files for Chapter 11 protection and keeps the lights on at reduced capacity. Its debt is restructured down to a fraction α (typically 0.1) — the rest is forgiven, and the shop is wounded, not killed. A small negative signal still flows through, so the gradient survives, and the shop can crawl back to life if a TikTok goes viral. Read the diagram left to right. The first column is the raw value x — each shop's profit at month's end. The second column is the leakage α — the fraction of the loss held over after restructuring (default 0.1, editable). The third column is the gate: 1 for shops still in the black, α for those operating under bankruptcy protection. The last column is the Leaky ReLU output: y = x · gate. Profitable shops pass through untouched; struggling ones shrink by a factor of α but still carry a sign. Five rows means five parallel shops, each evaluated independently. Like ReLU, this is an element-wise activation: every neuron's fate is decided on its own merits. #aibyhahd
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ReLU vs Leaky ReLU 👉 = ReLU = ReLU is the default activation in modern deep learning — cheap to compute, and stable enough to train networks hundreds of layers deep. To see what it does, picture five boba tea shops on the same block — 𝚊, 𝚋, 𝚌, 𝚍, 𝚎 — each running their own books. Each value is a shop's monthly profit — receipts minus rent, ingredients, and wages. When profit is positive, the shop stays open and the owner pockets every dollar. When profit turns negative, the shop runs out of cash and shutters — the lights go off, the books are wiped to zero. ReLU is exactly that rule, applied one shop at a time. Read the diagram left to right. The first column is the raw value x — each shop's profit at month's end. The second column is the gate: 1 if the shop is open (x > 0), 0 if it has shuttered. The last column is the ReLU output: open shops pass their profit through untouched, while shuttered ones are zeroed out. Five rows means five parallel shops on the same block, each evaluated independently. That's why ReLU is called an element-wise activation: every neuron decides its own fate. = LeakyRelu = Plain ReLU wipes negative values to zero — clean, but a shop that shutters can never recover, since both its output and its gradient stay pinned at zero. This is the dying ReLU problem, and in deep networks it can quietly kill a meaningful fraction of the units. Leaky ReLU is the one-line fix: instead of shuttering, the shop files for Chapter 11 protection and keeps the lights on at reduced capacity. Its debt is restructured down to a fraction α (typically 0.1) — the rest is forgiven, and the shop is wounded, not killed. A small negative signal still flows through, so the gradient survives, and the shop can crawl back to life if a TikTok goes viral. Read the diagram left to right. The first column is the raw value x — each shop's profit at month's end. The second column is the leakage α — the fraction of the loss held over after restructuring (default 0.1, editable). The third column is the gate: 1 for shops still in the black, α for those operating under bankruptcy protection. The last column is the Leaky ReLU output: y = x · gate. Profitable shops pass through untouched; struggling ones shrink by a factor of α but still carry a sign. Five rows means five parallel shops, each evaluated independently. Like ReLU, this is an element-wise activation: every neuron's fate is decided on its own merits. #aibyhahd

Tom Yeh

32,539 views • 3 months ago

Vector Database by Hand ✍️ Vector databases are revolutionizing how we search and analyze complex data. They have become the backbone of Retrieval Augmented Generation (#RAG). How do vector databases work? [1] Given ↳ A dataset of three sentences, each has 3 words (or tokens) ↳ In practice, a dataset may contain millions or billions of sentences. The max number of tokens may be tens of thousands (e.g., 32,768 mistral-7b). Process "how are you" [2] 🟨 Word Embeddings ↳ For each word, look up corresponding word embedding vector from a table of 22 vectors, where 22 is the vocabulary size. ↳ In practice, the vocabulary size can be tens of thousands. The word embedding dimensions are in the thousands (e.g., 1024, 4096) [3] 🟩 Encoding ↳ Feed the sequence of word embeddings to an encoder to obtain a sequence of feature vectors, one per word. ↳ Here, the encoder is a simple one layer perceptron (linear layer + ReLU) ↳ In practice, the encoder is a transformer or one of its many variants. [4] 🟩 Mean Pooling ↳ Merge the sequence of feature vectors into a single vector using "mean pooling" which is to average across the columns. ↳ The result is a single vector. We often call it "text embeddings" or "sentence embeddings." ↳ Other pooling techniques are possible, such as CLS. But mean pooling is the most common. [5] 🟦 Indexing ↳ Reduce the dimensions of the text embedding vector by a projection matrix. The reduction rate is 50% (4->2). ↳ In practice, the values in this projection matrix is much more random. ↳ The purpose is similar to that of hashing, which is to obtain a short representation to allow faster comparison and retrieval. ↳ The resulting dimension-reduced index vector is saved in the vector storage. [6] Process "who are you" ↳ Repeat [2]-[5] [7] Process "who am I" ↳ Repeat [2]-[5] Now we have indexed our dataset in the vector database. [8] 🟥 Query: "am I you" ↳ Repeat [2]-[5] ↳ The result is a 2-d query vector. [9] 🟥 Dot Products ↳ Take dot product between the query vector and database vectors. They are all 2-d. ↳ The purpose is to use dot product to estimate similarity. ↳ By transposing the query vector, this step becomes a matrix multiplication. [10] 🟥 Nearest Neighbor ↳ Find the largest dot product by linear scan. ↳ The sentence with the highest dot product is "who am I" ↳ In practice, because scanning billions of vectors is slow, we use an Approximate Nearest Neighbor (ANN) algorithm like the Hierarchical Navigable Small Worlds (HNSW).
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Vector Database by Hand ✍️ Vector databases are revolutionizing how we search and analyze complex data. They have become the backbone of Retrieval Augmented Generation (#RAG). How do vector databases work? [1] Given ↳ A dataset of three sentences, each has 3 words (or tokens) ↳ In practice, a dataset may contain millions or billions of sentences. The max number of tokens may be tens of thousands (e.g., 32,768 mistral-7b). Process "how are you" [2] 🟨 Word Embeddings ↳ For each word, look up corresponding word embedding vector from a table of 22 vectors, where 22 is the vocabulary size. ↳ In practice, the vocabulary size can be tens of thousands. The word embedding dimensions are in the thousands (e.g., 1024, 4096) [3] 🟩 Encoding ↳ Feed the sequence of word embeddings to an encoder to obtain a sequence of feature vectors, one per word. ↳ Here, the encoder is a simple one layer perceptron (linear layer + ReLU) ↳ In practice, the encoder is a transformer or one of its many variants. [4] 🟩 Mean Pooling ↳ Merge the sequence of feature vectors into a single vector using "mean pooling" which is to average across the columns. ↳ The result is a single vector. We often call it "text embeddings" or "sentence embeddings." ↳ Other pooling techniques are possible, such as CLS. But mean pooling is the most common. [5] 🟦 Indexing ↳ Reduce the dimensions of the text embedding vector by a projection matrix. The reduction rate is 50% (4->2). ↳ In practice, the values in this projection matrix is much more random. ↳ The purpose is similar to that of hashing, which is to obtain a short representation to allow faster comparison and retrieval. ↳ The resulting dimension-reduced index vector is saved in the vector storage. [6] Process "who are you" ↳ Repeat [2]-[5] [7] Process "who am I" ↳ Repeat [2]-[5] Now we have indexed our dataset in the vector database. [8] 🟥 Query: "am I you" ↳ Repeat [2]-[5] ↳ The result is a 2-d query vector. [9] 🟥 Dot Products ↳ Take dot product between the query vector and database vectors. They are all 2-d. ↳ The purpose is to use dot product to estimate similarity. ↳ By transposing the query vector, this step becomes a matrix multiplication. [10] 🟥 Nearest Neighbor ↳ Find the largest dot product by linear scan. ↳ The sentence with the highest dot product is "who am I" ↳ In practice, because scanning billions of vectors is slow, we use an Approximate Nearest Neighbor (ANN) algorithm like the Hierarchical Navigable Small Worlds (HNSW).

Tom Yeh

192,022 views • 2 years ago

[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]
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[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]

Tom Yeh

72,966 views • 2 years ago

Three years ago, I pitched a business to this Particular organization, and they told me they were not seeing the potential I was seeing. Just about an hour ago, I pitched the same business to the same particular organization, and the chairperson said, “Spirit, let’s get to work immediately on this; this is a big one.” What changed three years ago vs. today? ♟️Audience. My Point: There is an audience for everything. It requires wisdom to understand wisdom. The music is nothing if the audience is deaf. So why give up when you can just convince yourself that you are yet to be heard or seen by the right people? What was treated as useless three years ago is the same thing the same organization is saying: “This will put us on the map in the whole of Africa.” I made it possible. You too can. Happy July🥃.
0:18

Three years ago, I pitched a business to this Particular organization, and they told me they were not seeing the potential I was seeing. Just about an hour ago, I pitched the same business to the same particular organization, and the chairperson said, “Spirit, let’s get to work immediately on this; this is a big one.” What changed three years ago vs. today? ♟️Audience. My Point: There is an audience for everything. It requires wisdom to understand wisdom. The music is nothing if the audience is deaf. So why give up when you can just convince yourself that you are yet to be heard or seen by the right people? What was treated as useless three years ago is the same thing the same organization is saying: “This will put us on the map in the whole of Africa.” I made it possible. You too can. Happy July🥃.

🦉 🧘🏽‍♂️spiRituaL🧘🏽‍♂️

131,401 views • 1 year ago

Experiment ⬇️ „Dubai is empty“ When I post a picture or video, I have already left, for my security When I post, I make sure I choose a moment and angle, with no faces visible or edit them out of the content, for their security For the same security reasons, the UAE doesn’t want us to film and post sensitive footage People like to make up stories and look for faults, here is an experiment: A teacher writes down: 1+1=2 2+2=4 3+3=6 4+4=8 5+5=9 Every student raises their hand and points out the last mistake, instead of pointing out that 4/5 calculations are correct At the end, we are all human and must protect each other, instead of making each other vulnerable
0:09

Experiment ⬇️ „Dubai is empty“ When I post a picture or video, I have already left, for my security When I post, I make sure I choose a moment and angle, with no faces visible or edit them out of the content, for their security For the same security reasons, the UAE doesn’t want us to film and post sensitive footage People like to make up stories and look for faults, here is an experiment: A teacher writes down: 1+1=2 2+2=4 3+3=6 4+4=8 5+5=9 Every student raises their hand and points out the last mistake, instead of pointing out that 4/5 calculations are correct At the end, we are all human and must protect each other, instead of making each other vulnerable

Tima

17,337 views • 4 months ago

$4.4 trillion in PE assets under management Monitored by analysts who spend 500+ hours a year copying numbers from PDFs into Excel. Not analyzing. Copying and pasting. A fund has 10 portcos. One on NetSuite, one on QuickBooks, three on Excel, one CFO sending a paragraph in an email every quarter. Company A calls it "Revenue." Company B calls it "Net Sales." Company C doesn't even use the same EBITDA calculation. Before AI can do anything useful, you need four layers: 1. Ingestion: get the data out of PDFs, spreadsheets, emails, whatever format it shows up in 2. Normalization: make sure the same metric means the same thing across every company 3. Storage: structured database that can actually be queried, not a folder of files 4. Query layer: natural language interface so a non-technical partner can ask "which portco is trending down on margins?" and get a real answer Most companies jump straight to layer 4 and wonder why nothing works. The unlock is building layers 1-3 first. Once those exist, the AI part is MUCH easier. The firms that get their data infrastructure right first will be untouchable.
0:16

$4.4 trillion in PE assets under management Monitored by analysts who spend 500+ hours a year copying numbers from PDFs into Excel. Not analyzing. Copying and pasting. A fund has 10 portcos. One on NetSuite, one on QuickBooks, three on Excel, one CFO sending a paragraph in an email every quarter. Company A calls it "Revenue." Company B calls it "Net Sales." Company C doesn't even use the same EBITDA calculation. Before AI can do anything useful, you need four layers: 1. Ingestion: get the data out of PDFs, spreadsheets, emails, whatever format it shows up in 2. Normalization: make sure the same metric means the same thing across every company 3. Storage: structured database that can actually be queried, not a folder of files 4. Query layer: natural language interface so a non-technical partner can ask "which portco is trending down on margins?" and get a real answer Most companies jump straight to layer 4 and wonder why nothing works. The unlock is building layers 1-3 first. Once those exist, the AI part is MUCH easier. The firms that get their data infrastructure right first will be untouchable.

James Camp 🛠,🛠

19,235 views • 5 months ago

Jeff Bezos just described AI in three words that make most of the economy temporary. Bezos: “AI is real and it is going to change every industry. In fact it’s a very unusual technology in that regard in that it’s a horizontal enabling layer.” Horizontal enabling layer. Not a product. Not a platform. Not a feature. A layer. Underneath everything. Everyone is asking which AI company wins. Bezos is telling you that is the wrong question entirely. A horizontal layer does not produce winners. It produces a new floor. Everything standing on the old one either gets rebuilt or gets erased. This has happened exactly twice in modern history. Electricity. The internet. Both times the same pattern. The new layer appeared. The old economy kept running above it. Revenue held. Careers continued. Everything looked normal. Then quietly and permanently the entire structure reorganized around the new substrate. The people who did not move were not outcompeted. They were made structurally irrelevant. Not because they were wrong. Because the ground they stood on stopped being ground. Bezos is telling you it is happening a third time. Not with a product. Not with a platform. With intelligence itself becoming infrastructure. A horizontal layer does not compete with the expert. It makes expertise free. It hands a 22 year old with zero credentials the same cognitive output you spent a decade and a quarter million dollars learning to produce. For $20 a month. That is not disruption. Disruption replaces a product with a better product. This dissolves the scarcity your entire career was priced on. Not because the work disappeared. Because the wall around it did. Every profession that exists because knowledge is hard to acquire. Every company that profits because analysis takes time. Every industry that survives because complexity locks outsiders out. All of it rests on a single assumption. That cognition is scarce. AI does not challenge that assumption. It retires it. The people who understand this are already rebuilding. Quietly. Deliberately. While everyone else argues about whether the thing underneath them is real. Bezos did not give you a prediction. He gave you a position on a map. You are either above the new layer or beneath it.
0:16

Jeff Bezos just described AI in three words that make most of the economy temporary. Bezos: “AI is real and it is going to change every industry. In fact it’s a very unusual technology in that regard in that it’s a horizontal enabling layer.” Horizontal enabling layer. Not a product. Not a platform. Not a feature. A layer. Underneath everything. Everyone is asking which AI company wins. Bezos is telling you that is the wrong question entirely. A horizontal layer does not produce winners. It produces a new floor. Everything standing on the old one either gets rebuilt or gets erased. This has happened exactly twice in modern history. Electricity. The internet. Both times the same pattern. The new layer appeared. The old economy kept running above it. Revenue held. Careers continued. Everything looked normal. Then quietly and permanently the entire structure reorganized around the new substrate. The people who did not move were not outcompeted. They were made structurally irrelevant. Not because they were wrong. Because the ground they stood on stopped being ground. Bezos is telling you it is happening a third time. Not with a product. Not with a platform. With intelligence itself becoming infrastructure. A horizontal layer does not compete with the expert. It makes expertise free. It hands a 22 year old with zero credentials the same cognitive output you spent a decade and a quarter million dollars learning to produce. For $20 a month. That is not disruption. Disruption replaces a product with a better product. This dissolves the scarcity your entire career was priced on. Not because the work disappeared. Because the wall around it did. Every profession that exists because knowledge is hard to acquire. Every company that profits because analysis takes time. Every industry that survives because complexity locks outsiders out. All of it rests on a single assumption. That cognition is scarce. AI does not challenge that assumption. It retires it. The people who understand this are already rebuilding. Quietly. Deliberately. While everyone else argues about whether the thing underneath them is real. Bezos did not give you a prediction. He gave you a position on a map. You are either above the new layer or beneath it.

Dustin

103,988 views • 26 days ago

Karpathy method + Claude Code reading your whole Obsidian vault is the smartest second brain on earth. The method is simple and brutal. If you can’t build a thing from scratch, you don’t know it. Tutorials are fake learning and your brain deletes them in 3 days. Most people ignore this. They build a second brain that just sits there, folders of notes nobody reopens, dead text. Point Claude Code at the vault and it wakes up. 5,000 notes, one mind. It reads all of it and answers in your own words and your own proofs, not a model’s guess. Then the loop closes. Want to understand neural nets? Skip the 3-hour video and ask Claude Code to build a tiny one. 200 lines from scratch. Watch it train, break a layer, watch it fail, fix it. It clicks in 20 minutes instead of 3 weeks. The second it lands the note gets written. One idea per file, linked to 10 others, dropped into the vault while the memory is still hot. Now it compounds. Month 1: is 60 notes. Month 6 is 900. Every new note pulls in old ones, so you ask anything and the answer comes from your brain, not the internet. Before: 40 tabs, 6 half read PDF, 0 retained. After: build it once, own it for life. Setup takes 4 minutes. Plain text, no lock-in. A second brain nobody reads is a graveyard. Yours just started thinking.
0:13

Karpathy method + Claude Code reading your whole Obsidian vault is the smartest second brain on earth. The method is simple and brutal. If you can’t build a thing from scratch, you don’t know it. Tutorials are fake learning and your brain deletes them in 3 days. Most people ignore this. They build a second brain that just sits there, folders of notes nobody reopens, dead text. Point Claude Code at the vault and it wakes up. 5,000 notes, one mind. It reads all of it and answers in your own words and your own proofs, not a model’s guess. Then the loop closes. Want to understand neural nets? Skip the 3-hour video and ask Claude Code to build a tiny one. 200 lines from scratch. Watch it train, break a layer, watch it fail, fix it. It clicks in 20 minutes instead of 3 weeks. The second it lands the note gets written. One idea per file, linked to 10 others, dropped into the vault while the memory is still hot. Now it compounds. Month 1: is 60 notes. Month 6 is 900. Every new note pulls in old ones, so you ask anything and the answer comes from your brain, not the internet. Before: 40 tabs, 6 half read PDF, 0 retained. After: build it once, own it for life. Setup takes 4 minutes. Plain text, no lock-in. A second brain nobody reads is a graveyard. Yours just started thinking.

West Lord

590,875 views • 1 month ago

So I have been trying to do my own take on the 4-2-1-3. but it is not for my play style. Will try some more, later on. For now I ended up with a 5-2-1-2 that I like a lot. And it’s surprisingly good against the 4-2-1-3. Anyone wants to test? 🔥🏴‍☠️
0:17

So I have been trying to do my own take on the 4-2-1-3. but it is not for my play style. Will try some more, later on. For now I ended up with a 5-2-1-2 that I like a lot. And it’s surprisingly good against the 4-2-1-3. Anyone wants to test? 🔥🏴‍☠️

FC Pirate 🏴‍☠️

29,703 views • 1 year ago

This runner at first was caught in a pick off move by the pitcher. Pitcher throws to first and the first baseman fires to second and the umpire calls him out. He looked safe on the play. However, the umpire admits he was safe but said he called him out because the other team was losing 10-0 in the first inning. He said “he was so safe but I just gave it to them.” Basically saying we gotta’ get the game moving right? Fellow umpires, some coaches and parents said they respect the call and why. But many people said you are cheating that one runner by calling him out. They said no matter the score you have to have integrity even if it is 20-0. They said this is why kids grow up disliking umpires and why parents act the way they do. Tough one- I actually understand where he is coming from but if that were your kid, would you want him called out? I say call the game the right way 100% and let it play out the way it is supposed to. How is the other team supposed to get better if you are giving them calls? Do you agree with the umpire and why he did it? Or, are you totally against that and that should never happen?
0:18

This runner at first was caught in a pick off move by the pitcher. Pitcher throws to first and the first baseman fires to second and the umpire calls him out. He looked safe on the play. However, the umpire admits he was safe but said he called him out because the other team was losing 10-0 in the first inning. He said “he was so safe but I just gave it to them.” Basically saying we gotta’ get the game moving right? Fellow umpires, some coaches and parents said they respect the call and why. But many people said you are cheating that one runner by calling him out. They said no matter the score you have to have integrity even if it is 20-0. They said this is why kids grow up disliking umpires and why parents act the way they do. Tough one- I actually understand where he is coming from but if that were your kid, would you want him called out? I say call the game the right way 100% and let it play out the way it is supposed to. How is the other team supposed to get better if you are giving them calls? Do you agree with the umpire and why he did it? Or, are you totally against that and that should never happen?

👉M-Û-R-Č-H👈

44,446 views • 1 month ago