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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. #aibyhahdshow more

Tom Yeh

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$Softmax vs Sigmoid ✍️ Interact 👉 = Softmax = Softmax is how deep networks turn raw scores into a probability distribution — the final layer of every classifier, and the core of every attention head in a transformer. To see what it does, picture five boba tea shops on the same block, all competing for your dollar. Five candidates: a, b, c, d, e — different chains, different brewing styles, different pearls. A boba reviewer hands you a 𝘤𝘩𝘦𝘸𝘪𝘯𝘦𝘴𝘴 𝘴𝘤𝘰𝘳𝘦 for each — higher means perfectly chewy "QQ" pearls with the right bite (ask a Taiwanese friend to find out what QQ means). Negative scores are real: mushy bobas, overcooked pearls, a batch left sitting too long. How do you turn five chewiness scores into an allocation that adds to a whole dollar? You could spend everything at the chewiest shop, but that ignores how good the runners-up are. Softmax is the smooth alternative. Read the diagram left to right. First, raise each score to e^{x} — this does two things: it turns negative chewiness into small positives, and it stretches the gaps between scores exponentially. Then sum all five into a single total Z. Finally, divide each e^{x} by Z to get a probability. The five probabilities add up to one, so you can read them as percentages of your dollar. The chewiest shop gets the biggest slice — but never the whole dollar. That's the point of softmax: it ranks confidently while still leaving room for the others. = Sigmoid = Sigmoid squashes any real number into a probability between 0 and 1 — the classic activation for binary classification, and still the gating function inside LSTMs and GRUs. Same boba block as the previous Softmax example, narrowed to just two contenders — a hot new shop `a` with chewiness score x, and your usual go-to `b` whose score is pinned at zero (the neutral baseline you've come to expect). Sigmoid is just softmax with two players, one of them pinned to zero. Read the diagram left to right. First, raise each score to e^{x} — for the usual shop `b` whose score is zero, this is just e^0 = 1 (the constant baseline). Then sum the two into a total Z. Finally, divide each e^{x} by Z to get a probability. The two probabilities add up to one — the new shop wins more of your dollar when its pearls get chewier, and your usual keeps the rest. That's the point of sigmoid: it turns a single chewiness score into a clean 0-to-1 chance you'll try the new place over your usual. --- AI Math, Algorithms, Architectures by hand ✍️ Subscribe to my 60K+ reader newsletter 👉$

Softmax vs Sigmoid ✍️ Interact 👉 = Softmax = Softmax is how deep networks turn raw scores into a probability distribution — the final layer of every classifier, and the core of every attention head in a transformer. To see what it does, picture five boba tea shops on the same block, all competing for your dollar. Five candidates: a, b, c, d, e — different chains, different brewing styles, different pearls. A boba reviewer hands you a 𝘤𝘩𝘦𝘸𝘪𝘯𝘦𝘴𝘴 𝘴𝘤𝘰𝘳𝘦 for each — higher means perfectly chewy "QQ" pearls with the right bite (ask a Taiwanese friend to find out what QQ means). Negative scores are real: mushy bobas, overcooked pearls, a batch left sitting too long. How do you turn five chewiness scores into an allocation that adds to a whole dollar? You could spend everything at the chewiest shop, but that ignores how good the runners-up are. Softmax is the smooth alternative. Read the diagram left to right. First, raise each score to e^{x} — this does two things: it turns negative chewiness into small positives, and it stretches the gaps between scores exponentially. Then sum all five into a single total Z. Finally, divide each e^{x} by Z to get a probability. The five probabilities add up to one, so you can read them as percentages of your dollar. The chewiest shop gets the biggest slice — but never the whole dollar. That's the point of softmax: it ranks confidently while still leaving room for the others. = Sigmoid = Sigmoid squashes any real number into a probability between 0 and 1 — the classic activation for binary classification, and still the gating function inside LSTMs and GRUs. Same boba block as the previous Softmax example, narrowed to just two contenders — a hot new shop `a` with chewiness score x, and your usual go-to `b` whose score is pinned at zero (the neutral baseline you've come to expect). Sigmoid is just softmax with two players, one of them pinned to zero. Read the diagram left to right. First, raise each score to e^{x} — for the usual shop `b` whose score is zero, this is just e^0 = 1 (the constant baseline). Then sum the two into a total Z. Finally, divide each e^{x} by Z to get a probability. The two probabilities add up to one — the new shop wins more of your dollar when its pearls get chewier, and your usual keeps the rest. That's the point of sigmoid: it turns a single chewiness score into a clean 0-to-1 chance you'll try the new place over your usual. --- AI Math, Algorithms, Architectures by hand ✍️ Subscribe to my 60K+ reader newsletter 👉

Tom Yeh

73,787 görüntüleme • 2 ay önce

[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.

[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

48,356 görüntüleme • 2 yıl önce

[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)

[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

46,499 görüntüleme • 1 yıl önce

[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.

[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 görüntüleme • 2 yıl önce

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.

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

27,225 görüntüleme • 2 ay önce

$i made $83,000 by looking at one number not the price not the volume the spread α = Δ / (V_h − μ) α is the fraction of traders in the market who already know the correct answer spread 0.05 → α = 5% safe to enter spread 0.15 → α = 15% be careful spread 0.25 → α = 20% one in five knows more than you before this i entered markets with wide spreads i thought illiquid, inefficient, that's where the money is turns out a wide spread means smart money is already there and i was paying their bill every single time once i started filtering markets by this formula stopped entering anything where α > 12% $83,000 in the next two months same polymarket same markets i just stopped being someone else's α i track these markets in real time through a bot it calculates α for every market automatically and only alerts when the entry is clean did you know the spread tells you exactly who else is in the game?$

i made $83,000 by looking at one number not the price not the volume the spread α = Δ / (V_h − μ) α is the fraction of traders in the market who already know the correct answer spread 0.05 → α = 5% safe to enter spread 0.15 → α = 15% be careful spread 0.25 → α = 20% one in five knows more than you before this i entered markets with wide spreads i thought illiquid, inefficient, that's where the money is turns out a wide spread means smart money is already there and i was paying their bill every single time once i started filtering markets by this formula stopped entering anything where α > 12% $83,000 in the next two months same polymarket same markets i just stopped being someone else's α i track these markets in real time through a bot it calculates α for every market automatically and only alerts when the entry is clean did you know the spread tells you exactly who else is in the game?

self.dll

42,399 görüntüleme • 4 ay önce

Macy's on 34th in NYC . It was reported that a group of migrant gang members were allegedly shoplifting at the name-brand shop when they said the person recording the attacked the person. This is an ongoing issue at Macy's and other shops across NYC. The way this works is they send out crews to shoplift, then the stolen products are them sold by a different group . This is very organized and are making tons of money. ( sent in by a source)

Viral News NYC

54,978 görüntüleme • 1 yıl önce

Love for humanity is the core of love for life. It arises from the recognition of life’s value and beauty, from faith in humanity’s ability for greatness, and from the awareness that you are its child — and that it is dear and close to you. : The author places love for humanity at the heart of love for life itself. It springs from a clear recognition of life’s immense value and beauty, from an unwavering faith in humanity’s capacity for greatness, and from the intimate awareness that each person is humanity’s own child, bound to it by blood, spirit, and destiny. This love is not distant admiration. It is the quiet, fierce tenderness a child feels for the parent who gave it existence. Humanity is dear and close because it is the living source from which we draw breath, meaning, and possibility. To love life is to love the collective that carries it forward. To doubt humanity is to doubt life’s own worth. When we see ourselves as its children, gratitude replaces judgment. Hope replaces despair. Love for humanity becomes the deepest form of self-love, because we are not separate from it. It is the recognition that every stranger carries a piece of the same miracle we carry in ourselves. That recognition turns strangers into kin, and the world into home.

Love for humanity is the core of love for life. It arises from the recognition of life’s value and beauty, from faith in humanity’s ability for greatness, and from the awareness that you are its child — and that it is dear and close to you. : The author places love for humanity at the heart of love for life itself. It springs from a clear recognition of life’s immense value and beauty, from an unwavering faith in humanity’s capacity for greatness, and from the intimate awareness that each person is humanity’s own child, bound to it by blood, spirit, and destiny. This love is not distant admiration. It is the quiet, fierce tenderness a child feels for the parent who gave it existence. Humanity is dear and close because it is the living source from which we draw breath, meaning, and possibility. To love life is to love the collective that carries it forward. To doubt humanity is to doubt life’s own worth. When we see ourselves as its children, gratitude replaces judgment. Hope replaces despair. Love for humanity becomes the deepest form of self-love, because we are not separate from it. It is the recognition that every stranger carries a piece of the same miracle we carry in ourselves. That recognition turns strangers into kin, and the world into home.

Zafar Mirzo | Quotes

287,911 görüntüleme • 6 ay önce

JUST IN: Bank of America just told its clients to take profits. About 70% of its bear-market signals are flashing, a level it typically reaches only near market tops. Weeks earlier, BofA's own fund manager survey showed the largest one-month jump into stocks ever recorded, with cash down to 3.9%, under the 4% line the bank treats as a sell signal. Read those together. Investors made their biggest dash into equities in the survey's history at almost the exact moment BofA's own indicators say the top is near. But the number that should actually stop you is buried in the note, and almost nobody is quoting it. The companies driving this entire rally, the AI hyperscalers, are on track to spend nearly 100% of their operating cash flow on capex by year-end. In 2023 that figure was 40%. Sit with that. Big tech used to throw off cash and hand it back through buybacks, which lifted the stocks. Now it is pouring almost every dollar it generates into chips and data centers. BofA notes buybacks have slowed and cash conversion has flat-lined. The engine of the rally is consuming the fuel that powered the stocks. It is the same $725 billion build that companies are now blaming for layoffs. The whole market is priced on one bet, and that bet has grown large enough to eat the cash that used to support the share prices. This is not a crash call. BofA's year-end target is 7,100, about 4% below today, and the median outcome after this cash signal since 2011 has been a 1% dip, not a collapse. The posts screaming sell everything are wrong. The real message is quieter. You are being paid less and less to stay, while the engine runs hotter and hotter.

JUST IN: Bank of America just told its clients to take profits. About 70% of its bear-market signals are flashing, a level it typically reaches only near market tops. Weeks earlier, BofA's own fund manager survey showed the largest one-month jump into stocks ever recorded, with cash down to 3.9%, under the 4% line the bank treats as a sell signal. Read those together. Investors made their biggest dash into equities in the survey's history at almost the exact moment BofA's own indicators say the top is near. But the number that should actually stop you is buried in the note, and almost nobody is quoting it. The companies driving this entire rally, the AI hyperscalers, are on track to spend nearly 100% of their operating cash flow on capex by year-end. In 2023 that figure was 40%. Sit with that. Big tech used to throw off cash and hand it back through buybacks, which lifted the stocks. Now it is pouring almost every dollar it generates into chips and data centers. BofA notes buybacks have slowed and cash conversion has flat-lined. The engine of the rally is consuming the fuel that powered the stocks. It is the same $725 billion build that companies are now blaming for layoffs. The whole market is priced on one bet, and that bet has grown large enough to eat the cash that used to support the share prices. This is not a crash call. BofA's year-end target is 7,100, about 4% below today, and the median outcome after this cash signal since 2011 has been a 1% dip, not a collapse. The posts screaming sell everything are wrong. The real message is quieter. You are being paid less and less to stay, while the engine runs hotter and hotter.

Shanaka Anslem Perera ⚡

17,235 görüntüleme • 1 ay önce

On June 22, the United States signed one executive order to build a quantum computer and, the same day, another to defend against what a quantum computer can do. The first establishes a national effort to build a machine powerful enough to open a new era of scientific discovery, delivered to a Department of Energy lab. The second orders an accelerated national migration to post-quantum cryptography, because the same physics that makes the machine useful makes today's encryption breakable. Read the two orders against each other and the asymmetry is the entire story. The order to build the machine sets no delivery date and is explicitly subject to the availability of appropriations. The order to defend the data sets hard deadlines: a migration pilot due December 31, 2027, and high-value systems moved to post-quantum cryptography by 2030 and 2031. The machine is a national aspiration. The migration is a national deadline. This is the part almost no one is pricing. Even the government is treating the regulatory clock as the binding one, while the market keeps watching the hardware clock. A product does not need to be broken to lose its value. It only needs to become uncertifiable, and the date it becomes uncertifiable is now written into federal policy. The machine can stay distant. The proofs are already on the clock.

On June 22, the United States signed one executive order to build a quantum computer and, the same day, another to defend against what a quantum computer can do. The first establishes a national effort to build a machine powerful enough to open a new era of scientific discovery, delivered to a Department of Energy lab. The second orders an accelerated national migration to post-quantum cryptography, because the same physics that makes the machine useful makes today's encryption breakable. Read the two orders against each other and the asymmetry is the entire story. The order to build the machine sets no delivery date and is explicitly subject to the availability of appropriations. The order to defend the data sets hard deadlines: a migration pilot due December 31, 2027, and high-value systems moved to post-quantum cryptography by 2030 and 2031. The machine is a national aspiration. The migration is a national deadline. This is the part almost no one is pricing. Even the government is treating the regulatory clock as the binding one, while the market keeps watching the hardware clock. A product does not need to be broken to lose its value. It only needs to become uncertifiable, and the date it becomes uncertifiable is now written into federal policy. The machine can stay distant. The proofs are already on the clock.

Shanaka Anslem Perera ⚡

35,284 görüntüleme • 25 gün önce

They did not take cursive from the schools because children no longer needed it. They took it because of what it was quietly building in them. Consider what the exercise actually is. A child, six years old, is handed a pen and asked to draw a single unbroken line that becomes a word. The wrist must float. The fingers must hold a living pressure, never quite the same twice, always correcting. The eye must follow the ink forward and trust the hand to finish what it has begun. There is no lifting, no stopping, no starting over mid-word. The loop must close. The ascender must rise and return. The sentence must travel from one margin to the other as a single continuous gesture, and at the end of it the hand must still be steady. Twelve years of this. Every day. Ten thousand small acts of sustained, self-correcting attention, carried out below the level of conscious thought, until the motion belongs to the body and the body belongs to the motion. This is not penmanship. It is the slow construction of an interior form. The hand that has learned to carry a line without breaking it is the hand of a mind that has learned to carry a thought without breaking it. The two are not metaphors for one another. They are the same faculty, trained in the same child, by the same daily discipline. Continuity of the stroke becomes continuity of the reasoning. The patience of the loop becomes the patience of the argument. The commitment to finish a word one has started becomes the commitment to finish a sentence, a paragraph, a life's idea, without reaching for the nearest distraction halfway through. Print is a different creature entirely. Print lifts. Print stops. Print assembles a word out of separate, stamped, interchangeable pieces, each one beginning and ending in isolation. A mind raised only on print learns to think the way print is made, in discrete tokens, in replaceable units, in fragments that can be recombined by any outside hand without the owner noticing the substitution. It is precisely the shape of thought a language model produces. It is precisely the shape of thought a language model can steer. Cursive is kata. This is the whole of it. A form repeated daily, for years, not for the sake of the form but for what the repetition lays down in the practitioner beneath the form. The swordsman does not train kata so that one day he may fight in kata. He trains it so that when the moment comes and there is no time to think, the movement is already inside him, older and deeper than thought, and it rises on its own. Cursive was the kata of the literate mind, the daily quiet drilling of continuity, of patience, of a line held steady under the long pressure of its own length. And the signature it produced at the end, that small flourished mark unique to a single human being on earth, was only the outward proof of an inward form no machine and no other hand could ever reproduce. Take the kata away and the practitioner is left with vocabulary in place of faculty. He can recognise a whole thought when he encounters one. He cannot carry one himself. He can admire a finished argument. He cannot sustain one long enough to close its loop. He begins books he does not finish, sentences he does not end, ideas he abandons the moment the screen in his palm offers him a brighter one. And when the machine begins feeding him tokens in the exact shape his schooling taught him to receive, he meets it with no interior resistance at all, because no interior form was ever built in him to push back with. They removed it quietly, across a generation, and they removed it in the last years before the machines arrived. Twelve years of daily practice in unbroken, embodied, self-authored thought, gone from the curriculum of almost every child in the Western world, just as the instruments designed to complete their sentences for them came online. The hand forgets. The mind, having never been taught the kata, forgets a thing it never knew it had. That is what cursive was. That is what was taken. And that is why the thought of anyone who still writes by hand, in long unlifted lines, remains, quietly, stubbornly, and without their ever needing to announce it, their own. Now the question stands open. What else has been banned, phased out, quietly retired from the curriculum and from common life over these same decades, under the same soft excuses? Mental arithmetic. Memorisation of poetry. Latin. Logic as a formal subject. Map reading. Knot work. The keeping of a commonplace book. The reading aloud of long passages in class. Singing in parts. What was each of those actually building in the child, beneath the surface of the lesson, and whose interest was served by its disappearance?

They did not take cursive from the schools because children no longer needed it. They took it because of what it was quietly building in them. Consider what the exercise actually is. A child, six years old, is handed a pen and asked to draw a single unbroken line that becomes a word. The wrist must float. The fingers must hold a living pressure, never quite the same twice, always correcting. The eye must follow the ink forward and trust the hand to finish what it has begun. There is no lifting, no stopping, no starting over mid-word. The loop must close. The ascender must rise and return. The sentence must travel from one margin to the other as a single continuous gesture, and at the end of it the hand must still be steady. Twelve years of this. Every day. Ten thousand small acts of sustained, self-correcting attention, carried out below the level of conscious thought, until the motion belongs to the body and the body belongs to the motion. This is not penmanship. It is the slow construction of an interior form. The hand that has learned to carry a line without breaking it is the hand of a mind that has learned to carry a thought without breaking it. The two are not metaphors for one another. They are the same faculty, trained in the same child, by the same daily discipline. Continuity of the stroke becomes continuity of the reasoning. The patience of the loop becomes the patience of the argument. The commitment to finish a word one has started becomes the commitment to finish a sentence, a paragraph, a life's idea, without reaching for the nearest distraction halfway through. Print is a different creature entirely. Print lifts. Print stops. Print assembles a word out of separate, stamped, interchangeable pieces, each one beginning and ending in isolation. A mind raised only on print learns to think the way print is made, in discrete tokens, in replaceable units, in fragments that can be recombined by any outside hand without the owner noticing the substitution. It is precisely the shape of thought a language model produces. It is precisely the shape of thought a language model can steer. Cursive is kata. This is the whole of it. A form repeated daily, for years, not for the sake of the form but for what the repetition lays down in the practitioner beneath the form. The swordsman does not train kata so that one day he may fight in kata. He trains it so that when the moment comes and there is no time to think, the movement is already inside him, older and deeper than thought, and it rises on its own. Cursive was the kata of the literate mind, the daily quiet drilling of continuity, of patience, of a line held steady under the long pressure of its own length. And the signature it produced at the end, that small flourished mark unique to a single human being on earth, was only the outward proof of an inward form no machine and no other hand could ever reproduce. Take the kata away and the practitioner is left with vocabulary in place of faculty. He can recognise a whole thought when he encounters one. He cannot carry one himself. He can admire a finished argument. He cannot sustain one long enough to close its loop. He begins books he does not finish, sentences he does not end, ideas he abandons the moment the screen in his palm offers him a brighter one. And when the machine begins feeding him tokens in the exact shape his schooling taught him to receive, he meets it with no interior resistance at all, because no interior form was ever built in him to push back with. They removed it quietly, across a generation, and they removed it in the last years before the machines arrived. Twelve years of daily practice in unbroken, embodied, self-authored thought, gone from the curriculum of almost every child in the Western world, just as the instruments designed to complete their sentences for them came online. The hand forgets. The mind, having never been taught the kata, forgets a thing it never knew it had. That is what cursive was. That is what was taken. And that is why the thought of anyone who still writes by hand, in long unlifted lines, remains, quietly, stubbornly, and without their ever needing to announce it, their own. Now the question stands open. What else has been banned, phased out, quietly retired from the curriculum and from common life over these same decades, under the same soft excuses? Mental arithmetic. Memorisation of poetry. Latin. Logic as a formal subject. Map reading. Knot work. The keeping of a commonplace book. The reading aloud of long passages in class. Singing in parts. What was each of those actually building in the child, beneath the surface of the lesson, and whose interest was served by its disappearance?

SiriusB

441,606 görüntüleme • 2 ay önce

The occult begins with a single question. What do you see when your ordinary sight ends? 👁️✨ The occult is about the eye that sees what others refuse to see. The word occult comes from "oculus" ", the eye. The hidden. The unseen. The force that watches beneath the surface of reality. Long before books and rituals, power belonged to those who could see what others could not. From the beginning, the occult was born from sight. Not physical sight. Inner sight. The oculus. The capacity to perceive what the ordinary mind filters out. In Delphi, the priestesses entered trance to read the subtle currents beneath human fate. In Egypt, seers watched the movements of stars, interpreting the patterns of destiny. In Sumer, diviners read omens in flame, oil and shadow. In the Celtic lands, druids trained their vision through nature, dream and symbolic signs. In the East, mystics sharpened perception through breath, stillness and the awakening of the inner eye. Every culture had its own doorway, but the principle was the same. The true practitioner is the one who sees. They detect shifts before they manifest. They read intentions before words are spoken. They sense the path of a soul long before it chooses a direction. Clairvoyance is not fantasy. It is perception without filters. It is the eye that looks inward and outward at the same time. It is the ancient ability to read symbols, energies, intentions and the movements of fate long before they surface. The eye in magic represents mastery over awareness. To see is to know. To know is to choose. To choose is to shape reality. In every tradition, the awakened eye belongs to the practitioner, the healer, the warrior of consciousness. The one who refuses to move blindly. The one who sharpens intuition until it becomes vision. Follow The White Rabbit 🐇

The occult begins with a single question. What do you see when your ordinary sight ends? 👁️✨ The occult is about the eye that sees what others refuse to see. The word occult comes from "oculus" ", the eye. The hidden. The unseen. The force that watches beneath the surface of reality. Long before books and rituals, power belonged to those who could see what others could not. From the beginning, the occult was born from sight. Not physical sight. Inner sight. The oculus. The capacity to perceive what the ordinary mind filters out. In Delphi, the priestesses entered trance to read the subtle currents beneath human fate. In Egypt, seers watched the movements of stars, interpreting the patterns of destiny. In Sumer, diviners read omens in flame, oil and shadow. In the Celtic lands, druids trained their vision through nature, dream and symbolic signs. In the East, mystics sharpened perception through breath, stillness and the awakening of the inner eye. Every culture had its own doorway, but the principle was the same. The true practitioner is the one who sees. They detect shifts before they manifest. They read intentions before words are spoken. They sense the path of a soul long before it chooses a direction. Clairvoyance is not fantasy. It is perception without filters. It is the eye that looks inward and outward at the same time. It is the ancient ability to read symbols, energies, intentions and the movements of fate long before they surface. The eye in magic represents mastery over awareness. To see is to know. To know is to choose. To choose is to shape reality. In every tradition, the awakened eye belongs to the practitioner, the healer, the warrior of consciousness. The one who refuses to move blindly. The one who sharpens intuition until it becomes vision. Follow The White Rabbit 🐇

𝚃𝙷𝙴 𝚆𝙷𝙸𝚃𝙴 𝚁𝙰𝙱𝙱𝙸𝚃

16,266 görüntüleme • 7 ay önce

AN ANTHROPIC LEAD ENGINEER ACCIDENTALLY LEAKED HIS PERSONAL OBSIDIAN. INSIDE - NOT CODE OR PROMPTS, BUT A DIAGRAM OF HIS OWN BRAIN, ORGANIZED AS A NEURAL NETWORK 8,893 nodes. 4,729 connections. A $10/month app opens Obsidian. 21 inputs, ReLU on every layer. The first hidden layer has 26 neurons, followed by 33, then 24, and so on all the way to the output. Thousands of connections flash in real time this isn’t a conceptual diagram from a blog, but a living brain that powers decision-making within the company. 9,000 documents, each with its own semantic space, all interconnected it earns about $2m a year for sorting Markdown files into the right folders. The company that builds the world’s best AI maintains its internal knowledge base in the same app that a freshman uses for class notes three years of discipline and a single open Obsidian tab you’re reading this on a device where, tonight, you can open that same Obsidian and start building your own vault

AN ANTHROPIC LEAD ENGINEER ACCIDENTALLY LEAKED HIS PERSONAL OBSIDIAN. INSIDE - NOT CODE OR PROMPTS, BUT A DIAGRAM OF HIS OWN BRAIN, ORGANIZED AS A NEURAL NETWORK 8,893 nodes. 4,729 connections. A $10/month app opens Obsidian. 21 inputs, ReLU on every layer. The first hidden layer has 26 neurons, followed by 33, then 24, and so on all the way to the output. Thousands of connections flash in real time this isn’t a conceptual diagram from a blog, but a living brain that powers decision-making within the company. 9,000 documents, each with its own semantic space, all interconnected it earns about $2m a year for sorting Markdown files into the right folders. The company that builds the world’s best AI maintains its internal knowledge base in the same app that a freshman uses for class notes three years of discipline and a single open Obsidian tab you’re reading this on a device where, tonight, you can open that same Obsidian and start building your own vault

chewa.

312,842 görüntüleme • 4 gün önce

As of this morning, every brand-new Car sold in Europe is mandated by law to watch its “driver”, and the reason to worry is the opposite of what everyone is screaming about. The camera is not filming your face. The law explicitly bans that. It rather tracks your eyes. The danger is not what it does today. It is what it is now physically positioned to do tomorrow. This became binding across all 27 countries today, the 7th of July 2026, and no member state can opt out, because road safety is an EU competence and EU law overrides national law. Every new car and van, roughly 18 million of them a year, must now carry an infrared camera, usually on the steering column, that follows the driver's gaze. Look away too long, six seconds under 50 kilometers an hour, three and a half above it, and the car warns you with a sound, a light, or a buzz in the seat. The stated reason is real. Distraction causes up to 30 percent of crashes, and the Commission projects the wider safety package will save 25,000 lives by 2038. The outrage dissolves on contact with the actual text. The law actually fully forbids facial recognition and any biometric identification of anyone in the car, and the footage is legally barred from leaving the vehicle. No recording, no transmission, no police feed. As written today, this is a safety beeper, not a spy. But look at what already sits beside it. Think about it.. come on!! Europe's cars already run always-on systems that do transmit, the automatic crash caller that dials emergency services, the black-box event recorder, and over-the-air software that rewrites the car remotely overnight. The sensor was just made universal. The wall keeping it private is a single legal paragraph, and the same law already schedules its own review for 2027 to read cognitive state and body movement, while suppliers openly sell using the identical mandated camera to watch the passengers too. So this is the quiet architecture of every threshold. The permanent thing is physical, a camera now bolted into 18 million dashboards a year. The thing protecting you is a mere sentence, and sentences are the easiest part of any system to revise. Europe hardwired the eye. It left what the eye may see as the one part that can still be changed later. Hmm 🤨

Shanaka Anslem Perera ⚡

649,003 görüntüleme • 11 gün önce

Apparently, I saw this video online and I decided to share. What this worker is applying is called bitumen, or what many of us know as bituminous coating. Most people think a wall is a solid, impenetrable block, but in reality, it is more like a sponge. Concrete and blocks have microscopic pores that pull water from the earth through a process we call capillary action. This thick black substance is the shield that stops that water from climbing up into the house. It is not about making the wall look good because this part will be buried under the dirt forever. It is about creating a skin that water cannot breathe through. When do you need to do this? The need for this arises because the soil is a very aggressive environment. Water is not your only enemy.. The ground also contains salts and sulfates that want to eat away at the cement. If this moisture finds its way to the steel bars inside the columns, those bars will start to rust. And when steel rusts, it expands, and that expansion is what cracks the concrete from the inside out. This coating is the only thing standing between your foundation and that kind of slow destruction. Thats is why if you see wet patches at the bottom of your walls inside your house, it usually means someone skipped this step or did it poorly during construction. You can apply this anytime you are building parts of a structure that will stay in contact with the ground. It is common in areas where the water table is high or where the soil stays damp for most of the year. This is a one-shot opportunity. Once you backfill the soil, you can never go back to fix it without a lot of expense and a lot of digging. It is about having the foresight to protect the heart of the building while it is still exposed. Please don’t ignore this if you need to. If you ignore it now to save a bit of money, you will be funding the future decay of your own home. I hope this helps.

Apparently, I saw this video online and I decided to share. What this worker is applying is called bitumen, or what many of us know as bituminous coating. Most people think a wall is a solid, impenetrable block, but in reality, it is more like a sponge. Concrete and blocks have microscopic pores that pull water from the earth through a process we call capillary action. This thick black substance is the shield that stops that water from climbing up into the house. It is not about making the wall look good because this part will be buried under the dirt forever. It is about creating a skin that water cannot breathe through. When do you need to do this? The need for this arises because the soil is a very aggressive environment. Water is not your only enemy.. The ground also contains salts and sulfates that want to eat away at the cement. If this moisture finds its way to the steel bars inside the columns, those bars will start to rust. And when steel rusts, it expands, and that expansion is what cracks the concrete from the inside out. This coating is the only thing standing between your foundation and that kind of slow destruction. Thats is why if you see wet patches at the bottom of your walls inside your house, it usually means someone skipped this step or did it poorly during construction. You can apply this anytime you are building parts of a structure that will stay in contact with the ground. It is common in areas where the water table is high or where the soil stays damp for most of the year. This is a one-shot opportunity. Once you backfill the soil, you can never go back to fix it without a lot of expense and a lot of digging. It is about having the foresight to protect the heart of the building while it is still exposed. Please don’t ignore this if you need to. If you ignore it now to save a bit of money, you will be funding the future decay of your own home. I hope this helps.

A.Y.O

75,105 görüntüleme • 3 ay önce

Iran just called Trump’s bluff. Its supreme leader was assassinated. Its nuclear sites were bombed. And it is winning the war that is left. Washington walked into a trap with three locked doors. Trump cannot settle: a tentative 60-day ceasefire has stalled for a week while he demands changes Iran rejects. He cannot walk away: the strait stays shut and the bill keeps running. And the House just voted 215 to 208 to rein him in, with the Senate one vote behind. But the door he can least afford to open is escalation, and this is the part no one is pricing. America is draining two reserves at once. It has pulled its Strategic Petroleum Reserve down 12% to 365 million barrels to hold the oil price down, and it has fired roughly 1,100 Tomahawks and 1,200 Patriots, weapons it needs years to rebuild. Both gauges fall on the same clock. Neither refills fast: the oil reserve is not projected back to pre-war levels until 2028. And Iran can see all of it. That is why Iran will not move. A country this battered is winning the only contest left, the contest of who can afford to wait. The screen still looks calm. Brent is back above $100. US stocks sat at record highs days ago. But that calm is bought with a draining reserve and a spent arsenal, and neither comes back for years. Trump called the vote meaningless. The market shrugged. Iran read it as a green light. This war is not being won on the battlefield. It is being won by whoever outlasts the other’s reserves. For the first time, that is not Washington.

Iran just called Trump’s bluff. Its supreme leader was assassinated. Its nuclear sites were bombed. And it is winning the war that is left. Washington walked into a trap with three locked doors. Trump cannot settle: a tentative 60-day ceasefire has stalled for a week while he demands changes Iran rejects. He cannot walk away: the strait stays shut and the bill keeps running. And the House just voted 215 to 208 to rein him in, with the Senate one vote behind. But the door he can least afford to open is escalation, and this is the part no one is pricing. America is draining two reserves at once. It has pulled its Strategic Petroleum Reserve down 12% to 365 million barrels to hold the oil price down, and it has fired roughly 1,100 Tomahawks and 1,200 Patriots, weapons it needs years to rebuild. Both gauges fall on the same clock. Neither refills fast: the oil reserve is not projected back to pre-war levels until 2028. And Iran can see all of it. That is why Iran will not move. A country this battered is winning the only contest left, the contest of who can afford to wait. The screen still looks calm. Brent is back above $100. US stocks sat at record highs days ago. But that calm is bought with a draining reserve and a spent arsenal, and neither comes back for years. Trump called the vote meaningless. The market shrugged. Iran read it as a green light. This war is not being won on the battlefield. It is being won by whoever outlasts the other’s reserves. For the first time, that is not Washington.

Shanaka Anslem Perera ⚡

76,787 görüntüleme • 1 ay önce

This is the view from the Conscient Heritage Max Sector 102 flat we visited last week. My buyer has rejected it. I was not surprised. The moment we were asked to park outside the society gate and walk half a kilometre in 40°C, I knew this flat had already lost. I did not push him. When a buyer goes quiet inside a flat, the decision is already made. You just respect it. He is still looking. He is still going to buy. Just not here. Somewhere in this society, a flat owner is probably refreshing their portal listing right now, wondering why serious buyers are not coming back with a second visit. The answer is not inside the flat. The answer is at the gate. Their facility management is turning buyers away before the lift door opens. If you own a flat in either society and plan to sell in the next 1 to 2 years, the first call is not to a broker. It is to your facility management. Ask them why visitors are parking on the road. Then ask them what that is doing to your resale value. The view from the flat is fine. You can see it in the video. The flat lost the deal before the buyer saw it.

This is the view from the Conscient Heritage Max Sector 102 flat we visited last week. My buyer has rejected it. I was not surprised. The moment we were asked to park outside the society gate and walk half a kilometre in 40°C, I knew this flat had already lost. I did not push him. When a buyer goes quiet inside a flat, the decision is already made. You just respect it. He is still looking. He is still going to buy. Just not here. Somewhere in this society, a flat owner is probably refreshing their portal listing right now, wondering why serious buyers are not coming back with a second visit. The answer is not inside the flat. The answer is at the gate. Their facility management is turning buyers away before the lift door opens. If you own a flat in either society and plan to sell in the next 1 to 2 years, the first call is not to a broker. It is to your facility management. Ask them why visitors are parking on the road. Then ask them what that is doing to your resale value. The view from the flat is fine. You can see it in the video. The flat lost the deal before the buyer saw it.

Gurugrammer- Abhishek Bhardwaj

104,424 görüntüleme • 22 gün önce

BREAKING: Iran named a warship after the general who spent his career threatening to close the Strait of Hormuz. The US just lit it on fire in the Strait of Hormuz. The IRIS Shahid Sayyad Shirazi, a Soleimani-class corvette, is burning at Bandar Abbas right now. Footage is out. The smoke is visible from the port. Bandar Abbas is not a random target. It is Iran’s primary naval base. It sits directly at the mouth of the strait that carries 20% of the world’s oil. This is not a ship that was sunk in the Indian Ocean four thousand miles away. This is Iran’s naval guardian, on fire, at the gate it was built to defend. A week ago, Admiral Brad Cooper said the US had destroyed 17 Iranian ships. Then the IRIS Dena went down near Sri Lanka. Now a corvette is burning at the crown jewel of Iran’s entire naval posture. Here is what the Strait of Hormuz looks like right now. 85% reduction in maritime traffic. Iran threatening closure. The vessel specifically designed to enforce that threat is on fire at the base that commands the chokepoint. Iran cannot close the Strait. Iran cannot defend the Strait. Iran cannot patrol the Strait. The force built to do all three is being systematically destroyed at its own piers. Every tanker captain, every shipping insurer, every energy desk pricing this conflict as a 4-to-5-week regional event needs to look at that footage and ask a different question. Not when does the war end. When does the traffic come back. Those are not the same question. And only one of them is priced.

BREAKING: Iran named a warship after the general who spent his career threatening to close the Strait of Hormuz. The US just lit it on fire in the Strait of Hormuz. The IRIS Shahid Sayyad Shirazi, a Soleimani-class corvette, is burning at Bandar Abbas right now. Footage is out. The smoke is visible from the port. Bandar Abbas is not a random target. It is Iran’s primary naval base. It sits directly at the mouth of the strait that carries 20% of the world’s oil. This is not a ship that was sunk in the Indian Ocean four thousand miles away. This is Iran’s naval guardian, on fire, at the gate it was built to defend. A week ago, Admiral Brad Cooper said the US had destroyed 17 Iranian ships. Then the IRIS Dena went down near Sri Lanka. Now a corvette is burning at the crown jewel of Iran’s entire naval posture. Here is what the Strait of Hormuz looks like right now. 85% reduction in maritime traffic. Iran threatening closure. The vessel specifically designed to enforce that threat is on fire at the base that commands the chokepoint. Iran cannot close the Strait. Iran cannot defend the Strait. Iran cannot patrol the Strait. The force built to do all three is being systematically destroyed at its own piers. Every tanker captain, every shipping insurer, every energy desk pricing this conflict as a 4-to-5-week regional event needs to look at that footage and ask a different question. Not when does the war end. When does the traffic come back. Those are not the same question. And only one of them is priced.

Shanaka Anslem Perera ⚡

237,301 görüntüleme • 4 ay önce

There is a room in Málaga that was built to be the closest thing on earth to standing inside heaven. It is called the camarín of the Virgin of Victory, and it is hidden at the top of a tower inside the Santuario de la Victoria. To reach it, you climb and the ascent is the entire point... The building you are climbing through was completed in 1700, and it was designed as a single argument made in stone. At the bottom lies a crypt: a black chamber crowded with white plaster skeletons, a meditation on death and the brevity of life. From there a staircase rises, and as you climb it the light grows stronger and the imagery changes from bones to saints. The architects of the time understood this ascent as the soul's own journey, the dark crypt as the stage of penitence, the staircase as the stage of spiritual progress, and the room at the very top as the final stage: the union of the soul with the divine. That room at the top is the camarín, and its dome is one of the most extraordinary interiors in Spain... Every surface is covered in white and gold plasterwork. There is no empty space anywhere. The Baroque called this horror vacui, the horror of the void: the conviction that a space meant to represent heaven should not contain a single bare patch of stone. Out of that plasterwork emerge angels, flowers, birds, and mirrors. The mirrors are not decoration alone. They catch the light pouring in through the windows of the drum and throw it around the chamber, so that the gold seems to move and the whole room appears to shimmer and breathe. This wonder was built by people who believed that if you wanted to show a human being what heaven might feel like, you did not describe it to them. You built a room, and you let them climb into it... -- -- -- If you enjoyed this, I write a weekly newsletter read by over 50,000 people who love rediscovering the beauty of the past. You can join us here: If you'd like to support my work, a paid subscription is what makes it possible.

There is a room in Málaga that was built to be the closest thing on earth to standing inside heaven. It is called the camarín of the Virgin of Victory, and it is hidden at the top of a tower inside the Santuario de la Victoria. To reach it, you climb and the ascent is the entire point... The building you are climbing through was completed in 1700, and it was designed as a single argument made in stone. At the bottom lies a crypt: a black chamber crowded with white plaster skeletons, a meditation on death and the brevity of life. From there a staircase rises, and as you climb it the light grows stronger and the imagery changes from bones to saints. The architects of the time understood this ascent as the soul's own journey, the dark crypt as the stage of penitence, the staircase as the stage of spiritual progress, and the room at the very top as the final stage: the union of the soul with the divine. That room at the top is the camarín, and its dome is one of the most extraordinary interiors in Spain... Every surface is covered in white and gold plasterwork. There is no empty space anywhere. The Baroque called this horror vacui, the horror of the void: the conviction that a space meant to represent heaven should not contain a single bare patch of stone. Out of that plasterwork emerge angels, flowers, birds, and mirrors. The mirrors are not decoration alone. They catch the light pouring in through the windows of the drum and throw it around the chamber, so that the gold seems to move and the whole room appears to shimmer and breathe. This wonder was built by people who believed that if you wanted to show a human being what heaven might feel like, you did not describe it to them. You built a room, and you let them climb into it... -- -- -- If you enjoyed this, I write a weekly newsletter read by over 50,000 people who love rediscovering the beauty of the past. You can join us here: If you'd like to support my work, a paid subscription is what makes it possible.

James Lucas

69,219 görüntüleme • 1 ay önce

Thousands of CCTVs. Facial recognition on every corner. A surveillance network so dense it can track a jaywalker in seconds. Yet somehow… children still go missing. If a system this all-seeing still “fails,” what exactly is it seeing — and what is it choosing not to see? People who say “China is one of the safest countries in the world” are usually the ones who walk through society as guests, not locals — Western expats treated like a quiet upper caste. But safety is not measured by how the privileged feel. It’s measured by how anxious parents behave. And in China, look at the schools: crowds of parents and grandparents standing guard at the gates every single day. If the surveillance state is truly that safe, why does every school dismissal look like a mini-evacuation drill? When a country builds a panopticon yet ordinary families still don’t trust it… the question writes itself — is the danger outside, or inside the system?

Thousands of CCTVs. Facial recognition on every corner. A surveillance network so dense it can track a jaywalker in seconds. Yet somehow… children still go missing. If a system this all-seeing still “fails,” what exactly is it seeing — and what is it choosing not to see? People who say “China is one of the safest countries in the world” are usually the ones who walk through society as guests, not locals — Western expats treated like a quiet upper caste. But safety is not measured by how the privileged feel. It’s measured by how anxious parents behave. And in China, look at the schools: crowds of parents and grandparents standing guard at the gates every single day. If the surveillance state is truly that safe, why does every school dismissal look like a mini-evacuation drill? When a country builds a panopticon yet ordinary families still don’t trust it… the question writes itself — is the danger outside, or inside the system?

The Great Translation Movement 大翻译运动

41,497 görüntüleme • 7 ay önce