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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...

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Tom Yeh

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191,994 просмотров • 2 лет назад •via X (Twitter)

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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
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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

23,948 просмотров • 5 дней назад

[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

46,499 просмотров • 1 год назад

[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 просмотров • 2 лет назад

[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

48,356 просмотров • 2 лет назад

One cool thing about ColBERT-based search compared to the cosine-based vector retrieval is that you get interpretability for free as a byproduct of the MaxSim computation. It's kind of like the Lucene highlighter, letting you grab the most relevant snippets from a long document to show users where their query matches. With Jina-ColBERT-v1, which supports up to 8K token length, released by us earlier this Feb., the visualization of the late interaction between a query and a document is almost... artistic. The video shows the late interaction between the query "Elephants eat 150 kg of food per day." and the Wikipedia article about "Indian Elephant". Darker colors indicate stronger semantic matches. The darkest area corresponds to "The species is classified as a megaherbivore and consume up to 150 kg (330 lb) of plant matter per day." from the original article.
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One cool thing about ColBERT-based search compared to the cosine-based vector retrieval is that you get interpretability for free as a byproduct of the MaxSim computation. It's kind of like the Lucene highlighter, letting you grab the most relevant snippets from a long document to show users where their query matches. With Jina-ColBERT-v1, which supports up to 8K token length, released by us earlier this Feb., the visualization of the late interaction between a query and a document is almost... artistic. The video shows the late interaction between the query "Elephants eat 150 kg of food per day." and the Wikipedia article about "Indian Elephant". Darker colors indicate stronger semantic matches. The darkest area corresponds to "The species is classified as a megaherbivore and consume up to 150 kg (330 lb) of plant matter per day." from the original article.

Jina AI

22,268 просмотров • 2 лет назад

Researchers made KMeans 200x faster. And the new technique also beats approaches like cuML and FAISS. Flash-KMeans is an IO-aware implementation of exact KMeans that redesigns the algorithm around modern GPU bottlenecks. By attacking the memory bottlenecks directly, Flash-KMeans achieves: - 33x speedup over cuML - 200x speedup over FAISS This speedup comes from how it moves through GPU memory. Standard KMeans runs in two steps, and both are bottlenecked by reads and writes to GPU memory: 1) The first step matches every point to its nearest centroid. Standard KMeans computes the full point-to-centroid distance matrix, writes it out to GPU memory, then reads it back to find each nearest centroid. That write-then-read round trip is the bottleneck. Flash-KMeans combines the distance calculation with the nearest-centroid step, so the result is computed on-chip and the full matrix is never written out. 2) The second step recomputes each centroid by averaging the points assigned to it. Standard KMeans has thousands of threads writing into the same centroid slots at once, so they stall waiting for their turn. Flash-KMeans sorts points by cluster first, turning scattered writes into sequential reductions that read and write memory in one efficient pass. Using these two optimizations at the million-scale, Flash-KMeans completes a standard KMeans iteration in a few milliseconds. The video below depicts this in action. Several reasons why this is important: KMeans has always been an offline primitive. Something you run once to preprocess data and move on. These speedups make the approach viable in several runtime-critical systems. ↳ Vector indices like FAISS use KMeans to build search indices. Faster KMeans means you can re-index dynamically as data changes. ↳ LLM quantization methods need KMeans to find optimal weight codebooks, per layer, repeatedly. What takes hours could now take minutes. ↳ MoE models need fast token routing at inference time. Flash-KMeans makes it viable to run this inside the inference loop, not just in preprocessing. I have shared the paper in the replies. That said, memory is the real constraint Flash-KMeans solves, and the problem is not just limited to clustering. The vectors a RAG system stores after indexing create similar bottlenecks. I wrote a detailed walkthrough recently on cutting this vector memory by 32x with binary quantization, querying 36M+ vectors in a few milliseconds. Read it below.
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Researchers made KMeans 200x faster. And the new technique also beats approaches like cuML and FAISS. Flash-KMeans is an IO-aware implementation of exact KMeans that redesigns the algorithm around modern GPU bottlenecks. By attacking the memory bottlenecks directly, Flash-KMeans achieves: - 33x speedup over cuML - 200x speedup over FAISS This speedup comes from how it moves through GPU memory. Standard KMeans runs in two steps, and both are bottlenecked by reads and writes to GPU memory: 1) The first step matches every point to its nearest centroid. Standard KMeans computes the full point-to-centroid distance matrix, writes it out to GPU memory, then reads it back to find each nearest centroid. That write-then-read round trip is the bottleneck. Flash-KMeans combines the distance calculation with the nearest-centroid step, so the result is computed on-chip and the full matrix is never written out. 2) The second step recomputes each centroid by averaging the points assigned to it. Standard KMeans has thousands of threads writing into the same centroid slots at once, so they stall waiting for their turn. Flash-KMeans sorts points by cluster first, turning scattered writes into sequential reductions that read and write memory in one efficient pass. Using these two optimizations at the million-scale, Flash-KMeans completes a standard KMeans iteration in a few milliseconds. The video below depicts this in action. Several reasons why this is important: KMeans has always been an offline primitive. Something you run once to preprocess data and move on. These speedups make the approach viable in several runtime-critical systems. ↳ Vector indices like FAISS use KMeans to build search indices. Faster KMeans means you can re-index dynamically as data changes. ↳ LLM quantization methods need KMeans to find optimal weight codebooks, per layer, repeatedly. What takes hours could now take minutes. ↳ MoE models need fast token routing at inference time. Flash-KMeans makes it viable to run this inside the inference loop, not just in preprocessing. I have shared the paper in the replies. That said, memory is the real constraint Flash-KMeans solves, and the problem is not just limited to clustering. The vectors a RAG system stores after indexing create similar bottlenecks. I wrote a detailed walkthrough recently on cutting this vector memory by 32x with binary quantization, querying 36M+ vectors in a few milliseconds. Read it below.

Avi Chawla

89,234 просмотров • 1 месяц назад

Kedarnath is a tremendous space. The utterance of the sound “Shiva” attains a completely new dimension and significance in Kedar. It is a space which has been specially prepared for this particular sound. When we utter the word “Shiva,” it is the freedom of the uncreated, the liberation of one who is not created. It is almost like on this planet, the sound “Shiva” emanates from this place. For thousands of years, people have experienced that space as a reverberation of that sound. This is also a place that has witnessed thousands of Yogis and mystics of every kind. When I say every kind, you cannot imagine those kinds. These are people who made no attempt to teach anything to anyone. Their way of making an offering to the world was by leaving their energies, their path, their work – everything – in a certain way in these spaces.
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Kedarnath is a tremendous space. The utterance of the sound “Shiva” attains a completely new dimension and significance in Kedar. It is a space which has been specially prepared for this particular sound. When we utter the word “Shiva,” it is the freedom of the uncreated, the liberation of one who is not created. It is almost like on this planet, the sound “Shiva” emanates from this place. For thousands of years, people have experienced that space as a reverberation of that sound. This is also a place that has witnessed thousands of Yogis and mystics of every kind. When I say every kind, you cannot imagine those kinds. These are people who made no attempt to teach anything to anyone. Their way of making an offering to the world was by leaving their energies, their path, their work – everything – in a certain way in these spaces.

Sadhguru

57,706 просмотров • 3 месяцев назад

The UFO/UAP phenomenon is ancient. It has been here long before us, and it is connected to a grand hierarchy created by God. They are coming from higher dimensions, something that religions would describe as the Tree of Life. The phenomenon is part of us, and our soul is part of this grand system. We are currently in the lowest dimension, chakra, sefirot, or part of the soul, known as Malkhut in Kabbalah, Muladhara in Hinduism, and Khat in ancient Egypt. We are made of matter, but our soul is made of fire, and it is time for an upgrade. The Geophysical Event is connected to this transformation.
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The UFO/UAP phenomenon is ancient. It has been here long before us, and it is connected to a grand hierarchy created by God. They are coming from higher dimensions, something that religions would describe as the Tree of Life. The phenomenon is part of us, and our soul is part of this grand system. We are currently in the lowest dimension, chakra, sefirot, or part of the soul, known as Malkhut in Kabbalah, Muladhara in Hinduism, and Khat in ancient Egypt. We are made of matter, but our soul is made of fire, and it is time for an upgrade. The Geophysical Event is connected to this transformation.

Open Minded Approach

136,661 просмотров • 2 месяцев назад

As a gynecologist, one of the most frequently asked questions is about the ''hymen''. The hymen is not a structure located deep inside the vagina. It is a thin, flexible fold of tissue situated very close to the vaginal opening, anatomically at the entrance of the vaginal canal. It is typically found about 1–2 cm inside the vaginal opening, but in many women, it is almost at the surface. Therefore, the common belief that it is located deep inside is incorrect. One of the most important points is this: The hymen is not a closed membrane. It naturally has openings that allow menstrual blood to pass. Additionally, the structure of the hymen varies from person to person. Its thickness, elasticity, and shape are not standard. In some women, it may be very thin and elastic, while in others, it may be minimal or barely noticeable. This is completely a normal anatomical variation. A common misconception is that changes in the hymen occur only due to sexual intercourse. In reality, factors such as certain physical activities or tampon use can also lead to stretching or changes in this tissue. Therefore, the hymen is not a reliable indicator of a person’s sexual history or “virginity.” In summary, the hymen is a small and variable anatomical structure. The meanings attributed to it are largely shaped by sociocultural beliefs rather than medical facts.
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As a gynecologist, one of the most frequently asked questions is about the ''hymen''. The hymen is not a structure located deep inside the vagina. It is a thin, flexible fold of tissue situated very close to the vaginal opening, anatomically at the entrance of the vaginal canal. It is typically found about 1–2 cm inside the vaginal opening, but in many women, it is almost at the surface. Therefore, the common belief that it is located deep inside is incorrect. One of the most important points is this: The hymen is not a closed membrane. It naturally has openings that allow menstrual blood to pass. Additionally, the structure of the hymen varies from person to person. Its thickness, elasticity, and shape are not standard. In some women, it may be very thin and elastic, while in others, it may be minimal or barely noticeable. This is completely a normal anatomical variation. A common misconception is that changes in the hymen occur only due to sexual intercourse. In reality, factors such as certain physical activities or tampon use can also lead to stretching or changes in this tissue. Therefore, the hymen is not a reliable indicator of a person’s sexual history or “virginity.” In summary, the hymen is a small and variable anatomical structure. The meanings attributed to it are largely shaped by sociocultural beliefs rather than medical facts.

Op. Dr. Mehmet Bekir Şen

116,046 просмотров • 3 месяцев назад

[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

72,891 просмотров • 2 лет назад

I built MatmulFlow ( — an interactive tool that makes matrix multiplication dimensions visual, part of my AI by Hand ✍️ series. Matrix multiplication dimensions are confusing. Which is the inner dimension? Columns of the first or rows of the second? And when you chain five multiplications together, it gets worse. The idea: represent matrices as rectangles. Shift the second matrix up and to the right. The edges that must align become obvious. The result fills in the remaining space. No memorization. You can see it. It extends to chains. Stack vertically for left-multiplication. Stack horizontally for right-multiplication. Resize any matrix and watch the dimensions "flow" through the entire chain. Give it a try!
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I built MatmulFlow ( — an interactive tool that makes matrix multiplication dimensions visual, part of my AI by Hand ✍️ series. Matrix multiplication dimensions are confusing. Which is the inner dimension? Columns of the first or rows of the second? And when you chain five multiplications together, it gets worse. The idea: represent matrices as rectangles. Shift the second matrix up and to the right. The edges that must align become obvious. The result fills in the remaining space. No memorization. You can see it. It extends to chains. Stack vertically for left-multiplication. Stack horizontally for right-multiplication. Resize any matrix and watch the dimensions "flow" through the entire chain. Give it a try!

Tom Yeh

26,269 просмотров • 3 месяцев назад

Added context to my tiny diffusion model to enable sequential generation of longer outputs! Currently the context is a quarter of the sequence length (seq_len=256, context_len=64). I have a theory that the less semantic-value-per-token, the worse the “curse of parallel decoding” is. With parallel decoding, we independently predict multiple tokens in one step. With the sentence “My poker hand was a ___ ___”, two valid predictions are “two pair” and “straight flush”. Because each token prediction is independent though, we can end up with a nonsensical output like “two flush”. This seems to be exacerbated with low semantic-value-per-token, as now you need more tokens to express the same concept. Instead of needing to independently predict two tokens, we might need to predict 10 instead (which is of course much harder). The model currently has noticeably worse output compared to nanogpt (similar size) and I believe this is a main reason. I’ll try adding confidence-aware parallel decoding (from NVIDIA’s Fast-dLLM paper) and other tricks and see how much they improve generation quality.
0:12

Added context to my tiny diffusion model to enable sequential generation of longer outputs! Currently the context is a quarter of the sequence length (seq_len=256, context_len=64). I have a theory that the less semantic-value-per-token, the worse the “curse of parallel decoding” is. With parallel decoding, we independently predict multiple tokens in one step. With the sentence “My poker hand was a ___ ___”, two valid predictions are “two pair” and “straight flush”. Because each token prediction is independent though, we can end up with a nonsensical output like “two flush”. This seems to be exacerbated with low semantic-value-per-token, as now you need more tokens to express the same concept. Instead of needing to independently predict two tokens, we might need to predict 10 instead (which is of course much harder). The model currently has noticeably worse output compared to nanogpt (similar size) and I believe this is a main reason. I’ll try adding confidence-aware parallel decoding (from NVIDIA’s Fast-dLLM paper) and other tricks and see how much they improve generation quality.

Nathan Barry

89,040 просмотров • 9 месяцев назад

The Hidden Language of Diffusion Models paper page: tackle the challenge of understanding concept representations in text-to-image models by decomposing an input text prompt into a small set of interpretable elements. This is achieved by learning a pseudo-token that is a sparse weighted combination of tokens from the model's vocabulary, with the objective of reconstructing the images generated for the given concept. Applied over the state-of-the-art Stable Diffusion model, this decomposition reveals non-trivial and surprising structures in the representations of concepts. For example, we find that some concepts such as "a president" or "a composer" are dominated by specific instances (e.g., "Obama", "Biden") and their interpolations. Other concepts, such as "happiness" combine associated terms that can be concrete ("family", "laughter") or abstract ("friendship", "emotion"). In addition to peering into the inner workings of Stable Diffusion, our method also enables applications such as single-image decomposition to tokens, bias detection and mitigation, and semantic image manipulation
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The Hidden Language of Diffusion Models paper page: tackle the challenge of understanding concept representations in text-to-image models by decomposing an input text prompt into a small set of interpretable elements. This is achieved by learning a pseudo-token that is a sparse weighted combination of tokens from the model's vocabulary, with the objective of reconstructing the images generated for the given concept. Applied over the state-of-the-art Stable Diffusion model, this decomposition reveals non-trivial and surprising structures in the representations of concepts. For example, we find that some concepts such as "a president" or "a composer" are dominated by specific instances (e.g., "Obama", "Biden") and their interpolations. Other concepts, such as "happiness" combine associated terms that can be concrete ("family", "laughter") or abstract ("friendship", "emotion"). In addition to peering into the inner workings of Stable Diffusion, our method also enables applications such as single-image decomposition to tokens, bias detection and mitigation, and semantic image manipulation

AK

41,746 просмотров • 3 лет назад

If you are an USM student, Alumni, Fan, or a resident of the Pinebelt/surrounding areas you need to be at The Rock this Saturday vs Texas State, and in 2 weeks vs Troy. The Eags are 7-2. They are 5-0 in the Sunbelt. People have wanted a winning product, and Huff has delivered by flipping a 1-11 team over night basically. The Eags not only have a chance to win the west, and play for a conference championship. But win out and with some help there is a small outside chance of being the G5 team in the playoffs. Which is crazy to say, but it’s not impossible. The team is fun to watch, and KujForCongress brings the energy to make it a good time for everyone. Don’t miss out! Need tickets call Tyler Cochran ! #SMTTT
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If you are an USM student, Alumni, Fan, or a resident of the Pinebelt/surrounding areas you need to be at The Rock this Saturday vs Texas State, and in 2 weeks vs Troy. The Eags are 7-2. They are 5-0 in the Sunbelt. People have wanted a winning product, and Huff has delivered by flipping a 1-11 team over night basically. The Eags not only have a chance to win the west, and play for a conference championship. But win out and with some help there is a small outside chance of being the G5 team in the playoffs. Which is crazy to say, but it’s not impossible. The team is fun to watch, and KujForCongress brings the energy to make it a good time for everyone. Don’t miss out! Need tickets call Tyler Cochran ! #SMTTT

Attack Eagles🦅

13,011 просмотров • 8 месяцев назад

As someone who is pretty up to date in AI I’d say there are 2 times a year where I am genuinely blown away by something. A breakthrough that keeps me up at night. This is one of them. I mean the video of will smith genuinely freaks me out by how good it is. 2.5 years of AI progress and you think it’s hitting a wall. There’s no point in trying to convince people where this is going. The writing is on the wall. I can bring a horse to water but I can’t force him to drink.
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As someone who is pretty up to date in AI I’d say there are 2 times a year where I am genuinely blown away by something. A breakthrough that keeps me up at night. This is one of them. I mean the video of will smith genuinely freaks me out by how good it is. 2.5 years of AI progress and you think it’s hitting a wall. There’s no point in trying to convince people where this is going. The writing is on the wall. I can bring a horse to water but I can’t force him to drink.

Chris

53,717 просмотров • 5 месяцев назад

This is the second of two posts I’m making about the teaching of Andy Stanley because I have a burden to warn people to be like the Bereans "examining the Scriptures daily to see if these things were so." (Acts 17:11). I have attached a short video clip where Stanley says we don’t know Jesus rose from the dead because the bible tells us so. He says it’s the other way around. Now how do we know Jesus bodily rose from the dead? Did any of us see it happen? No, it happened 2000 years ago. But haven’t people researched the resurrection and found all sorts of evidence consistent with Him rising from the dead. Yes, but such evidence, though powerful, and we can certainly use in our witnessing, does not ultimately prove He rose from the dead. In fact, no matter what evidence we point to in geology, biology, astronomy etc., none of this proves in an ultimate sense the bible is true. Now it is certainly true such evidence properly interpreted does confirm the bible’s history. For instance, the molecule of heredity DNA is a complex information system and language system. No one has seen matter produce information or a language from matter by natural processes. Our observations and experience show information and language have to come from an intelligence. Such evidence confirms an intelligence behind life. This certainly confirms the first verse of the bible, “In the beginning God created… .” But nonetheless, it’s not absolute proof. Think about it. We are finite beings living in the present. We don’t know everything. We don’t know how much we don’t know or do know in relation to whatever there is to know! When we try to interpret evidence of the present in relation to the past, how do we know we have all the relevant information to make the correct interpretation. Some information we don’t have could totally change our interpretation. That has certainly happened with scientists solving crimes using circumstantial evidence. When new evidence comes along, some of the interpretations change and certain people thought to be guilty were found they were innocent after-all. We need to have all the information needed. But we can’t know everything. However we have a book that claims over three thousand times to be the Word of God. This book claims that God moved people by His spirit to write His Word, what He wants revealed to us about life, the universe and history. This book, the bible, tells us that God knows everything, He is infinite in knowledge and wisdom. He has all information. “In whom are hidden all the treasures of wisdom and knowledge” (Colossians 2:3). If God’s Word is what it claims to be (and it is), then the infinite Creator God has revealed to us the key information we need to know to have the ability to correctly interpret this world in relation to the past, present and its purpose and meaning. “Therefore, we never stop thanking God that when you received his message from us, you didn’t think of our words as mere human ideas. You accepted what we said as the very word of God—which, of course, it is. And this word continues to work in you who believe” (1 Thessalonians 2:13). This means if we build our thinking on God’s Word, we build a Christian worldview to enable us to look at the world through “biblical glasses” and have the ability to correctly interpret and understand it. And Genesis 1-11 is the history that is foundational to the rest of the bible and thus our worldview. So, when we start with God’s Word we learn that the God revealed to us in the bible is the One Who created all things. Now by just looking at the world, for instance at DNA, we might deduce that there’s an intelligence behind life. But we would not know who that intelligence is unless revealed to us. The bible reveals who that intelligence is, God the father, Son, and Holy Spirit. But, if we just looked at the world with all its death, suffering and disease, we could assume that the intelligence behind life must be an ogre to make such a violent disease ridden suffering world. But when we start from God’s Word, we understand there was no death or disease to start with, but these entered the world because of sin. We also find man has a problem called sin which alienated him from God. We even find in Genesis that God promised someone would come to save us from our sin and restore our relationship with God (Genesis 3:15; 3:21). We learn later on that “someone” is Jesus--the one who became flesh for us, the babe in a manger 2000 years ago. It's important to understand we can’t know anything absolutely unless an absolute authority has revealed to us what we need to know. Now Andy Stanley claims we don’t know Jesus rose from the dead because the bible tells us so, but claims it’s the other way round, that because Jesus rose from the dead, we can believe what is says about this in the bible. In reality, Andy Stanley is actually claiming he knows all information about the resurrection to know it’s true so then he can proclaim what the bible says about the resurrection is true. This is not so. And remember from the previous post, Andy Stanley accepts man’s view of evolution and millions of years as true to declare what Genesis records about creation is not all true. So why shouldn't people take the word of others who claim Jesus didn't rise from the dead to then declare the account of the resurrection in the gospels can't be true. Stanley, as a finite fallen human being with very limited knowledge, starts outside the bible to go to the bible to make pronouncements over God’s written Word. No wonder he rejects a literal Genesis. Sadly, this is the case for the majority of our church leaders and Christian academics, particularly when it comes to Genesis. Think about it. Really Stanley is acting in accord with our sin nature because of what happened in Genesis 3. Part of our sin nature concerns us wanting to be our own god. Consider Genesis 3:1 and Genesis 3:5, the temptation by the devil. Satan tempted Adam and Eve to question God’s Word, and be want to be like God to decide good and evil, truth, etc., for themselves. In actuality, the statements Andy Stanley is making about Christianity and God’s Word are reflecting this sin problem we have. He is letting his sin nature master over him in this instance instead of letting God’s Word tell us clearly what we should believe. And I would say that about all Christians who reinterpret parts of the bible (like Genesis) because of beliefs from outside the bible. Now the whole bible is actually about Jesus, from the very first verse, that Jesus is the Creator (Colossians 1:16 “For by him all things were created,”), & and he is the Savior (Revelation 5:9), to the very last verse, “He who testifies to these things says, “Surely I am coming soon.” Amen. Come, Lord Jesus! The grace of the Lord Jesus be with all. Amen” (Revelation 22:20–21) God reveals all we need to know about Jesus in His Word. We know Jesus rose from the dead because the bible tells us so! We know we are sinners because the bible tells us so. We know we can be saved through faith in Christ because the bible tells us so. We know we need to repent of sin because the bible tells us so. As Christians we know we will spend eternity in Heaven because the bible tells us so. “So faith comes from hearing, and hearing through the word of God” (Romans 10:17). I still remember singing the chorus as a child Jesus loves me this I know, for the bible tells me so. Yes, the bible tells me so – that’s how know who Jesus is, that He is the Creator, that he died and rose from the dead, and that He is our Savior.
0:14

This is the second of two posts I’m making about the teaching of Andy Stanley because I have a burden to warn people to be like the Bereans "examining the Scriptures daily to see if these things were so." (Acts 17:11). I have attached a short video clip where Stanley says we don’t know Jesus rose from the dead because the bible tells us so. He says it’s the other way around. Now how do we know Jesus bodily rose from the dead? Did any of us see it happen? No, it happened 2000 years ago. But haven’t people researched the resurrection and found all sorts of evidence consistent with Him rising from the dead. Yes, but such evidence, though powerful, and we can certainly use in our witnessing, does not ultimately prove He rose from the dead. In fact, no matter what evidence we point to in geology, biology, astronomy etc., none of this proves in an ultimate sense the bible is true. Now it is certainly true such evidence properly interpreted does confirm the bible’s history. For instance, the molecule of heredity DNA is a complex information system and language system. No one has seen matter produce information or a language from matter by natural processes. Our observations and experience show information and language have to come from an intelligence. Such evidence confirms an intelligence behind life. This certainly confirms the first verse of the bible, “In the beginning God created… .” But nonetheless, it’s not absolute proof. Think about it. We are finite beings living in the present. We don’t know everything. We don’t know how much we don’t know or do know in relation to whatever there is to know! When we try to interpret evidence of the present in relation to the past, how do we know we have all the relevant information to make the correct interpretation. Some information we don’t have could totally change our interpretation. That has certainly happened with scientists solving crimes using circumstantial evidence. When new evidence comes along, some of the interpretations change and certain people thought to be guilty were found they were innocent after-all. We need to have all the information needed. But we can’t know everything. However we have a book that claims over three thousand times to be the Word of God. This book claims that God moved people by His spirit to write His Word, what He wants revealed to us about life, the universe and history. This book, the bible, tells us that God knows everything, He is infinite in knowledge and wisdom. He has all information. “In whom are hidden all the treasures of wisdom and knowledge” (Colossians 2:3). If God’s Word is what it claims to be (and it is), then the infinite Creator God has revealed to us the key information we need to know to have the ability to correctly interpret this world in relation to the past, present and its purpose and meaning. “Therefore, we never stop thanking God that when you received his message from us, you didn’t think of our words as mere human ideas. You accepted what we said as the very word of God—which, of course, it is. And this word continues to work in you who believe” (1 Thessalonians 2:13). This means if we build our thinking on God’s Word, we build a Christian worldview to enable us to look at the world through “biblical glasses” and have the ability to correctly interpret and understand it. And Genesis 1-11 is the history that is foundational to the rest of the bible and thus our worldview. So, when we start with God’s Word we learn that the God revealed to us in the bible is the One Who created all things. Now by just looking at the world, for instance at DNA, we might deduce that there’s an intelligence behind life. But we would not know who that intelligence is unless revealed to us. The bible reveals who that intelligence is, God the father, Son, and Holy Spirit. But, if we just looked at the world with all its death, suffering and disease, we could assume that the intelligence behind life must be an ogre to make such a violent disease ridden suffering world. But when we start from God’s Word, we understand there was no death or disease to start with, but these entered the world because of sin. We also find man has a problem called sin which alienated him from God. We even find in Genesis that God promised someone would come to save us from our sin and restore our relationship with God (Genesis 3:15; 3:21). We learn later on that “someone” is Jesus--the one who became flesh for us, the babe in a manger 2000 years ago. It's important to understand we can’t know anything absolutely unless an absolute authority has revealed to us what we need to know. Now Andy Stanley claims we don’t know Jesus rose from the dead because the bible tells us so, but claims it’s the other way round, that because Jesus rose from the dead, we can believe what is says about this in the bible. In reality, Andy Stanley is actually claiming he knows all information about the resurrection to know it’s true so then he can proclaim what the bible says about the resurrection is true. This is not so. And remember from the previous post, Andy Stanley accepts man’s view of evolution and millions of years as true to declare what Genesis records about creation is not all true. So why shouldn't people take the word of others who claim Jesus didn't rise from the dead to then declare the account of the resurrection in the gospels can't be true. Stanley, as a finite fallen human being with very limited knowledge, starts outside the bible to go to the bible to make pronouncements over God’s written Word. No wonder he rejects a literal Genesis. Sadly, this is the case for the majority of our church leaders and Christian academics, particularly when it comes to Genesis. Think about it. Really Stanley is acting in accord with our sin nature because of what happened in Genesis 3. Part of our sin nature concerns us wanting to be our own god. Consider Genesis 3:1 and Genesis 3:5, the temptation by the devil. Satan tempted Adam and Eve to question God’s Word, and be want to be like God to decide good and evil, truth, etc., for themselves. In actuality, the statements Andy Stanley is making about Christianity and God’s Word are reflecting this sin problem we have. He is letting his sin nature master over him in this instance instead of letting God’s Word tell us clearly what we should believe. And I would say that about all Christians who reinterpret parts of the bible (like Genesis) because of beliefs from outside the bible. Now the whole bible is actually about Jesus, from the very first verse, that Jesus is the Creator (Colossians 1:16 “For by him all things were created,”), & and he is the Savior (Revelation 5:9), to the very last verse, “He who testifies to these things says, “Surely I am coming soon.” Amen. Come, Lord Jesus! The grace of the Lord Jesus be with all. Amen” (Revelation 22:20–21) God reveals all we need to know about Jesus in His Word. We know Jesus rose from the dead because the bible tells us so! We know we are sinners because the bible tells us so. We know we can be saved through faith in Christ because the bible tells us so. We know we need to repent of sin because the bible tells us so. As Christians we know we will spend eternity in Heaven because the bible tells us so. “So faith comes from hearing, and hearing through the word of God” (Romans 10:17). I still remember singing the chorus as a child Jesus loves me this I know, for the bible tells me so. Yes, the bible tells me so – that’s how know who Jesus is, that He is the Creator, that he died and rose from the dead, and that He is our Savior.

Ken Ham

233,976 просмотров • 3 лет назад

𝙏𝙝𝙚 𝙬𝙞𝙡𝙡 𝙤𝙛 𝙢𝙮 𝙁𝙖𝙩𝙝𝙚𝙧 For this is the will of my Father, that whosoever shall see the Son, and believe on him, have eternal life, and I will raise him up at the last day” (John 6:40). That "last day" is described in 1 Thessalonians 4:15-17 "For this we say to you by the word of the Lord, We who are alive and remain until the coming of the Lord shall by no means precede those who are asleep, for the Lord Himself shall descend from heaven with a signal, with the shouting of the archangel, and with the sound of the trump of God; and they that are dead in Christ shall rise first; then we who are alive and remain shall be caught up together with them in the clouds in the twinkling of an eye to meet the Lord in the air, and so shall we ever be with the Lord.”
0:18

𝙏𝙝𝙚 𝙬𝙞𝙡𝙡 𝙤𝙛 𝙢𝙮 𝙁𝙖𝙩𝙝𝙚𝙧 For this is the will of my Father, that whosoever shall see the Son, and believe on him, have eternal life, and I will raise him up at the last day” (John 6:40). That "last day" is described in 1 Thessalonians 4:15-17 "For this we say to you by the word of the Lord, We who are alive and remain until the coming of the Lord shall by no means precede those who are asleep, for the Lord Himself shall descend from heaven with a signal, with the shouting of the archangel, and with the sound of the trump of God; and they that are dead in Christ shall rise first; then we who are alive and remain shall be caught up together with them in the clouds in the twinkling of an eye to meet the Lord in the air, and so shall we ever be with the Lord.”

Benjamin Rapture Ready

13,449 просмотров • 6 месяцев назад

This is Tehran. Today, right around 10:15 AM. I want the world to hear this: life is flowing here. We are actually doing fine. For years, this occupying regime has choked our city in a permanent, toxic smog. We never get to see a blue sky. But look up today. The air is beautifully clear. The only darkness in the sky is the black pillar of smoke rising exactly where they struck the regime's oil depot. The poison is finally burning. The politicians and pundits in the West are terrified of escalation. They are begging for peace. But walking these streets, seeing the iron of our cage melting before our eyes, we are not afraid of the fire. We only have one true, suffocating fear: we are terrified that the strikes will stop before the rescue mission is finished. We are afraid of this regime's survival. And more than anything, we are afraid of losing our one real chance to end them for good.
0:14

This is Tehran. Today, right around 10:15 AM. I want the world to hear this: life is flowing here. We are actually doing fine. For years, this occupying regime has choked our city in a permanent, toxic smog. We never get to see a blue sky. But look up today. The air is beautifully clear. The only darkness in the sky is the black pillar of smoke rising exactly where they struck the regime's oil depot. The poison is finally burning. The politicians and pundits in the West are terrified of escalation. They are begging for peace. But walking these streets, seeing the iron of our cage melting before our eyes, we are not afraid of the fire. We only have one true, suffocating fear: we are terrified that the strikes will stop before the rescue mission is finished. We are afraid of this regime's survival. And more than anything, we are afraid of losing our one real chance to end them for good.

Decado

955,774 просмотров • 4 месяцев назад