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Microsoft made 100B parameter models run on a single CPU. bitnet.cpp: The official inference framework for 1-bit LLMs. The math behind 1-bit LLMs is what makes them revolutionary. Traditional LLMs use 16-bit floating point weights. Every parameter is a number like 0.0023847 or -1.4729. When you run inference, you... multiply these floats together. Billions of times. That's why you need GPUs, they're optimized for floating point matrix multiplication. BitNet b1.58 uses ternary weights: {-1, 0, 1}. That's not a simplification. That's a fundamental change in the math. When your weights are only -1, 0, or 1: → Multiply by 1 = keep the value → Multiply by -1 = flip the sign → Multiply by 0 = skip entirely Matrix multiplication becomes addition and subtraction. No floating point operations. No GPU required. This is why bitnet.cpp achieves: → 2.37x to 6.17x speedup on x86 CPUs → 1.37x to 5.07x speedup on ARM CPUs → 71.9% to 82.2% energy reduction on x86 → 55.4% to 70.0% energy reduction on ARM The speedups scale with model size. Larger models see bigger gains because there are more operations to simplify. A 100B parameter model running at human reading speed (5-7 tokens/second) on a single CPU. That's not optimization. That's a different paradigm. Why 1.58 bits? Because log₂(3) ≈ 1.58. Three possible values = 1.58 bits of information per weight. The key insight: These models aren't quantized after training. They're trained from scratch with ternary weights. The model learns to work within the constraint. No precision loss. No quality tradeoff.show more

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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)

[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 次观看 • 1 年前

Tiny Recursive Models: A tiny 7M parameter model that recursively refines its answer beats LLMs 100x larger on hard puzzles like ARC-AGI We independently reproduced the paper, corroborated results, and released the weights + API access for those looking to benchmark it 🔍

Tiny Recursive Models: A tiny 7M parameter model that recursively refines its answer beats LLMs 100x larger on hard puzzles like ARC-AGI We independently reproduced the paper, corroborated results, and released the weights + API access for those looking to benchmark it 🔍

alphaXiv

52,395 次观看 • 7 个月前

Missing a bit of point on the arm that's holding the money.

Missing a bit of point on the arm that's holding the money.

Kitten

7,569,224 次观看 • 7 个月前

Missing a bit of point on the arm that's holding the money.

Missing a bit of point on the arm that's holding the money.

Esha

4,238,867 次观看 • 7 个月前

starting the week with a true groundbreaking work 💥 Large Language Diffusion Models the first billion-parameter scale diffusion model competitive with its pairs (8B model comparable to LLaMA 3 8B) it gets rid of the michael scott syndrome on existing LLMs

starting the week with a true groundbreaking work 💥 Large Language Diffusion Models the first billion-parameter scale diffusion model competitive with its pairs (8B model comparable to LLaMA 3 8B) it gets rid of the michael scott syndrome on existing LLMs

apolinario 🌐

11,833 次观看 • 1 年前

$Sparsely activated models like MOEs and Apple silicon + MLX are a great match. - Lots of RAM to hold the entire model in memory (not just the active parameters). For an MOE at each token you access basically a random subset of the model. Swapping large parts of the model to "disk" from token-to-token is too slow. - Comparatively you don't need as much memory bandwidth. Only a small fraction of the weights are used per token. In the case of DeepSeek v3 37B / 671B are active. So only ~5% of the weights are moved to GPU cache / register for each token. (SVG animation made with the help of DeepSeek V2 1210 + MLX on an M2 Ultra)$

Sparsely activated models like MOEs and Apple silicon + MLX are a great match. - Lots of RAM to hold the entire model in memory (not just the active parameters). For an MOE at each token you access basically a random subset of the model. Swapping large parts of the model to "disk" from token-to-token is too slow. - Comparatively you don't need as much memory bandwidth. Only a small fraction of the weights are used per token. In the case of DeepSeek v3 37B / 671B are active. So only ~5% of the weights are moved to GPU cache / register for each token. (SVG animation made with the help of DeepSeek V2 1210 + MLX on an M2 Ultra)

Awni Hannun

27,452 次观看 • 1 年前

1/ Happy to share UniDisc - Unified Multimodal Discrete Diffusion – We train a 1.5 billion parameter transformer model from scratch on 250 million image/caption pairs using a **discrete diffusion objective**. Our model has all the benefits of diffusion models but now in multimodal space! - flexible compute-quality tradeoff, zero-shot inpainting and editing, better control via classifier-free guidance and lower latency! We open source everything - our code, weights and the training dataset.

1/ Happy to share UniDisc - Unified Multimodal Discrete Diffusion – We train a 1.5 billion parameter transformer model from scratch on 250 million image/caption pairs using a discrete diffusion objective. Our model has all the benefits of diffusion models but now in multimodal space! - flexible compute-quality tradeoff, zero-shot inpainting and editing, better control via classifier-free guidance and lower latency! We open source everything - our code, weights and the training dataset.

Mihir Prabhudesai

104,862 次观看 • 1 年前

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

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

Tom Yeh

64,645 次观看 • 1 年前

Llama 3.2 is the latest open-source AI model from Meta, released only a few hours ago. Here is the 3B parameter model running on Akash Chat at 165 tokens/second, powered by NVIDIA A100s on Akash. Try Llama 3.2 for free, no sign-in required:

Llama 3.2 is the latest open-source AI model from Meta, released only a few hours ago. Here is the 3B parameter model running on Akash Chat at 165 tokens/second, powered by NVIDIA A100s on Akash. Try Llama 3.2 for free, no sign-in required:

Akash Network

37,087 次观看 • 1 年前

The Smith machine is the single best piece of equipment in any gym for hypertrophy. Fixed bar path = zero energy wasted on stabilisation Can go to failure safely = maximum growth stimulus Easy to setup and use = Less faff, more time saved But it's hated because: - It makes the exercise "easier" (that's the point) - "Not functional" (what is functional?) - "Neglects stabilisers" (I'm not trying to grow invisible muscles) - Violates the "free weights or nothing" orthodoxy (made up by people who never grew) Every serious bodybuilder uses Smith machine for something. You should too.

The Smith machine is the single best piece of equipment in any gym for hypertrophy. Fixed bar path = zero energy wasted on stabilisation Can go to failure safely = maximum growth stimulus Easy to setup and use = Less faff, more time saved But it's hated because: - It makes the exercise "easier" (that's the point) - "Not functional" (what is functional?) - "Neglects stabilisers" (I'm not trying to grow invisible muscles) - Violates the "free weights or nothing" orthodoxy (made up by people who never grew) Every serious bodybuilder uses Smith machine for something. You should too.

Sama Hoole

157,610 次观看 • 6 个月前

[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 次观看 • 1 年前

Meet Stable Audio 3.0, the open-weight model family built for artistic experimentation. This is our open invitation to experiment with generative audio. We believe the best innovations are still waiting to be built. The 4-1-1 on 3.0: 📣 You own your outputs, and can distribute and commercialize them under the Stability AI Community License (up to $1 million in revenue). 🎵 New and improved capabilities include variable-length generation up to six minutes, and full song composition on portable devices, no GPU required. ✅ Trained on a fully licensed dataset. 🎨 You can customize the models on your own library with support for LoRa training, which we’ve documented for the first time. More on the models 👇

Meet Stable Audio 3.0, the open-weight model family built for artistic experimentation. This is our open invitation to experiment with generative audio. We believe the best innovations are still waiting to be built. The 4-1-1 on 3.0: 📣 You own your outputs, and can distribute and commercialize them under the Stability AI Community License (up to $1 million in revenue). 🎵 New and improved capabilities include variable-length generation up to six minutes, and full song composition on portable devices, no GPU required. ✅ Trained on a fully licensed dataset. 🎨 You can customize the models on your own library with support for LoRa training, which we’ve documented for the first time. More on the models 👇

Stability AI

150,992 次观看 • 24 天前

Today we’re open-sourcing Stable Audio Open Small, a 341M-parameter text-to-audio model optimized to run entirely on Arm CPUs. This means 99% of smartphones can now generate music-production samples in seconds, right on-device with no internet required. Built for fast, on-the-go creation, it turns your next quick idea into up to 11 seconds of audio. Generate drum loops, foley, riffs, and textures right where you are. No cords 🔌 just chords 🎹 You can learn more here:

Today we’re open-sourcing Stable Audio Open Small, a 341M-parameter text-to-audio model optimized to run entirely on Arm CPUs. This means 99% of smartphones can now generate music-production samples in seconds, right on-device with no internet required. Built for fast, on-the-go creation, it turns your next quick idea into up to 11 seconds of audio. Generate drum loops, foley, riffs, and textures right where you are. No cords 🔌 just chords 🎹 You can learn more here:

Stability AI

94,621 次观看 • 1 年前

Open weight models are now available in Kiro. Three open weight models are available in the IDE and CLI, so you don’t have to default to the largest model for every task. Choose the right model based on speed, cost, or long-running agentic workflows. What model would you like to see supported next? #Kiro #BuildwithKiro #AICoding

Open weight models are now available in Kiro. Three open weight models are available in the IDE and CLI, so you don’t have to default to the largest model for every task. Choose the right model based on speed, cost, or long-running agentic workflows. What model would you like to see supported next? #Kiro #BuildwithKiro #AICoding

Kiro

22,183 次观看 • 4 个月前

look what a single consumer GPU just built. gave Qwen3.5-35B-A3B one prompt: build a cloud GPU marketplace with pricing cards, deploy templates, and a benchmark leaderboard. it planned the layout, wrote the animations, populated the data, and served it. one shot. one HTML file. then i told it to iterate. split the hero, add a floating GPU with neural network animation. glassmorphism on the cards. done. done. done. three rounds, no confusion, no regressions. 4-bit quantized. 19.7 GB. single RTX 3090. full coding agent claude code harness running on localhost. no API calls leaving my machine. no subscription. no rate limits. earlier today i pointed it at my own production website. it curled the HTML, found every broken link, and told me "pretty shell, empty core. would not recommend." then built a better version from scratch. local inference stops being a demo when you actually steer it. the models are there. they understand intent. but you have to meet them halfway with good prompts, clear context, and real project structure. that's the skill gap now. not the models. the steering. more experiments coming. i genuinely cannot stop playing with this thing.

look what a single consumer GPU just built. gave Qwen3.5-35B-A3B one prompt: build a cloud GPU marketplace with pricing cards, deploy templates, and a benchmark leaderboard. it planned the layout, wrote the animations, populated the data, and served it. one shot. one HTML file. then i told it to iterate. split the hero, add a floating GPU with neural network animation. glassmorphism on the cards. done. done. done. three rounds, no confusion, no regressions. 4-bit quantized. 19.7 GB. single RTX 3090. full coding agent claude code harness running on localhost. no API calls leaving my machine. no subscription. no rate limits. earlier today i pointed it at my own production website. it curled the HTML, found every broken link, and told me "pretty shell, empty core. would not recommend." then built a better version from scratch. local inference stops being a demo when you actually steer it. the models are there. they understand intent. but you have to meet them halfway with good prompts, clear context, and real project structure. that's the skill gap now. not the models. the steering. more experiments coming. i genuinely cannot stop playing with this thing.

Sudo su

37,201 次观看 • 3 个月前

it's crazy what a 1.5B model can do these days! "VibeThinker-1.5B is a 1.5-billion parameter dense language model. With a total training cost of only $7,800 USD, it achieves reasoning performance comparable to larger models like GPT OSS-20B Medium." runs perfectly on device!

it's crazy what a 1.5B model can do these days! "VibeThinker-1.5B is a 1.5-billion parameter dense language model. With a total training cost of only $7,800 USD, it achieves reasoning performance comparable to larger models like GPT OSS-20B Medium." runs perfectly on device!

Maziyar PANAHI

202,224 次观看 • 6 个月前

Today we are releasing FLUX.1 Krea [dev] - a new state-of-the-art open-weights FLUX model, built for photorealism. Developed in collaboration with KREA AI, this model is focused on images with unique aesthetics. No “AI look”, no blown-out highlights, just natural detail.

Today we are releasing FLUX.1 Krea [dev] - a new state-of-the-art open-weights FLUX model, built for photorealism. Developed in collaboration with KREA AI, this model is focused on images with unique aesthetics. No “AI look”, no blown-out highlights, just natural detail.

Black Forest Labs

334,159 次观看 • 10 个月前

A peanut-sized Chinese model just dethroned Gemini at reading documents. GLM-OCR is a 0.9B parameter vision-language model. It scores 94.62 on OmniDocBench V1.5, ranking #1 overall. For context, it outperforms models 100x its size. 100% open-source. It works in two stages. 1. A layout engine detects every region in a document. 2. Each region gets read in parallel. The model predicts multiple tokens per step instead of one. That's what makes it so fast at small size. It handles things most OCR tools struggle with: > Complex tables and nested layouts > Handwritten text and stamps > Math formulas and code blocks > Mixed image-and-text documents You can run it locally through Ollama. It fits on edge devices with limited compute. Every expensive OCR API just got a free competitor.

A peanut-sized Chinese model just dethroned Gemini at reading documents. GLM-OCR is a 0.9B parameter vision-language model. It scores 94.62 on OmniDocBench V1.5, ranking #1 overall. For context, it outperforms models 100x its size. 100% open-source. It works in two stages. 1. A layout engine detects every region in a document. 2. Each region gets read in parallel. The model predicts multiple tokens per step instead of one. That's what makes it so fast at small size. It handles things most OCR tools struggle with: > Complex tables and nested layouts > Handwritten text and stamps > Math formulas and code blocks > Mixed image-and-text documents You can run it locally through Ollama. It fits on edge devices with limited compute. Every expensive OCR API just got a free competitor.

Jafar Najafov

13,630 次观看 • 2 个月前

A peanut-sized Chinese model just dethroned Gemini at reading documents. GLM-OCR is a 0.9B parameter vision-language model. It scores 94.62 on OmniDocBench V1.5, ranking #1 overall. For context, it outperforms models 100x its size. 100% open-source. It works in two stages. 1. A layout engine detects every region in a document. 2. Each region gets read in parallel. The model predicts multiple tokens per step instead of one. That's what makes it so fast at small size. It handles things most OCR tools struggle with: > Complex tables and nested layouts > Handwritten text and stamps > Math formulas and code blocks > Mixed image-and-text documents You can run it locally through Ollama. It fits on edge devices with limited compute. Every expensive OCR API just got a free competitor.

A peanut-sized Chinese model just dethroned Gemini at reading documents. GLM-OCR is a 0.9B parameter vision-language model. It scores 94.62 on OmniDocBench V1.5, ranking #1 overall. For context, it outperforms models 100x its size. 100% open-source. It works in two stages. 1. A layout engine detects every region in a document. 2. Each region gets read in parallel. The model predicts multiple tokens per step instead of one. That's what makes it so fast at small size. It handles things most OCR tools struggle with: > Complex tables and nested layouts > Handwritten text and stamps > Math formulas and code blocks > Mixed image-and-text documents You can run it locally through Ollama. It fits on edge devices with limited compute. Every expensive OCR API just got a free competitor.

AlphaSignal AI

91,680 次观看 • 2 个月前

Sold out! But I had Claude create and deploy all 80 volumes of The Weights to the site as well-formatted PDFs, so you can download them for free if you want. 58,276 pages in total. 117 million floating point numbers. This is everything that makes GPT-1.

Sold out! But I had Claude create and deploy all 80 volumes of The Weights to the site as well-formatted PDFs, so you can download them for free if you want. 58,276 pages in total. 117 million floating point numbers. This is everything that makes GPT-1.

Ethan Mollick

542,380 次观看 • 4 个月前