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Trained a single layer neural network in C to predict AND GATE from scratch using gradient descent and Batch training of dataset in almost 300K epochs

AADITYANSHA

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81,395 görüntüleme • 5 ay önce •via X (Twitter)

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Implemented a visualization for the neural network today. This is a neural network being trained to learn the snake game in a terminal. It's built in Rust using Ratatui More input details in thread

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ℏεsam

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ℏεsam

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I vibecoded this neural network visualization for my students and open sourced it. It shows a simple MLP trained on MNIST handwritten digits at several training steps. The visualization is using Three.js and it comes with training code in PyTorch . Link + repo 👇

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Gradient descent doesn't find the global minimum - it finds whatever valley it falls into first. Every LLM trained today gets stuck in a local minimum and nobody can prove the solution it found is anywhere near optimal. The loss landscape of GPT-4 has more dimensions than atoms in the observable universe. Convex optimization guarantees a global minimum exists and gradient descent finds it. Non-convex optimization - the kind every neural network uses - offers no such guarantee. The entire field of deep learning is built on the empirical observation that local minima are good enough. 22 minutes. Bookmark & watch today. The math behind every AI training run - and why nobody fully understands why it works.

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Ollin Boer Bohan

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With Helix 02, Figure has introduced a new foundational layer for whole-body control that replaces 109k lines of hand-engineered C++ with a single neural prior for stable, natural motion. - Learned from 1,000+ hours of human motion data and sim-to-real RL across 200,000+ parallel environments. - A 10M-parameter neural network that takes full-body joint state and base motion as input and outputs joint-level actuator commands at 1 kHz (1,000 times a second).

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randy

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Motion planning in complex tasks is hard and still done via slow, explicit, traditional planners. We present a generalist Neural Motion Planner -- a single neural network that plans complex dynamic motions quickly and accurately at test time. Building upon our lab's sim2real efforts, the key idea is to create many complex scenes in simulation and then distill classical motion planner trajectories into a single reactive neural network policy. More details in the thread below! 👇 Open-sourced:

Motion planning in complex tasks is hard and still done via slow, explicit, traditional planners. We present a generalist Neural Motion Planner -- a single neural network that plans complex dynamic motions quickly and accurately at test time. Building upon our lab's sim2real efforts, the key idea is to create many complex scenes in simulation and then distill classical motion planner trajectories into a single reactive neural network policy. More details in the thread below! 👇 Open-sourced:

Deepak Pathak

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Backpropagation by hand ✍️ ~ 11 steps walkthrough below Backpropagation is the algorithm that actually trains a neural network, and it is where most people stop following along. It is not calculus you cannot do. It is matrix multiplication, working backward, one layer at a time. So I drew and calculated one entirely by hand. Goal: push the loss gradient back through a 3-layer network and land on a new value for every weight and bias. = 1. Given = A 3-layer perceptron, an input X, predictions Ypred = [0.5, 0.5, 0], and the truth Ytarget = [0, 1, 0]. = 2. Backprop gradient cells = Let us draw empty cells for every gradient we are about to compute. The shape of the answer comes first. = 3. Layer 3 softmax = We get dL/dz3 straight from Ypred minus Ytarget = [0.5, -0.5, 0]. No chain rule needed, and that shortcut is the whole reason softmax and cross-entropy are paired. = 4. Layer 3 weights and biases = Let us multiply dL/dz3 by [a2 | 1]. One multiplication gives the gradient for W3 and b3 together. = 5. Layer 2 activations = We multiply dL/dz3 by W3 to get dL/da2. The gradient moves back across a layer the same way the signal moved forward. = 6. Layer 2 ReLU = Let us pass it through the gate: keep the gradient where the activation was positive, zero it everywhere else. = 7. Layer 2 weights and biases = We multiply dL/dz2 by [a1 | 1]. The same figure as step 4, one layer up. = 8. Layer 1 activations = Let us multiply dL/dz2 by W2. = 9. Layer 1 ReLU = We apply the same gate again, now on a1. = 10. Layer 1 weights and biases = Let us multiply dL/dz1 by [x | 1], and every weight in the network now has a gradient. = 11. Update = We subtract, and the network has learned. In practice a learning rate scales this step. The gradients: dL/dz3 = [0.5, -0.5, 0] dL/da1 = [1, -2, 2, -1] dL/dz1 = [0, -2, 2, -1] The takeaway: matrix multiplication is all you need. Just like the forward pass, backpropagation is matrix multiplications end to end. You can do every one by hand, slowly and imperfectly, which is exactly why a GPU's ability to do them fast mattered so much to deep learning. 💾 Save this post!

Backpropagation by hand ✍️ ~ 11 steps walkthrough below Backpropagation is the algorithm that actually trains a neural network, and it is where most people stop following along. It is not calculus you cannot do. It is matrix multiplication, working backward, one layer at a time. So I drew and calculated one entirely by hand. Goal: push the loss gradient back through a 3-layer network and land on a new value for every weight and bias. = 1. Given = A 3-layer perceptron, an input X, predictions Ypred = [0.5, 0.5, 0], and the truth Ytarget = [0, 1, 0]. = 2. Backprop gradient cells = Let us draw empty cells for every gradient we are about to compute. The shape of the answer comes first. = 3. Layer 3 softmax = We get dL/dz3 straight from Ypred minus Ytarget = [0.5, -0.5, 0]. No chain rule needed, and that shortcut is the whole reason softmax and cross-entropy are paired. = 4. Layer 3 weights and biases = Let us multiply dL/dz3 by [a2 | 1]. One multiplication gives the gradient for W3 and b3 together. = 5. Layer 2 activations = We multiply dL/dz3 by W3 to get dL/da2. The gradient moves back across a layer the same way the signal moved forward. = 6. Layer 2 ReLU = Let us pass it through the gate: keep the gradient where the activation was positive, zero it everywhere else. = 7. Layer 2 weights and biases = We multiply dL/dz2 by [a1 | 1]. The same figure as step 4, one layer up. = 8. Layer 1 activations = Let us multiply dL/dz2 by W2. = 9. Layer 1 ReLU = We apply the same gate again, now on a1. = 10. Layer 1 weights and biases = Let us multiply dL/dz1 by [x | 1], and every weight in the network now has a gradient. = 11. Update = We subtract, and the network has learned. In practice a learning rate scales this step. The gradients: dL/dz3 = [0.5, -0.5, 0] dL/da1 = [1, -2, 2, -1] dL/dz1 = [0, -2, 2, -1] The takeaway: matrix multiplication is all you need. Just like the forward pass, backpropagation is matrix multiplications end to end. You can do every one by hand, slowly and imperfectly, which is exactly why a GPU's ability to do them fast mattered so much to deep learning. 💾 Save this post!

Tom Yeh

961,186 görüntüleme • 1 ay önce