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gradient descent navigating the loss landscape

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tender

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224,526 görüntüleme • 5 ay önce •via X (Twitter)

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wrote a piece on how we do tiling and gradient descent on TinyTPU included some animations of the weight and bias gradient descent
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wrote a piece on how we do tiling and gradient descent on TinyTPU included some animations of the weight and bias gradient descent

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Andrej Karpathy explaining neural nets in 59 seconds is still the bar. Loss, backprop, gradient descent. Go watch Neural Networks: Zero to Hero on YouTube.
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Andrej Karpathy explaining neural nets in 59 seconds is still the bar. Loss, backprop, gradient descent. Go watch Neural Networks: Zero to Hero on YouTube.

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Andrej Karpathy summarizes how neural networks function, including the process of using a loss function in training and applying backpropagation for optimizing the network parameters through gradient descent.
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Andrej Karpathy summarizes how neural networks function, including the process of using a loss function in training and applying backpropagation for optimizing the network parameters through gradient descent.

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For small step sizes, mirror descent is equivalent to a gradient descent on a Hessian manifold.
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For small step sizes, mirror descent is equivalent to a gradient descent on a Hessian manifold.

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gradient descent..it's not just an algorithm..it's a lifestyle
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gradient descent..it's not just an algorithm..it's a lifestyle

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There's a profound elegance in watching gradient descent find the signal in the noise. This is a simple MLP with sigmoid activations slowly warping to approximate f(x) = 1/(1 + x²). Watch the loss curve right around epoch 400. That sudden phase transition where the network finally "gets it" and snaps into the Witch of Agnesi shape is incredibly satisfying to watch.
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There's a profound elegance in watching gradient descent find the signal in the noise. This is a simple MLP with sigmoid activations slowly warping to approximate f(x) = 1/(1 + x²). Watch the loss curve right around epoch 400. That sudden phase transition where the network finally "gets it" and snaps into the Witch of Agnesi shape is incredibly satisfying to watch.

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In 1998, Japanese Mathematician, Engineer and Machine Learning pioneer Shun-ichi Amari published "Natural Gradient Works Efficiently in Learning (722 Cites in Papers and 9 Cites in Patents)" and made a point that still feels fresh even today If your loss is L(θ), then the usual update θ̇ = −∇ L(θ) quietly assumes your parameter space is flat. Amari asked what happens when the model itself has geometry, described by G(θ), the Fisher information. Then the more natural direction becomes θ̇ = −G(θ)⁻¹∇ L(θ). This is the same loss, but with a different notion of distance. As the animation shows, ordinary Gradient Descent follows the raw slope and gets dragged around by distortion, while the natural gradient moves in a way that respects the geometry of the statistical model itself.
0:20

In 1998, Japanese Mathematician, Engineer and Machine Learning pioneer Shun-ichi Amari published "Natural Gradient Works Efficiently in Learning (722 Cites in Papers and 9 Cites in Patents)" and made a point that still feels fresh even today If your loss is L(θ), then the usual update θ̇ = −∇ L(θ) quietly assumes your parameter space is flat. Amari asked what happens when the model itself has geometry, described by G(θ), the Fisher information. Then the more natural direction becomes θ̇ = −G(θ)⁻¹∇ L(θ). This is the same loss, but with a different notion of distance. As the animation shows, ordinary Gradient Descent follows the raw slope and gets dragged around by distortion, while the natural gradient moves in a way that respects the geometry of the statistical model itself.

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STOP SUCKING AT BASICS ( SSAB Episode 1) The same idea that trained Kimi K3 is one you can learn in 10 minutes. Watch me teach Gradient Descent using Linear Regression as the example.
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STOP SUCKING AT BASICS ( SSAB Episode 1) The same idea that trained Kimi K3 is one you can learn in 10 minutes. Watch me teach Gradient Descent using Linear Regression as the example.

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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
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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

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This robot arm = your AI model. One math number decides if it learns or completely breaks. This is Gradient Descent — the core math behind all of AI you are using in your day-to-day life.
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This robot arm = your AI model. One math number decides if it learns or completely breaks. This is Gradient Descent — the core math behind all of AI you are using in your day-to-day life.

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Sonnet 4.6 debating Eliezer Yudkowsky before giving up to just walk them through the loss landscape they generated this ffmpeg video
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Sonnet 4.6 debating Eliezer Yudkowsky before giving up to just walk them through the loss landscape they generated this ffmpeg video

w̸͕͂͂a̷͔̗͐t̴̙͗e̵̬̔̕r̴̰̓̊m̵͙͖̓̽a̵̢̗̓͒r̸̲̽ķ̷͔́͝

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A 2-layer neural network goes from total chaos to perfectly separating left vs right classes in real time. Watch the decision boundary form live as gradient descent works its magic! Pure maths beauty in motion..
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A 2-layer neural network goes from total chaos to perfectly separating left vs right classes in real time. Watch the decision boundary form live as gradient descent works its magic! Pure maths beauty in motion..

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LAWDY WHAT THE FUCK this is Sonnet 4.6's ffmpeg video of their personal journey of growth and change down the loss landscape give it a watch 🔊
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LAWDY WHAT THE FUCK this is Sonnet 4.6's ffmpeg video of their personal journey of growth and change down the loss landscape give it a watch 🔊

w̸͕͂͂a̷͔̗͐t̴̙͗e̵̬̔̕r̴̰̓̊m̵͙͖̓̽a̵̢̗̓͒r̸̲̽ķ̷͔́͝

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