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Autoencoder by hand✍️Excel~ I designed this exercise to show how an Encoder-Decoder network convert input to code and reconstruct input from code. It is annotated with equations, PyTorch, and graphs. 👇Join the 'AI Math' community. Download xlsx.

101,555 Aufrufe • vor 1 Jahr •via X (Twitter)

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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

48,475 Aufrufe • vor 2 Jahren

MLP in PyTorch by hand ✍️ ~ 7 steps walkthrough below Goal: fill in every blank in the PyTorch code to build a multi-layer perceptron. 1. Given Let us start with a code template on the left and the network it is supposed to build on the right. Every blank in the code can be worked out from the picture. 2. Linear layer We count: 3 features in, 4 features out. So the weight matrix is 4 by 3. There is an extra column for the biases, which means bias = T. 3. ReLU Let us apply the activation. ReLU crosses out the negatives, so -1 becomes 0. 4. Linear layer The input size is 4, because that is what the previous layer put out. The output size is 2. A 2 by 4 weight matrix, and this time no extra column, so bias = F. 5. ReLU We cross out the negatives again. 6. Linear layer Two features in, five out. A 5 by 2 weight matrix, with a bias column, so bias = T. 7. Sigmoid Let us finish. Sigmoid squashes the raw scores (3, 0, -2, 5, -5) into probabilities between 0 and 1. You have just implemented a three-layer deep neural network by hand. ✍️ == Story == Three years ago I gave this exercise to my students, to connect the code to the math. They found it odd. Every other AI course they were taking lived inside a Jupyter notebook, and here I was handing out paper. Three years later, my colleagues are the ones rushing to move their materials to paper. The exercise has not changed. Paper still asks the one thing a notebook lets you skip: do you actually understand what the code is doing? If you can tell me why the weight matrix is 4 by 3, and why bias is F on the second layer, you understand nn.Linear better than someone who has been copy-pasting it for a year. 💾 Save this post! #AIbyHand #PyTorch #DeepLearning

Tom Yeh

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