MachineLearningToGo
@machinelearningtogo • 27,700 subscribers
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➡️ Part 9 of learning ML code from scratch Six weights, one wrong answer, and not one of them knows it was at fault. Backpropagation is how they find out. Two questions guide the video: what even is backpropagation, and why do models need it? Step 1, the forward pass. Two numbers go into a tiny network, run through a hidden layer, and one number comes out. Ours says 0.700. We wanted 1.0, so square the difference and the loss is 0.09. That single number is how wrong the model is. Step 2, the question. Six weights produced that answer together. Which of them is to blame, and by how much? Step 3, the one idea. Change a single weight by a tiny amount and watch the error move. How much the error changes per unit of weight is the gradient of that weight. In the video you can see it happen: the weight wobbles and the error bar answers. Step 4, the shortcut. Every weight running into the same neuron starts from one shared number, the blame of that neuron. Multiply that blame by the value each weight carried and you have its gradient. One blame, computed once, and every weight into that neuron gets its own gradient from it. That is why backpropagation is fast enough to train anything at all. Step 5, backwards. The blame starts at the output and every layer hands its share to the layer in front of it, back through the same network the data came forward through. It goes layer by layer, and inside one layer every neuron is done together. Step 6, the update. The optimizer moves every weight against its own gradient, the whole weight matrix in one go, so no weight waits for its turn. All six gradients here are negative, so all six weights go up. After one step the answer reads 0.769. After sixty it reads 0.968 and the error is down to 0.001. The honest part: every gradient in the video was checked against the measured change of the error. Move that one weight, see what the error does, divide. Backprop and the measurement agree to nine decimal places, otherwise nothing would have rendered. #machinelearning #backpropagation #neuralnetworks #python #coding
MachineLearningToGo209,900 просмотров • 1 месяц назад
➡️ Machine Learning from Scratch, part 31: the transformer. A transformer turns every token into a list of numbers, adds its position, and then lets every token look at the others. That step is called attention: each token has a query (what am I looking for), a key (what do I contain) and a value (what I pass on). The better a query matches a key, the more of that value flows in. Real transformers repeat this in many layers with several attention heads each. The design comes from the 2017 Google paper "Attention Is All You Need" by Ashish Vaswani and colleagues, first used for translation. A large language model is a transformer trained to predict the next token, again and again, on a huge amount of text. Our own run, nothing downloaded. attention.py is one self-attention layer in 16 lines of numpy. Every word gets a query, a key and a value of 8 numbers, starting random, trained from scratch with hand-written backpropagation on 192 made-up sentences like "the dog ate the carrot because it was hungry". The task: find out which pet "it" means. On 64 new test sentences "it" puts 99.95 percent of its attention on the right word on average (the lowest single sentence gets 99.9 percent; the program prints this as 100%). Before training it was 10 percent, spread evenly. The cat sentence from the video is one of the test sentences. Honest notes: our task is easy on purpose. Every sentence has exactly one pet, so "it" only has to learn to look for pets, and it learns that within the first pass. Real sentences with two candidates need more context, which is what many layers are for. Our small version has no positions, no scaling, no mask, one head, and only "it" asks a question. Every word of the test sentences also appears in training; the combinations are new. The 3D space in the video shows the real keys of our model, projected to three axes (two of them stretched so you can see them). The stacked layers are a sketch. #machinelearning #ai #transformer #python #llm
MachineLearningToGo79,400 просмотров • 1 месяц назад
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