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The second is a fancy function that turns the elements of your matrix. Output vector into a valid probability distribution (all entries sum to one, all are greater than zero). Changing the entries of your matrix changes your 10 hyperplanes. Your output is your input ‘image’ dot Nice Oh The Places You’ll Go When You Read Shirt. The biggest value is what you say the number was. So the act of training your logistic regression classifier is. Effectively the act of finding the perfect 10 hyperplanes, where any hand-written digit sent in. Will be farthest off the hyperplane representing that number. Most people who study that stuff aren’t doing original math. They’re learning so they can understand the methods they need to use to do cool stuff. That’s a perfectly acceptable reason to pursue math, there are whole generations. Of engineers seriously benefited from the math they’ve known.

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It sounds to me like you aren’t sure what your WORK will be yet. From the sounds of it, it’ll at least be math adjacent. A math major would likely serve you well in all kinds of other fields, but if you could figure out your deeper interests (what area of math? Is it pure math you’re Nice Oh The Places You’ll Go When You Read Shirt first place? Maybe you’re more practical than that?) then maybe. You’ll be able to more directly head towards what you’re interested in. This kind of math is the way that artificial intelligence often approaches automated theorem proving. You can take math ‘code’ like that, and turn it into a graph, and then have a graph neural network (GNN) do its magic. Theorems as vector embeddings, chewed through by networks not all that different by the simple logistic regression deal I described above. Nonsense, it’s crazy that it can work.

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