I'm very surprised that this worked with the small amount of training data he provided! (he "provided the algorithm ten images containing hand written digits..." - if we generously estimate that each image has 10 training images, that's only 100 training examples)
Using Neural Networks to Evaluate Handwritten Mathematical Expressions
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Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#12I'm very surprised that this worked with the small amount of training data he provided! (he "provided the algorithm ten images containing hand written digits..." - if we generously estimate that each image has 10 training images, that's only 100 training examples)
Author here: I'm equally surprised it worked so well with such little training data. Each image contained 1 example of each character (18 total characters * 10 images = 180 examples). Having said that, I don't think it would generalize well to other people's handwriting until I provided a (lot) more training data.
Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#13Earlier quoted context omitted.
Having a single ANN do everything is the best way to end up with a system that works wonders 95% of the time, but then you give it a simple 1+1 question and it answers 42. It would also require way more neurons, and a lot of processing power. Consider the curse of dimensionality: he's working with a 5000ish dimensions vector, you have to make it simpler on the machine at some point!
But I can also recognize digits by correlating them against a database of millions of test-characters. Recognizing perfectly cropped characters is not a hard problem. The only benefit of an ANN is the compactness of the representation. So, unfortunately, as a non-expert, I would say this is only a minor step in the direction of true artificial intelligence. The application looks quite fun and interesting though.
That's because you're confusing ANN with General/Hard AI. It's not. ANN's are a tool which excells in clasically difficult tasks (pattern matching, for example). But since the AI winters we've learend that, as good as they're for pattern matching, we can't rely on them to do all the work.
And I would like to disagree with you. A system, with many small subsystems dedicated to specific tasks, is not only simpler to develop, but also better from an engineering point of view.
To put in a practical example: do you use the same "parts" of the brain to read a poem and to interpret a mathematical formula? If you would, you'd be quite bad at both things. your brain has specialized "parts" (not necesarily physical parts) to interpret correctly different things. Why should we not do the same with our AI systems?
Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#14I'm very surprised that this worked with the small amount of training data he provided! (he "provided the algorithm ten images containing hand written digits..." - if we generously estimate that each image has 10 training images, that's only 100 training examples)
Author here: I'm equally surprised it worked so well with such little training data. Each image contained 1 example of each character (18 total characters * 10 images = 180 examples). Having said that, I don't think it would generalize well to other people's handwriting until I provided a (lot) more training data.
Did you use any regularization? Did you train until the training accuracy converged?
I feel like the network has enough capacity to overfit 180 training samples
Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#15Earlier quoted context omitted.
Author here: I'm equally surprised it worked so well with such little training data. Each image contained 1 example of each character (18 total characters * 10 images = 180 examples). Having said that, I don't think it would generalize well to other people's handwriting until I provided a (lot) more training data.
Did you use any regularization? Did you train until the training accuracy converged? I feel like the network has enough capacity to overfit 180 training samples
I experimented with a few regularization factors and ultimately settled on a lambda of 0.1. Rather than using a stopping criteria, I ran a fixed number of training iterations (~100) and just eyeballed the cost function results. Since my total training time was fairly brief (~2 minutes, tops), I had the luxury of designing the ANN somewhat heuristically.
Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#16Finally, a method to compile all that whiteboard interview code.
Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#17Finally, a method to compile all that whiteboard interview code.
I can see it now: Syntax error.
Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#18Next step is have it output the LaTeX code. Wouldn't that be nice!
Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#19Will someone please build this into a mobile (tablet!) first version of Jupyter? Stop doing all these slightly-better-in-some-way-but-not-really things (Zeppelin, etc). You've lost. But I'm so frustrated trying to use Jupyter on a tablet. The compute model is perfect for using my tablet, but the UI just doesn't work that well.
What are you using Jupyter for that can actually be done on a tablet?
I couldn't imagine writing any new code on one...
Re: Using Neural Networks to Evaluate Handwritten Mathematical Expressions
#20Earlier quoted context omitted.
Having a single ANN do everything is the best way to end up with a system that works wonders 95% of the time, but then you give it a simple 1+1 question and it answers 42. It would also require way more neurons, and a lot of processing power. Consider the curse of dimensionality: he's working with a 5000ish dimensions vector, you have to make it simpler on the machine at some point!
But I can also recognize digits by correlating them against a database of millions of test-characters. Recognizing perfectly cropped characters is not a hard problem. The only benefit of an ANN is the compactness of the representation. So, unfortunately, as a non-expert, I would say this is only a minor step in the direction of true artificial intelligence. The application looks quite fun and interesting though.
The author probably could have used an ANN to segment the images as well before feeding it into another NN to classify the images. This has the benefit of re-using the character recognition network, which would better simulate what humans do, since we read new equations character by character into memory (unless we've seen so many that we begin chunking them like speed readers do with word groups)