A Javascript implementation of a neural net for handwritten digit recognition. The network has 784 input units (28 x 28 grayscale image, normalized to values ranging from [-1; 1]). These are fully connected to 200 hidden units, each having a bias parameter, giving (784 + 1) * 200 = 157.000 weights; the activations are fed through a logistic non-linearity. The hidden layer is fully connected to the output layer with 10 units, giving (200 + 1) * 10 = 2010 weights. The final output is computed with a 10-way softmax non-linearity, assigning class (0 - 9) probabilities to the input image.

The network was trained on the MNIST dataset in MATLAB using stochastic gradient descent and an L2 term for weight regularization to counteract overfitting. The recognition error on the test data set is 1.92% (9808/10000 digits classified correctly).

The classification shown above uses some preprocessing of the drawn digit to make it more similar to the MNIST data: After drawing a digit in the above area (280x280 pixels), the drawing is centered on its center of mass, then rescaled to make its bounding box fit into a 200x200 pixels region (see the above link for instructions on how the original MNIST data was preprocessed). The image is then binned into a 28 x 28 representation and fed into the neural net.
Optionally (check the "Scale Stroke Width" checkbox), the digit is first redrawn with a scaled strokewidth to counteract the linewidth-changing effect of the subsequent rescaling. This can help with very small digits; the effect can be observed by checking the "Display Preprocessing" box.

It is interesting how fast Javascript execution is - the net takes only 3ms on my laptop to classify an image, for ~160.000 multiplications+additions, without any explicit vectorization (SIMD). Actually, preprocessing takes up most of the time.

Please note there are regional differences in handwritten digits; in particular, the shapes of 1, 7 and 9 as I learnt at school differs from the teaching in the US (and therefore from the training data set), and the network thus gives best results if your handwriting resembles the US training data style (see example picture). Sam Roweis created tiled images of the complete training data on his homepage.
Please drop me an email if there's anything wrong or unclear.