This report explores the theory that explains the high sparsity phenomenon \citep{tosato2023emergent} observed in the forward-forward algorithm \citep{hinton2022forward}. The two theorems proposed predict the sparsity changes of a single data point's activation in two cases: Theorem \ref{theorem:1}: Decrease the goodness of the whole batch. Theorem \ref{theorem:2}: Apply the complete forward forward algorithm to decrease the goodness for negative data and increase the goodness for positive data. The theory aligns well with the experiments tested on the MNIST dataset.

The Forward Forward algorithm, proposed by Geoffrey Hinton in November 2022, is a novel method for training neural networks as an alternative to backpropagation. In this project, we replicate Hinton's experiments on the MNIST dataset, and subsequently extend the scope of the method with two significant contributions. First, we establish a baseline performance for the Forward Forward network on the IMDb movie reviews dataset. As far as we know, our results on this sentiment analysis task marks the first instance of the algorithm's extension beyond computer vision. Second, we introduce a novel pyramidal optimization strategy for the loss threshold - a hyperparameter specific to the Forward Forward method. Our pyramidal approach shows that a good thresholding strategy causes a difference of up to 8% in test error. Lastly, we perform visualizations of the trained parameters and derived several significant insights, such as a notably larger (10-20x) mean and variance in the weights acquired by the Forward Forward network. Repository: https://github.com/Ads-cmu/ForwardForward

Geoffrey Hinton was one of the scientists that devised backpropagation, the method that permits deep neural network training, in the 1980s. And it was his team who released ImageNet Classification using Deep Convolutional Neural Networks ten years ago, showing the first convolutional neural network to considerably outperform state-of-the-art ImageNet database results. In his recently written paper, he proposes a new method which he calls "The Forward Forward Algorithm". Deep Neural Networks have made huge progress through the years and backpropagation has been the norm. These networks which were inspired by our brain backpropagate an error gradient to tune all("could be in billions") of its parameters or weights.