Neural message-passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of this utilized neighbourhood is hard to extend. This paper uses the relationship between graph convolutional networks (GCN) and PageRank to derive an improved propagation scheme based on personalized PageRank. We utilize this propagation procedure to construct a simple model, personalized propagation of neural predictions (PPNP), and its fast approximation, APPNP. Our model's training time is on par or faster and its number of parameters is on par or lower than previous models. It leverages a large, adjustable neighbourhood for classification and can be easily combined with any neural network. We show that this model outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models.

**GHM-R** is a loss function designed to balance the gradient flow for bounding box refinement. The GHM first performs statistics on the number of examples with similar attributes w.r.t their gradient density and then attaches a harmonizing parameter to the gradient of each example according to the density. The modification of gradient can be equivalently implemented by reformulating the loss function. Embedding the GHM into the bounding box regression branch is denoted as GHM-R loss.

GHM-R

Gradient Harmonized Single-stage Detector

APPNP

Predict then Propagate: Graph Neural Networks meet Personalized PageRank

**Stochastic Gradient Descent** is an iterative optimization technique that uses minibatches of data to form an expectation of the gradient, rather than the full gradient using all available data. That is for weights $w$ and a loss function $L$ we have:

$$ w\_{t+1} = w\_{t} - \eta\hat{\nabla}\_{w}{L(w\_{t})} $$

Where $\eta$ is a learning rate. SGD reduces redundancy compared to batch gradient descent - which recomputes gradients for similar examples before each parameter update - so it is usually much faster.

(Image Source: [here](http://rasbt.github.io/mlxtend/user_guide/general_concepts/gradient-optimization/))

Source	Predict then Propagate: Graph Neural Networks meet Personalized PageRank
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com