# Visualizing the Loss Landscape of Neural Nets: Meaning of the word 'filter'?

I found myself scratching my head when I read the following phrase in the paper Visualizing the Loss Landscape of Neural Nets:

To remove this scaling effect, we plot loss functions using filter-wise normalized directions. To obtain such directions for a network with parameters $$\theta$$, we begin by producing a random Gaussian direction vector $$d$$ with dimensions compatible with $$\theta$$. Then, we normalize each filter in $$d$$ to have the same norm of the corresponding filter in $$\theta$$. In other words, we make the replacement $$d_{i,j} \leftarrow d_{i,j} \| d_{i,j}\| \| \theta_{i,j}\|$$

I'm completely unclear what the authors are referring to when they refer to the filters of the vector $$d$$ in weight space. As far as I can tell, the vector $$d$$ is a standard vector in weight space ($$W$$) with a number of components equal to the number of changeable weights in the network. In my opinion, it could be said that each layer in the network can be visualized as a vector in weight space ($$\theta_{i}$$) with:

$$\theta = \sum_{i}\theta_{i}$$

and then maybe these vectors $$\theta_{i}$$ are called filters? But how this would have anything to do with the random vector $$d$$, generated in this space, remains a complete mystery to me.