# Operation modes in neural turing machine (Graves, 2014)

I am reading the paper "Neural Turing Machines" of Alex Graves (2014) and there are two points that are unclear to me. I would be very grateful if someone could help me out.

More specifically, my questions are about the last step performed by the write head (underlines in green) :

1. What do authors mean by leakage or dispersion ? I feel like adding the sharpening operation should not be required.
2. (Second green part) Why cannot we focus on the exact same location by having a shift of zero ? I am missing something here

2. To be concrete, let's say $$i$$ is the current location, $$j$$ is proposed by the content addressing, and $$k$$ is the shift proposed by the location addressing. For simplicity, pretend these are integers, even though both systems actually specify a distribution over addresses. Then the three "modes" (note that all three modes are implemented in a single system shown in Fig 2.) are
• goto $$j$$
• goto $$j+k$$
• goto $$i+k$$
In particular, "focusing on the same location" would be achieved by the third mode, using $$k=0$$