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Great title!
> Great title! Second it!
I think the paper is also nice. :)
I think this is a great paper. I like how the subject is presented, in particular the state of the art and the motivation are well-written. In my humble opinion, more papers should have an introduction as well-written as this. Although one has to readily accept that having to compare large graphs together is an important task, once this is accepted there is no ambiguity about where the authors want to lead the reader. There is a good overview of the problems with common methods in the literature, clear enough that the reader knows what is going on, yet simple enough not to feel overwhelming. Then, the authors clearly state how they positioned themselves in regard to these problems. The problem statement, in section 3, also follows this pattern of clearly exposing what is what and then using this information to expose what their contribution is. Now, I am not an expert on the subject so I can't make any serious judgment on the scope of the contribution. Some parts about scaling to large graphs seems a bit underwhelming to me, as the authors point out themselves that the Taylor expansion "provides a rather dubious approximation". Still, the theoretical work is well exposed and well developped. Thus, I expect anyone in this field could use this as a great starting point to improve on the experimental results. Overall, I wish more papers were written with such clarity. The authors took time to clearly state their problem, which enabled me, an outsider to such questions of graph comparison techniques, to easily follow their argument. This was an enjoyable read.
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This is not a usual scientific paper, not a metaphysical tractatus either. It is accessible for for people with different backgrounds. Author tries to convince us that "the core of the human mind is simple and its structure is comprehensible". If I understand correctly, he believes that we (humanity or an individual?) will eventually develop a mathematical theory allowing us to understand our own understanding. Nevertheless, we should surmount a strange barrier of unclear shape and unknown size to achieve the goal. The power of our imagination could help... Who knows ? Some phrases are very remarkable, for example : * *In reality, no matter how hard some mathematicians try to achieve the contrary, subexponential time suffices for deciphering their papers.* * *For instance, an intelligent human and an equally intelligent gigantic squid may not agree on which of the above three blobs are abstract and which are concrete.* * *To see what iterations of self-references do, try it with "the meaning of". The first iteration "meaning of meaning" tells you what the (distributive) meaning really is. But try it two more times, and what come out of it, "meaning of meaning of meaning of meaning" strikes you as something meaningless.* The mind experiment from the third point suggests that our brain uses some type of hash function dealing with self-referential iterations. The special hash function that have the following property: it is possible to take a inverse of such hash, but it takes some time; inversion of a double hash becomes more complicated; its virtually impossible to inverse a triple-hash application. If "hash inversion" and "understanding" are linked in some way, this could lead to something interesting... The hash function in this case works like a lossy compression algorithm.
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