The semantic vector of a sentence is approximately the sum of the word vectors, not the product. It is not exact because it does not account for word order. John + loves + Mary = Mary + loves + John.
On Wed, Jun 18, 2014 at 8:47 AM, YKY (Yan King Yin, 甄景贤) <[email protected]> wrote: > > Words or concepts can be extracted as vectors using Google's word2vec > algorithm: > https://code.google.com/p/word2vec/ > > To express a complex thought composed of simpler concepts, a mathematically > natural way is to multiply them together, for example "John loves Mary" = > john x loves x mary. > > I'm wondering if forming the tensor products from word2vec vectors could be > meaningful. > > The tensor product is a bi-linear form (the most universal such bi-linear > mappings). So it may preserve the linearity of the original vector space > (in other words, the scalar multiplication in the original vector space). > If the scalar multiplication is meaningful in the word2vec space, then its > meaning would be preserved by the tensor product. > > The dimension of the tensor product space is also much higher (as the > product of the dimensions of the original spaces; this is even greater than > the Cartesian product which is the sum of the dimensions of the original > spaces.) Computationally, I wonder what is the advantage of using tensor > products as opposed to Cartesian products...? > > Or perhaps the extra richness of tensor structure can be exploited > differently... > > -- > YKY > "The ultimate goal of mathematics is to eliminate any need for intelligent > thought" -- Alfred North Whitehead > > -- > You received this message because you are subscribed to the Google Groups > "Genifer" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > For more options, visit https://groups.google.com/d/optout. -- -- Matt Mahoney, [email protected] ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
