On Saturday, 28 September 2019 19:43:23 UTC+2, Gagandeep Singh (B17CS021) wrote: > > When I skimmed through the paper, I had the following queries: > > 1. Is integration really a tree to tree translation? Because, neural > network is predicting the resulting expression tree for the input equation. > However, integration is not a predictive operation. Moreover, how can we > define that whether the model is over-fitting or not on the training data? > What was the size of the training data set? >
They claim they write the expression tree into a sequence using Polish-notation. <https://en.wikipedia.org/wiki/Polish_notation>After that they train a sequence-to-sequence model developed by Google for machine translation (I have previously posted a link to a notebook containing an example of that model used for Portuguese to English translation). They discuss the possibility that the resulting sequence in Polish-notation may not be parseable into an expression tree, but they claim that this rarely occurs. Any correct result for the equation is OK, as long as it is correct. The current SymPy integrator only returns one result (even if there are multiple). > 2. Does the data set of equations contains noise? Is there any uncertainty > in the data set? For example, while translating from one language to > another there are chances that one word can be mapped to different ones > having the same meaning. However, here, it is not the case, there may be > multiple results but we can check whether they are correct or not with 100% > surety. > It would be interesting to see how many results are actually parseable (let alone correct). If a translation gives you a grammar mistake, you can still read the text, but it doesn't work like that on expression trees. > 3. Is this model able to generalise over any mathematical expression. The > way they generated data sets is algorithmic and deterministic. It is not > random(random number generators are itself deterministic). So, how can we > say that this model is the one that outperforms any CAS? > I really doubt it will outperform CAS algorithms, but let's wait for their results first. > Neural Networks don't learn, the way human beings do. They just imitate > the underlying distribution of the data. But, I don't think that > mathematical expressions have any such underlying distribution. Well, we > can take a subset of those expressions which can have a distribution and I > think that's the case with their model. > I think it's more promising to use mixtures of ML and rules. For example, you have many possible rules to apply and use ML/neural networks to decide which rules to try first. I'm always a bit skeptical of neural networks, in the end they work as huge black boxes. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/644a1d7a-48e7-4bcb-842d-223ba225091b%40googlegroups.com.
