f(x1,x2)=x1⋅Swish(x2)=x1⋅(x2⋅σ(x2))
Recall that a barycentric coordinate system is given with respect to a -dimensional simplex, where is no larger than the dimensional space. Given a set of scattered points, it’s possible to create a tessellation of the space by forming simplices from the points, such that any input point that lies within the convex hull of the scattered set can be expressed in terms of the enclosing simplex and its corresponding barycentric coordinates2. This can be understood as a kind of triangulated irregular network (TIN).
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One challenge is having enough training data. Another is that the training data needs to be free of contamination. For a model trained up till 1900, there needs to be no information from after 1900 that leaks into the data. Some metadata might have that kind of leakage. While it’s not possible to have zero leakage - there’s a shadow of the future on past data because what we store is a function of what we care about - it’s possible to have a very low level of leakage, sufficient for this to be interesting.