what is black-box function evaluations? about neuralmath

[ForoughA]

black-box function evaluations refers to input-output examples of mathematical functions when the function is treated as a "black-box". To be more clear the input-output pair ($\pi/2$, 1) is a an evaluation for the sine function. Sine is treated as a black-box because we do not care how we got the pair ($\pi/2$, 1), we just use the pair as a black-box evaluation for the function. We use a few such pairs for all the mathematical functions and combine them with the symbolic representation of the functions (e.g. sin^2(x)+cos^2(x)=1).

[jiangnanhugo]

@ForoughA Really thanks for your detailed explanations. Personally, I really like your solid works on building structural models. By the way, I am still confused about the "function evaluation expressions" part. you claim that this is auto-encoder, but from your figure 1(b), I only see this is more similar to siamse network not autoencoder. Also, you mention that $W^-1_{num}$ is the decoder params, does this matrix used to transform "dense embedding into scalar"?. Why not directly do "vector-vecctor product" to calculate the cos similarity?