Clarification on the discrepancy between Eq. (9) and the public implementation

[1666178607]

Thank you for releasing the code for CGBC. I am currently reproducing the Adaptive Soft-Trim likelihood in Sec. 4.2, and I noticed a discrepancy between Eq. (9) in the paper and the public implementation.

According to Eq. (9), the concept weight appears to be:

w_{i,j} = sigmoid(
- log((1 - rho_hat_i) / rho_hat_i)
* |S_{i,j} - m_i|
* k / MAD_i
)

where the paper states that k = exp(4.6).

However, the public implementation appears to use:

kappa = log((1 - rhohat) / rhohat).clamp(0.1, 4.0)
z = -kappa * (similarities - median) / mad
weights = 1 / (1 + exp(z))

which is equivalent to:

w_{i,j} = sigmoid(
kappa_i * (S_{i,j} - m_i) / MAD_i
)

[less-and-less-bugs]

Thanks for your interest and for catching this.

We tried both versions in practice. The implementation in our released code gives slightly better results, although the difference is not significant.

Our intuition is that concepts with higher similarity scores are more likely to be high-quality concepts, which may be why this version works a bit better empirically. That said, both choices are reasonable.

The formulation in the paper is the one that is consistent with our theoretical bound.