gtsam retraction in droid-slam

[JzHuai0108]

Thank you for open sourcing the great work.
I am reading the code, and get baffled with the gtsam retraction here.
My (wrong) derivation indicates that the chi should be negative,

self.last_state = x0.retract(-gtsam_delta)

It follows from the below observations.
Here we are optimizing w_T_b, its update is defined as w_T_b \leftarrow w_T_b exp(epsilon).
In droid-slam, the ba optimizes c_T_w, its update is defined as c_T_w \leftarrow exp(nu) c_T_w.
By comparing nerfslam droid_kernels.cu and droid-slam droid_kernels.cu, I see that they are using the same observations (gru flow) and the same Hessians and residuals.
So following droid slam, denote the delta chi by nu, we will update w_T_b by w_T_b \leftarrow b_T_w exp(-nu).

Can you please clarify this?