  We introduce the two-way Gaussian interference channel in which there are
four nodes with four independent messages: two-messages to be transmitted over
a Gaussian interference channel in the $\rightarrow$ direction, simultaneously
with two-messages to be transmitted over an interference channel (in-band,
full-duplex) in the $\leftarrow$ direction. In such a two-way network, all
nodes are transmitters and receivers of messages, allowing them to adapt
current channel inputs to previously received channel outputs. We propose two
new outer bounds on the symmetric sum-rate for the two-way Gaussian
interference channel with complex channel gains: one under full adaptation (all
4 nodes are permitted to adapt inputs to previous outputs), and one under
partial adaptation (only 2 nodes are permitted to adapt, the other 2 are
restricted). We show that simple non-adaptive schemes such as the Han and
Kobayashi scheme, where inputs are functions of messages only and not past
outputs, utilized in each direction are sufficient to achieve within a constant
gap of these fully or partially adaptive outer bounds for all channel regimes.
