at res4 decreased performance, removing the module at res4 from the fpn1-5 & res3,4 model caused a significant decrease in performance, as the row of fpn1-5 & res3 shows. This result further reinforces the importance of multi-hop dependency modeling, as even efficient attention modules which cannot improve performance independently can make contributions when collaborating with other efficient attention modules. The low complexities of the efficient attention module enable multiple insertion and realize this previously hypothetical advantage of attention.

  Layer(s)                 Box AP       Mask AP         Input size
  ----------------- ------------- ------------- ------------------
  None                     $39.4$        $35.1$                  -
  res3                $\bm{40.2}$   $\bm{36.0}$     $56 \times 80$
  res4                     $39.1$        $34.8$     $28 \times 40$
  fpn1                     $39.9$        $35.8$   $224 \times 320$
  fpn2                     $39.7$        $35.7$   $112 \times 160$
  fpn3                     $39.7$        $35.5$     $56 \times 80$
  fpn4                     $39.7$        $35.4$     $28 \times 40$
  fpn5                     $39.6$        $35.3$     $14 \times 20$
  fpn1-5                   $40.6$        $36.2$                  -
  fpn1-5 & res3            $40.8$        $36.3$                  -
  fpn1-5 & res3,4     $\bm{41.2}$   $\bm{36.7}$                  -

  : **Comparison between insertions at different layers.**[]{data-label="tab:layer"}

### Dimensionality of the Keys {#sec:channels}

These experiments tested the impact of the dimensionality of the keys on the effect of efficient attention. As in Table \[tab:channels\], decreasing the dimensionality of the keys from 128 to 32 caused minimal performance change. This 