There are several reasons why Liverpool started the season conceding more goals before facing Arsenal.
-Liverpool underestimated opponents considered weaker, such as Newcastle and Bournemouth.
-Liverpool is adapting to a new formation with several new players.
The improvement against Arsenal suggests that the second reason may be Liverpool's somewhat weak defense. Liverpool also shouldn't be complacent despite their improvements, but Chelsea could be a strong contender this time around
I totally disagree with this your first reason, how can you suggest that Liverpool underestimated teams like Bournemouth and Newcastle when they are full aware of the kind of offset these teams can produce at anytime. Those team played in a level and capacity that they are capable of winning any team but Liverpool just played better and eventually won. Your second reason is what I agree with, because these players are still taking time to know and play with themselves.