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max_allowed_packetis set in mysql config, not on php side

[mysqld]
max_allowed_packet=16M 

You can see its curent value in mysql like this:
SHOW VARIABLES LIKE max_allowed_packet
You can try to change it like this, but its unlikely this will work on shared hosting:
SET GLOBAL max_allowed_packet=16777216;
You can read about it here http://dev.mysql.com/doc/refman/5.1/en/packet-too-large.html