▁sufficient ). ▁Therefore , ▁many ▁math ▁libraries ▁such ▁as ▁IT ++ ▁provide ▁a ▁default ▁routine ▁of ▁L SE ▁and ▁use ▁this ▁formula ▁internally . ▁ ▁where ▁ ▁A ▁strictly ▁convex ▁log - sum - exp ▁type ▁function ▁▁ ▁L SE ▁is ▁convex ▁but ▁not ▁strictly ▁convex . ▁We ▁can ▁define ▁a ▁ ▁strictly ▁convex ▁log - sum - exp ▁type ▁function ▁by ▁adding ▁an ▁extra ▁argument ▁set ▁to ▁zero : ▁▁▁▁▁ <0x09> ▁This ▁function ▁is ▁a ▁proper ▁B reg man ▁generator ▁( str ict ly ▁convex ▁and ▁differenti able ). ▁ ▁It ▁is ▁encountered ▁in ▁machine ▁learning , ▁for ▁example , ▁as ▁the ▁cum ul ant ▁of ▁the ▁mult in omial / bin omial ▁family . ▁ ▁See ▁also ▁▁ ▁Log arith mic ▁mean ▁ ▁Log ▁sem iring ▁ ▁Sm ooth ▁maximum ▁ ▁So ft max ▁function ▁ ▁References ▁▁▁▁▁▁ ▁Category : Log arith ms <0x0A> </s> ▁El ly ▁J annes ▁( Nov ember ▁ 1 5 , ▁ 1 9 0 7 ▁– ▁February ▁ 1 1 , ▁ 2 0 0 6 ) ▁was ▁ ▁a ▁Swedish ▁writer ▁and ▁journalist . ▁ ▁Biography ▁ ▁J annes ▁was ▁born ▁in ▁Ö re bro ▁in ▁November ▁ 1 9 0 7 . ▁She ▁was ▁the ▁daughter ▁of ▁Jan ne ▁Pet ter son ▁and ▁his ▁wife ▁Anna ▁Land ström . ▁She ▁grew ▁up ▁in ▁Bre vens ▁bru k ▁in ▁K ils mo . ▁Her ▁up br ing ing ▁at ▁the ▁mill ▁character ized ▁her ▁life ▁and ▁writing . ▁She ▁often ▁used ▁the ▁simple ▁life