Neural
Nets Solve
Differential
Equations
Deep Math
I
F COLLEGE STUDENTS
could obtain a copy of
Facebook’s latest neura l
network—a series of algo-
rithms that resemble the
human brain—they could
cheat all the way through
Calculus 300. At the least, they
could solve the following dif-
fe r e nt i a l e q u a t i on i n u n d e r
one second:It may not replace Wolfram
Alpha anytime soon, but Face-
book’s neural net is the first to
solve complex calculus prob-
lems. It’s a considerable leap
forward in computers’ abilities
to understand math logic.
Two Facebook researchers in
Paris, Guillaume Lample and
François Charton, described the
breakthrough in a recent paper,
“Deep Learning for Symbolic
Mathematics.” They noted that
while neural nets can perform
everyday calculations, like arith-
metic, they don’t exactly have
a whiz-kid reputation when it
comes to calculations with sym-
bolic data—basically information
you can’t add, multiply, or other-
wise use in operations.“All the data used by comput-
ers are numbers,” Lample and
Charton say. “Most of the time,
they represent quantities, such
as the intensity of a color in an
image, or the amount of sales of
a product. But sometimes the
numbers are used as symbols to
represent objects or classes. For
instance, an individual’s age
group might be represented by
a number.”
Let’s say you are planning
a birthday party and you’d like
to assign the kids’ seats by age.
There are three categories: kids
under 10, kids aged 10 to 13, and
13- to 18-year-olds. A computer
wouldn’t understand an input of
“children, preteens, and teenag-
ers,” so you might use numbers
to represent the groups. Any-
one under 10 is represented
with a “1,” preteens with a “2,”and teenagers with a “3.” The
numerals present our symbolic
data—the age groups—in a lan-
guage computers understand.
The neural net has made
strides in solving differential
equations due to the pair’s wiz-
ardry with symbolic data. A
refresher: Differential equations
are used to solve for one or more
derivatives of a given function.
They can be used to calculate
the rate of change within a pop-
ulation or wavering demand for
a particular product. An inte-
gral, meanwhile, is known as
the anti-derivative since it’s
the inverse process of differen-
tiation. Finding the integral of
a function with respect to “x”
means finding the area from the
x-a x is to the cur ve.
The Facebook neural net
can solve these kinds of equa- CREATED^ BY^ ELENI^DIMOUUSINGSCIENCEPHOTO^ LIBRARY^ -SCIEPRO/GETTYIMAGES16 May/June 2020// B Y C O U R T N E Y L I N D E R //5
16x^3 -42x^2 +2 x
y^1 =
(-16x^8 +1 1 2 x^7 -20 4 x^6 +28 x^5 -x^4 +1)