<s>
Backpropagation	B-Algorithm
through	I-Algorithm
time	I-Algorithm
(	O
BPTT	B-Algorithm
)	O
is	O
a	O
gradient-based	O
technique	O
for	O
training	O
certain	O
types	O
of	O
recurrent	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
.	O
</s>
<s>
The	O
training	O
data	O
for	O
a	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
is	O
an	O
ordered	O
sequence	O
of	O
input-output	O
pairs	O
,	O
.	O
</s>
<s>
BPTT	B-Algorithm
begins	O
by	O
unfolding	O
a	O
recurrent	B-Algorithm
neural	I-Algorithm
network	I-Algorithm
in	O
time	O
.	O
</s>
<s>
Then	O
the	O
backpropagation	B-Algorithm
algorithm	O
is	O
used	O
to	O
find	O
the	O
gradient	O
of	O
the	O
cost	O
with	O
respect	O
to	O
all	O
the	O
network	O
parameters	O
.	O
</s>
<s>
Consider	O
an	O
example	O
of	O
a	O
neural	O
network	O
that	O
contains	O
a	O
recurrent	B-Algorithm
layer	O
and	O
a	O
feedforward	B-Algorithm
layer	O
.	O
</s>
<s>
The	O
figure	O
above	O
shows	O
how	O
the	O
cost	O
at	O
time	O
can	O
be	O
computed	O
,	O
by	O
unfolding	O
the	O
recurrent	B-Algorithm
layer	O
for	O
three	O
time	O
steps	O
and	O
adding	O
the	O
feedforward	B-Algorithm
layer	O
.	O
</s>
<s>
Pseudocode	O
for	O
a	O
truncated	O
version	O
of	O
BPTT	B-Algorithm
,	O
where	O
the	O
training	O
data	O
contains	O
input-output	O
pairs	O
,	O
but	O
the	O
network	O
is	O
unfolded	O
for	O
time	O
steps	O
:	O
</s>
<s>
BPTT	B-Algorithm
tends	O
to	O
be	O
significantly	O
faster	O
for	O
training	O
recurrent	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
than	O
general-purpose	O
optimization	O
techniques	O
such	O
as	O
evolutionary	B-Algorithm
optimization	O
.	O
</s>
<s>
BPTT	B-Algorithm
has	O
difficulty	O
with	O
local	O
optima	O
.	O
</s>
<s>
With	O
recurrent	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
,	O
local	O
optima	O
are	O
a	O
much	O
more	O
significant	O
problem	O
than	O
with	O
feed-forward	B-Algorithm
neural	I-Algorithm
networks	I-Algorithm
.	O
</s>
<s>
The	O
recurrent	B-Algorithm
feedback	O
in	O
such	O
networks	O
tends	O
to	O
create	O
chaotic	O
responses	O
in	O
the	O
error	O
surface	O
which	O
cause	O
local	O
optima	O
to	O
occur	O
frequently	O
,	O
and	O
in	O
poor	O
locations	O
on	O
the	O
error	O
surface	O
.	O
</s>
