LiFT compiles formula of neural network to executable code. LiFT can be seen as Theano with ranks , though LiFT does not work with NumPy. It emits C code instead. With ranks, LiFT does not need as many built-in functionality as Theano do. As you can see in the quickstart section, dot product can be expressed without a built-in dot.
As you might have already found out, this will lead to a hugh 8x8x8 intermediate array. So BE CAUTIOUS when trying in the Python shell. However, when compiled, it will be eliminated. LiFT depends solely on isl to eliminate unnecessary arrays and to optimize, so that all OpenCL code is generated rather than hand-written.
A very simple matrix dot product example.
matmul.model
A :: (in 8 8)
B :: (out 8 8)
B := (((reduce 1 +)"2) (A (*"1 2) A))matmul.c
#include <stdio.h>
#ifdef USE_OPENCL
#include "matmul_cl.h"
#else
#include "matmul_c.h"
#endif
int
main(){
float A[8][8];
float B[8][8];
struct matmul_state state = {.A = A, .B = B};
for(int i=0; i<8; i++)
for(int j=0; j<8; j++)
A[i][j] = i*8+j;
matmul(&state);
for(int i=0; i<8; i++) {
for(int j=0; j<8; j++)
printf("%5.0f ", B[i][j]);
printf("\n");
}
return 0;
}compile and run
$ python -m lift --emit opencl --sizes '{ kernel[i] -> grid[2,2]; kernel[i] -> block[2,2]; kernel[i] -> tile[2,2,2]}' matmul matmul.model
$ gcc -DUSE_OPENCL -o matmul.elf -Wl,--format=binary matmul.cl -Wl,--format=default matmul.c matmul_cl.c -lOpenCL
$ ./matmul.elf
1120 1148 1176 1204 1232 1260 1288 1316
2912 3004 3096 3188 3280 3372 3464 3556
4704 4860 5016 5172 5328 5484 5640 5796
6496 6716 6936 7156 7376 7596 7816 8036
8288 8572 8856 9140 9424 9708 9992 10276
10080 10428 10776 11124 11472 11820 12168 12516
11872 12284 12696 13108 13520 13932 14344 14756
13664 14140 14616 15092 15568 16044 16520 16996- --dump-schedule
print schedule to stderr
- --schedule FILE
use schedule from FILE.
Because schedule generation would take very very long time, you might want to reuse previously generated schedule.
- --emit {schedule,c,opencl}
choose schedule to save schedule
OpenCL backend is ported from ppcg .
- --sizes SIZES
see 'Specifying tile, grid and block sizes' section in README of ppcg .
Besides compilation, we can also run them in the Python shell, but much slower and consume lots more memory than you might expected.
>>> from lift import *
>>>
>>> SOURCE = """
... A :: (in 8 8)
... B :: (out 8 8)
... B := (((reduce 1 +)"2) (A (*"1 2) A))
... """
>>> A = Array((8,8),range(64))
>>> exec load_source(SOURCE)
>>> B
Array((8, 8), [1120.0, 1148.0, 1176.0, 1204.0, 1232.0, 1260.0, 1288.0, 1316.0, 2912.0, 3004.0, 3096.0, 3188.0, 3280.0, 3372.0, 3464.0, 3556.0, 4704.0, 4860.0, 5016.0, 5172.0, 5328.0, 5484.0, 5640.0, 5796.0, 6496.0, 6716.0, 6936.0, 7156.0, 7376.0, 7596.0, 7816.0, 8036.0, 8288.0, 8572.0, 8856.0, 9140.0, 9424.0, 9708.0, 9992.0, 10276.0, 10080.0, 10428.0, 10776.0, 11124.0, 11472.0, 11820.0, 12168.0, 12516.0, 11872.0, 12284.0, 12696.0, 13108.0, 13520.0, 13932.0, 14344.0, 14756.0, 13664.0, 14140.0, 14616.0, 15092.0, 15568.0, 16044.0, 16520.0, 16996.0])
>>>J
A =: 1 2 3
B =: +/ A
B6
LiFT
Reduce has been extended to multiple dimensions in LiFT, thus we have 1 here.
>>> SOURCE = """
... A :: (in 3)
... B :: (out)
... B := ((reduce 1 +) A)
... """
>>> A = Array((3,), [1,2,3])
>>> exec load_source(SOURCE)
>>> B
Array((), [6.0])
>>>J
A =: 2 3 $ 1 2 3 4 5 6
B =: +/ A
B5 7 9
LiFT
>>> SOURCE = """
... A :: (in 2 3)
... B :: (out 3)
... B := ((reduce 1 +) A)
... """
>>> A = Array((3,2), [1,2,3,4,5,6])
>>> exec load_source(SOURCE)
>>> B
Array((3,), [5.0, 7.0, 9.0])
>>>J
A =: 2 3 $ 1 2 3 4 5 6
B =: (+/)"1 A6 15
LiFT
>>> SOURCE = """
... A :: (in 2 3)
... B :: (out 2)
... B := (((reduce 1 +)"1) A)
... """
>>> A = Array((3,2), [1,2,3,4,5,6])
>>> exec load_source(SOURCE)
>>> B
Array((2,), [6.0, 15.0])
>>>J
A =: 1 2
B =: 3 4
C =: A + B4 6
LiFT
>>> SOURCE = """
... A :: (in 2)
... B :: (in 2)
... C :: (out 2)
... C := (A + B)
... """
>>> A = Array((2,),[1,2])
>>> B = Array((2,),[3,4])
>>> exec load_source(SOURCE)
>>> C
Array((2,), [4, 6])
>>>J
A =: 1 3
B =: 3 4
C =: A (+"0 1) B4 5 6 7
LiFT
>>> SOURCE = """
... A :: (in 2)
... B :: (in 2)
... C :: (out 2 2)
... C := (A (+"0 1) B)
... """
>>> A = Array((2,),[1,3])
>>> B = Array((2,),[3,4])
>>> exec load_source(SOURCE)
>>> C
Array((2, 2), [4, 5, 6, 7])
>>>We have automatic differentiation in LiFT. The example here is taken from A Step by Step Backpropagation Example .
dW1 :: (grad Loss W1) means dW1 is the derivative of Loss with respect to W1
>>> from lift import *
>>> SOURCE = """
... Input :: (in 2)
... W1 :: (in 2 2)
... B1 :: (in)
... W2 :: (in 2 2)
... B2 :: (in)
... Output :: (out 2)
...
... sigmoid"0 := (1 / ((exp (0 - y)) + 1))
... dot"1 1 := ((reduce 1 +) (x * y))
...
... Hidden := (sigmoid ((W1 dot Input) + B1))
... Output := (sigmoid ((W2 dot Hidden) + B2))
...
... Target :: (in 2)
... Loss :: (out)
...
... Loss := ((reduce 1 +) (0.5 * ((Target - Output) ** 2)))
...
... dW1 :: (grad Loss W1)
... dW2 :: (grad Loss W2)
...
... nW1 :: (out 2 2)
... nW2 :: (out 2 2)
...
... nW1 := (W1 - (0.5 * dW1))
... nW2 := (W2 - (0.5 * dW2))
... """
>>> W1 = Array((2,2), [0.15,0.20,0.25,0.30])
>>> B1 = Array((), [0.35])
>>> W2 = Array((2,2), [0.40,0.45,0.50,0.55])
>>> B2 = Array((), [0.60])
>>> Input = Array((2,), [0.05,0.10])
>>> Target = Array((2,), [0.01,0.99])
>>> exec load_source(SOURCE)
>>> Output
Array((2,), [0.7513650695523157, 0.7729284653214625])
>>> Loss
Array((), [0.2983711087600027])
>>> nW1
Array((2, 2), [0.1497807161327628, 0.19956143226552567, 0.24975114363236958, 0.29950228726473915])
>>> nW2
Array((2, 2), [0.35891647971788465, 0.4086661860762334, 0.5113012702387375, 0.5613701211079891])
>>>- x + y
plus
- x - y
minus
- x * y
multiply
- x / y
divide
- x ** y
power
- log y
log
- exp y
exp
- x <. y
min
- x >. y
max
- reduce
1-dimension reduce
A1 2 3
(reduce 1 +) A
6
2-dimension reduce
B1 2 3 4
(reduce 2 +) B
10
- oblique
oblique in LiFT goes in a different direction than in J.
A0 1 2 4 5 6 7 8 9 (oblique 1 +) A 7 12 14 7 2 (oblique 1 >.) A 7 8 9 6 2 (oblique 1 <.) A 7 4 0 1 2
- duplicate
duplicate
(duplicate 2) 11 1
(duplicate 2 2) 1
1 1 1 1
- trim
trim
A- 1 2 1
(trim 1) A
2
B
- 1 1 2 1 1
(trim 2) B
2
C
1 1 1 1 2 1 1 1 1 (trim 1 1) C 2
- stride
stride
A- 1 2 1
(stride 2) A
1 1
B
- 1 2 1 2 1
(stride 2) B
1 1 1
C
- 1 2 2 1
(stride 3) C
1 1
D
1 2 1 2 2 2 1 2 1 (stride 2 2) D 1 1 1 1
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