“New Methods for Implementation of 2-D Convolution for Convolutional Neural Networks,” a Presentation from Santa Clara University

© 2020 SPRL, SoE, Santa Clara University
New Methods for Implementation of 2-D
Convolution for Convolutional Neural
Network (CNN)
Tokunbo Ogunfunmi
Signal Processing Research Lab (SPRL),
Electrical & Computer Engr. (ECEN) Dept.,
School of Engineering,
Santa Clara University.
September 2020

Outline
➢ Motivation
➢ Challenges in Implementing 2-D Convolution for CNNs
➢ Method #1
➢ Method #2
➢ Future Work
➢ Summary and Conclusions
2

Convolutional Neural Networks
• CNNs are most popular for vision tasks like image classification and segmentation.
• CNNs are computationally intensive.
• Computation and data movement requires energy.
• Data read and write major energy consumer.
• Activations, partial sums and weights constitute the most amount of data moved.
3

2D Convolution Operation
• Weights multiplied by input feature
map and accumulated.
• Kernel or weights are synonymous.
• Filters in CNNs convolve over
multiple channels.
Image Source: https://cedar.buffalo.edu/~srihari/CSE574/Chap5/Chap5.5.6-ConvolutionalNetworks.pdf
4

Challenges in FPGA Implementation of DNNs
Computation Engine
PE PE
PE PE
On chip
Output
buffer
External
Memory
FPGA
Input image
And weights
Input pixels
and weights
Input pixels
and weights
Output
Feature
Map
Pixel
Input size
Loop Tiling Loop Unrolling
Output feature size
Loop Tiling
On chip
buffer for
input and
weights
2 3 2
External
Memory
1
1 Challenge 1 : Huge Memory Transfer (Input and Output)
2 Challenge 2 : Large Onchip Buffers (Input and Output)
3 Challenge 3: Large Compute
4 Challenge 4: Complicated Scheduling and Dataflow Control
4
1
5

Method #1
FIFO Based

Convolution – Tile Based
• Conv. with 3x3 kernel
• Need to read at least 3
rows of pixels into line buffers.
• Better tile based
processing with 4 line
buffers.
7

Proposed Dataflow
• Method proposed for VGG16 which has only 3x3 kernel
• Can be extended to other kernel sizes as well
• The proposed method aims to reduce the read and write bandwidth.
• Aims to read the input feature map only once.
[4]. A. Ardakani, C. Condo, M. Ahmadi, and W. J. Gross, “An architecture to accelerate convolution in deep neural networks,”
IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 65, no. 4, pp. 1349–1362, 2017.
8

The Basic Idea and an Example
Partial sum
FIFO1
Output
FIFO
Partial sum
FIFO2
33
14
4
16
7
23
1
21
0
12
7
14
5
14
9
19
5
20
4
87
11
2
10
0
75 85
67 95 75 65 82
90
11
5
14
3
23
2
17
8
1 0 -1 2 0 -2 1 0 -1
-23
-53
-43
-22
-44
-67
-50
-
100
-
153
-55
-
110
-
153
-13
-26
-48
-13
-80
9

Processing Element (PE)
• Uses 3 FIFOs to compute convolution output
• Partial sums are stored in 2 FIFOs.
• 3rd FIFO used to accumulate outputs
• Partial sum FIFO size = width of the input image.
• Rounded up to 256 in case of VGG16
• 2 such FIFOs
• Output FIFO used to combine output of Processing elements
• Output FIFO size for VGG16 =>256x256 = 64k
10

Processing Element (PE) Architecture
11

Parallel Implementation
• Example of how 64 channel Input Feature (IF) map is processed in groups of 4.
12

Hardware Platform
• XILINX PYNQZ1 has a ZNYQ
7000 soc.
• Has an ARM processor
running at 650 MHz.
• Programable logic works at
100 MHz.
• Programmable logic can be
controlled using Python code
Image source : https://reference.digilentinc.com/_media/reference/programmable-logic/pynq-z1/pynq-z1-1.png

Architecture Implementation
• The architecture was implemented using C++
• HLS used to convert C++ to hardware.
• RTL IP created and built into block design
• Xilinx Vivado used to synthesize, place and route the block design
• Fixed point 16 format was used for the weights and partial sums.
• Python code using PYNQ library used to implement the Conv. Layer operation.
14

FPGA Utilization
Includes the space required for
AXI DMAs, Block RAMs other
blocks.
15

Results and Comparisons
[10] Y. Chen, T. Krishna, J.S. Emer and V. Sze, “Eyeriss: An energy-efficient reconfigurable accelerator for deep
convolutional neural networks” IEEE Journal of Solid State Circuits, vol. 52, no. 1, pp. 127-138, January 2017.
[4]. A. Ardakani, C. Condo, M. Ahmadi, and W. J. Gross, “An architecture to accelerate convolution in deep neural networks,”
16

Method #2
Single Partial Product 2-D
(SPP2D)

Convolution Operation
i0 i1 i2 i3 i4
i5 i6 i7 i8 i9
i10 i11 i12 i13 i14
i15 i16 i17 i18 i19
i20 i21 i22 i23 i24
i0*w0 i1*w1 i2*w2
i5*w3 i6*w4 i7*w5
i10*w6 i11*w7 i12*w8
Input
o0 o1 o2
o3 o4 o5
o6 o7 o8
w0 w1 w2
w3 w4 w5
w6 w7 w8
Kernel Output
i1*w0 i2*w1 i3*w2
i6*w3 i7*w4 i8*w5
i11*w6 i12*w7 i13*w8
i2*w0 i3*w1 i4*w2
i7*w3 i8*w4 i9*w5
i12*w6 i13*w7 i14*w8
i5*w0 i6*w1 i7*w2
i10*w3 i11*w4 i12*w5
i15*w6 i16*w7 i17*w8
i6*w0 i7*w1 i8*w2
i11*w3 i12*w4 i13*w5
i16*w6 i17*w7 i18*w8
i7*w0 i8*w1 i9*w2
i12*w3 i13*w4 i14*w5
i17*w6 i18*w7 i19*w8
i10*w0 i11*w1 i12*w2
i15*w3 i16*w4 i17*w5
i20*w6 i21*w7 i22*w8
i11*w0 i12*w1 i13*w2
i16*w3 i17*w4 i18*w5
i21*w6 i22*w7 i23*w8
Σ
i12*w0 i13*w1 i14*w2
i17*w3 i18*w4 i19*w5
i22*w6 i23*w7 i24*w8
Consider and input of size 5x5,kernel of size 3x3.We consider a convolution operation
with stride 1 and with zero padding.
18

o0 o1 o2
o3 o4 o5
o6 o7 o8
o0 o1 o2
o3 o4 o5
o6 o7 o8
o0 o1 o2
o3 o4 o5
o6 o7 o8
i0 i1 i2 i3 i4
i5 i6 i7 i8 i9
i10 i11 i12 i13 i14
i15 i16 i17 i18 i19
i20 i21 i22 i23 i24
i0 i1 i2 i3 i4
i5 i6 i7 i8 i9
i10 i11 i12 i13 i14
i15 i16 i17 i18 i19
i20 i21 i22 i23 i24
i0 i1 i2 i3 i4
i5 i6 i7 i8 i9
i10 i11 i12 i13 i14
i15 i16 i17 i18 i19
i20 i21 i22 i23 i24
Frequency of use of an input pixels is N(x) where x is the frequency itself. For example i0 has frequency 1
19

We use the notation N(x) to convey the frequency of use for an input pixel, here x is the frequency.
For example, pixel i12 has frequency N(9). It is the input pixel that is used 9 times with all 9 kernel
elements.
20

Pattern of Input Pixel Frequency in Sliding Window
Pattern of the frequency with which input pixels are needed in the existing* implementation
N(9) pixels always lies in the center of the input ( (N-4)x(N-4) where N is input dimension) while all the
other frequencies lie on the periphery boundary which is two pixels deep.
21

Patterns in Existing Implementation
Pattern of the frequency with which input pixels are needed in the existing* implementation
N(3) pixels always lies in the center of the input while all the other frequencies lie on top and bottom
and are two pixels deep
A. Ardakani, C. Condo, M. Ahmadi, and W. J. Gross, “An architecture to accelerate convolution in deep neural networks,”
22

Generalized Equation for Pattern of Input Pixels for Sliding
Window Operation
N(9)
N(6)
N(3)
N(4)
N(2)
N(1)
N pixels
N pixels
2 columns 2 columns
2 rows
2 rows
input size N(9) N(6) and N(3) N(4) and N(1) N(2)
5 1 4 4 8
6 4 8 4 8
7 9 12 4 8
10 36 24 4 8
14 100 40 4 8
28 576 96 4 8
56 2704 208 4 8
112 11664 432 4 8
224 48400 880 4 8
Number of inputs with N(x) Generalized Expression
N(9) (Hinput – 2) x (Winput – 2)
N(6) and N(3) ((Hinput – 4) x 2 ) + ((Winput – 4)x2)
N(4) and N(1) 4
N(2) 2x4
Hinput and Winput are dimension of input and are N
pixels in this example
23

SPP2D – Input stream
• Only i12 occupies all the multipliers with the 9 weight
• Complementary Sets : (i7,i22), (i17,i2), (i11,i 14), (i6,i19,i21,i24), (i16,i1,i19,i4),
(i13, i10), (i8,i5,i23,i20), (i18,i3,i15,i0)
24

SPP2D – Optimized Input stream
Two benefits of combining input pixels into complementary
sets
1. All multipliers are occupied
2. Arrive at output faster. Theoretically in 9 cycles for this
arrangement
i0 i1 i2 i3 i4
i5 i6 i7 i8 i9
i10 i11 i12 i13 i14
i15 i16 i17 i18 i19
i20 i21 i22 i23 i24
o0 o1 o2
o3 o4 o5
o6 o7 o8
w0 w1 w2
w3 w4 w5
w6 w7 w8
Kernel Output
Input
clock cycles 1 2 3 4 5 6 7 8 9
N(x) N(4),N(2),N(1) N(4),N(2),N(1) N(6),N(3) N(4),N(2),N(1) N(4),N(2),N(1) N(6),N(3) N(6),N(3) N(6),N(3) N(9)
weights
Complementary
sets
i18+i3+i15+i0 i16+i1+i19+i4 i17 +i2 i8+i5 +i23+i20 i6+i19+i21+i24 i7 +i22 i13 + i10 i11 +i14 i12
w0 w0i0 w0i1 w0i2 w0i5 w0i6 w0i7 w0i10 w0i11 w0i12
w3 w3i15 w3i16 w3i17 w3i5 w3i6 w3i7 w3i10 w3ii11 w3i12
25

w0
2
w1
2
w2
3
w3
1
w4
2
w5
1
w6
1
w7
3
w8
1
SPP2D – Partial Products Sorted into their Outputs
The highlighted partial
products in red
contribute to the first
output pixel
Output
o0
77
o1
75
o2
93
o3
69
o4
68
o5
82
o6
81
o7
98
o8
85
i18+i3+i15+i0 6 4 4 2 3 3 2 3 3
i16+i1+i19+i4 5 5 6 1 1 3 1 1 3
i17 +i2 7 7 7 8 8 8 8 8 8
i8+i5 +i23+i20 8 1 1 8 1 1 9 2 2
i6+i19+i21+i24 2 2 5 2 2 5 9 9 4
i7 +i22 8 8 8 8 8 8 10 10 10
i13 + i10 5 9 9 5 9 9 5 9 9
i11 +i 14 2 2 8 2 2 8 2 2 8
i12 3 3 3 3 3 3 3 3 3
Σ 12 10 21 8 4 8 5 6 3
26

SPP2D – Hardware Architecture
External
Memory
Weight
Buffer
Input Buffer
Selector
Accumulator
Output
Buffer
9 weights
Multiplier
Input Stream
27

SPP2D – Hardware Architecture
• Delivers output in 9 cycles for an
input of 5x5 and kernel of size 3x3.
• Architecture involves blowing up an
input matrix of 25 pixels to 81 pixels.
• The selector accumulator for this
example is designed for a 5x5 input
and 3x3 weights. Need to scale it to
an input size of 224x224 for VGG16
example.
28
5x5 input
results
25 pixels
Would require a
big buffer to
accommodate
81 pixels
The mux selector
accumulator
needs to scale to
an input of size
224x224

Results and Comparisons
Our Algorithm is 9x faster than the sliding window and 3x faster than the Warren Gross
Implementation
[1] A. Ardakani, C. Condo, M. Ahmadi, and W. J. Gross, “An architecture to accelerate convolution in deep neural networks,”
29

Future Work

Future work (1)
• Use Compression: CNNs can be compressed to INT8 with minimal impact on accuracy.
• More Processing Elements (PEs) can be implemented.
• Faster operation
• Compress weights and activations to reduce bandwidth requirement.
• The utilization percentage of Method #1 FIFOs for the later layers of the CNNs is low
31

Future work (2)
• Better utilization of FIFOs for later layers of CNNs of Method #1.
• Better utilization of Multipliers for layers of CNNs of Method #2.
• These two methods can be utilized for other non-FPGA platforms e.g. ASICs, CPUs,
GPUs, etc.
• Demonstrate scalability to practical sizes such as 224x224.
32

Summary and Conclusions

Summary and Conclusions
• We presented two new methods for 2-D convolution that offer considerable reduction
in power, computational complexity and efficiency offering a considerably better
architecture.
• The first method is based on using FIFOs and computes convolution results using row-
wise inputs as opposed to traditional tile-based processing giving considerably
reduced latency.
• The second method Single Partial Product 2-D (SPP2D) Convolution prevents
recalculation of partial weights and reduces input reuse.
• Hardware implementation results with improvements are presented.
34

References & Acknowledgements
35
Reference 1
A FIFO Based Accelerator for CNNs
Reference 2
A Fast 2-D Convolution Technique for
Deep Neural Networks
Acknowledgements
Xilinx University Program
Vineet Panchbaiyye, Santa Clara
University
Anaam Ansari, Santa Clara University

Questions & Answers
36
Contact Information:
Tokunbo Ogunfunmi
Santa Clara University
Email: Togunfunmi@scu.edu

“New Methods for Implementation of 2-D Convolution for Convolutional Neural Networks,” a Presentation from Santa Clara University

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