IEEE Circuits and Systems Magazine - Q3 2023 - 26
Figure 15. Algorithm and system co-design reduces the training memory from 303 MB (PyTorch) to 149KB with the same transfer
learning accuracy, leading to 2077× reduction. The numbers are measured with MobilenetV2-w0.35 [4], batch size 1 and
resolution 128×128. It can be deployed to a microcontroller with 256 KB SRAM.
Figure 16. The quantized model has a very different weight/gradient norm ratio (i.e., W G/) compared to the floating-point
model at training time (left). QAS stabilizes the
WG/
QAS. QAS effectively helps convergence, leading to better accuracy (right). The results are from updating the last two blocks of
the MCUNet model on the Cars dataset. (a) Weight/gradient norm ratio. (b) Training convergence.
ratio and helps optimization. The validation loss curves w/ and w/o
distorts the gradient update. To verify the idea, Figure
16 plot the ratio between weight norm and gradient
norm (i.e.,
WG
/) for each tensor at the beginning
of the training on the CIFAR dataset [147]. The ratio
curve is very different after quantization: (1) the ratio is
much larger (could be addressed by adjusting the learning
rate) and (2) the ratio has a different pattern after
quantization. Take the highlighted area (red box) as an
example, the quantized ratios have a zigzag pattern, differing
from the floating-point curve. If all the tensors
are updated with a fixed learning rate, then the update
speed of each tensor would be very different compared
to the floating-point case, leading to inferior accuracy.
Even adaptive-learning rate optimizers like Adam [148]
cannot fully address the issue, as shown in Table 7.
2) Hyperparameter-Free Gradient Scaling. To address
the problem, a hyper-parameter-free learning rate scaling
rule, QAS, is proposed. Consider a 2D weight matrix
of a linear layer W∈
×cc
26
IEEE CIRCUITS AND SYSTEMS MAGAZINE
output channel. To perform per-tensor quantization4 a
scaling rate sW ∈ R is computed, such that W′s largest
magnitude is 27 − 1 = 127:
WW WGW WW (2)
=⋅() ≈⋅ ≈⋅G
ss ssWW W
/,
quantize
The process (roughly) preserves the mathematical
functionality during the forward (Equation 1)], but it
distorts the magnitude ratio between the weight and its
corresponding gradient:
WG WG WG (3)// .
//W WW WW≈⋅ =⋅−
ss s 2
The weight and gradient ratios are off by sW
−2, leading
to the distorted pattern in Figure 16: (1) the scaling factor
is far smaller than 1, making the weight-gradient ratio
much larger and (2) weights and biases have different
12 , where c1,c2 are the input and
4For simplicity. In practice, per-channel quantization [146] is used and
the scaling factor is a vector of size C2.
THIRD QUARTER 2023
IEEE Circuits and Systems Magazine - Q3 2023
Table of Contents for the Digital Edition of IEEE Circuits and Systems Magazine - Q3 2023
Contents
IEEE Circuits and Systems Magazine - Q3 2023 - Cover1
IEEE Circuits and Systems Magazine - Q3 2023 - Cover2
IEEE Circuits and Systems Magazine - Q3 2023 - Contents
IEEE Circuits and Systems Magazine - Q3 2023 - 2
IEEE Circuits and Systems Magazine - Q3 2023 - 3
IEEE Circuits and Systems Magazine - Q3 2023 - 4
IEEE Circuits and Systems Magazine - Q3 2023 - 5
IEEE Circuits and Systems Magazine - Q3 2023 - 6
IEEE Circuits and Systems Magazine - Q3 2023 - 7
IEEE Circuits and Systems Magazine - Q3 2023 - 8
IEEE Circuits and Systems Magazine - Q3 2023 - 9
IEEE Circuits and Systems Magazine - Q3 2023 - 10
IEEE Circuits and Systems Magazine - Q3 2023 - 11
IEEE Circuits and Systems Magazine - Q3 2023 - 12
IEEE Circuits and Systems Magazine - Q3 2023 - 13
IEEE Circuits and Systems Magazine - Q3 2023 - 14
IEEE Circuits and Systems Magazine - Q3 2023 - 15
IEEE Circuits and Systems Magazine - Q3 2023 - 16
IEEE Circuits and Systems Magazine - Q3 2023 - 17
IEEE Circuits and Systems Magazine - Q3 2023 - 18
IEEE Circuits and Systems Magazine - Q3 2023 - 19
IEEE Circuits and Systems Magazine - Q3 2023 - 20
IEEE Circuits and Systems Magazine - Q3 2023 - 21
IEEE Circuits and Systems Magazine - Q3 2023 - 22
IEEE Circuits and Systems Magazine - Q3 2023 - 23
IEEE Circuits and Systems Magazine - Q3 2023 - 24
IEEE Circuits and Systems Magazine - Q3 2023 - 25
IEEE Circuits and Systems Magazine - Q3 2023 - 26
IEEE Circuits and Systems Magazine - Q3 2023 - 27
IEEE Circuits and Systems Magazine - Q3 2023 - 28
IEEE Circuits and Systems Magazine - Q3 2023 - 29
IEEE Circuits and Systems Magazine - Q3 2023 - 30
IEEE Circuits and Systems Magazine - Q3 2023 - 31
IEEE Circuits and Systems Magazine - Q3 2023 - 32
IEEE Circuits and Systems Magazine - Q3 2023 - 33
IEEE Circuits and Systems Magazine - Q3 2023 - 34
IEEE Circuits and Systems Magazine - Q3 2023 - 35
IEEE Circuits and Systems Magazine - Q3 2023 - 36
IEEE Circuits and Systems Magazine - Q3 2023 - 37
IEEE Circuits and Systems Magazine - Q3 2023 - 38
IEEE Circuits and Systems Magazine - Q3 2023 - 39
IEEE Circuits and Systems Magazine - Q3 2023 - 40
IEEE Circuits and Systems Magazine - Q3 2023 - 41
IEEE Circuits and Systems Magazine - Q3 2023 - 42
IEEE Circuits and Systems Magazine - Q3 2023 - 43
IEEE Circuits and Systems Magazine - Q3 2023 - 44
IEEE Circuits and Systems Magazine - Q3 2023 - 45
IEEE Circuits and Systems Magazine - Q3 2023 - 46
IEEE Circuits and Systems Magazine - Q3 2023 - 47
IEEE Circuits and Systems Magazine - Q3 2023 - 48
IEEE Circuits and Systems Magazine - Q3 2023 - 49
IEEE Circuits and Systems Magazine - Q3 2023 - 50
IEEE Circuits and Systems Magazine - Q3 2023 - 51
IEEE Circuits and Systems Magazine - Q3 2023 - 52
IEEE Circuits and Systems Magazine - Q3 2023 - 53
IEEE Circuits and Systems Magazine - Q3 2023 - 54
IEEE Circuits and Systems Magazine - Q3 2023 - 55
IEEE Circuits and Systems Magazine - Q3 2023 - 56
IEEE Circuits and Systems Magazine - Q3 2023 - 57
IEEE Circuits and Systems Magazine - Q3 2023 - 58
IEEE Circuits and Systems Magazine - Q3 2023 - 59
IEEE Circuits and Systems Magazine - Q3 2023 - 60
IEEE Circuits and Systems Magazine - Q3 2023 - 61
IEEE Circuits and Systems Magazine - Q3 2023 - 62
IEEE Circuits and Systems Magazine - Q3 2023 - 63
IEEE Circuits and Systems Magazine - Q3 2023 - 64
IEEE Circuits and Systems Magazine - Q3 2023 - 65
IEEE Circuits and Systems Magazine - Q3 2023 - 66
IEEE Circuits and Systems Magazine - Q3 2023 - 67
IEEE Circuits and Systems Magazine - Q3 2023 - 68
IEEE Circuits and Systems Magazine - Q3 2023 - 69
IEEE Circuits and Systems Magazine - Q3 2023 - 70
IEEE Circuits and Systems Magazine - Q3 2023 - 71
IEEE Circuits and Systems Magazine - Q3 2023 - 72
IEEE Circuits and Systems Magazine - Q3 2023 - 73
IEEE Circuits and Systems Magazine - Q3 2023 - 74
IEEE Circuits and Systems Magazine - Q3 2023 - 75
IEEE Circuits and Systems Magazine - Q3 2023 - 76
IEEE Circuits and Systems Magazine - Q3 2023 - 77
IEEE Circuits and Systems Magazine - Q3 2023 - 78
IEEE Circuits and Systems Magazine - Q3 2023 - 79
IEEE Circuits and Systems Magazine - Q3 2023 - 80
IEEE Circuits and Systems Magazine - Q3 2023 - 81
IEEE Circuits and Systems Magazine - Q3 2023 - 82
IEEE Circuits and Systems Magazine - Q3 2023 - 83
IEEE Circuits and Systems Magazine - Q3 2023 - 84
IEEE Circuits and Systems Magazine - Q3 2023 - 85
IEEE Circuits and Systems Magazine - Q3 2023 - 86
IEEE Circuits and Systems Magazine - Q3 2023 - 87
IEEE Circuits and Systems Magazine - Q3 2023 - 88
IEEE Circuits and Systems Magazine - Q3 2023 - Cover3
IEEE Circuits and Systems Magazine - Q3 2023 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2023Q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2022Q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021Q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2021q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2020q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2019q1
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q4
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q3
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q2
https://www.nxtbook.com/nxtbooks/ieee/circuitsandsystems_2018q1
https://www.nxtbookmedia.com