Why Input Responsiveness?
Why Input Responsiveness?
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
5%
10%
15%
20%
25%
30%
35% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(a) 4×2 tiling approximation (5.9× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
16% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(b) 8×8 tiling (22× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
Missed Opportunity Fast + High Quality TOQ = 90%
TOQ Violation
(c) 16×16 tiling (83× speedup)
Proportion of Inputs
Figure 2. Histograms of the accuracy of three tiling approximations applied to the same 800 images; some mix of missed opportunities and unacceptably low accuracy are present in each approximation
100% 95% 90% 85% 80% 75% 70%
0%
10%
20%
30%
40%
50% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
Proportion of Inputs
(a) Output quality achieved Output Quality
0%
2%
4%
6%
8%
10%
0× 100× 200× 300× 400×
Proportion of Inputs
(b) Speedup achieved (average is 61×) Speedup
0%
5%
10%
15%
(c) Tiling method chosen
Proportion of Inputs 16×16 8×16 16×32 8×32 32×32 4×16 8×8 16×64 32×16 32×64 64×128 4×8 4×32 16×128 32×128 4×4 8×64 8×4 24 others
Figure 3. A dynamic oracle approximation system using the most effective tiling approximation method (fastest without violating TOQ) achieves an average speedup of 61× and uses 42 different approximation options
results in an average speedup of 10.2× across our 13 test applications with small accuracy losses in program outputs.
IRA outperforms oracle versions of two classes of prior work while delivering the same level of accuracy, achieving more than 4× the speedup of oracle calibration techniques and 2× the speedup of oracle static profiling.
2. The Case for Input Driven Dynamism
The ability of approximate computation to produce high-quality results is one of the keys to making approximation broadly deployable in real systems. Many techniques for preserving result accuracy when choosing how to approx-imate focus on the worst case, resulting in overly conser-vative approximation for other cases. Here we discuss the opportunity available in the presence of a technique that dy-namically controls approximation for individual inputs.
2.1 Input Matters for Output Quality
Input is an important part of the accuracy of an approximate computation. To illustrate this, we detail the output quality produced by three different tiling approximations [50] of an image processing application called gamma correction [42]
applied to 800 input images. Tiling is based on the assump-tion that, in many applicaassump-tion domains such as image and video processing, elements nearby one another (e.g., pix-els in an image) are likely to have similar values. Instead of computing each element of the output, a tiling
approxi-mation computes a single output element and projects that output onto the surrounding elements to form a tile. Tiling can be tuned to trade off lower accuracy for better perfor-mance by increasing the size of the tile.
Figure 2 presents histograms of the output quality for 800 different images across three tile sizes. For the purposes of illustration, we assume that the target output quality1 (TOQ) of the approximation is 90%. As shown in the figure, for all three tile sizes, different inputs can result in very differ-ent output qualities. For example, across these inputs 8×8 tiling (Figure 2(b)) results in output qualities ranging from 78%-99% because the assumption made by the approxima-tion technique (that nearby pixels are similar to one another) holds true to a different extent depending on the compo-sition of the input. Furthermore, we have observed that a wide range in output quality across inputs is not unique to tiling approximation and gamma correction, occurring across many applications and approximation techniques.
2.2 Limitations of Conventional Approaches
A common approach used to choose how to approximate is to select a single approximation option for some program and apply that approximation to multiple inputs. This ap-proach to approximation suffers from a form of the prob-lem of aggregation, in which aggregate behavior (average or
1Target output quality (TOQ) is the minimum acceptable result accu-racy [49], supplied by the user of the application.
163
Output Quality100% 95% 90% 85% 80% 75% 70%
0%
5%
10%
15%
20%
25%
30%
35% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(a) 4×2 tiling approximation (5.9× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
16% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(b) 8×8 tiling (22× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
Missed Opportunity Fast + High Quality TOQ = 90%
TOQ Violation
(c) 16×16 tiling (83× speedup)
Proportion of Inputs
Figure 2. Histograms of the accuracy of three tiling approximations applied to the same 800 images; some mix of missed opportunities and unacceptably low accuracy are present in each approximation
100% 95% 90% 85% 80% 75% 70%
0%
10%
20%
30%
40%
50% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
Proportion of Inputs
(a) Output quality achieved
Output Quality
0%
2%
4%
6%
8%
10%
0× 100× 200× 300× 400×
Proportion of Inputs
(b) Speedup achieved (average is 61×)
Speedup
0%
5%
10%
15%
(c) Tiling method chosen
Proportion of Inputs 16×16 8×16 16×32 8×32 32×32 4×16 8×8 16×64 32×16 32×64 64×128 4×8 4×32 16×128 32×128 4×4 8×64 8×4 24 others
Figure 3. A dynamic oracle approximation system using the most effective tiling approximation method (fastest without violating TOQ) achieves an average speedup of 61 × and uses 42 different approximation options
results in an average speedup of 10.2 × across our 13 test applications with small accuracy losses in program outputs.
IRA outperforms oracle versions of two classes of prior work while delivering the same level of accuracy, achieving more than 4 × the speedup of oracle calibration techniques and 2 × the speedup of oracle static profiling.
2. The Case for Input Driven Dynamism
The ability of approximate computation to produce high-quality results is one of the keys to making approximation broadly deployable in real systems. Many techniques for preserving result accuracy when choosing how to approx-imate focus on the worst case, resulting in overly conser-vative approximation for other cases. Here we discuss the opportunity available in the presence of a technique that dy-namically controls approximation for individual inputs.
2.1 Input Matters for Output Quality
Input is an important part of the accuracy of an approximate computation. To illustrate this, we detail the output quality produced by three different tiling approximations [50] of an image processing application called gamma correction [42]
applied to 800 input images. Tiling is based on the assump-tion that, in many applicaassump-tion domains such as image and video processing, elements nearby one another (e.g., pix-els in an image) are likely to have similar values. Instead of computing each element of the output, a tiling
approxi-mation computes a single output element and projects that output onto the surrounding elements to form a tile. Tiling can be tuned to trade off lower accuracy for better perfor-mance by increasing the size of the tile.
Figure 2 presents histograms of the output quality for 800 different images across three tile sizes. For the purposes of illustration, we assume that the target output quality
1(TOQ) of the approximation is 90%. As shown in the figure, for all three tile sizes, different inputs can result in very differ-ent output qualities. For example, across these inputs 8 ×8 tiling (Figure 2(b)) results in output qualities ranging from 78%-99% because the assumption made by the approxima-tion technique (that nearby pixels are similar to one another) holds true to a different extent depending on the compo-sition of the input. Furthermore, we have observed that a wide range in output quality across inputs is not unique to tiling approximation and gamma correction, occurring across many applications and approximation techniques.
2.2 Limitations of Conventional Approaches
A common approach used to choose how to approximate is to select a single approximation option for some program and apply that approximation to multiple inputs. This ap-proach to approximation suffers from a form of the prob-lem of aggregation, in which aggregate behavior (average or
1
Target output quality (TOQ) is the minimum acceptable result accu-racy [49], supplied by the user of the application.
163
4x2 tiling, 5.9x speedup 8x8 tiling, 22x speedup 16x16 tiling, 83x speedup
• Example: gamma correction, 3 tiling approximations, 800 inputs
• What if we take full advantage of the differences among inputs?
Why Input Responsiveness?
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
5%
10%
15%
20%
25%
30%
35% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(a) 4×2 tiling approximation (5.9× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
16% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(b) 8×8 tiling (22× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
Missed Opportunity Fast + High Quality TOQ = 90%
TOQ Violation
(c) 16×16 tiling (83× speedup)
Proportion of Inputs
Figure 2. Histograms of the accuracy of three tiling approximations applied to the same 800 images; some mix of missed opportunities and unacceptably low accuracy are present in each approximation
100% 95% 90% 85% 80% 75% 70%
0%
10%
20%
30%
40%
50% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
Proportion of Inputs
(a) Output quality achieved Output Quality
0%
2%
4%
6%
8%
10%
0× 100× 200× 300× 400×
Proportion of Inputs
(b) Speedup achieved (average is 61×) Speedup
0%
5%
10%
15%
(c) Tiling method chosen
Proportion of Inputs 16×16 8×16 16×32 8×32 32×32 4×16 8×8 16×64 32×16 32×64 64×128 4×8 4×32 16×128 32×128 4×4 8×64 8×4 24 others
Figure 3. A dynamic oracle approximation system using the most effective tiling approximation method (fastest without violating TOQ) achieves an average speedup of 61× and uses 42 different approximation options
results in an average speedup of 10.2× across our 13 test applications with small accuracy losses in program outputs.
IRA outperforms oracle versions of two classes of prior work while delivering the same level of accuracy, achieving more than 4× the speedup of oracle calibration techniques and 2× the speedup of oracle static profiling.
2. The Case for Input Driven Dynamism
The ability of approximate computation to produce high-quality results is one of the keys to making approximation broadly deployable in real systems. Many techniques for preserving result accuracy when choosing how to approx-imate focus on the worst case, resulting in overly conser-vative approximation for other cases. Here we discuss the opportunity available in the presence of a technique that dy-namically controls approximation for individual inputs.
2.1 Input Matters for Output Quality
Input is an important part of the accuracy of an approximate computation. To illustrate this, we detail the output quality produced by three different tiling approximations [50] of an image processing application called gamma correction [42]
applied to 800 input images. Tiling is based on the assump-tion that, in many applicaassump-tion domains such as image and video processing, elements nearby one another (e.g., pix-els in an image) are likely to have similar values. Instead of computing each element of the output, a tiling
approxi-mation computes a single output element and projects that output onto the surrounding elements to form a tile. Tiling can be tuned to trade off lower accuracy for better perfor-mance by increasing the size of the tile.
Figure 2 presents histograms of the output quality for 800 different images across three tile sizes. For the purposes of illustration, we assume that the target output quality1 (TOQ) of the approximation is 90%. As shown in the figure, for all three tile sizes, different inputs can result in very differ-ent output qualities. For example, across these inputs 8×8 tiling (Figure 2(b)) results in output qualities ranging from 78%-99% because the assumption made by the approxima-tion technique (that nearby pixels are similar to one another) holds true to a different extent depending on the compo-sition of the input. Furthermore, we have observed that a wide range in output quality across inputs is not unique to tiling approximation and gamma correction, occurring across many applications and approximation techniques.
2.2 Limitations of Conventional Approaches
A common approach used to choose how to approximate is to select a single approximation option for some program and apply that approximation to multiple inputs. This ap-proach to approximation suffers from a form of the prob-lem of aggregation, in which aggregate behavior (average or
1Target output quality (TOQ) is the minimum acceptable result accu-racy [49], supplied by the user of the application.
163
Output Quality100% 95% 90% 85% 80% 75% 70%
0%
5%
10%
15%
20%
25%
30%
35% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(a) 4×2 tiling approximation (5.9× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
16% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(b) 8×8 tiling (22× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
Missed Opportunity Fast + High Quality TOQ = 90%
TOQ Violation
(c) 16×16 tiling (83× speedup)
Proportion of Inputs
Figure 2. Histograms of the accuracy of three tiling approximations applied to the same 800 images; some mix of missed opportunities and unacceptably low accuracy are present in each approximation
100% 95% 90% 85% 80% 75% 70%
0%
10%
20%
30%
40%
50% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
Proportion of Inputs
(a) Output quality achieved
Output Quality
0%
2%
4%
6%
8%
10%
0× 100× 200× 300× 400×
Proportion of Inputs
(b) Speedup achieved (average is 61×)
Speedup
0%
5%
10%
15%
(c) Tiling method chosen
Proportion of Inputs 16×16 8×16 16×32 8×32 32×32 4×16 8×8 16×64 32×16 32×64 64×128 4×8 4×32 16×128 32×128 4×4 8×64 8×4 24 others
Figure 3. A dynamic oracle approximation system using the most effective tiling approximation method (fastest without violating TOQ) achieves an average speedup of 61 × and uses 42 different approximation options
results in an average speedup of 10.2 × across our 13 test applications with small accuracy losses in program outputs.
IRA outperforms oracle versions of two classes of prior work while delivering the same level of accuracy, achieving more than 4 × the speedup of oracle calibration techniques and 2 × the speedup of oracle static profiling.
2. The Case for Input Driven Dynamism
The ability of approximate computation to produce high-quality results is one of the keys to making approximation broadly deployable in real systems. Many techniques for preserving result accuracy when choosing how to approx-imate focus on the worst case, resulting in overly conser-vative approximation for other cases. Here we discuss the opportunity available in the presence of a technique that dy-namically controls approximation for individual inputs.
2.1 Input Matters for Output Quality
Input is an important part of the accuracy of an approximate computation. To illustrate this, we detail the output quality produced by three different tiling approximations [50] of an image processing application called gamma correction [42]
applied to 800 input images. Tiling is based on the assump-tion that, in many applicaassump-tion domains such as image and video processing, elements nearby one another (e.g., pix-els in an image) are likely to have similar values. Instead of computing each element of the output, a tiling
approxi-mation computes a single output element and projects that output onto the surrounding elements to form a tile. Tiling can be tuned to trade off lower accuracy for better perfor-mance by increasing the size of the tile.
Figure 2 presents histograms of the output quality for 800 different images across three tile sizes. For the purposes of illustration, we assume that the target output quality
1(TOQ) of the approximation is 90%. As shown in the figure, for all three tile sizes, different inputs can result in very differ-ent output qualities. For example, across these inputs 8 ×8 tiling (Figure 2(b)) results in output qualities ranging from 78%-99% because the assumption made by the approxima-tion technique (that nearby pixels are similar to one another) holds true to a different extent depending on the compo-sition of the input. Furthermore, we have observed that a wide range in output quality across inputs is not unique to tiling approximation and gamma correction, occurring across many applications and approximation techniques.
2.2 Limitations of Conventional Approaches
A common approach used to choose how to approximate is to select a single approximation option for some program and apply that approximation to multiple inputs. This ap-proach to approximation suffers from a form of the prob-lem of aggregation, in which aggregate behavior (average or
1
Target output quality (TOQ) is the minimum acceptable result accu-racy [49], supplied by the user of the application.
163
4x2 tiling, 5.9x speedup 8x8 tiling, 22x speedup 16x16 tiling, 83x speedup
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
5%
10%
15%
20%
25%
30%
35% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(a) 4×2 tiling approximation (5.9× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
16% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
(b) 8×8 tiling (22× speedup)
Proportion of Inputs
Output Quality
100% 95% 90% 85% 80% 75% 70%
0%
2%
4%
6%
8%
10%
12%
14%
Missed Opportunity Fast + High Quality TOQ = 90%
TOQ Violation
(c) 16×16 tiling (83× speedup)
Proportion of Inputs
Figure 2. Histograms of the accuracy of three tiling approximations applied to the same 800 images; some mix of missed opportunities and unacceptably low accuracy are present in each approximation
100% 95% 90% 85% 80% 75% 70%
0%
10%
20%
30%
40%
50% Missed Opportunity
Fast + High Quality TOQ = 90%
TOQ Violation
Proportion of Inputs
(a) Output quality achieved Output Quality
0%
2%
4%
6%
8%
10%
0× 100× 200× 300× 400×
Proportion of Inputs
(b) Speedup achieved (average is 61×) Speedup
0%
5%
10%
15%
(c) Tiling method chosen
Proportion of Inputs 16×16 8×16 16×32 8×32 32×32 4×16 8×8 16×64 32×16 32×64 64×128 4×8 4×32 16×128 32×128 4×4 8×64 8×4 24 others
Figure 3. A dynamic oracle approximation system using the most effective tiling approximation method (fastest without violating TOQ) achieves an average speedup of 61× and uses 42 different approximation options
results in an average speedup of 10.2× across our 13 test applications with small accuracy losses in program outputs.
IRA outperforms oracle versions of two classes of prior work while delivering the same level of accuracy, achieving more than 4× the speedup of oracle calibration techniques and 2× the speedup of oracle static profiling.
2. The Case for Input Driven Dynamism
The ability of approximate computation to produce high-quality results is one of the keys to making approximation broadly deployable in real systems. Many techniques for preserving result accuracy when choosing how to approx-imate focus on the worst case, resulting in overly conser-vative approximation for other cases. Here we discuss the opportunity available in the presence of a technique that dy-namically controls approximation for individual inputs.
2.1 Input Matters for Output Quality
Input is an important part of the accuracy of an approximate computation. To illustrate this, we detail the output quality produced by three different tiling approximations [50] of an image processing application called gamma correction [42]
applied to 800 input images. Tiling is based on the assump-tion that, in many applicaassump-tion domains such as image and video processing, elements nearby one another (e.g., pix-els in an image) are likely to have similar values. Instead of computing each element of the output, a tiling
approxi-mation computes a single output element and projects that output onto the surrounding elements to form a tile. Tiling can be tuned to trade off lower accuracy for better perfor-mance by increasing the size of the tile.
Figure 2 presents histograms of the output quality for 800 different images across three tile sizes. For the purposes of illustration, we assume that the target output quality1 (TOQ) of the approximation is 90%. As shown in the figure, for all three tile sizes, different inputs can result in very differ-ent output qualities. For example, across these inputs 8×8 tiling (Figure 2(b)) results in output qualities ranging from 78%-99% because the assumption made by the approxima-tion technique (that nearby pixels are similar to one another) holds true to a different extent depending on the compo-sition of the input. Furthermore, we have observed that a wide range in output quality across inputs is not unique to tiling approximation and gamma correction, occurring across many applications and approximation techniques.
2.2 Limitations of Conventional Approaches
A common approach used to choose how to approximate is to select a single approximation option for some program and apply that approximation to multiple inputs. This ap-proach to approximation suffers from a form of the prob-lem of aggregation, in which aggregate behavior (average or
1Target output quality (TOQ) is the minimum acceptable result accu-racy [49], supplied by the user of the application.