Genetic Programming for Energy-Efficient and Energy-Scalable Approximate Feature Computation in Embedded Inference Systems

With the increasing interest in deploying embedded sensors in a range of applications, there is also interest in deploying embedded inference capabilities. Doing so under the strict and often variable energy constraints of the embedded platforms requires algorithmic, in addition to circuit and architectural, approaches to reducing energy. A broad approach that has recently received considerable attention in the context of inference systems is approximate computing. This stems from the observation that many inference systems exhibit various forms of tolerance to data noise. While some systems have demonstrated significant approximation-versus-energy knobs to exploit this, they have been applicable to specific kernels and architectures; the more generally available knobs have been relatively weak, resulting in large data noise for relatively modest energy savings (e.g., voltage overscaling, bit-precision scaling). In this work, we explore the use of genetic programming (GP) to compute approximate features. Further, we leverage a method that enhances tolerance to feature-data noise through directed retraining of the inference stage. Previous work in GP has shown that it generalizes well to enable approximation of a broad range of computations, raising the potential for broad applicability of the proposed approach. The focus on feature extraction is deliberate because they involve diverse, often highly nonlinear, operations, challenging general applicability of energy-reducing approaches. We evaluate the proposed methodologies through two case studies, based on energy modeling of a custom low-power microprocessor with a classification accelerator. The first case study is on electroencephalogram-based seizure detection. We find that the choice of two primitive functions (square root, subtraction) out of seven possible primitive functions (addition, subtraction, multiplication, logarithm, exponential, square root, and square) enables us to approximate features in 0.41<inline-formula><tex-math notation="LaTeX">$mJ$</tex-math><alternatives> <inline-graphic xlink:href="lu-ieq1-2738642.gif"/></alternatives></inline-formula> per feature vector (FV), as compared to 4.79<inline-formula><tex-math notation="LaTeX">$mJ$</tex-math><alternatives> <inline-graphic xlink:href="lu-ieq2-2738642.gif"/></alternatives></inline-formula> per FV required for baseline feature extraction. This represents a feature extraction energy reduction of 11.68<inline-formula><tex-math notation="LaTeX"> $\times$</tex-math><alternatives><inline-graphic xlink:href="lu-ieq3-2738642.gif"/></alternatives></inline-formula>. The important system-level performance metrics for seizure detection are sensitivity, latency, and number of false alarms per hour. Our set of GP models achieves 100 percent sensitivity, 4.37 second latency, and 0.15 false alarms per hour. The baseline performance is 100 percent sensitivity, 3.84 second latency, and 0.06 false alarms per hour. The second case study is on electrocardiogram-based arrhythmia detection. In this case, just one primitive function (multiplication) suffices to approximate features in 1.13<inline-formula><tex-math notation="LaTeX">$\mu J$</tex-math> <alternatives><inline-graphic xlink:href="lu-ieq4-2738642.gif"/></alternatives></inline-formula> per FV, as compared to 11.69<inline-formula><tex-math notation="LaTeX">$\mu J$</tex-math><alternatives> <inline-graphic xlink:href="lu-ieq5-2738642.gif"/></alternatives></inline-formula> per FV required for baseline feature extraction. This represents a feature extraction energy reduction of 10.35<inline-formula><tex-math notation="LaTeX"> $\times$</tex-math><alternatives><inline-graphic xlink:href="lu-ieq6-2738642.gif"/></alternatives></inline-formula>. The important system-level metrics in this case are sensitivity, specificity, and accuracy. Our set of GP models achieves 81.17 percent sensitivity, 80.63 percent specificity, and 81.86 percent accuracy, whereas the baseline achieves 82.05 percent sensitivity, 88.12 percent specificity, and 87.92 percent accuracy. These case studies demonstrate the possibility of a significant reduction in feature extraction energy at the expense of a slight degradation in system performance.