Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Anand Raghunathan

Committee Chair

Anand Raghunathan

Committee Member 1

Cheng-Kok Koh

Committee Member 2

Kaushik Roy

Committee Member 3

Vijay Raghunathan


A new design approach, called approximate computing (AxC), leverages the flexibility provided by intrinsic application resilience to realize hardware or software implementations that are more efficient in energy or performance. Approximate computing techniques forsake exact (numerical or Boolean) equivalence in the execution of some of the application’s computations, while ensuring that the output quality is acceptable. While early efforts in approximate computing have demonstrated great potential, they consist of ad hoc techniques applied to a very narrow set of applications, leaving in question the applicability of approximate computing in a broader context.

The primary objective of this thesis is to develop an integrated cross-layer approach to approximate computing, and to thereby establish its applicability to a broader range of applications. The proposed framework comprises of three key components: (i) At the circuit level, systematic approaches to design approximate circuits, or circuits that realize a slightly modified function with improved efficiency, (ii) At the architecture level, utilize approximate circuits to build programmable approximate processors, and (iii) At the software level, methods to apply approximate computing to machine learning classifiers, which represent an important class of applications that are being utilized across the computing spectrum. Towards this end, the thesis extends the state-of-the-art in approximate computing in the following important directions.

Synthesis of Approximate Circuits: First, the thesis proposes a rigorous framework for the automatic synthesis of approximate circuits , which are the hardware building blocks of approximate computing platforms. Designing approximate circuits involves making judicious changes to the function implemented by the circuit such that its hardware complexity is lowered without violating the specified quality constraint. Inspired by classical approaches to Boolean optimization in logic synthesis, the thesis proposes two synthesis tools called SALSA and SASIMI that are general, i.e., applicable to any given circuit and quality specification. The framework is further extended to automatically design quality configurable circuits , which are approximate circuits with the capability to reconfigure their quality at runtime. Over a wide range of arithmetic circuits, complex modules and complete datapaths, the circuits synthesized using the proposed framework demonstrate significant benefits in area and energy.

Programmable AxC Processors: Next, the thesis extends approximate computing to the realm of programmable processors by introducing the concept of quality programmable processors (QPPs). A key principle of QPPs is that the notion of quality is explicitly codified in their HW/SW interface i.e., the instruction set. Instructions in the ISA are extended with quality fields, enabling software to specify the accuracy level that must be met during their execution. The micro-architecture is designed with hardware mechanisms to understand these quality specifications and translate them into energy savings. As a first embodiment of QPPs, the thesis presents a quality programmable 1D/2D vector processor QP-Vec, which contains a 3-tiered hierarchy of processing elements. Based on an implementation of QP-Vec with 289 processing elements, energy benefits up to 2.5X are demonstrated across a wide range of applications.

Software and Algorithms for AxC: Finally, the thesis addresses the problem of applying approximate computing to an important class of applications viz. machine learning classifiers such as deep learning networks. To this end, the thesis proposes two approaches—AxNN and scalable effort classifiers. Both approaches leverage domain- specific insights to transform a given application to an energy-efficient approximate version that meets a specified application output quality. In the context of deep learning networks, AxNN adapts backpropagation to identify neurons that contribute less significantly to the network’s accuracy, approximating these neurons (e.g., by using lower precision), and incrementally re-training the network to mitigate the impact of approximations on output quality. On the other hand, scalable effort classifiers leverage the heterogeneity in the inherent classification difficulty of inputs to dynamically modulate the effort expended by machine learning classifiers. This is achieved by building a chain of classifiers of progressively growing complexity (and accuracy) such that the number of stages used for classification scale with input difficulty. Scalable effort classifiers yield substantial energy benefits as a majority of the inputs require very low effort in real-world datasets. In summary, the concepts and techniques presented in this thesis broaden the applicability of approximate computing, thus taking a significant step towards bringing approximate computing to the mainstream. (Abstract shortened by ProQuest.)