Approximate circuits often achieve exceptional trade-offs between computational accuracy and hardware efficiency, making them attractive for deployment as reusable Intellectual Property (IP) cores. However, safeguarding such circuits against piracy is critical for enabling sustainable commercialization of approximate computing. This work addresses the emerging challenge of IP protection and piracy detection in the context of approximate hardware. We introduce a novel adversarial threat model, approximate obfuscation, in which an attacker not only conceals the design through structural obfuscation but also introduces functional modifications to ensure that the resulting circuit exhibits nearly identical error characteristics and hardware metrics as the original IP. To counter this threat, we propose an automated framework that extracts and compares statistical error profiles of protected IP cores and suspicious circuits, enabling systematic detection of potential IP theft. Through extensive experiments on a diverse set of approximate multipliers, we analyze the resilience of different approximate multipliers against approximate obfuscation. Our results provide new insights into the interplay between obfuscation, approximation, and IP protection.

A new field programmable gate array (FPGA)-based emulation platform is proposed to accelerate fault tolerance analysis of inference accelerators of convolutional neural networks (CNN). For a given CNN model, hardware accelerator architecture, and FT analysis target, an FPGA-based CNN implementation is generated (with the help of the Tengine framework), and fault injection logic is added. In our first case study, we report how the classification accuracy drop depends on the faults injected into multipliers used in Multiply-and-Accumulate Units of NVDLA inference accelerator executing ResNet-18 CNN. The FT analysis emulated on Zynq UltraScale+ SoC is an order of magnitude faster than software emulation.

Hardware-aware neural architecture search (HW-aware NAS) methods are crucial for designing and optimizing convolutional neural networks (CNNs) and their efficient deployment on hardware accelerators. In this work, we analyze two HW-aware NAS methods, EvoApproxNAS and ApproxDARTS, and investigate the impact of precise hardware parameter measurement on the performance of resulting CNNs. In particular, we compare the precise measurement of inference energy using the extended Timeloop tool with the original approach employed by EvoApproxNAS and ApproxDARTS, which relies on a simple analytical energy estimation based on the number of multiplications performed during the inference. The analysis demonstrates how improved energy measurements can enhance the search process of HW-aware NAS methods, resulting in more energy-efficient architectures. Our results show that without precise hardware parameter measurement, the HW-aware NAS can produce acceptable results but may fail to fully exploit the potential of hardware accelerator, especially if the 8×N -bit approximate multipliers are implemented in convolutional layers.

Approximate computing offers promising energy efficiency benefits for error-tolerant applications, but discovering optimal approximations requires extensive design space exploration (DSE). Predicting the accuracy of circuits composed of approximate components without performing complete synthesis remains a challenging problem. Current machine learning approaches used to automate this task require retraining for each new circuit configuration, making them computationally expensive and time-consuming.This paper presents ApproxGNN, a construction methodology for a pre-trained graph neural network model predicting QoR and HW cost of approximate accelerators employing approximate adders from a library. This approach is applicable in DSE for assignment of approximate components to operations in accelerator. Our approach introduces novel component feature extraction based on learned embeddings rather than traditional error metrics, enabling improved transferability to unseen circuits. ApproxGNN models can be trained with a small number of approximate components, supports transfer to multiple prediction tasks, utilizes precomputed embeddings for efficiency, and significantly improves accuracy of the prediction of approximation error. On a set of image convolutional filters, our experimental results demonstrate that the proposed embeddings improve prediction accuracy (mean square error) by 50% compared to conventional methods. Furthermore, the overall prediction accuracy is 30% better than statistical machine learning approaches without fine-tuning and 54% better with fast fine-tuning. The proposed methodology effectively addresses the challenge of transferring knowledge across different circuit designs without requiring expensive retraining. We provide our implementation, including the graph generation tools and pretrained models, as an open-source library to facilitate further research in this area.

The increasing demand for energy-efficient solutions has led to the emergence of an approximate computing paradigm that enables power-efficient implementations in various application areas such as image and data processing. The median filter, widely used in image processing and computer vision, is of immense importance in these domains. We propose a systematic design methodology for the design of power-efficient median networks suitable for on-chip or FPGA-based implementations. A search-based design method is used to obtain approximate medians that show the desired trade-offs between accuracy, power consumption and area on chip. A new metric tailored to this problem is proposed to quantify the accuracy of approximate medians. Instead of the simple error rate, our method analyses the rank error. A significant improvement in implementation cost is achieved. For example, compared to the well-optimized high-throughput implementation of the exact 9-input median, a 30% reduction in area and a 36% reduction in power consumption was achieved by introducing an error by one position (i.e., allowing the 4th or 6th lowest input to be returned instead of the median).

A fundamental assumption for search-based circuit approximation methods is the ability to massively and efficiently traverse the search space and evaluate candidate solutions. For complex approximate circuits (adders and multipliers), common error metrics, and error analysis approaches (SAT solving, BDD analysis), we perform a detailed analysis to understand the behavior of the error analysis methods under constrained resources, such as limited execution time. In addition, we show that when evaluating the error of a candidate approximate circuit, it is highly beneficial to reuse knowledge obtained during the evaluation of previous circuit instances to reduce the total design time. When an adaptive search strategy that drives the search towards promptly verifiable approximate circuits is employed, the method can discover circuits that exhibit better trade-offs between error and desired parameters (such as area) than the same method with unconstrained verification resources and within the same overall time budget. For 16-bit and 20-bit approximate multipliers, it was possible to achieve a 75% reduction in area when compared with the baseline method.

Energy efficiency and memory footprint of a convolutional neural network (CNN) implemented on a CNN inference accelerator depend on many factors, including a weight quantization strategy (i.e., data types and bit-widths) and mapping (i.e., placement and scheduling of DNN elementary operations on hardware units of the accelerator). We show that enabling rich mixed quantization schemes during the implementation can open a previously hidden space of mappings that utilize the hardware resources more effectively. CNNs utilizing quantized weights and activations and suitable mappings can significantly improve trade-offs among the accuracy, energy, and memory requirements compared to less carefully optimized CNN implementations. To find, analyze, and exploit these mappings, we: (i) extend a general-purpose state-of-the-art mapping tool (Timeloop) to support mixed quantization, which is not currently available; (ii) propose an efficient multi-objective optimization algorithm to find the most suitable bit-widths and mapping for each DNN layer executed on the accelerator; and (iii) conduct a detailed experimental evaluation to validate the proposed method. On two CNNs (MobileNetV1 and MobileNetV2) and two accelerators (Eyeriss and Simba) we show that for a given quality metric (such as the accuracy on ImageNet), energy savings are up to 37% without any accuracy drop.

Printed electronics offer ultra-low manufacturing costs and the potential for on-demand fabrication of flexible hardware. However, significant intrinsic constraints stemming from their large feature sizes and low integration density pose design challenges that hinder their practicality. In this work, we conduct a holistic exploration of printed neural network accelerators, starting from the analog-to-digital interface---a major area and power sink for sensor processing applications---and extending to networks of ternary neurons and their implementation. We propose bespoke ternary neural networks using approximate popcount and popcount-compare units, developed through a multi-phase evolutionary optimization approach and interfaced with sensors via customizable analog-to-binary converters. Our evaluation results show that the presented designs outperform the state of the art, achieving at least 6× improvement in area and 19× in power. To our knowledge, they represent the first open-source digital printed neural network classifiers capable of operating with existing printed energy harvesters.

Integrating the principles of approximate computing into the design of hardware-aware deep neural networks (DNN) has led to DNNs implementations showing good output quality and highly optimized hardware parameters such as low latency or inference energy. In this work, we present ApproxDARTS, a neural architecture search (NAS) method enabling the popular differentiable neural architecture search method called DARTS to exploit approximate multipliers and thus reduce the power consumption of generated neural networks. We showed on the CIFAR-10 data set that the ApproxDARTS is able to perform a complete architecture search within less than 10 GPU hours and produce competitive convolutional neural networks (CNN) containing approximate multipliers in convolutional layers. For example, ApproxDARTS created a CNN showing an energy consumption reduction of (a) 53.84% in the arithmetic operations of the inference phase compared to the CNN utilizing the native 32-bit floating-point multipliers and (b) 5.97% compared to the CNN utilizing the exact 8-bit fixed-point multipliers, in both cases with a negligible accuracy drop. Moreover, the ApproxDARTS is 2.3× faster than a similar but evolutionary algorithm-based method called EvoApproxNAS.

The energy efficiency of hardware implementations of convolutional neural networks (CNNs) is critical to their widespread deployment in low-power mobile devices. Recently, a number of methods have been proposed for providing energy-optimal mappings of CNNs onto diverse hardware accelerators. Their estimated energy consumption is related to specific implementation details and hardware parameters, which does not allow for machine-independent exploration of CNN energy measures. In this letter, we introduce a simplified theoretical energy complexity model for CNNs, based on only a two-level memory hierarchy that captures asymptotically all important sources of energy consumption for different CNN hardware implementations. In this model, we derive a simple energy lower bound and calculate the energy complexity of evaluating a CNN layer for two common data flows, providing corresponding upper bounds. According to statistical tests, the theoretical energy upper and lower bounds we present fit asymptotically very well with the real energy consumption of CNN implementations on the Simba and Eyeriss hardware platforms, estimated by the Timeloop/Accelergy program, which validates the proposed energy complexity model for CNNs.

Levodopa, a drug used to treat symptoms of Parkin-son's disease, is connected to side effects known as Levodopa-induced dyskinesia (LID). LID is difficult to classify during a physician's visit. A wearable device allowing long-term and continuous classification would significantly help with dosage adjustments. This paper deals with an automated design of energy-efficient hardware accelerators for such LID classifiers. The proposed accelerator consists of a feature extractor and a classifier co-designed using genetic programming. Improvements are achieved by introducing a variable bit width for arithmetic operators, eliminating redundant registers, and using precise energy consumption estimation for Pareto front creation. Evolved solutions reduce energy consumption while maintaining classification accuracy comparable to the state of the art.

Taking levodopa, a drug used to treat symptoms of Parkinson’s disease, is often connected with severe side effects, known as Levodopa-induced dyskinesia (LID). It can fluctuate in severity throughout the day and thus is difficult to classify during a short period of a physician’s visit. A low-power wearable classifier enabling long-term and continuous LID classification would thus significantly help with LID detection and dosage adjustment. This paper deals with an automated design of energy-efficient hardware accelerators of LID classifiers that can be implemented in wearable devices. The accelerator consists of a feature extractor and a classification circuit co-designed using genetic programming (GP). We also introduce and evaluate a fast and accurate energy consumption estimation method for the target architecture of considered classifiers. In a multiobjective design scenario, GP evolves solutions showing the best trade-offs between accuracy and energy. Compared to the state-of-the-art solutions, the proposed method leads to classifiers showing a comparable accuracy while the energy consumption is reduced by 49 %.

The goal of this tutorial is to introduce functional hardware approximation techniques employing machine learning methods. Functional approximation changes the function of a circuit slightly in order to reduce its power consumption. Machine learning models can help to estimate the error and the resulting circuit power consumption. The use of these techniques will be presented at multiple levels - at the individual component level and the higher level of HW accelerator synthesis.

Design methodologies developed for optimizing hardware implementations of convolutional neural networks (CNN) or searching for new hardware-aware neural architectures rely on the fast and reliable estimation of key hardware parameters, such as the energy needed for one inference. Utilizing approximate circuits in hardware accelerators of CNNs faces the designers with new problems during their simulation — commonly used tools (TimeLoop, Accelergy, Maestro) do not support approximate arithmetic operations. This work addresses the fast and efficient prediction of consumed energy in hardware accelerators of CNNs that utilize approximate circuits such as approximate multipliers. First, we extend the state-of-the-art software frameworks TimeLoop and Accelergy to predict the inference energy when exact multipliers are replaced with various approximate implementations. The energies obtained using the modified tools are then considered the ground truth (reference) values. Then, we propose and evaluate, using two accelerators (Eyeriss and Simba) and two types of networks (CNNs generated by EvoApproxNAS and standard ResNet CNNs), two predictors of inference energy. We conclude that a simple predictor based on summing the energies needed for all multiplications highly correlates with the reference values if the CNN’s architecture is fixed. For complex CNNs with variable architectures typically generated by neural architecture search algorithms, a more sophisticated predictor based on a machine learning model has to be employed. The proposed predictors are 420-533× faster than reference solutions.

In this paper, we propose an interpretable electroencephalogram (EEG)-based solution for the diagnostics of major depressive disorder (MDD). The acquisition of EEG experimental data involved 32 MDD patients and 29 healthy controls. A feature matrix is constructed involving frequency decomposition of EEG data based on power spectrum density (PSD) using the Welch method. Those PSD features were selected, which were statistically significant. To improve interpretability, the best features are first selected from feature space via the non-dominated sorting genetic (NSGA-II) evolutionary algorithm. The best features are utilized for support vector machine (SVM), and k-nearest neighbors (k-NN) classifiers, and the results are then correlated with features to improve the interpretability. The results show that the features (gamma bands) extracted from the left temporal brain regions can distinguish MDD patients from control significantly. The proposed best solution by NSGA-II gives an average sensitivity of 93.3%, specificity of 93.4% and accuracy of 93.5%. The complete framework is published as open-source at https://github.com/ehw-fit/eeg-mdd.

Generation and exploration of approximate circuits and accelerators has been a prominent research domain to achieve energy-efficiency and/or performance improvements. This research has predominantly focused on ASICs, while not achieving similar gains when deployed for FPGA-based accelerator systems, due to the inherent architectural differences between the two. In this work, we propose a novel framework, Xel-FPGAs, which leverages statistical or machine learning models to effectively explore the architecture-space of state-of-the-art ASIC-based approximate circuits to cater them for FPGA-based systems given a simple RTL description of the target application. We have also evaluated the scalability of our framework on a multi-stage application using a hierarchical search strategy. The Xel-FPGAs framework is capable of reducing the exploration time by up to 95%, when compared to the default synthesis, place, and route approaches, while identifying an improved set of Pareto-optimal designs for a given application, when compared to the state-of-the-art. The complete framework is open-source and available online at https://github.com/ehw-fit/xel-fpgas.

Generators of arithmetic circuits can automatically deliver various implementations of arithmetic circuits that show different tradeoffs between the key circuit parameters (delay, area, power consumption). However, existing (freely-)available generators are limited if more complex circuits with a hierarchical structure and additional architecture optimization are requested. Furthermore, they support only a few output formats. In order to overcome the above-mentioned limitations, we developed a new generator of arithmetic circuits called ArithsGen. ArithsGen can generate specific architectures of signed and unsigned adders and multipliers using basic building elements such as wires and gates. Compared to existing generators, the user can, for example, specify the type of adders used in multipliers. The tool supports various outputs formats (Verilog, BLIF, C/C++, or integer netlists). ArithsGen was evaluated in the synthesis and optimization of generic customizable accurate and approximate adders and multipliers. Furthermore, we used the circuits generated by ArithsGen as seeds for a tool developed to automatically create approximate implementations of arithmetic circuits. We show that different initial circuits (generated by ArithsGen) significantly impact the properties of these approximate implementations. The tool is available online at https://github.com/ehw-fit/ariths-gen.

Approximate circuits trading the power consumption for the quality of results play a key role in the development of energy-aware systems. Designing complex approximate circuits is, however, a very difficult and computationally demanding process. When deploying approximate circuits, various error metrics (e.g., mean average error, worst-case error, error rate), as well as other constraints (e.g., correct multiplication by 0), have to be considered. The state-of-the-art approximation methods typically focus on a single metric which significantly limits the applicability of the resulting circuits. In this paper, we experimentally investigate how various error metrics and their combinations affect the reduction of the power consumption that can be achieved. To this end, we extend evolutionary-driven techniques that allow us to effectively explore the design space of the approximate circuits. We identify principal limitations when complex error constraints are required as well as important correlations among the error metrics enabling the construction of circuits providing the best-known trade-offs between the power reduction and combined error constraints.

Deep neural networks (DNNs) have been established as the state-of-the-art method for advanced machine learning applications. Recently proposed by the Google Brain's team, the capsule networks (CapsNets) have improved the generalization ability, as compared to DNNs, due to their multidimensional capsules and preserving the spatial relationship between different objects. However, they pose significantly high computational and memory requirements, making their energy-efficient inference a challenging task. This article provides, for the first time, an in-depth analysis to highlight the design and runtime challenges for the (on-chip scratchpad) memories deployed in hardware accelerators executing fast CapsNets inference. To enable an efficient design, we propose an application-specific memory architecture, called DESCNet, which minimizes the off-chip memory accesses, while efficiently feeding the data to the hardware accelerator executing CapsNets inference. We analyze the corresponding on-chip memory requirement and leverage it to propose a methodology for exploring different scratchpad memory (SPM) designs and their energy/area tradeoffs. Afterward, an application-specific power-gating technique for the on-chip SPM is employed to further reduce its energy consumption, depending upon the mapped dataflow of the CapsNet and the utilization across different operations of its processing. We integrated our DESCNet memory design, as well as another state-of-the-art memory design Marchisio et al. [2018] for comparison studies, with an opensource DNN accelerator executing Google's CapsNet model Sabour et al. [2017] for the MNIST dataset. We also enhanced the design to execute the recent deep CapsNet model Rajasegaran et al. [2019] for the CIFAR10 dataset. Note: we use the same benchmarks and test conditions for which these CapsNets have been proposed and evaluated by their respective teams. The complete hardware is synthesized for a 32-nm CMOS technology using the ASIC-design flow with Synopsys tools and CACTI-P, and detailed area, performance, and power/energy estimation is performed using different configurations. Our results for a selected Pareto-optimal solution demonstrate no performance loss and an energy reduction of 79% for the complete accelerator, including computational units and memories, when compared to the state-of-the-art design.

In the past few years, Capsule Networks (CapsNets) have taken the spotlight compared to traditional convolutional neural networks (CNNs) for image classification. Unlike CNNs, CapsNets have the ability to learn the spatial relationship between features of the images. However, their complexity grows because of their heterogeneous capsule structure and the dynamic routing, which is an iterative algorithm to dynamically learn the coupling coefficients of two consecutive capsule layers. This necessitates specialized hardware accelerators for CapsNets. Moreover, a high-performance and energy-efficient design of CapsNet accelerators requires exploration of different design decisions (such as the size and configuration of the processing array and the structure of the processing elements). Toward this, we make the following key contributions: 1) FEECA, a novel methodology to explore the design space of the (micro)architectural parameters of a CapsNet hardware accelerator and 2) CapsAcc, the first specialized RTL-level hardware architecture to perform CapsNets inference with high performance and high energy efficiency. Our CapsAcc achieves significant performance improvement, compared to an optimized GPU implementation, due to its efficient implementation of key activation functions, such as squash and softmax, and an efficient data reuse for the dynamic routing. The FEECA methodology employs the Non-dominated Sorting Genetic Algorithm (NSGA-II) to explore the Pareto-optimal points with respect to area, performance, and energy consumption. This requires analytical modeling of the number of clock cycles required to perform each operation of the CapsNet inference and the memory accesses to enable a fast yet accurate design space exploration. We synthesized the complete accelerator architecture in a 45-nm CMOS technology using Synopsys design tools and evaluated it for the MNIST benchmark (as done by the original CapsNet paper from Google Brain's team) and for a more complex data set, the German Traffic Sign Recognition Benchmark (GTSRB).

There has been abundant research on the development of Approximate Circuits (ACs) for ASICs. However, previous studies have illustrated that ASIC-based ACs offer asymmetrical gains in FPGA-based accelerators. Therefore, an AC that might be pareto-optimal for ASICs might not be pareto-optimal for FPGAs. In this work, we present the ApproxFPGAs methodology that uses machine learning models to reduce the exploration time for analyzing the state-of-the-art ASIC-based ACs to determine the set of pareto-optimal FPGA-based ACs. We also perform a case-study to illustrate the benefits obtained by deploying these pareto-optimal FPGA-based ACs in a state-of-the-art automation framework to systematically generate pareto-optimal approximate accelerators that can be deployed in FPGA-based systems to achieve high performance or low-power consumption.

Recent advances in Capsule Networks (CapsNets) have shown their superior learning capability, compared to the traditional Convolutional Neural Networks (CNNs). However, the extremely high complexity of CapsNets limits their fast deployment in real-world applications. Moreover, while the resilience of CNNs have been extensively investigated to enable their energy-efficient implementations, the analysis of CapsNets' resilience is a largely unexplored area, that can provide a strong foundation to investigate techniques to overcome the CapsNets' complexity challenge.Following the trend of Approximate Computing to enable energy-efficient designs, we perform an extensive resilience analysis of the CapsNets inference subjected to the approximation errors. Our methodology models the errors arising from the approximate components (like multipliers), and analyze their impact on the classification accuracy of CapsNets. This enables the selection of approximate components based on the resilience of each operation of the CapsNet inference. We modify the TensorFlow framework to simulate the injection of approximation noise (based on the models of the approximate components) at different computational operations of the CapsNet inference. Our results show that the CapsNets are more resilient to the errors injected in the computations that occur during the dynamic routing (the softmax and the update of the coefficients), rather than other stages like convolutions and activation functions. Our analysis is extremely useful towards designing efficient CapsNet hardware accelerators with approximate components. To the best of our knowledge, this is the first proof-of-concept for employing approximations on the specialized CapsNet hardware.

Energy efficiency of hardware accelerators of deep neural networks (DNN) can be improved by introducing approximate arithmetic circuits. In order to quantify the error introduced by using these circuits and avoid the expensive hardware prototyping, a software emulator of the DNN accelerator is usually executed on CPU or GPU. However, this emulation is typically two or three orders of magnitude slower than a software DNN implementation running on CPU or GPU and operating with standard floating point arithmetic instructions and common DNN libraries. The reason is that there is no hardware support for approximate arithmetic operations on common CPUs and GPUs and these operations have to be expensively emulated. In order to address this issue, we propose an efficient emulation method for approximate circuits utilized in a given DNN accelerator which is emulated on GPU. All relevant approximate circuits are implemented as look-up tables and accessed through a texture memory mechanism of CUDA capable GPUs. We exploit the fact that the texture memory is optimized for irregular read-only access and in some GPU architectures is even implemented as a dedicated cache. This technique allowed us to reduce the inference time of the emulated DNN accelerator approximately 200 times with respect to an optimized CPU version on complex DNNs such as ResNet. The proposed approach extends the TensorFlow library and is available online at github.com/ehw-fit/tf-approximate.

Despite many successful applications, Cartesian Genetic Programming (CGP) suffers from limited scalability, especially when used for evolutionary circuit design. Considering the multiplier design problem, for example, the 5×5-bit multiplier represents the most complex circuit evolved from a randomly generated initial population. The efficiency of CGP highly depends on the performance of the point mutation operator, however, this operator is purely stochastic. This contrasts with the recent developments in Genetic Programming (GP), where advanced informed approaches such as semantic-aware operators are incorporated to improve the search space exploration capability of GP. In this paper, we propose a semantically-oriented mutation operator (SOMO) suitable for the evolutionary design of combinational circuits. SOMO uses semantics to determine the best value for each mutated gene. Compared to the common CGP and its variants as well as the recent versions of Semantic GP, the proposed method converges on common Boolean benchmarks substantially faster while keeping the phenotype size relatively small. The successfully evolved instances presented in this paper include 10-bit parity, 10+10-bit adder and 5×5-bit multiplier. The most complex circuits were evolved in less than one hour with a single-thread implementation running on a common CPU.

Deep Neural Networks (DNNs) have made significant improvements to reach the desired accuracy to be employed in a wide variety of Machine Learning (ML) applications. Recently the Google Brain's team demonstrated the ability of Capsule Networks (CapsNets) to encode and learn spatial correlations between different input features, thereby obtaining superior learning capabilities compared to traditional (i.e., non-capsule based) DNNs. However, designing CapsNets using conventional methods is a tedious job and incurs significant training effort. Recent studies have shown that powerful methods to automatically select the best/optimal DNN model configuration for a given set of applications and a training dataset are based on the Neural Architecture Search (NAS) algorithms. Moreover, due to their extreme computational and memory requirements, DNNs are employed using the specialized hardware accelerators in IoT-Edge/CPS devices.

Improving the accuracy of a neural network (NN) usually requires using larger hardware that consumes more energy. However, the error tolerance of NNs and their applications allow approximate computing techniques to be applied to reduce implementation costs. Given that multiplication is the most resource-intensive and power-hungry operation in NNs, more economical approximate multipliers (AMs) can significantly reduce hardware costs. In this article, we show that using AMs can also improve the NN accuracy by introducing noise. We consider two categories of AMs: 1) deliberately designed and 2) Cartesian genetic programing (CGP)-based AMs. The exact multipliers in two representative NNs, a multilayer perceptron (MLP) and a convolutional NN (CNN), are replaced with approximate designs to evaluate their effect on the classification accuracy of the Mixed National Institute of Standards and Technology (MNIST) and Street View House Numbers (SVHN) data sets, respectively. Interestingly, up to 0.63% improvement in the classification accuracy is achieved with reductions of 71.45% and 61.55% in the energy consumption and area, respectively. Finally, the features in an AM are identified that tend to make one design outperform others with respect to NN accuracy. Those features are then used to train a predictor that indicates how well an AM is likely to work in an NN.

Approximate computing is an emerging paradigm for developing highly energy-efficient computing systems such as various accelerators. In the literature, many libraries of elementary approximate circuits have already been proposed to simplify the design process of approximate accelerators. Because these libraries contain from tens to thousands of approximate implementations for a single arithmetic operation it is intractable to find an optimal combination of approximate circuits in the library even for an application consisting of a few operations. An open problem is "how to effectively combine circuits from these libraries to construct complex approximate accelerators". This paper proposes a novel methodology for searching, selecting and combining the most suitable approximate circuits from a set of available libraries to generate an approximate accelerator for a given application. To enable fast design space generation and exploration, the methodology utilizes machine learning techniques to create computational models estimating the overall quality of processing and hardware cost without performing full synthesis at the accelerator level. Using the methodology, we construct hundreds of approximate accelerators (for a Sobel edge detector) showing different but relevant tradeoffs between the quality of processing and hardware cost and identify a corresponding Pareto-frontier. Furthermore, when searching for approximate implementations of a generic Gaussian filter consisting of 17 arithmetic operations, the proposed approach allows us to identify approximately 103 highly relevant implementations from 1023 possible solutions in a few hours, while the exhaustive search would take four months on a high-end processor.

We propose an application-tailored data-driven fully automated method for functional approximation of combinational circuits. We demonstrate how an application-level error metric such as the classification accuracy can be translated to a component-level error metric needed for an efficient and fast search in the space of approximate low-level components that are used in the application. This is possible by employing a weighted mean error distance (WMED) metric for steering the circuit approximation process which is conducted by means of genetic programming. WMED introduces a set of weights (calculated from the data distribution measured on a selected signal in a given application) determining the importance of each input vector for the approximation process. The method is evaluated using synthetic benchmarks and application-specific approximate MAC (multiply-and-accumulate) units that are designed to provide the best trade-offs between the classification accuracy and power consumption of two image classifiers based on neural networks.

The state-of-the-art approaches employ approximate computing to reduce the energy consumption of DNN hardware. Approximate DNNs then require extensive retraining afterwards to recover from the accuracy loss caused by the use of approximate operations. However, retraining of complex DNNs does not scale well. In this paper, we demonstrate that efficient approximations can be introduced into the computational path of DNN accelerators while retraining can completely be avoided. ALWANN provides highly optimized implementations of DNNs for custom low-power accelerators in which the number of computing units is lower than the number of DNN layers. First, a fully trained DNN (e.g., in TensorFlow) is converted to operate with 8-bit weights and 8-bit multipliers in convolutional layers. A suitable approximate multiplier is then selected for each computing element from a library of approximate multipliers in such a way that (i) one approximate multiplier serves several layers, and (ii) the overall classification error and energy consumption are minimized. The optimizations including the multiplier selection problem are solved by means of a multiobjective optimization NSGA-II algorithm. In order to completely avoid the computationally expensive retraining of DNN, which is usually employed to improve the classification accuracy, we propose a simple weight updating scheme that compensates the inaccuracy introduced by employing approximate multipliers. The proposed approach is evaluated for two architectures of DNN accelerators with approximate multipliers from the open-source “EvoApprox” library, while executing three versions of ResNet on CIFAR-10. We report that the proposed approach saves 30% of energy needed for multiplication in convolutional layers of ResNet-50 while the accuracy is degraded by only 0.6% (0.9% for the ResNet-14). The proposed technique and approximate layers are available as an open-source extension of TensorFlow at https://github.com/ehw-fit/tf-approximate.

Randomness testing is an important procedure that bit streams, produced by critical cryptographic primitives such as encryption functions and hash functions, have to undergo. In this paper, a new hardware platform for the randomness testing is proposed. The platform exploits the principles of genetic programming, which is a machine learning technique developed for the automated program and circuit design. The platform is capable of evolving efficient randomness distinguishers directly on a chip. Each distinguisher is represented as a Boolean polynomial in the algebraic normal form. The randomness testing is conducted for bit streams that are either stored in an on-chip memory or generated by a circuit placed on the chip. The platform is developed with a Xilinx Zynq-7000 All Programmable System on Chip that integrates a field programmable gate array with on-chip ARM processors. The platform is evaluated in terms of the quality of randomness testing, performance, and resources utilization. With power budget less than 3 W, the platform provides comparable randomness testing capabilities with the standard testing batteries running on a personal computer.

Approximate circuits with relaxed requirements on functional correctness play an important role in the development of resource-efficient computer systems. Designing approximate circuits is a very complex and time-demanding process trying to find optimal trade-offs between the approximation error and resource savings. In this paper, we present ADAC—a novel framework for automated design of approximate arithmetic circuits. ADAC integrates in a unique way efficient simulation and formal methods for approximate equivalence checking into a search-based circuit optimisation. To make ADAC easily accessible, it is implemented as a module of the ABC tool: a state-of-the-art system for circuit synthesis and verification. Within several hours, ADAC is able to construct high-quality Pareto sets of complex circuits (including even 32-bit multipliers), providing useful trade-offs between the resource consumption and the error that is formally guaranteed. This demonstrates outstanding performance and scalability compared with other existing approaches.

The security of cryptographic algorithms (such as block ciphers and hash functions) is often evaluated in terms of their output randomness. This paper presents a novel method for the statistical randomness testing of cryptographic primitives, which is based on the evolutionary construction of the so-called randomness distinguisher. Each distinguisher is represented as a Boolean polynomial in the Algebraic Normal Form. The previous approach, in which the distinguishers were developed in two phases by means of the brute-force method, is replaced with a more scalable evolutionary algorithm (EA). On seven complex datasets, this EA provided distinguishers of the same quality as the previous approach, but the execution time was in practice reduced 40 times. This approach allowed us to perform a more efficient search in the space of Boolean distinguishers and to obtain more complex high-quality distinguishers than the previous approach.

Approximate circuits and approximate circuit design methodologies attracted a significant attention of researchers as well as industry in recent years. In order to accelerate the approximate circuit and system design process and to support a fair benchmarking of circuit approximation methods, we propose a library of approximate adders and multipliers called EvoApprox8b. This library contains 430 non-dominated 8-bit approximate adders created from 13 conventional adders and 471 non-dominated 8-bit approximate multipliers created from 6 conventional multipliers. These implementations were evolved by a multi-objective Cartesian genetic programming. The EvoApprox8b library provides Verilog, Matlab and C models of all approximate circuits. In addition to standard circuit parameters, the error is given for seven different error metrics.

Video processing performed directly on IoT nodes is one of the most performance as well as energy demanding applications for current IoT technology. In order to support real-time high-definition video, energy-reduction optimizations have to be introduced at all levels of the video processing chain. This paper deals with an efficient implementation of Discrete Cosine Transform (DCT) blocks employed in video compression based on the High Efficiency Video Coding (HEVC) standard. The proposed multiplierless 4-input DCT implementations contain approximate adders and subtractors that were obtained using genetic programming. In order to manage the complexity of evolutionary approximation and provide formal guarantees in terms of errors of key circuit components, the worst and average errors were determined exactly by means of Binary decision diagrams. Under conditions of our experiments, approximate 4-input DCTs show better quality/power trade-offs than relevant implementations available in the literature. For example, 25% power reduction for the same error was obtained in comparison with a recent highly optimized implementation.

We present a novel method allowing one to approximate complex arithmetic circuits with formal guarantees on the approximation error. The method integrates in a unique way formal techniques for approximate equivalence checking into a search-based circuit optimisation algorithm. The key idea of our approach is to employ a novel search strategy that drives the search towards promptly verifiable approximate circuits. The method was implemented within the ABC tool and extensively evaluated on functional approximation of multipliers (with up to 32-bit operands) and adders (with up to 128-bit operands). Within a few hours, we constructed a high-quality Pareto set of 32-bit multipliers providing trade-offs between the circuit error and size. This is for the first time when such complex approximate circuits with formal error guarantees have been derived, which demonstrates an outstanding performance and scalability of our approach compared with existing methods that have either been applied to the approximation of multipliers limited to 8-bit operands or statistical testing has been used only. Our approach thus significantly improves capabilities of the existing methods and paves a way towards an automated design process of provably-correct circuit approximations.

Artificial neural networks (NN) have shown a significant promise in difficult tasks like image classification or speech recognition. Even well-optimized hardware implementations of digital NNs show significant power consumption. It is mainly due to non-uniform pipeline structures and inherent redundancy of numerous arithmetic operations that have to be performed to produce each single output vector. This paper provides a methodology for the design of well-optimized power-efficient NNs with a uniform structure suitable for hardware implementation. An error resilience analysis was performed in order to determine key constraints for the design of approximate multipliers that are employed in the resulting structure of NN. By means of a search based approximation method, approximate multipliers showing desired tradeoffs between the accuracy and implementation cost were created. Resulting approximate NNs, containing the approximate multipliers, were evaluated using standard benchmarks (MNIST dataset) and a real-world classification problem of Street-View House Numbers. Significant improvement in power efficiency was obtained in both cases with respect to regular NNs. In some cases, 91% power reduction of multiplication led to classification accuracy degradation of less than 2.80%. Moreover, the paper showed the capability of the back propagation learning algorithm to adapt with NNs containing the approximate multipliers.

In order to satisfy a constant need of reducing energy consumption of electronic devices, the approximate computing paradigm has been introduced in recent years. This paradigm is based on the fact that there are applications that are inherently capable of absorbing some errors in computation. Multimedia signal processing represents a typical example that allows for quality to be traded off for power. Typicaly, the approximate circuits are designed at gate level. This paper introduces an automatic design method that is able to operate directly at transistor level which offers a great potential for discovering novel implementations of approximate circuits. The method combines a stochastic search algorithm with transistor-level circuit simulator and is able to handle the circuits consisting of hundreds of transistors. The goal of the search strategy is to improve the power consumption. To estimate power consumption, an algorithm based on transistor switching activity is proposed. A design of 4-bit multiplier was chosen as a case study. Two scenarios were considered. Firstly, the proposed method is applied to improve the power consumption of a common 4-bit multiplier and a 4-bit multiplier consisting of manually designed 2-bit multipliers. In both cases, approx. 3% power reduction was achieved. Then, it is demonstrated that a noticeable improvement can be obtained when the multipliers are designed using a hybrid approach operating at transistor as well as gate level. We discovered a novel implementation of an approximate 4-bit multiplier which has approximately by 40% better power-delay product and exhibits 14% lower worst-case error compared to the best known 4-bit multiplier consisting of 2-bit manually optimized approximate multipliers.