We propose a novel hybrid bit parallel-serial processing technique calledTALIPOTin order to reduce energy consumption of deep neural networks (DNNs).TALIPOTworks as computation booster and has inborn ability of quality adjusting tradeoff between accuracy and energy consumption of DNNs. The core principal ofTALIPOTis keeping the serial number of bits same in the entire computing process, so the energy is consumed effectively without extra waiting times between inputs and outputs of the computing blocks (adders, multipliers, and activation blocks). To achieve this, we implement activation rounding which scales down the accumulation of parallel bits at the output of the hidden layers of DNN.TALIPOTutilizes most significant bit first (MSB-first) fashion, so we obtain the most valuable bit information first, between the layers of DNN, which ensures the activation rounding process done accurately and efficiently. Thanks to this method, we optimize operating accuracy/energy point by cutting off bits at the output whenever we obtain the desired accuracy. Simulations using the MNIST and CIFAR-10 datasets show thatTALIPOToutperforms the state-of-the-art computation techniques in terms of energy consumption.TALIPOTperforms the MNIST classification with the energy efficiency of 25.3 TOPS/W and the accuracy of 98.2% in ASIC environment using 40 nm CMOS process.

Switching lattices, consisting of four-terminal switches, present an alternative structure for the realization of Boolean logic functions. Although promising algorithms have been introduced to find a realization of a logic function using a switching lattice with the fewest number of four-terminal switches, the delay of a switching lattice has not been examined yet. In this article, we generate a switching lattice using a recently proposed CMOS-compatible four-terminal device model and formulate the delay of a path in a switching lattice. It is observed that the delay of a design realizing a logic function on a switching lattice heavily depends on the number of four-terminal switches in the critical path. With this motivation, we introduce optimization algorithms, called PHAEDRA and TROADES, which can find the realization of a logic function on a switching lattice with the fewest number of switches under a delay constraint given in terms of the number of switches in the critical path. While PHAEDRA is a dichotomic search algorithm that can obtain solutions with a small number of switches on small size logic functions, TROADES is a divide-and-conquer method that can find a solution using less computational effort and can easily handle larger size logic functions with respect to PHAEDRA. The experimental results show that the proposed algorithms can reduce the delay of a lattice realization of a logic function significantly at a cost of an increase in the number of switches. They can explore alternative lattice realizations of a logic function by changing the delay constraint, enabling a designer to choose the one that fits best in an application.

In this paper, we first summarize our research activities done through our European Union’s Horizon-2020 project between 2015 and 2019. The project has a goal of developing synthesis and performance optimization techniques for nanocrossbar arrays. For this purpose, different computing models including diode, memristor, FET, and four-terminal switch based models, within different technologies including carbon nanotubes, nanowires, and memristors as well as the CMOS technology have been investigated. Their capabilities to realize logic functions and to tolerate faults have been deeply analyzed. From these experiences, we think that instead of replacing CMOS with a completely new crossbar based technology, developing CMOS compatible crossbar technologies and computing models is a more viable solution to overcome challenges in CMOS miniaturization. At this point, four-terminal switch based arrays, called switching lattices, come forward with their CMOS compatibility feature as well as with their area efficient device and circuit realizations. We have showed that switching lattices can be efficiently implemented using a standard CMOS process to implement logic functions by doing experiments in a 65nm CMOS process. Further in this paper, we make an introduction of realizing memory arrays with switching lattices including ROMs and RAMs. Also we discuss challenges and promises in realizing switching lattices for under 30nm CMOS technologies including FinFET technologies.

Switching lattices consisting of four-terminal switches are introduced as area-efficient structures to realize logic functions. Many optimization algorithms have been proposed, including exact ones, realizing logic functions on lattices with the fewest number of four-terminal switches, as well as heuristic ones. Hence, the computing potential of switching lattices has been justified adequately in the literature. However, the same thing cannot be said for their physical implementation. There have been conceptual ideas for the technology development of switching lattices, but no concrete and directly applicable technology has been proposed yet. In this study, we show that switching lattices can be directly and efficiently implemented using a standard CMOS process. To realize a given logic function on a switching lattice, we propose static and dynamic logic solutions. The proposed circuits as well as the compared conventional ones are designed and simulated in the Cadence environment using TSMC 65nm CMOS process. Experimental post layout results on logic functions show that switching lattices occupy much smaller area than those of the conventional CMOS implementations, while they have competitive delay and power consumption values.

Over the years, efficient algorithms have been proposed to realize logic functions on two-dimensional arrays of four-terminal switches, called switching lattices, using the fewest number of switches. Although existing algorithms can easily find a solution on logic functions with a small number of inputs and products, they can hardly handle large size instances. In order to cope with such logic functions, in this paper, we introduce SISYPHUS that exploits Boolean decomposition techniques and incorporates a state-of-art algorithm designed for the realization of logic functions using switching lattices. Experimental results indicate that SISYPHUS can find competitive solutions on logic functions with a small number of inputs and products when compared to those of previously proposed algorithms. Moreover, its solutions on large size functions are obtained using a little computational effort and are significantly better than the best solutions found so far.

This paper presents techniques and design structures to reduce the time-multiplexed hardware complexity of a feed-forward artificial neural network (ANN). After the weights of ANN are determined in a training phase, in a post-training stage, initially, the minimum quantization value used to convert the floating-point weights to integers is found. Then, the integer weights related to each neuron are tuned to reduce the hardware complexity in the time-multiplexed design avoiding a loss on the ANN accuracy in hardware. Also, at each layer of ANN, the multiplications of integer weights by an input variable at each time are realized under the shift-adds architecture using a minimum number of adders and subtractors. It is observed that the application of the post-training stage yields a significant reduction in area, latency, and energy consumption on the time-multiplexed designs including multipliers. Moreover, the multiplierless design of ANN whose weights are found in the post-training stage leads to a further reduction in area and energy consumption, increasing the latency slightly.

Two-dimensional switching lattices including four-terminal switches are introduced as alternative structures to realize logic functions, aiming to outperform the designs consisting of one-dimensional two-terminal switches. Exact and approximate algorithms have been proposed for the problem of finding a switching lattice which implements a given logic function and has the minimum size, i.e., a minimum number of switches. In this article, we present an approximate algorithm, called JANUS, that explores the search space in a dichotomic search manner. It iteratively checks if the target function can be realized using a given lattice candidate, which is formalized as a satisfiability (SAT) problem. As the lattice size and the number of literals and products in the given target function increase, the size of a SAT problem grows dramatically, increasing the run-time of a SAT solver. To handle the instances that JANUS cannot cope with, we introduce a divide and conquer method called MEDEA. It partitions the target function into smaller sub-functions, finds the realizations of these sub-functions on switching lattices using JANUS, and explores alternative realizations of these subfunctions which may reduce the size of the final lattice. Moreover, we describe the realization of multiple functions in a single lattice. Experimental results show that JANUS can find better solutions than the existing approximate algorithms, even than the exact algorithm which cannot determine a minimum solution in a given time limit. On the other hand, MEDEA can find better solutions on relatively large size instances using a little computational effort when compared to the previously proposed algorithms. Moreover, on instances that the existing methods cannot handle, MEDEA can easily find a solution which is significantly better than the available solutions.

In recent years the realization of a logic function on two-dimensional arrays of four-terminal switches, called switching lattices, has attracted considerable interest. Exact and approximate methods have been proposed for the problem of synthesizing Boolean functions on switching lattices with minimum size, called lattice synthesis (LS) problem. However, the exact method can only handle relatively small instances and the approximate methods may find solutions that are far from the optimum. This paper introduces an approximate algorithm, called JANUS, that formalizes the problem of realizing a logic function on a given lattice, called lattice mapping (LM) problem, as a satisfiability problem and explores the search space of the LS problem in a dichotomic search manner, solving LM problems for possible lattice candidates. This paper also presents three methods to improve the initial upper bound and an efficient way to realize multiple logic functions on a single lattice. Experimental results show that JANUS can find solutions very close to the minimum in a reasonable time and obtain better results than the existing approximate methods. The solutions of JANUS can also be better than those of the exact method, which cannot be determined to be optimal due to the given time limit, where the maximum gain on the number of switches reaches up to 25%.

Our European Union's Horizon-2020 project aims to develop a complete synthesis and performance optimization methodology for switching nano-crossbar arrays that leads to the design and construction of an emerging nanocomputer. Within the project, we investigate different computing models based on either two-terminal switches, realized with field effect transistors, resistive and diode devices, or four-terminal switches. Although a four-terminal switch based model offers a significant area advantage, its realization at the technology level needs further justifications and raises a number of questions about its feasibility. In this study, we answer these questions. First, by using three dimensional technology computer-aided design (TCAD) simulations, we show that four-terminal switches can be directly implemented with the CMOS technology. For this purpose, we try different semiconductor gate materials in different formations of geometric shapes. Then, by fitting the TCAD simulation data to the standard CMOS current-voltage equations, we develop a Spice model of a four-terminal switch. Finally, we successfully perform Spice circuit simulations on four-terminal switches with different sizes. As a follow-up work within the project, we will proceed to the fabrication step.

In reversible circuits, a fault as a change in logic value at a circuit node always alters an output logic value, so observability of faults at the output is 100%. In other words, reversible circuits are latent-fault-free. Our motivation is to incorporate this unique feature of reversible circuits to design CMOS circuits having perfect or 100% Concurrent Error Detection (CED). For this purpose we propose a new, fault preservative, and reversible gate library called Even Target - Mixed Polarity Multiple Control Toffoli (ET-MPMCT). By using ET-MPCT, we ensure that the parity, even or odd, is preserved at all levels including the output level unless there is a faulty node. Our design strategy has two steps for a reversible function: 1) implement the reversible functions with the ET-MPMCT library; and 2) apply reversible-to-CMOS gate conversion. In case an irreversible function needs to be synthesized then its reversible form is used followed by the two design steps. As a result, we have come up with a CMOS circuit having 100% CED. The performance of our approach is compared with other CED schemes in the literature in terms of area, detection rate, and power consumption. Simulations are done with Cadence Genus tool using TSMC 0.18 μm technology. Clearly, results are in favor of our proposed technique.

Contrary to abundant memory related studies of memristive crossbar structures, logic oriented applications are only gaining popularity in recent years. In this paper, we study logic synthesis, regarding both two-level and multi level designs, and defect aspects of memristor based crossbar architectures. First, we introduce our two-level and multi-level logic synthesis techniques. We elaborate on advantages and disadvantages of both approaches with experimental results regarding area cost. After that, we devise a defect model in alignment with the conventional stuck-at open and closed paradigm. In addition, we determine the effects of defects to the operational capacity of the crossbar. Furthermore, we propose a preliminary defect tolerant Boolean logic mapping approach. In order to evaluate our approach, we conduct extensive Monte Carlo simulations with industrial benchmarks. Finally, we discuss future directions concerning both existing two-level and prospective multi-level logic designs as well as defect tolerance with area redundancy.

Nano-crossbar arrays have emerged as a strong candidate technology to replace CMOS in near future. They are regular and dense structures, and can be fabricated such that each crosspoint can be used as a conventional electronic component such as a diode, a FET, or a switch. This is a unique opportunity that allows us to integrate well developed conventional circuit design techniques into nano-crossbar arrays. Motivated by this, our project aims to develop a complete synthesis and performance optimization methodology for switching nano-crossbar arrays that leads to the design and construction of an emerging nanocomputer. First two work packages of the project are presented in this paper. These packages are on logic synthesis that aims to implement Boolean functions with nano-crossbar arrays with area optimization, and fault tolerance that aims to provide a full methodology in the presence of high fault densities and extreme parametric variations in nano-crossbar architectures.

This paper studies fault tolerance in switching reconfigurable nano-crossbar arrays. Both permanent and transient faults are taken into account by independently assigning stuck-open and stuck-closed fault probabilities into crosspoints. In the presence of permanent faults, a fast and accurate heuristic algorithm is proposed that uses the techniques of index sorting, backtracking, and row matching. The algorithm's effectiveness is demonstrated on standard benchmark circuits in terms of runtime, success rate, and accuracy. In the presence of transient faults, tolerance analysis is performed by formally and recursively determining tolerable fault positions. In this way, we are able to specify fault tolerance performances of nano-crossbars without relying on randomly generated faults that is relatively costly regarding that the number of fault distributions in a crossbar grows exponentially with the crossbar size.

Beyond CMOS, new technologies are emerging to extend electronic systems with features unavailable to silicon-based devices. Emerging technologies provide new logic and interconnection structures for computation, storage and communication that may require new design paradigms, and therefore trigger the development of a new generation of design automation tools. In the last decade, several emerging technologies have been proposed and the time has come for studying new ad-hoc techniques and tools for logic synthesis, physical design and testing. The main goal of this project is developing a complete synthesis and optimization methodology for switching nano-crossbar arrays that leads to the design and construction of an emerging nanocomputer. New models for diode, FET, and four-terminal switch based nanoarrays are developed. The proposed methodology implements both arithmetic and memory elements, necessitated by achieving a computer, by considering performance parameters such as area, delay, power dissipation, and reliability. With combination of arithmetic and memory elements a synchronous state machine (SSM), representation of a computer, is realized. The proposed methodology targets variety of emerging technologies including nanowire/nanotube crossbar arrays, magnetic switch-based structures, and crossbar memories. The results of this project will be a foundation of nano-crossbar based circuit design techniques and greatly contribute to the construction of emerging computers beyond CMOS. The topic of this project can be considered under the research area of "Emerging Computing Models" or "Computational Nanoelectronics", more specifically the design, modeling, and simulation of new nanoscale switches beyond CMOS.

In this paper, we study implementation of Boolean functions with crossbar nanoarrays where each cross point behaves as a switch. This study has two main parts "formulation" and "optimization". In the first part of formulation, we investigate nanoarray based implementation methodologies in the literature. We classify them as two-terminal or four-terminal switch based. We generalize these methodologies to be applicable for any given Boolean function by offering array size formulations. In the second part of optimization, we focus on four-terminal switch based implementations, we propose a synthesis method to implement Boolean functions with optimal array sizes. Finally, we perform synthesis trials on standard benchmark circuits to evaluate the proposed optimal method in comparison with previous nanoarray based implementation methods. The proposed synthesis method gives by far the smallest array sizes and offers a new design paradigm for nanoarray based computing architectures.

This paper studies the implementation of Boolean functions by lattices of four-terminal switches. Each switch is controlled by a Boolean literal. If the literal takes the value 1, the corresponding switch is connected to its four neighbors; else it is not connected. A Boolean function is implemented in terms of connectivity across the lattice: it evaluates to 1 iff there exists a connected path between two opposing edges of the lattice. The paper addresses the following synthesis problem: how should one assign literals to switches in a lattice in order to implement a given target Boolean function? The goal is to minimize the lattice size, measured in terms of the number of switches. An efficient algorithm for this task is presented-one that does not exhaustively enumerate paths but rather exploits the concept of Boolean function duality. The algorithm produces lattices with a size that grows linearly with the number of products of the target Boolean function in ISOP form. It runs in time that grows polynomially. Synthesis trials are performed on standard benchmark circuits. The synthesis results are compared to a lower-bound calculation on the lattice size.

This paper studies the implementation of Boolean functions with lattices of two-dimensional switches. Each switch is controlled by a Boolean literal. If the literal is 1, the switch is connected to its four neighbours; else it is not connected. Boolean functions are implemented in terms of connectivity across the lattice: a Boolean function evaluates to 1 iff there exists a top-to-bottom path. The paper addresses the following synthesis problem: how should we map literals to switches in a lattice in order to implement a given target Boolean function? We seek to minimize the number of switches. Also, we aim for an efficient algorithm -- one that does not exhaustively enumerate paths. We exploit the concept of lattice and Boolean function duality. We demonstrate a synthesis method that produces lattices with a number of switches that grows linearly with the number of product terms in the function. Our algorithm runs in time that grows polynomially.

In this study, we apply a novel synthesis technique for implementing robust digital computation in nanoscale lattices with random interconnects: percolation theory on random graphs. We exploit the non-linearity that occurs through percolation to produce Boolean functionality. We show that the error margins, defined in terms of the steepness of the non-linearity, translate into the degree of defect tolerance. We study the problem of mapping Boolean functions onto lattices with good error margins.

In this paper, improved CMRR, high gain CMOS current-mode operational amplifier (COA) is presented. A new class AB input stage is used in order to obtain very low input resistance. The proposed COA is operated under ±1.5 V voltage supplies and designed with 0.35-μm CMOS process. Results of simulation indicate a 107 dB DC gain, 123 Ω input resistance, common mode rejection ratio exceeding 110dB and a gain-bandwidth product at about 100 MHz.