The Posit number system provides a promising alternative to traditional floating-point (FP) formats for deep neural network (DNN) training by offering tapered precision and a wide dynamic range, addressing key limitations of conventional FP formats. While recent research has demonstrated the advantages of Posit-enabled training and inference for fixed-precision applications, the development of mixed-precision frameworks has been hindered by the absence of rounding algorithms for transitioning between Posit formats. This dependency has limited the practical adoption of Posits in DNN workflows. In this article, we present a Posit-based Mixed Precision Training and Inference (PMP) framework, leveraging Posit32, Posit16, and Posit8 for distinct computational stages. Posit32 ensures numerical stability in critical operations, Posit16 balances precision and efficiency for intermediate computations, and Posit8 significantly reduces memory usage during inference. Specifically, we introduce algorithms for converting Posit32 representations into Posit16 and Posit8 , and vice versa, under two rounding modes: deterministic and stochastic. Stochastic rounding is employed to mitigate precision loss in low-precision arithmetic. Furthermore, we propose a hardware-efficient Posit Multiply-Accumulate (pMAC) Unit that integrates deterministic and stochastic rounding modules, enabling efficient mixed-precision computations. We validate our framework on ResNet-18, ResNet-50, ResNet-152, MobileNet-v2, VGG-16, and EfficientNet-B7 (trained on ImageNet), YOLOv2 (trained on PASCAL VOC 2012), and BERT (trained on WikiText-2). Experimental results demonstrate up to 1.5× training speedup with Posit16 -based PMP framework and up to 6.5× training speedup with Posit8 -based PMP framework when compared with fixed-precision FP32 training, while maintaining comparable or superior accuracy. Moreover, hardware results show that the design overhead of integrating proposed deterministic and stochastic rounding modules with the pMAC unit is estimated to be around 4.6% only.

This paper presents a Posit-based Mixed Precision (PMP) framework for deep neural network (DNN) training and inference, leveraging Posit32, Posit16, and Posit8 across different computational stages. We develop deterministic and stochastic rounding algorithms to enable high-to-low bit conversions between Posit formats, and integrate them into a hardware-efficient Posit Multiply-Accumulate (pMAC) unit. Evaluation results preformed on ResNet-50 and YOLOv2 model demonstrates up to 14× training speedup with Posit8, while maintaining accuracy comparable to FP32. Further, the additional hardware overhead for rounding support is limited to 4.6%.

Approximate computing (AxC) reduces power consumption with minimal accuracy loss, benefiting error-tolerant, compute-intensive tasks such as machine learning, deep learning, and image processing. However, existing AxC methods often ignore the vulnerability to soft errors. Such errors can interact with approximation-induced errors, causing system failures or unexpected exceptions. To our knowledge, no work has addressed both soft error resilience and exception avoidance in approximate floating-point computing. This gap is particularly critical in deep neural network (DNN) inference, where soft error-induced errors or exceptions can significantly affect the stability and accuracy of computations.In this paper, we introduce SERA-Float, an approximate floating-point format resilient to soft errors. Specifically, it is designed to protect floating-point computations from soft error-induced errors and exception-triggering bit-flips. Unlike prior floating-point formats, SERA-Float protects the sign and exponent bits using error-correcting codes and relies on storing 8 valid bits of mantissa rather than performing coarse truncation. Additionally, by tracking critical bits in the floating-point representation, SERA-Float prevents overflow, underflow, and NaN exceptions. Our evaluation demonstrates that SERA-Float improves the reliability of floating-point operations during DNN inference by significantly reducing exceptions and ensuring the stability of computations. Moreover, it enables energy-efficient arithmetic by leveraging narrower arithmetic units, yielding up to 80.3% energy savings per multiplication with a 0.9% reduction in DNN inference accuracy.

Approximate arithmetic circuits have gained prominence in modern computing systems due to their ability to trade accuracy for improved performance and energy efficiency. However, their susceptibility to stealthy Trojan attacks poses a significant security concern. This work analyzes Trojan attacks on approximate circuits, focusing specifically on approximate adders and multipliers. We propose SATGuard, a boolean satisfiability (SAT)-based methodology to identify Trojan activating inputs (TAIs) for all approximate adder and multiplier families. We also claim that TAIs for approximate circuits are analogous to test input patterns for accurate circuits. Subsequently, we propose design-specific countermeasures to safeguard approximate circuits. The proposed countermeasures nullify the Hardware Trojan Horse (HTH)-based accuracy degradation, thus upholding the application-level accuracy requirements. We conduct experiments where potential Trojans are implanted into various approximate adders and multipliers. We evaluate their impact on the error metrics and the quality of results in real-world applications such as image processing and deep neural networks (DNNs). Our findings demonstrate that the proposed methodology successfully reverses the HTH-based accuracy degradation by 99.4%, and 99.8% in approximate adders and multipliers, respectively. This improvement is achieved with an average area overhead of 5.3% and a power-delay-product overhead of 7.6% in approximate adders and 1.7% and 1.9% in multipliers, respectively.

Approximate computing (AC) techniques provide overall performance gains in terms of power and energy savings at the cost of minor loss in application accuracy. For this reason, AC has emerged as a viable method for efficiently supporting several compute-intensive applications, e.g., machine learning, deep learning, and image processing, that can tolerate bounded errors in computations. However, most prior techniques do not consider the possibility of soft errors or malicious bit-flips in AC systems. These errors may interact with approximation-introduced errors in unforeseen ways, leading to disastrous consequences, such as the failure of computing systems. A recent research effort, FTApprox (DATE’21) proposes an error-resilient approximate data format. FTApprox stores two blocks, starting from the one containing the most significant valid (MSV) bit. It also stores location of the MSV block and protects them using error-correcting bits (ECBs). However, FTApprox has crucial limitations such as lack of flexibility, redundantly storing zeros in the MSV, etc. In this paper, we propose a novel storage format named Versatile Approximate Data Format (VADF) for storing approximate integer numbers while providing resilience to soft errors. VADF prescribes rules for storing, for example, a 32-bit number in either 8-bit, 12-bit or 16-bit numbers. VADF identifies the MSV bit and stores a certain number of bits following the MSV bit. It also stores the location of the MSV bit and protects it by ECBs. VADF does not explicitly store the MSB bit itself and this prevents VADF from accruing significant errors. VADF incurs lower error than both truncation methodologies and FTApprox. We further evaluate five image-processing and machine-learning applications and confirm that VADF provides higher application quality than FTApprox in the presence and absence of soft errors. Finally, VADF allows the use of narrow arithmetic units. For example, instead of using a 32-bit multiplier/adder, one can first use VADF (or FTApprox) to compress the data and then use a 8-bit multiplier/adder. Through this approach, VADF facilitates 95.97% and 79.3% energy savings in multiplication and addition, respectively. However, the subsequent re-conversion of the 8-bit output data to 32-bit data using Inv-VADF(16,3,32) diminishes the energy savings by 9.6% for addition and 0.56% for multiplication operation, respectively. The code is available at https://github.com/CandleLabAI/VADF-ApproximateDataFormat-TECS .

This paper proposes a novel merged-accumulation-based approximate MAC (multiply-accumulate) unit, MEGA-MAC, for accelerating error-resilient applications. MEGA-MAC utilizes a novel rearrangement and compression strategy in the multiplication stage and a novel approximate "carry predicting adder" (CPA) in the accumulation stage. Addition and multiplication operations are merged, which reduces the delay. MEGA-MAC provides knobs to exercise a tradeoff between accuracy and resource overhead. Compared to the accurate MAC unit, MEGA-MAC(8,6) (i.e., a MEGA-MAC unit with a chunk size of 6 bits, operating on 8-bit input operands) reduces the power-delay-product (PDP) by 49.4%, while incurring a mean error percentage of only 4.2%. Compared to state-of-art approximate MAC units, MEGA-MAC achieves a better balance between resource-saving and accuracy-loss. The source code is available at https://sites.google.com/view/mega-mac-approximate-mac-unit/.

In recent times, approximate computing has emerged as a promising technique to achieve significant power and energy benefits in computational systems. It is widely employed in fault-tolerant computationally intensive applications that require large arithmetic blocks. Applications such as image processing and machine learning often invoke the Multiply-Accumulate (MAC) unit for convolution operations. This paper proposes a novel architecture for an (unsigned × unsigned) approximate rounding and truncation based MAC unit named ART-MAC. It replaces the accurate multiplier architecture with an approximate multiplier proposed along with this work, thus improving the overall Quality of Results (QoR). The proposed design consumes 35.35% less power and showcases a significant speedup of 1.23 times when compared to the conventional MAC unit. On an average, the ART-MAC consumes 7.44% lesser on-chip area and showcases 13.49% lesser power-delay-product (PDP) compared to existing state-of-the-art designs.

Approximate Computing aims at achieving better performance at a marginal loss of accuracy in error-resilient applications. Several approximate arithmetic circuits have been proposed in the past which use carry prediction schemes, block-based approaches and genetic algorithms. However, these architectures are usually non power-aware and often incur large area overhead with the introduction of re-configurability. This work explores a new facet of approximation, which involves using the Unified Power Format (UPF) model to introduce approximation on additions. We call this methodology AxLEAP. Further, we validate the proposed methodology on a new approximate adder, which we term as AxL-Add. AxL-Add has a simple and re-configurable design with a marginal area overhead of 1.69% over accurate adder. After extensive evaluation, we show that our methodology is up to 67% better in terms of power consumption while providing near accurate results at the end application.

In recent times, approximate computing has found significant use in applications that can tolerate partially inaccurate results. This tolerance can be exploited to design simpler hardware aimed at getting area and energy benefits. In this work, we propose a novel technique to multiply two unsigned binary numbers through a Segmentation based Approximate Multiplier (SAM). The proposed design reduces the size of the Partial Products Matrix (PPM) in the order of n × (2n — 1) to a Reduced Partial Product Matrix (R-PPM) of the order 4 × 2n. Additionally, it also eliminates the extra hardware required for compression and rearrangement of partial products. μ-SAM, an optimized version of our basic design is also proposed along with this work. μ-SAM further minimizes the on-chip area and power consumption of the basic design. The basic design consumes 32.43% lesser on-chip area when compared to the conventional Wallace tree multiplier [1] and produces results that are 89.1% more accurate when compared to other existing state-of-the-art designs such as TOSAM [2], LETAM [3], and DQ4:2C4 [4].

In this paper, we derive accurate outage probability and bit error rate expressions for a high altitude platform station (HAPS) assisted terrestrial communication system. In particular, HAPS is deployed as a relay node to assist two ground stations for data transmission. Each ground station-to-HAPS communication link works on a hybrid radio frequency (RF) and free space optics (FSO) mode. Selection combining is performed at the HAPS and the destination ground station to select either RF or FSO link based on the instantaneous channel signal-to-noise ratio (SNR). The derived expressions provide insights on system design and assist analyzing HAPS-terrestrial integrated network supported by hybrid RF/FSO system. The accuracy of the derived outage probability and bit error rate expressions are validated with extensive computer simulations.

Approximate computing has in recent times found significant applications towards lowering power, area, and time requirements for arithmetic operations. Several works done in recent years have furthered approximate computing along these directions. In this work, we propose a new approximate adder that employs a carry prediction method. This allows parallel propagation of the carry allowing faster calculations. In addition to the basic adder design, we also propose a rectification logic which would enable higher accuracy for larger computations. Experimental results show that our adder produces results 91.2% faster than the conventional ripple-carry adder. In terms of accuracy, the addition of rectification logic to the basic design produces results that are more accurate than state-of-the-art adders like SARA[13] and BCSA[5] by 74%.