Related papers: Efficient, arbitrarily high precision hardware log…
Single-precision floating point (FP32) data format, defined by the IEEE 754 standard, is widely employed in scientific computing, signal processing, and deep learning training, where precision is critical. However, FP32 multiplication is…
We propose a new instruction (FPADDRE) that computes the round-off error in floating-point addition. We explain how this instruction benefits high-precision arithmetic operations in applications where double precision is not sufficient.…
Recently, the demand of low-power deep-learning hardware for industrial applications has been increasing. Most existing artificial intelligence (AI) chips have evolved to rely on new chip technologies rather than on radically new hardware…
We present an algorithm to compute arbitrary multi-loop massive Feynman diagrams in the region where the typical energy scale \sqrt{s} is much larger than the typical mass scale M, i.e. s>>M^2, while various different energy and mass…
In this work, we provide energy-efficient architectural support for floating point accuracy. Our goal is to provide accuracy that is far greater than that provided by the processor's hardware floating point unit (FPU). Specifically, for…
Traditional digital implementations of neural accelerators are limited by high power and area overheads, while analog and non-CMOS implementations suffer from noise, device mismatch, and reliability issues. This paper introduces a CMOS…
In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks…
We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error…
Analog mixed-signal (AMS) devices promise faster, more energy-efficient deep neural network (DNN) inference than their digital counterparts. However, recent studies show that DNNs on AMS devices with fixed-point numbers can incur an…
CNNs have been shown to maintain reasonable classification accuracy when quantized to lower precisions. Quantizing to sub 8-bit activations and weights can result in accuracy falling below an acceptable threshold. Techniques exist for…
We present algorithms for real and complex dot product and matrix multiplication in arbitrary-precision floating-point and ball arithmetic. A low-overhead dot product is implemented on the level of GMP limb arrays; it is about twice as fast…
Representing deep neural networks (DNNs) in low-precision is a promising approach to enable efficient acceleration and memory reduction. Previous methods that train DNNs in low-precision typically keep a copy of weights in high-precision…
Iterative algorithms are widely used in digital signal processing applications. With the case study of radio astronomy calibration processing, this work contributes towards revealing and exploiting the intrinsic error resilience of…
We present an optimal rate convergence analysis for a second order accurate in time, fully discrete finite difference scheme for the Cahn-Hilliard-Navier-Stokes (CHNS) system, combined with logarithmic Flory-Huggins energy potential. The…
In the numerical linear algebra community, it was suggested that to obtain nearly optimal bounds for various problems such as rank computation, finding a maximal linearly independent subset of columns (a basis), regression, or low-rank…
In modern computing units, division operations are generally slower than other arithmetic operations and require more resources, such as area and power, than multiplication. To reduce the delay, fast division algorithms use an initial…
With the proliferation of embedded systems requiring intelligent behavior, custom number systems to optimize performance per Watt of the entire system become essential components for successful commercial products. We present the Universal…
A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…
In this paper, we propose LoopLynx, a scalable dataflow architecture for efficient LLM inference that optimizes FPGA usage through a hybrid spatial-temporal design. The design of LoopLynx incorporates a hybrid temporal-spatial architecture,…
Approximate computing (AC) leverages the inherent error resilience and is used in many big-data applications from various domains such as multimedia, computer vision, signal processing, and machine learning to improve systems performance…