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When training deep neural networks, keeping all tensors in high precision (e.g., 32-bit or even 16-bit floats) is often wasteful. However, keeping all tensors in low precision (e.g., 8-bit floats) can lead to unacceptable accuracy loss.…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
The use of low-precision fixed-point arithmetic along with stochastic rounding has been proposed as a promising alternative to the commonly used 32-bit floating point arithmetic to enhance training neural networks training in terms of…
We propose basic and natural assumptions under which iterative optimization methods with compressed iterates can be analyzed. This problem is motivated by the practice of federated learning, where a large model stored in the cloud is…
Lossy compression plays a growing role in scientific simulations where the cost of storing their output data can span terabytes. Using error bounded lossy compression reduces the amount of storage for each simulation; however, there is no…
Block Floating-Point (BFP) is emerging as an attractive data format for edge Neural Processing Units (NPUs), combining wide dynamic range with high hardware efficiency. However, its behavior under hardware faults and suitability for…
Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…
In this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. So far, various window functions…
There are a prohibitively large number of floating-point time series data generated at an unprecedentedly high rate. An efficient, compact and lossless compression for time series data is of great importance for a wide range of scenarios.…
An alternative approach to two-part 'critical compression' is presented. Whereas previous results were based on summing a lossless code at reduced precision with a lossy-compressed error or noise term, the present approach uses a similar…
Fast Fourier Transform (FFT) is an essential tool in scientific and engineering computation. The increasing demand for mixed-precision FFT has made it possible to utilize half-precision floating-point (FP16) arithmetic for faster speed and…
Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…
FP-Growth algorithm is a Frequent Pattern Min- ing (FPM) algorithm that has been extensively used to study correlations and patterns in large scale datasets. While several researchers have designed distributed memory FP-Growth algorithms,…
The typical processors used for scientific computing have fixed-width data-paths. This implies that mathematical libraries were specifically developed to target each of these fixed precisions (binary16, binary32, binary64). However, to…
In scientific simulations, observations, and experiments, the cost of transferring data to and from disk and across networks has become a significant bottleneck that particularly impacts subsequent data analysis and visualization. To…
This paper studies the joint data and semantics lossy compression problem, i.e., an extension of the hidden lossy source coding problem that entails recovering both the hidden and observable sources. We aim to study the nonasymptotic and…
Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
Increasingly, visual signals such as images, videos and point clouds are being captured solely for the purpose of automated analysis by computer vision models. Applications include traffic monitoring, robotics, autonomous driving, smart…
We propose a scheme for reduced-precision representation of floating point data on a continuum between IEEE-754 floating point types. Our scheme enables the use of lower precision formats for a reduction in storage space requirements and…