Related papers: Block Format Error Bounds and Optimal Block Size S…

Large Language Models (LLMs) have intensified the need for low-precision formats that enable efficient, large-scale inference. The Open Compute Project (OCP) Microscaling (MX) standard is attractive due to its favorable hardware efficiency,…

We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance…

Deep Neural Networks (DNN) represent a performance-hungry application. Floating-Point (FP) and custom floating-point-like arithmetic satisfies this hunger. While there is need for speed, inference in DNNs does not seem to have any need for…

GPU-based fast Fourier transform (FFT) is extremely important for scientific computing and signal processing. However, we find the inefficiency of existing FFT libraries and the absence of fault tolerance against soft error. To address…

Inner and outer bounds are derived on the optimal performance of fixed length block codes on discrete memoryless channels with feedback and errors-and-erasures decoding. First an inner bound is derived using a two phase encoding scheme with…

Fluid dynamics simulations with the lattice Boltzmann method (LBM) are very memory-intensive. Alongside reduction in memory footprint, significant performance benefits can be achieved by using FP32 (single) precision compared to FP64…

In a large class of deep learning models, including vector embedding models such as word and database embeddings, we observe that floating point exponent values cluster around a few unique values, permitting entropy based data compression.…

Low-precision training is considered an effective strategy for reducing both training and downstream inference costs. Previous scaling laws for precision mainly focus on integer quantization, which pay less attention to the constituents in…

Deep Feedforward Neural Networks' (DFNNs) weights estimation relies on the solution of a very large nonconvex optimization problem that may have many local (no global) minimizers, saddle points and large plateaus. As a consequence,…

Recently, a class of fractal surface codes (FSCs), has been constructed on fractal lattices with Hausdorff dimension $2+\epsilon$, which admits a fault-tolerant non-Clifford CCZ gate. We investigate the performance of such FSCs as…

Discrete diffusion language models have shown strong potential for text generation, yet standard supervised fine-tuning (SFT) misaligns with their semi-autoregressive inference: training randomly masks tokens across the entire response,…

This preliminary white paper proposes a novel 8-bit floating-point data format HiFloat8 (abbreviated as HiF8) for deep learning. HiF8 features tapered precision. For normal value encoding, it provides 7 exponent values with 3-bit mantissa,…

Deep neural networks are commonly developed and trained in 32-bit floating point format. Significant gains in performance and energy efficiency could be realized by training and inference in numerical formats optimized for deep learning.…

FP8 low-precision formats have gained significant adoption in Transformer inference and training. However, existing digital compute-in-memory (DCIM) architectures face challenges in supporting variable FP8 aligned-mantissa bitwidths, as…

As LLMs scale, low-bit floating-point formats like MXFP and NVFP4 offer new opportunities for precision and efficiency. In this work, we evaluate HiFloat (HiF8 and HiF4), a family of formats tailored for Ascend NPUs. Through rigorous…

When quantizing neural networks for efficient inference, low-bit integers are the go-to format for efficiency. However, low-bit floating point numbers have an extra degree of freedom, assigning some bits to work on an exponential scale…

Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models…

Limited magnitude asymmetric error model is well suited for flash memory. In this paper, we consider the construction of asymmetric codes correcting single error over $\mathbb{Z}_{2^{k}r}$ and which are based on so called $B_{1}[4](2^{k}r)$…

Kernel methods are widespread in machine learning; however, they are limited by the quadratic complexity of the construction, application, and storage of kernel matrices. Low-rank matrix approximation algorithms are widely used to address…

We establish a general formula for the maximum size of finite length block codes with minimum pairwise distance no less than $d$. The achievability argument involves an iterative construction of a set of radius-$d$ balls, each centered at a…