Silviu-Ioan Filip

Silviu-Ioan Filip, Yuji Nakatsukasa, Lloyd N. Trefethen et al.

Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far more robust algorithms than previously available can be developed by making use of rational barycentric representations whose support points are chosen in an adaptive fashion as the approximant is computed. Three variants of this barycentric strategy are all shown to be powerful: (1) a classical Remez algorithm, (2) a "AAA-Lawson" method of iteratively reweighted least-squares, and (3) a differential correction algorithm. Our preferred combination, implemented in the Chebfun MINIMAX code, is to use (2) in an initial phase and then switch to (1) for generically quadratic convergence. By such methods we can calculate approximations up to type (80, 80) of $|x|$ on $[-1, 1]$ in standard 16-digit floating point arithmetic, a problem for which Varga, Ruttan, and Carpenter required 200-digit extended precision.

Cédric Gernigon, Silviu-Ioan Filip, Olivier Sentieys et al.

One of the major bottlenecks in high-resolution Earth Observation (EO) space systems is the downlink between the satellite and the ground. Due to hardware limitations, on-board power limitations or ground-station operation costs, there is a strong need to reduce the amount of data transmitted. Various processing methods can be used to compress the data. One of them is the use of on-board deep learning to extract relevant information in the data. However, most ground-based deep neural network parameters and computations are performed using single-precision floating-point arithmetic, which is not adapted to the context of on-board processing. We propose to rely on quantized neural networks and study how to combine low precision (mini) floating-point arithmetic with a Quantization-Aware Training methodology. We evaluate our approach with a semantic segmentation task for ship detection using satellite images from the Airbus Ship dataset. Our results show that 6-bit floating-point quantization for both weights and activations can compete with single-precision without significant accuracy degradation. Using a Thin U-Net 32 model, only a 0.3% accuracy degradation is observed with 6-bit minifloat quantization (a 6-bit equivalent integer-based approach leads to a 0.5% degradation). An initial hardware study also confirms the potential impact of such low-precision floating-point designs, but further investigation at the scale of a full inference accelerator is needed before concluding whether they are relevant in a practical on-board scenario.

El-Mehdi El Arar, Massimiliano Fasi, Silviu-Ioan Filip et al.

Stochastic rounding (SR) is a probabilistic rounding mode that mitigates errors in large-scale numerical computations, especially when prone to stagnation effects. Beyond numerical analysis, SR has shown significant benefits in practical applications such as deep learning and climate modelling. The definition of classical SR requires that results of arithmetic operations are known with infinite precision. This is often not possible, and when it is, the resulting hardware implementation can become prohibitively expensive in terms of energy, area, and latency. A more practical alternative is limited-precision SR, which only requires that the outputs of arithmetic operations are available in higher, finite, precision. We extend previous work on limited-precision SR presented in [El Arar et al., SIAM J. Sci. Comput. 47(5) (2025), B1227-B1249], which developed a framework to evaluate the trade-off between accuracy and hardware resource cost in SR implementations. Within this framework, we study the Horner algorithm and pairwise summation, providing both theoretical insights and practical experiments in these settings when using limited-precision SR.

Cédric Gernigon, Silviu-Ioan Filip, Olivier Sentieys et al.

Large-scale deep neural networks (DNNs) have achieved remarkable success in many application scenarios. However, high computational complexity and energy costs of modern DNNs make their deployment on edge devices challenging. Model quantization is a common approach to deal with deployment constraints, but searching for optimized bit-widths can be challenging. In this work, we present Adaptive Bit-Width Quantization Aware Training (AdaQAT), a learning-based method that automatically optimizes weight and activation signal bit-widths during training for more efficient DNN inference. We use relaxed real-valued bit-widths that are updated using a gradient descent rule, but are otherwise discretized for all quantization operations. The result is a simple and flexible QAT approach for mixed-precision uniform quantization problems. Compared to other methods that are generally designed to be run on a pretrained network, AdaQAT works well in both training from scratch and fine-tuning scenarios.Initial results on the CIFAR-10 and ImageNet datasets using ResNet20 and ResNet18 models, respectively, indicate that our method is competitive with other state-of-the-art mixed-precision quantization approaches.

El-Mehdi El Arar, Silviu-Ioan Filip, Theo Mary et al.

This work proposes a mathematically founded mixed precision accumulation strategy for the inference of neural networks. Our strategy is based on a new componentwise forward error analysis that explains the propagation of errors in the forward pass of neural networks. Specifically, our analysis shows that the error in each component of the output of a layer is proportional to the condition number of the inner product between the weights and the input, multiplied by the condition number of the activation function. These condition numbers can vary widely from one component to the other, thus creating a significant opportunity to introduce mixed precision: each component should be accumulated in a precision inversely proportional to the product of these condition numbers. We propose a practical algorithm that exploits this observation: it first computes all components in low precision, uses this output to estimate the condition numbers, and recomputes in higher precision only the components associated with large condition numbers. We test our algorithm on various networks and datasets and confirm experimentally that it can significantly improve the cost--accuracy tradeoff compared with uniform precision accumulation baselines.