Enrique S. Quintana–Ort́ı

Guillermo Alaejos, Adrián Castelló, Pedro Alonso-Jordá et al.

We explore the utilization of the Apache TVM open source framework to automatically generate a family of algorithms that follow the approach taken by popular linear algebra libraries, such as GotoBLAS2, BLIS and OpenBLAS, in order to obtain high-performance blocked formulations of the general matrix multiplication (GEMM). % In addition, we fully automatize the generation process, by also leveraging the Apache TVM framework to derive a complete variety of the processor-specific micro-kernels for GEMM. This is in contrast with the convention in high performance libraries, which hand-encode a single micro-kernel per architecture using Assembly code. % In global, the combination of our TVM-generated blocked algorithms and micro-kernels for GEMM 1)~improves portability, maintainability and, globally, streamlines the software life cycle; 2)~provides high flexibility to easily tailor and optimize the solution to different data types, processor architectures, and matrix operand shapes, yielding performance on a par (or even superior for specific matrix shapes) with that of hand-tuned libraries; and 3)~features a small memory footprint.

Jie Lei, José Flich, Enrique S. Quintana-Ortí

The remarkable positive impact of Deep Neural Networks on many Artificial Intelligence (AI) tasks has led to the development of various high performance algorithms as well as specialized processors and accelerators. In this paper we address this scenario by demonstrating that the principles underlying the modern realization of the general matrix multiplication (GEMM) in conventional processor architectures, are also valid to achieve high performance for the type of operations that arise in deep learning (DL) on an exotic accelerator such as the AI Engine (AIE) tile embedded in Xilinx Versal platforms. In particular, our experimental results with a prototype implementation of the GEMM kernel, on a Xilinx Versal VCK190, delivers performance close to 86.7% of the theoretical peak that can be expected on an AIE tile, for 16-bit integer operands.

Alberto Fernández-Hernández, Jose I. Mestre, Manuel F. Dolz et al.

We introduce the Overfitting-Underfitting Indicator (OUI), a novel tool for monitoring the training dynamics of Deep Neural Networks (DNNs) and identifying optimal regularization hyperparameters. Specifically, we validate that OUI can effectively guide the selection of the Weight Decay (WD) hyperparameter by indicating whether a model is overfitting or underfitting during training without requiring validation data. Through experiments on DenseNet-BC-100 with CIFAR- 100, EfficientNet-B0 with TinyImageNet and ResNet-34 with ImageNet-1K, we show that maintaining OUI within a prescribed interval correlates strongly with improved generalization and validation scores. Notably, OUI converges significantly faster than traditional metrics such as loss or accuracy, enabling practitioners to identify optimal WD (hyperparameter) values within the early stages of training. By leveraging OUI as a reliable indicator, we can determine early in training whether the chosen WD value leads the model to underfit the training data, overfit, or strike a well-balanced trade-off that maximizes validation scores. This enables more precise WD tuning for optimal performance on the tested datasets and DNNs. All code for reproducing these experiments is available at https://github.com/AlbertoFdezHdez/OUI.

Jose Duato, Jose I. Mestre, Manuel F. Dolz et al.

The number and complexity of artificial intelligence (AI) applications is growing relentlessly. As a result, even with the many algorithmic and mathematical advances experienced over past decades as well as the impressive energy efficiency and computational capacity of current hardware accelerators, training the most powerful and popular deep neural networks comes at very high economic and environmental costs. Recognising that additional optimisations of conventional neural network training is very difficult, this work takes a radically different approach by proposing GreenLightningAI, a new AI system design consisting of a linear model that is capable of emulating the behaviour of deep neural networks by subsetting the model for each particular sample. The new AI system stores the information required to select the system subset for a given sample (referred to as structural information) separately from the linear model parameters (referred to as quantitative knowledge). In this paper we present a proof of concept, showing that the structural information stabilises far earlier than the quantitative knowledge. Additionally, we show experimentally that the structural information can be kept unmodified when re-training the AI system with new samples while still achieving a validation accuracy similar to that obtained when re-training a neural network with similar size. Since the proposed AI system is based on a linear model, multiple copies of the model, trained with different datasets, can be easily combined. This enables faster and greener (re)-training algorithms, including incremental re-training and federated incremental re-training.

Jose I. Mestre, Alberto Fernández-Hernández, Cristian Pérez-Corral et al.

In this work we introduce GreenLightningAI (GLAI), a new architectural block designed as an alternative to conventional MLPs. The central idea is to separate two types of knowledge that are usually entangled during training: (i) *structural knowledge*, encoded by the stable activation patterns induced by ReLU activations; and (ii) *quantitative knowledge*, carried by the numerical weights and biases. By fixing the structure once stabilized, GLAI reformulates the MLP as a combination of paths, where only the quantitative component is optimized. This reformulation retains the universal approximation capabilities of MLPs, yet achieves a more efficient training process, reducing training time by ~40% on average across the cases examined in this study. Crucially, GLAI is not just another classifier, but a generic block that can replace MLPs wherever they are used, from supervised heads with frozen backbones to projection layers in self-supervised learning or few-shot classifiers. Across diverse experimental setups, GLAI consistently matches or exceeds the accuracy of MLPs with an equivalent number of parameters, while converging faster. Overall, GLAI establishes a new design principle that opens a direction for future integration into large-scale architectures such as Transformers, where MLP blocks dominate the computational footprint.

Héctor Martínez, Adrián Castelló, Francisco D. Igual et al.

Recent advances in deep learning (DL) have led to a shift from traditional 64-bit floating point (FP64) computations toward reduced-precision formats, such as FP16, BF16, and 8- or 16-bit integers, combined with mixed-precision arithmetic. This transition enhances computational throughput, reduces memory and bandwidth usage, and improves energy efficiency, offering significant advantages for resource-constrained edge devices. To support this shift, hardware architectures have evolved accordingly, now including adapted ISAs (Instruction Set Architectures) that expose mixed-precision vector units and matrix engines tailored for DL workloads. At the heart of many DL and scientific computing tasks is the general matrix-matrix multiplication gemm, a fundamental kernel historically optimized using axpy vector instructions on SIMD (single instruction, multiple data) units. However, as hardware moves toward mixed-precision dot-product-centric operations optimized for quantized inference, these legacy approaches are being phased out. In response to this, our paper revisits traditional high-performance gemm and describes strategies for adapting it to mixed-precision integer (MIP) arithmetic across modern ISAs, including x86_64, ARM, and RISC-V. Concretely, we illustrate novel micro-kernel designs and data layouts that better exploit today's specialized hardware and demonstrate significant performance gains from MIP arithmetic over floating-point implementations across three representative CPU architectures. These contributions highlight a new era of gemm optimization-driven by the demands of DL inference on heterogeneous architectures, marking what we term as the "Cambrian period" for matrix multiplication.

Alberto Fernández-Hernández, Jose I. Mestre, Manuel F. Dolz et al.

Initialization plays a critical role in Deep Neural Network training, directly influencing convergence, stability, and generalization. Common approaches such as Glorot and He initializations rely on randomness, which can produce uneven weight distributions across layer connections. In this paper, we introduce the Sinusoidal initialization, a novel deterministic method that employs sinusoidal functions to construct structured weight matrices expressly to improve the spread and balance of weights throughout the network while simultaneously fostering a more uniform, well-conditioned distribution of neuron activation states from the very first forward pass. Because Sinusoidal initialization begins with weights and activations that are already evenly and efficiently utilized, it delivers consistently faster convergence, greater training stability, and higher final accuracy across a wide range of models, including convolutional neural networks, vision transformers, and large language models. On average, our experiments show an increase of 4.9% in final validation accuracy and 20.9% in convergence speed. By replacing randomness with structure, this initialization provides a stronger and more reliable foundation for Deep Learning systems.

Rafael Rodríguez-Sánchez, Enrique S. Quintana-Ortí

Low-power asymmetric multicore processors (AMPs) attract considerable attention due to their appealing performance-power ratio for energy-constrained environments. However, these processors pose a significant programming challenge due to the integration of cores with different performance capabilities, asking for an asymmetry-aware scheduling solution that carefully distributes the workload. The recent HEVC standard, which offers several high-level parallelization strategies, is an important application that can benefit from an implementation tailored for the low-power AMPs present in many current mobile or hand-held devices. In this scenario, we present an architecture-aware implementation of an HEVC decoder that embeds a criticality-aware scheduling strategy tuned for a Samsung Exynos 5422 system-on-chip furnished with an ARM big.LITTLE AMP. The performance and energy efficiency of our solution is further enhanced by exploiting the NEON vector engine available in the ARM big.LITTLE architecture. Experimental results expose a 1080p real-time HEVC decoding at 24 frames/sec, and a reduction of energy consumption over 20%.

Sandra Catalán, Francisco D. Igual, Rafael Mayo et al.

Asymmetric multicore processors (AMPs) have recently emerged as an appealing technology for severely energy-constrained environments, especially in mobile appliances where heterogeneity in applications is mainstream. In addition, given the growing interest for low-power high performance computing, this type of architectures is also being investigated as a means to improve the throughput-per-Watt of complex scientific applications. In this paper, we design and embed several architecture-aware optimizations into a multi-threaded general matrix multiplication (gemm), a key operation of the BLAS, in order to obtain a high performance implementation for ARM big.LITTLE AMPs. Our solution is based on the reference implementation of gemm in the BLIS library, and integrates a cache-aware configuration as well as asymmetric--static and dynamic scheduling strategies that carefully tune and distribute the operation's micro-kernels among the big and LITTLE cores of the target processor. The experimental results on a Samsung Exynos 5422, a system-on-chip with ARM Cortex-A15 and Cortex-A7 clusters that implements the big.LITTLE model, expose that our cache-aware versions of gemm with asymmetric scheduling attain important gains in performance with respect to its architecture-oblivious counterparts while exploiting all the resources of the AMP to deliver considerable energy efficiency.

Matthias Petschow, Enrique Quintana-Orti, Paolo Bientinesi

The real symmetric tridiagonal eigenproblem is of outstanding importance in numerical computations; it arises frequently as part of eigensolvers for standard and generalized dense Hermitian eigenproblems that are based on a reduction to tridiagonal form. For its solution, the algorithm of Multiple Relatively Robust Representations (MRRR) is among the fastest methods. Although fast, the solvers based on MRRR do not deliver the same accuracy as competing methods like Divide & Conquer or the QR algorithm. In this paper, we demonstrate that the use of mixed precisions leads to improved accuracy of MRRR-based eigensolvers with limited or no performance penalty. As a result, we obtain eigensolvers that are not only equally or more accurate than the best available methods, but also -in most circumstances- faster and more scalable than the competition.