arXiv subjects

Gioele Gottardo

Publications and source records attributed to Gioele Gottardo.

3 recordsLinked to original sources

arXiv2026

Fast and Stable Triangular Inversion for Delta-Rule Linear Transformers

Linear attention has emerged as a cornerstone for efficient long-context architectures, as evidenced by its integration into state-of-the-art open-source models including Qwen3.5/3.6, Kimi Linear, and RWKV-7. Models that incorporate linear attention layers with the so-called Delta-Rule involve the inversion of triangular matrices as a core sub-routine. This operation often forms a performance bottleneck, and, due to its high-sensitivity to numerical errors, it can significantly deteriorate end-to-end model accuracy if it is not carefully implemented. This work provides a systematic analysis of both direct and iterative triangular inversion algorithms, targeting methods that are rich in matrix products, and, therefore, have the potential to efficiently utilize modern hardware. To that end, our analysis covers a broad spectrum of mathematical and practical aspects, with a heavy focus on numerical stability, computational complexity, and, ultimately, hardware efficiency and practical considerations. We provide a rigorous experimental evaluation to verify these properties in practical scenarios, and in low-precision floating-point representations, highlighting the strengths and limitations of each method. Performance benchmarks on NPUs reveal up to $4.3\times$ speed-up against the state-of-the-art implementations of SGLang for triangular matrix inversion, leading to significant performance improvements on the entire layer level, while maintaining full end-to-end model accuracy.

cs.LG↗

arXiv2025

PerfDojo: Automated ML Library Generation for Heterogeneous Architectures

The increasing complexity of machine learning models and the proliferation of diverse hardware architectures (CPUs, GPUs, accelerators) make achieving optimal performance a significant challenge. Heterogeneity in instruction sets, specialized kernel requirements for different data types and model features (e.g., sparsity, quantization), and architecture-specific optimizations complicate performance tuning. Manual optimization is resource-intensive, while existing automatic approaches often rely on complex hardware-specific heuristics and uninterpretable intermediate representations, hindering performance portability. We introduce PerfLLM, a novel automatic optimization methodology leveraging Large Language Models (LLMs) and Reinforcement Learning (RL). Central to this is PerfDojo, an environment framing optimization as an RL game using a human-readable, mathematically-inspired code representation that guarantees semantic validity through transformations. This allows effective optimization without prior hardware knowledge, facilitating both human analysis and RL agent training. We demonstrate PerfLLM's ability to achieve significant performance gains across diverse CPU (x86, Arm, RISC-V) and GPU architectures.

cs.PF↗

arXiv2025

Parallel Scan on Ascend AI Accelerators

We design and implement parallel prefix sum (scan) algorithms using Ascend AI accelerators. Ascend accelerators feature specialized computing units: the cube units for efficient matrix multiplication and the vector units for optimized vector operations. A key feature of the proposed scan algorithms is their extensive use of matrix multiplications and accumulations enabled by the cube unit. To showcase the effectiveness of these algorithms, we also implement and evaluate several scan-based operators commonly used in AI workloads, including sorting, tensor masking, and top-$k$ / top-$p$ sampling. Our single-core results demonstrate substantial performance improvements, with speedups ranging from $5\times$ to $9.6\times$ compared to vector-only implementations for sufficiently large input lengths. Additionally, we present a multi-core scan algorithm that fully utilizes both the cube and vector units of Ascend, reaching up to 74.9\% of the memory bandwidth achieved by memory copy. Furthermore, our radix sort implementation, which utilizes matrix multiplications for its parallel splits, showcases the potential of matrix engines to enhance complex operations, offering up to $3.3\times$ speedup over the vector-only baseline.

cs.DC↗