Computational linear algebra over finite fields

We present here algorithms for efficient computation of linear algebra problems over finite fields

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

ViTCoD: Vision Transformer Acceleration via Dedicated Algorithm and Accelerator Co-Design

Vision Transformers (ViTs) have achieved state-of-the-art performance on various vision tasks. However, ViTs' self-attention module is still arguably a major bottleneck, limiting their achievable hardware efficiency. Meanwhile, existing accelerators dedicated to NLP Transformers are not optimal for ViTs. This is because there is a large difference between ViTs and NLP Transformers: ViTs have a relatively fixed number of input tokens, whose attention maps can be pruned by up to 90% even with fixed sparse patterns; while NLP Transformers need to handle input sequences of varying numbers of tokens and rely on on-the-fly predictions of dynamic sparse attention patterns for each input to achieve a decent sparsity (e.g., >=50%). To this end, we propose a dedicated algorithm and accelerator co-design framework dubbed ViTCoD for accelerating ViTs. Specifically, on the algorithm level, ViTCoD prunes and polarizes the attention maps to have either denser or sparser fixed patterns for regularizing two levels of workloads without hurting the accuracy, largely reducing the attention computations while leaving room for alleviating the remaining dominant data movements; on top of that, we further integrate a lightweight and learnable auto-encoder module to enable trading the dominant high-cost data movements for lower-cost computations. On the hardware level, we develop a dedicated accelerator to simultaneously coordinate the enforced denser/sparser workloads and encoder/decoder engines for boosted hardware utilization. Extensive experiments and ablation studies validate that ViTCoD largely reduces the dominant data movement costs, achieving speedups of up to 235.3x, 142.9x, 86.0x, 10.1x, and 6.8x over general computing platforms CPUs, EdgeGPUs, GPUs, and prior-art Transformer accelerators SpAtten and Sanger under an attention sparsity of 90%, respectively.Comment: Accepted to HPCA 202

Analysis and Synthesis of Digital Dyadic Sequences

We explore the space of matrix-generated (0, m, 2)-nets and (0, 2)-sequences in base 2, also known as digital dyadic nets and sequences. In computer graphics, they are arguably leading the competition for use in rendering. We provide a complete characterization of the design space and count the possible number of constructions with and without considering possible reorderings of the point set. Based on this analysis, we then show that every digital dyadic net can be reordered into a sequence, together with a corresponding algorithm. Finally, we present a novel family of self-similar digital dyadic sequences, to be named $\xi$-sequences, that spans a subspace with fewer degrees of freedom. Those $\xi$-sequences are extremely efficient to sample and compute, and we demonstrate their advantages over the classic Sobol (0, 2)-sequence.Comment: 17 pages, 11 figures. Minor improvement of exposition; references to earlier proofs of Theorems 3.1 and 3.3 adde