Mike Heddes

Mike Heddes, Igor Nunes, Pere Vergés et al.

Hyperdimensional computing (HD), also known as vector symbolic architectures (VSA), is a framework for computing with distributed representations by exploiting properties of random high-dimensional vector spaces. The commitment of the scientific community to aggregate and disseminate research in this particularly multidisciplinary area has been fundamental for its advancement. Joining these efforts, we present Torchhd, a high-performance open source Python library for HD/VSA. Torchhd seeks to make HD/VSA more accessible and serves as an efficient foundation for further research and application development. The easy-to-use library builds on top of PyTorch and features state-of-the-art HD/VSA functionality, clear documentation, and implementation examples from well-known publications. Comparing publicly available code with their corresponding Torchhd implementation shows that experiments can run up to 100x faster. Torchhd is available at: https://github.com/hyperdimensional-computing/torchhd.

Pere Vergés, Mike Heddes, Igor Nunes et al.

Hyperdimensional Computing (HDC) is a bio-inspired computing framework that has gained increasing attention, especially as a more efficient approach to machine learning (ML). This work introduces the \name{} compiler, the first open-source compiler that translates high-level descriptions of HDC classification methods into optimized C code. The code generated by the proposed compiler has three main features for embedded systems and High-Performance Computing: (1) it is self-contained and has no library or platform dependencies; (2) it supports multithreading and single instruction multiple data (SIMD) instructions using C intrinsics; (3) it is optimized for maximum performance and minimal memory usage. \name{} is designed like a modern compiler, featuring an intuitive and descriptive input language, an intermediate representation (IR), and a retargetable backend. This makes \name{} a valuable tool for research and applications exploring HDC for classification tasks on embedded systems and High-Performance Computing. To substantiate these claims, we conducted experiments with HDCC on several of the most popular datasets in the HDC literature. The experiments were run on four different machines, including different hyperparameter configurations, and the results were compared to a popular prototyping library built on PyTorch. The results show a training and inference speedup of up to 132x, averaging 25x across all datasets and machines. Regarding memory usage, using 10240-dimensional hypervectors, the average reduction was 5x, reaching up to 14x. When considering vectors of 64 dimensions, the average reduction was 85x, with a maximum of 158x less memory utilization.

Igor Nunes, Mike Heddes, Tony Givargis et al.

Hyperdimensional Computing (HDC) developed by Kanerva is a computational model for machine learning inspired by neuroscience. HDC exploits characteristics of biological neural systems such as high-dimensionality, randomness and a holographic representation of information to achieve a good balance between accuracy, efficiency and robustness. HDC models have already been proven to be useful in different learning applications, especially in resource-limited settings such as the increasingly popular Internet of Things (IoT). One class of learning tasks that is missing from the current body of work on HDC is graph classification. Graphs are among the most important forms of information representation, yet, to this day, HDC algorithms have not been applied to the graph learning problem in a general sense. Moreover, graph learning in IoT and sensor networks, with limited compute capabilities, introduce challenges to the overall design methodology. In this paper, we present GraphHD$-$a baseline approach for graph classification with HDC. We evaluate GraphHD on real-world graph classification problems. Our results show that when compared to the state-of-the-art Graph Neural Networks (GNNs) the proposed model achieves comparable accuracy, while training and inference times are on average 14.6$\times$ and 2.0$\times$ faster, respectively.

Igor Nunes, Mike Heddes, Tony Givargis et al.

Hyperdimensional Computing (HDC) is a computation framework based on properties of high-dimensional random spaces. It is particularly useful for machine learning in resource-constrained environments, such as embedded systems and IoT, as it achieves a good balance between accuracy, efficiency and robustness. The mapping of information to the hyperspace, named encoding, is the most important stage in HDC. At its heart are basis-hypervectors, responsible for representing the smallest units of meaningful information. In this work we present a detailed study on basis-hypervector sets, which leads to practical contributions to HDC in general: 1) we propose an improvement for level-hypervectors, used to encode real numbers; 2) we introduce a method to learn from circular data, an important type of information never before addressed in machine learning with HDC. Empirical results indicate that these contributions lead to considerably more accurate models for both classification and regression with circular data.

Pere Verges, Igor Nunes, Mike Heddes et al.

Our work introduces an innovative approach to graph learning by leveraging Hyperdimensional Computing. Graphs serve as a widely embraced method for conveying information, and their utilization in learning has gained significant attention. This is notable in the field of chemoinformatics, where learning from graph representations plays a pivotal role. An important application within this domain involves the identification of cancerous cells across diverse molecular structures. We propose an HDC-based model that demonstrates comparable Area Under the Curve results when compared to state-of-the-art models like Graph Neural Networks (GNNs) or the Weisfieler-Lehman graph kernel (WL). Moreover, it outperforms previously proposed hyperdimensional computing graph learning methods. Furthermore, it achieves noteworthy speed enhancements, boasting a 40x acceleration in the training phase and a 15x improvement in inference time compared to GNN and WL models. This not only underscores the efficacy of the HDC-based method, but also highlights its potential for expedited and resource-efficient graph learning.

Mike Heddes, Narayan Srinivasa, Tony Givargis et al.

The excessive computational requirements of modern artificial neural networks (ANNs) are posing limitations on the machines that can run them. Sparsification of ANNs is often motivated by time, memory and energy savings only during model inference, yielding no benefits during training. A growing body of work is now focusing on providing the benefits of model sparsification also during training. While these methods greatly improve the training efficiency, the training algorithms yielding the most accurate models still materialize the dense weights, or compute dense gradients during training. We propose an efficient, always-sparse training algorithm with excellent scaling to larger and sparser models, supported by its linear time complexity with respect to the model width during training and inference. Moreover, our guided stochastic exploration algorithm improves over the accuracy of previous sparse training methods. We evaluate our method on CIFAR-10/100 and ImageNet using ResNet, VGG, and ViT models, and compare it against a range of sparsification methods.

Mike Heddes, Igor Nunes, Tony Givargis et al.

Tensor network contraction is a fundamental mathematical operation that generalizes the dot product and matrix multiplication. It finds applications in numerous domains, such as database systems, graph theory, machine learning, probability theory, and quantum mechanics. Tensor network contractions are computationally expensive, in general requiring exponential time and space. Sketching methods include a number of dimensionality reduction techniques that are widely used in the design of approximation algorithms. The existing sketching methods for tensor network contraction, however, only support acyclic tensor networks. We present the first method capable of approximating arbitrary tensor network contractions, including those of cyclic tensor networks. Additionally, we show that the existing sketching methods require a computational complexity that grows exponentially with the number of contractions. We present a second method, for acyclic tensor networks, whose space and time complexity depends only polynomially on the number of contractions.

Mike Heddes, Adel Javanmard, Kyriakos Axiotis et al.

Transformer networks have achieved remarkable success across diverse domains, leveraging a variety of architectural innovations, including residual connections. However, traditional residual connections, which simply sum the outputs of previous layers, can dilute crucial information. This work introduces DeepCrossAttention (DCA), an approach that enhances residual learning in transformers. DCA employs learnable, input-dependent weights to dynamically combine layer outputs, enabling the model to selectively focus on the most relevant information in any of the previous layers. Furthermore, DCA incorporates depth-wise cross-attention, allowing for richer interactions between layers at different depths. Our language modeling experiments show that DCA achieves improved perplexity for a given training time. Moreover, DCA obtains the same model quality up to 3x faster while adding a negligible number of parameters. Theoretical analysis confirms that DCA provides an improved trade-off between accuracy and model size when the ratio of collective layer ranks to the ambient dimension falls below a critical threshold.