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.

With the increasing rate of data generated by critical systems, estimating functions on streaming data has become essential. This demand has driven numerous advancements in algorithms designed to efficiently query and analyze one or more data streams while operating under memory constraints. The primary challenge arises from the rapid influx of new items, requiring algorithms that enable efficient incremental processing of streams in order to keep up. A prominent algorithm in this domain is the AMS sketch. Originally developed to estimate the second frequency moment of a data stream, it can also estimate the cardinality of the equi-join between two relations. Since then, two important advancements are the Count sketch, a method which significantly improves upon the sketch update time, and secondly, an extension of the AMS sketch to accommodate multi-join queries. However, combining the strengths of these methods to maintain sketches for multi-join queries while ensuring fast update times is a non-trivial task, and has remained an open problem for decades as highlighted in the existing literature. In this work, we successfully address this problem by introducing a novel sketching method which has fast updates, even for sketches capable of accurately estimating the cardinality of complex multi-join queries. We prove that our estimator is unbiased and has the same error guarantees as the AMS-based method. Our experimental results confirm the significant improvement in update time complexity, resulting in orders of magnitude faster estimates, with equal or better estimation accuracy.

Hyperdimensional Computing (HDC) is a computation framework based on random vector spaces, particularly useful for machine learning in resource-constrained environments. The encoding of information to the hyperspace is the most important stage in HDC. At its heart are basis-hypervectors, responsible for representing atomic information. We present a detailed study on basis-hypervectors, leading to broad contributions to HDC: 1) an improvement for level-hypervectors, used to encode real numbers; 2) a method to learn from circular data, an important type of information never before addressed in HDC. Results indicate that these contributions lead to considerably more accurate models for classification and regression.

Metrics for set similarity are a core aspect of several data mining tasks. To remove duplicate results in a Web search, for example, a common approach looks at the Jaccard index between all pairs of pages. In social network analysis, a much-celebrated metric is the Adamic-Adar index, widely used to compare node neighborhood sets in the important problem of predicting links. However, with the increasing amount of data to be processed, calculating the exact similarity between all pairs can be intractable. The challenge of working at this scale has motivated research into efficient estimators for set similarity metrics. The two most popular estimators, MinHash and SimHash, are indeed used in applications such as document deduplication and recommender systems where large volumes of data need to be processed. Given the importance of these tasks, the demand for advancing estimators is evident. We propose DotHash, an unbiased estimator for the intersection size of two sets. DotHash can be used to estimate the Jaccard index and, to the best of our knowledge, is the first method that can also estimate the Adamic-Adar index and a family of related metrics. We formally define this family of metrics, provide theoretical bounds on the probability of estimate errors, and analyze its empirical performance. Our experimental results indicate that DotHash is more accurate than the other estimators in link prediction and detecting duplicate documents with the same complexity and similar comparison time.

Hyperdimensional computing (HDC) is a novel computing framework that has gained significant attention for its ability to accelerate machine learning algorithms. Its fast learning and inference capabilities make it an ideal technique for various fields, including machine learning. HDC utilizes high-dimensional holographic vectors, which are vectors with independent and identically distributed dimensions, to represent information. This unique representation allows HDC to leverage highly parallelizable arithmetic operations such as bundling, binding and permute. These simple and highly optimizable operations make HDC an efficient framework for classification in embedded systems. HDC has demonstrated remarkable accuracy in learning patterns from sequenced data. In this paper, we propose a method to enhance the permute operation, which is crucial for maintaining the order of symbols or measures in real-time data. Our method enhances the efficiency of HDC's permute operations by a factor of 10×. Furthermore, by applying the same idea to n-gram encoding, we achieve a speedup of 14×, resulting in up to 26.8× speedup on a real application, compared to a state-of-the-art HDC prototyping library. To achieve this improvement, we utilized SIMD operations and shifted entire SIMD data blocks rather than individual elements. As a result, we demonstrate that real-time inference can be conducted rapidly in applications that are utilized in embedded systems with constrained computational and memory resources, such as those for recognizing emotions, gestures, and language.

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.

Most cloud services and distributed applications rely on hashing algorithms that allow dynamic scaling of a robust and efficient hash table. Examples include AWS, Google Cloud and BitTorrent. Consistent and rendezvous hashing are algorithms that minimize key remapping as the hash table resizes. While memory errors in large-scale cloud deployments are common, neither algorithm offers both efficiency and robustness. Hyperdimensional Computing is an emerging computational model that has inherent efficiency, robustness and is well suited for vector or hardware acceleration. We propose Hyperdimensional (HD) hashing and show that it has the efficiency to be deployed in large systems. Moreover, a realistic level of memory errors causes more than 20% mismatches for consistent hashing while HD hashing remains unaffected.

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.