Symbolic Representation and Learning With Hyperdimensional Computing

Abstract

It has been proposed that machine learning techniques can benefit from symbolic representations and reasoning systems. We describe a method in which the two can be combined in a natural and direct way by use of hyperdimensional vectors and hyperdimensional computing. By using hashing neural networks to produce binary vector representations of images, we show how hyperdimensional vectors can be constructed such that vector-symbolic inference arises naturally out of their output. We design the Hyperdimensional Inference Layer (HIL) to facilitate this process and evaluate its performance compared to baseline hashing networks. In addition to this, we show that separate network outputs can directly be fused at the vector symbolic level within HILs to improve performance and robustness of the overall model. Furthermore, to the best of our knowledge, this is the first instance in which meaningful hyperdimensional representations of images are created on real data, while still maintaining hyperdimensionality.

A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges

“…When compared to the standard aggregation methods in (mobile robotics) place recognition experiments, HVs of the aggregated descriptors demonstrated average performance better than alternative methods (except the exhaustive pair-wise comparison). A very similar concept was demonstrated in [Mitrokhin et al, 2020] using an image classification task, see also Table 15. One of the proposed ways of forming image HV used the superposition of three binary HVs obtained from three different hashing neural networks.…”

“…For example, as mentioned in Section 3.4.3 in [Kleyko et al, 2021c], it is very common to use activations of convolutional neural networks to form HVs of images. This is commonly done using the standard pre-trained neural networks [Yilmaz, 2015b], [Mitrokhin et al, 2020], . Two challenges here are to increase the dimensionality and change the format of the neural network representations to conform with the HV format requirements.…”

“…Two challenges here are to increase the dimensionality and change the format of the neural network representations to conform with the HV format requirements. Some neural networks already produce binary vectors (see [Mitrokhin et al, 2020]), and the transformation to HVs was in randomly repeated those components to get the necessary dimensionality. In [Karunaratne et al, 2021b], the authors first guided a convolutional neural network to produce HDC/VSA-conforming vectors with the aid of proper attention and sharpening functions, and then just used the sign function to transform those real-valued vectors to bipolar HVs (of the same dimensionality).…”

Robust high-dimensional memory-augmented neural networks

“…Besides the few shot classification task that we highlighted in this work, there are several tantalizing prospects for the HD learned patterns in the key memory. They form vector-symbolic representations that can directly be used for reasoning, or multimodal fusion across separate networks 38 . The key-value memory also becomes the central ingredient in many recent models for unsupervised and contrastive learning [39][40][41] where a huge number of prototype vectors should be efficiently stored, compared, compressed, and retrieved.…”

Spiking Hyperdimensional Network: Neuromorphic Models Integrated with Memory-Inspired Framework

“…The human brain remains the most sophisticated processing component that has ever existed. The ever-growing research in biological vision, cognitive psychology, and neuroscience has given rise to many concepts that have led to prolific advancement in artificial intelligent accomplishing cognitive tasks [41][42][43].…”