The idea of disentangled representations is to reduce the data to a set of generative factors that produce it. Typically, such representations are vectors in latent space, where each coordinate corresponds to one of the generative factors. The object can then be modified by changing the value of a particular coordinate, but it is necessary to determine which coordinate corresponds to the desired generative factor -- a difficult task if the vector representation has a high dimension. In this article, we propose ArSyD (Architecture for Symbolic Disentanglement), which represents each generative factor as a vector of the same dimension as the resulting representation. In ArSyD, the object representation is obtained as a superposition of the generative factor vector representations. We call such a representation a \textit{symbolic disentangled representation}. We use the principles of Hyperdimensional Computing (also known as Vector Symbolic Architectures), where symbols are represented as hypervectors, allowing vector operations on them. Disentanglement is achieved by construction, no additional assumptions about the underlying distributions are made during training, and the model is only trained to reconstruct images in a weakly supervised manner. We study ArSyD on the dSprites and CLEVR datasets and provide a comprehensive analysis of the learned symbolic disentangled representations. We also propose new disentanglement metrics that allow comparison of methods using latent representations of different dimensions. ArSyD allows to edit the object properties in a controlled and interpretable way, and the dimensionality of the object property representation coincides with the dimensionality of the object representation itself.

Hyperdimensional Computing (HDC) has obtained abundant attention as an emerging non von Neumann computing paradigm. Inspired by the way human brain functions, HDC leverages high dimensional patterns to perform learning tasks. Compared to neural networks, HDC has shown advantages such as energy efficiency and smaller model size, but sub-par learning capabilities in sophisticated applications. Recently, researchers have observed when combined with neural network components, HDC can achieve better performance than conventional HDC models. This motivates us to explore the deeper insights behind theoretical foundations of HDC, particularly the connection and differences with neural networks. In this paper, we make a comparative study between HDC and neural network to provide a different angle where HDC can be derived from an extremely compact neural network trained upfront. Experimental results show such neural network-derived HDC model can achieve up to 21% and 5% accuracy increase from conventional and learning-based HDC models respectively. This paper aims to provide more insights and shed lights on future directions for researches on this popular emerging learning scheme.

This article reviews recent progress in the development of the computing framework Vector Symbolic Architectures (also known as Hyperdimensional Computing). This framework is well suited for implementation in stochastic, nanoscale hardware and it naturally expresses the types of cognitive operations required for Artificial Intelligence (AI). We demonstrate in this article that the ring-like algebraic structure of Vector Symbolic Architectures offers simple but powerful operations on high-dimensional vectors that can support all data structures and manipulations relevant in modern computing. In addition, we illustrate the distinguishing feature of Vector Symbolic Architectures, "computing in superposition," which sets it apart from conventional computing. This latter property opens the door to efficient solutions to the difficult combinatorial search problems inherent in AI applications. Vector Symbolic Architectures are Turing complete, as we show, and we see them acting as a framework for computing with distributed representations in myriad AI settings. This paper serves as a reference for computer architects by illustrating techniques and philosophy of VSAs for distributed computing and relevance to emerging computing hardware, such as neuromorphic computing.

Various non-classical approaches of distributed information processing, such as neural networks, computation with Ising models, reservoir computing, vector symbolic architectures, and others, employ the principle of collective-state computing. In this type of computing, the variables relevant in a computation are superimposed into a single high-dimensional state vector, the collective-state. The variable encoding uses a fixed set of random patterns, which has to be stored and kept available during the computation. Here we show that an elementary cellular automaton with rule 90 (CA90) enables space-time tradeoff for collective-state computing models that use random dense binary representations, i.e., memory requirements can be traded off with computation running CA90. We investigate the randomization behavior of CA90, in particular, the relation between the length of the randomization period and the size of the grid, and how CA90 preserves similarity in the presence of the initialization noise. Based on these analyses we discuss how to optimize a collective-state computing model, in which CA90 expands representations on the fly from short seed patterns - rather than storing the full set of random patterns. The CA90 expansion is applied and tested in concrete scenarios using reservoir computing and vector symbolic architectures. Our experimental results show that collective-state computing with CA90 expansion performs similarly compared to traditional collective-state models, in which random patterns are generated initially by a pseudo-random number generator and then stored in a large memory.

Heretofore, neural networks with external memory are restricted to single memory with lossy representations of memory interactions. A rich representation of relationships between memory pieces urges a high-order and segregated relational memory. In this paper, we propose to separate the storage of individual experiences (item memory) and their occurring relationships (relational memory). The idea is implemented through a novel Self-attentive Associative Memory (SAM) operator. Found upon outer product, SAM forms a set of associative memories that represent the hypothetical high-order relationships between arbitrary pairs of memory elements, through which a relational memory is constructed from an item memory. The two memories are wired into a single sequential model capable of both memorization and relational reasoning. We achieve competitive results with our proposed two-memory model in a diversity of machine learning tasks, from challenging synthetic problems to practical testbeds such as geometry, graph, reinforcement learning, and question answering.