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Motivated by recent innovations in biologically inspired neuromorphic hardware, this article presents a novel unsupervised machine learning algorithm named Hyperseed that draws on the principles of vector symbolic architectures (VSAs) for fast learning of a topology preserving feature map of unlabeled data. It relies on two major operations of VSA, binding and bundling. The algorithmic part of Hyperseed is expressed within the Fourier holographic reduced representations (FHRR) model, which is specifically suited for implementation on spiking neuromorphic hardware. The two primary contributions of the Hyperseed algorithm are few-shot learning and a learning rule based on single vector operation. These properties are empirically evaluated on synthetic datasets and on illustrative benchmark use cases, IRIS classification, and a language identification task using the $n$ -gram statistics. The results of these experiments confirm the capabilities of Hyperseed and its applications in neuromorphic hardware.

Multilayer neural networks set the current state of the art for many technical classification problems. But, these networks are still, essentially, black boxes in terms of analyzing them and predicting their performance. Here, we develop a statistical theory for the one-layer perceptron and show that it can predict performances of a surprisingly large variety of neural networks with different architectures. A general theory of classification with perceptrons is developed by generalizing an existing theory for analyzing reservoir computing models and connectionist models for symbolic reasoning known as vector symbolic architectures. Our statistical theory offers three formulas leveraging the signal statistics with increasing detail. The formulas are analytically intractable, but can be evaluated numerically. The description level that captures maximum details requires stochastic sampling methods. Depending on the network model, the simpler formulas already yield high prediction accuracy. The quality of the theory predictions is assessed in three experimental settings, a memorization task for echo state networks (ESNs) from reservoir computing literature, a collection of classification datasets for shallow randomly connected networks, and the ImageNet dataset for deep convolutional neural networks. We find that the second description level of the perceptron theory can predict the performance of types of ESNs, which could not be described previously. Furthermore, the theory can predict deep multilayer neural networks by being applied to their output layer. While other methods for prediction of neural networks performance commonly require to train an estimator model, the proposed theory requires only the first two moments of the distribution of the postsynaptic sums in the output neurons. Moreover, the perceptron theory compares favorably to other methods that do not rely on training an estimator model.

Memory-augmented neural networks enhance a neural network with an external key-value (KV) memory whose complexity is typically dominated by the number of support vectors in the key memory. We propose a generalized KV memory that decouples its dimension from the number of support vectors by introducing a free parameter that can arbitrarily add or remove redundancy to the key memory representation. In effect, it provides an additional degree of freedom to flexibly control the tradeoff between robustness and the resources required to store and compute the generalized KV memory. This is particularly useful for realizing the key memory on in-memory computing hardware where it exploits nonideal, but extremely efficient nonvolatile memory devices for dense storage and computation. Experimental results show that adapting this parameter on demand effectively mitigates up to 44% nonidealities, at equal accuracy and number of devices, without any need for neural network retraining.

Variable binding is a cornerstone of symbolic reasoning and cognition. But how binding can be implemented in connectionist models has puzzled neuroscientists, cognitive psychologists, and neural network researchers for many decades. One type of connectionist model that naturally includes a binding operation is vector symbolic architectures (VSAs). In contrast to other proposals for variable binding, the binding operation in VSAs is dimensionality-preserving, which enables representing complex hierarchical data structures, such as trees, while avoiding a combinatoric expansion of dimensionality. Classical VSAs encode symbols by dense randomized vectors, in which information is distributed throughout the entire neuron population. By contrast, in the brain, features are encoded more locally, by the activity of single neurons or small groups of neurons, often forming sparse vectors of neural activation. Following Laiho et al. (2015), we explore symbolic reasoning with a special case of sparse distributed representations. Using techniques from compressed sensing, we first show that variable binding in classical VSAs is mathematically equivalent to tensor product binding between sparse feature vectors, another well-known binding operation which increases dimensionality. This theoretical result motivates us to study two dimensionality-preserving binding methods that include a reduction of the tensor matrix into a single sparse vector. One binding method for general sparse vectors uses random projections, the other, block-local circular convolution, is defined for sparse vectors with block structure, sparse block-codes. Our experiments reveal that block-local circular convolution binding has ideal properties, whereas random projection based binding also works, but is lossy. We demonstrate in example applications that a VSA with block-local circular convolution and sparse block-codes reaches similar performance as classical VSAs. Finally, we discuss our results in the context of neuroscience and neural networks.