Hyperdimensional (HD) computing (also referred to as vector symbolic architectures, VSAs) offers a method for encoding symbols into vectors, allowing for those symbols to be combined in different ways to form other vectors in the same vector space. The vectors and operators form a compositional algebra, such that composite vectors can be decomposed back to their constituent vectors. Many useful algorithms have implementations in HD computing, such as classification, spatial navigation, language modeling, and logic. In this letter, we propose a spiking implementation of Fourier holographic reduced representation (FHRR), one of the most versatile VSAs. The phase of each complex number of an FHRR vector is encoded as a spike time within a cycle. Neuron models derived from these spiking phasors can perform the requisite vector operations to implement an FHRR. We demonstrate the power and versatility of our spiking networks in a number of foundational problem domains, including symbol binding and unbinding, spatial representation, function representation, function integration, and memory (i.e., signal delay).

Predictive coding (PC) networks are a biologically interesting class of neural networks. Their layered hierarchy mimics the reciprocal connectivity pattern observed in the mammalian cortex, and they can be trained using local learning rules that approximate backpropagation (Bogacz, 2017). However, despite having feedback connections that enable information to flow down the network hierarchy, discriminative PC networks are not typically generative. Clamping the output class and running the network to equilibrium yields an input sample that usually does not resemble the training input. This letter studies this phenomenon and proposes a simple solution that promotes the generation of input samples that resemble the training inputs. Simple decay, a technique already in wide use in neural networks, pushes the PC network toward a unique minimum two-norm solution, and that unique solution provably (for linear networks) matches the training inputs. The method also vastly improves the samples generated for nonlinear networks, as we demonstrate on MNIST.

The processes of evolution and learning interact. Learning is an evolved strategy that improves fitness, especially in a world where some aspects cannot realistically be encoded in the genome. We endeavored to see if evolution could sculpt a generic neuroplasticity mechanism into a learning rule that would give virtual organisms an advantage in a simulated foraging environment. Our virtual organisms have brains with nine neurons. The connections between those neurons are adjusted by a plasticity rule that is computed by another fixed neural network. Evolution experiments repeatedly found plasticity networks that conferred an adaptive advantage, even outperforming populations that were given a parametric Hebbian plasticity mechanism. Evolution also favored the inclusion of genetically encoded heterogeneity. We also investigate how behavior is influenced by various brainand movement-related energy penalty terms in the fitness function.

In a real brain, the act of perception is a bidirectional process, depending on both feedforward sensory pathways and feedback pathways that carry expectations. We are interested in how such a neural network might emerge from a biologically plausible learning rule. Other neural network learning methods either only apply to feedforward networks, or employ assumptions (such as weight copying) that render them unlikely in a real brain. Predictive estimators (PEs) offer a better solution to this bidirectional learning scenario. However, PEs also depend on weight copying. In this paper, we propose the symmetric PE (SPE), an architecture that can learn both feedforward and feedback connection weights individually using only locally available information. We demonstrate that the SPE can learn complicated mappings without the use of weight copying. The SPE networks also show promise in deeper architectures.

This paper presents a nearest neighbor partitioning method designed to improve the performance of a neural-network classifier. For neural-network classifiers, usually the number, positions, and labels of centroids are fixed in partition space before training. However, that approach limits the search for potential neural networks during optimization; the quality of a neural network classifier is based on how clear the decision boundaries are between classes. Although attempts have been made to generate floating centroids automatically, these methods still tend to generate sphere-like partitions and cannot produce flexible decision boundaries. We propose the use of nearest neighbor classification in conjunction with a neural-network classifier. Instead of being bound by sphere-like boundaries (such as the case with centroid-based methods), the flexibility of nearest neighbors increases the chance of finding potential neural networks that have arbitrarily shaped boundaries in partition space. Experimental results demonstrate that the proposed method exhibits superior performance on accuracy and average f-measure.

One of the main tasks in neuroscience research is to interpret the activity of neurons. Given some neuroscientific data, such as spike trains, one tries to decipher how the activity of the neurons relate to the outside world and/or the behaviour of the animal. The discovery of place cells and grid cells are great examples - discoveries that garnered a Nobel Prize in 2014. However, the spatial patterns exhibited by such cells are only the beginning of our understanding of spatial representation in the brain. In this paper, we apply an evolutionary algorithm to discover spatial patterns exhibited in cells from the entorhinal cortex to see (1) if we can automatically deduce an accurate model for the hexagonal-grid pattern, and (2) if we can discover a more general model that also incorporates grid-cell-like variants that have been observed, but not understood.

Evolution is extremely creative. The mere availability of a mechanism for synaptic change seems to be enough for evolution to derive a learning rule. Many simulations of evolution have evolved learning in a highly guided manner. Either by constraining the update function to a Hebbian form, or by supplying an error/teaching signal. In this paper, we aim to evolve a more general learning rule. And since neural networks are so versatile, we construct the learning function itself out of a neural network. Our evolved networks excel at the foraging task they evolved in. Amazingly, they even function robustly when tested outside of their historical niche. The same cannot be said for the Hebbian learning networks we compare to.

In gene expression programming, diversity can be reduced during evolution, sometimes resulting in premature convergence because of non-coding regions, leading to substantial reproduction of repeated individuals. In order to increase the diversity of the population and to avoid premature convergence, we propose a new diversity preservation tournament operator, adopting a tree-based similarity measurement and global probability weights. Furthermore, the proposed tournament operator is embedded into a hybrid evolution architecture to search for a parsimonious model for the firing pattern of grid cells, neurons in the mammalian brain involved in navigation. Experimental results demonstrate that the proposed diversity preservation tournament improves the performance of gene expression programming for evolving a model for grid-cell data.

Navigation and path integration in rodents seems to involve place cells, grid cells, and theta oscillations (4-12 Hz) in the local field potential. Two main theories have been proposed to explain the neurological underpinnings of how these phenomena relate to navigation and to each other. Attractor network (AN) models revolve around the idea that local excitation and long-range inhibition connectivity can spontaneously generate grid-cell-like activity patterns. Oscillator interference (OI) models propose that spatial patterns of activity are caused by the interference patterns between neural oscillators. In rats, these oscillators have a frequency close to the theta frequency. Recent studies have shown that bats do not exhibit a theta cycle when they crawl, and yet they still have grid cells. This has been interpreted as a criticism of OI models. However, OI models do not require theta oscillations. We explain why the absence of theta oscillations does not contradict OI models and discuss how the two families of models might be distinguished experimentally.

Many registration scenarios involve aligning more than just two images. These image sets-called ensembles-are conventionally registered by choosing one image as a template, and every other image is registered to it. This pairwise approach is problematic because results depend on which image is chosen as the template. The issue is particularly acute for multisensor ensembles because different sensors create images with different features. Also, pairwise methods use only a fraction of the available data at a time. In this paper, we propose a maximum-likelihood clustering method that registers all the images in a multisensor ensemble simultaneously. Experiments involving rigid-body and affine transformations show that the clustering method is more robust and accurate than competing pairwise registration methods. Moreover, the clustering results can be used to form a rudimentary segmentation of the image ensemble.

This paper describes an automated image restoration algorithm. The technique is based on the Stockwell transform (ST) and its discrete version, the discrete orthonormal Stockwell transform (DOST). These mathematical transforms provide a multiresolution spatial-frequency representation of a signal or image. First, we give a brief introduction to the Stockwell transform, and the DOST. Then we describe a restoration method using the DOST based on the total variation (TV) minimization model. The results show that the DOST restoration outperforms the wavelet restoration by giving a higher Peak Signal to Noise Ratio (PSNR).

Nonlocal-means (NL-means) is an image denoising method that replaces each pixel by a weighted average of all the pixels in the image. Unfortunately, the method requires the computation of the weighting terms for all possible pairs of pixels, making it computationally expensive. Some short-cuts assign a weight of zero to any pixel pairs whose neighbourhood averages are too dissimilar. In this paper, we propose an alternative strategy that uses the SVD to more efficiently eliminate pixel pairs that are dissimilar. Experiments comparing this method against other NL-means speed-up strategies show that its refined discrimination between similar and dissimilar pixel neighbourhoods significantly improves the denoising effect.

This paper introduces a novel approach to the problem of image inpainting through the use of nonlocal-means. In traditional inpainting techniques, only local information around the target regions are used to fill in the missing information, which is insufficient in many cases. More recent inpainting techniques based on the concept of exemplar-based synthesis utilize nonlocal information but in a very limited way. In the proposed algorithm, we use nonlocal image information from multiple samples within the image. The contribution of each sample to the reconstruction of a target pixel is determined using an weighted similarity function and aggregated to form the missing information. Experimental results show that the proposed method yields quantitative and qualitative improvements compared to the current exemplar-based approach. The proposed approach can also be integrated into existing exemplar-based inpainting techniques to provide improved visual quality.

This paper presents a fast Fourier transform (FFT)-accelerated approach designed to handle many of the difficulties associated with the registration of optical and light detection and ranging (LIDAR) images. The proposed algorithm utilizes an exhaustive region correspondence search technique to determine the correspondence between regions of interest from the optical image with the LIDAR image over all translations for various rotations. The computational cost associated with exhaustive search is greatly reduced by exploiting the FFT. The substantial differences in intensity mappings between optical and LIDAR images are addressed through local feature mapping transformation optimization. Geometric distortions in the underlying images are dealt with through a geometric transformation estimation process that handles various transformations such as translation, rotation, scaling, shear, and perspective transformations. To account for mismatches caused by factors such as severe contrast differences, the proposed algorithm attempts to prune such outliers using the random sample consensus technique to improve registration accuracy. The proposed algorithm has been tested using various optical and LIDAR images and evaluated based on its registration accuracy. The results indicate that the proposed algorithm is suitable for the multimodal invariant registration of optical and LIDAR images.

Current multimodal registration methods almost always rely on local gradient-descent type optimization strategies. Such registration methods often converge to an incorrect local optimum, especially when the initial misregistration is large. There are monomodal image registration methods that employ global optimization techniques. This paper introduces the use of these global optimization methods for multimodal image registration. The goal is to robustly bring the images into close enough registration that a local optimization method could fine-tune the solution. The method proposed here is based on edge information extracted from the images. Positive results from a modest set of test cases suggests that this approach is promising.

There are many image registration situations in which the initial misalignment of the two images is large. These registration problems, often involving comparison of the two images only within a region of interest (ROI), are difficult to solve. Most intensity-based registration methods perform local optimization of their cost function and often miss the global optimum when the initial misregistration is large. The registration of multimodal images makes the problem even more difficult since it limits the choice of available cost functions. We have developed an efficient method, capable of multimodal rigid-body registration within an ROI, that performs an exhaustive search over all integer translations, and a local search over rotations. The method uses the fast Fourier transform to efficiently compute the sum of squared differences cost function for all possible integer pixel shifts, and for each shift models the relationship between the intensities of the two images using linear regression. Test cases involving medical imaging, remote sensing and forensic science applications show that the method consistently brings the two images into close registration so that a local optimization method should have no trouble fine-tuning the solution.

In clinical applications where structural asymmetries between homologous shapes have been correlated with pathology, the questions of definition and quantification of "asymmetry" arise naturally. When not only the degree but the position of deformity is thought relevant, asymmetry localization must also be addressed. Asymmetries between paired shapes have already been formulated in terms of (nonrigid) diffeomorphisms between the shapes. For the infinity of such maps possible for a given pair, we define optimality as the minimization of deviation from isometry under the constraint of piecewise deformation homogeneity. We propose a novel variational formulation for segmenting asymmetric regions from surface pairs based on the minimization of a functional of both the deformation map and the segmentation boundary, which defines the regions within which the homogeneity constraint is to be enforced. The functional minimization is achieved via a quasi-simultaneous evolution of the map and the segmenting curve, conducted on and between two-dimensional surface parametric domains. We present examples using both synthetic data and pairs of left and right hippocampal structures and demonstrate the relevance of the extracted features through a clinical epilepsy classification analysis.