We compare 10 methods of classifying fMRI volumes by applying them to data from a longitudinal study of stroke recovery: adaptive Fisher's linear and quadratic discriminant; gaussian naive Bayes; support vector machines with linear, quadratic, and radial basis function (RBF) kernels; logistic regression; two novel methods based on pairs of restricted Boltzmann machines (RBM); and K-nearest neighbors. All methods were tested on three binary classification tasks, and their out-of-sample classification accuracies are compared. The relative performance of the methods varies considerably across subjects and classification tasks. The best overall performers were adaptive quadratic discriminant, support vector machines with RBF kernels, and generatively trained pairs of RBMs.

Naturally occurring sensory stimuli are dynamic. In this letter, we consider how spiking neural populations might transmit information about continuous dynamic stimulus variables. The combination of simple encoders and temporal stimulus correlations leads to a code in which information is not readily available to downstream neurons. Here, we explore a complex encoder that is paired with a simple decoder that allows representation and manipulation of the dynamic information in neural systems. The encoder we present takes the form of a biologically plausible recurrent spiking neural network where the output population recodes its inputs to produce spikes that are independently decodeable. We show that this network can be learned in a supervised manner by a simple local learning rule.

Uncertainty coming from the noise in its neurons and the ill-posed nature of many tasks plagues neural computations. Maybe surprisingly, many studies show that the brain manipulates these forms of uncertainty in a probabilistically consistent and normative manner, and there is now a rich theoretical literature on the capabilities of populations of neurons to implement computations in the face of uncertainty. However, one major facet of uncertainty has received comparatively little attention: time. In a dynamic, rapidly changing world, data are only temporarily relevant. Here, we analyze the computational consequences of encoding stimulus trajectories in populations of neurons. For the most obvious, simple, instantaneous encoder, the correlations induced by natural, smooth stimuli engender a decoder that requires access to information that is nonlocal both in time and across neurons. This formally amounts to a ruinous representation. We show that there is an alternative encoder that is computationally and representationally powerful in which each spike contributes independent information; it is independently decodable, in other words. We suggest this as an appropriate foundation for understanding time-varying population codes. Furthermore, we show how adaptation to temporal stimulus statistics emerges directly from the demands of simple decoding.

Attractor networks, which map an input space to a discrete output space, are useful for pattern completion—cleaning up noisy or missing input features. However, designing a net to have a given set of attractors is notoriously tricky; training procedures are CPU intensive and often produce spurious attractors and ill-conditioned attractor basins. These difficulties occur because each connection in the network participates in the encoding of multiple attractors. We describe an alternative formulation of attractor networks in which the encoding of knowledge is local, not distributed. Although localist attractor networks have similar dynamics to their distributed counterparts, they are much easier to work with and interpret. We propose a statistical formulation of localist attractor net dynamics, which yields a convergence proof and a mathematical interpretation of model parameters. We present simulation experiments that explore the behavior of localist attractor networks, showing that they yield few spurious attractors, and they readily exhibit two desirable properties of psychological and neurobiological models: priming (faster convergence to an attractor if the attractor has been recently visited) and gang effects (in which the presence of an attractor enhances the attractor basins of neighboring attractors).

We present a general encoding-decoding framework for interpreting the activity of a population of units. A standard population code interpretation method, the Poisson model, starts from a description as to how a single value of an underlying quantity can generate the activities of each unit in the population. In casting it in the encoding-decoding framework, we find that this model is too restrictive to describe fully the activities of units in population codes in higher processing areas, such as the medial temporal area. Under a more powerful model, the population activity can convey information not only about a single value of some quantity but also about its whole distribution, including its variance, and perhaps even the certainty the system has in the actual presence in the world of the entity generating this quantity. We propose a novel method for forming such probabilistic interpretations of population codes and compare it to the existing method.

Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the parameters to maximize the probability of the observed patterns. We describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations. Our method can be viewed as a form of hierarchical self-supervised learning that may relate to the function of bottom-up and top-down cortical processing pathways.

If different causes can interact on any occasion to generate a set of patterns, then systems modeling the generation have to model the interaction too. We discuss a way of combining multiple causes that is based on the Integrated Segmentation and Recognition architecture of Keeler et al. (1991). It is more cooperative than the scheme embodied in the mixture of experts architecture, which insists that just one cause generate each output, and more competitive than the noisy-or combination function, which was recently suggested by Saund (1994a,b). Simulations confirm its efficacy.

The minimum description length (MDL) principle can be used to train the hidden units of a neural network to extract a representation that is cheap to describe but nonetheless allows the input to be reconstructed accurately. We show how MDL can be used to develop highly redundant population codes. Each hidden unit has a location in a low-dimensional implicit space. If the hidden unit activities form a bump of a standard shape in this space, they can be cheaply encoded by the center of this bump. So the weights from the input units to the hidden units in an autoencoder are trained to make the activities form a standard bump. The coordinates of the hidden units in the implicit space are also learned, thus allowing flexibility, as the network develops a discontinuous topography when presented with different input classes.

Despite the fact that complex visual scenes contain multiple, overlapping objects, people perform object recognition with ease and accuracy. One operation that facilitates recognition is an early segmentation process in which features of objects are grouped and labeled according to which object they belong. Current computational systems that perform this operation are based on predefined grouping heuristics. We describe a system called MAGIC that learns how to group features based on a set of presegmented examples. In many cases, MAGIC discovers grouping heuristics similar to those previously proposed, but it also has the capability of finding nonintuitive structural regularities in images. Grouping is performed by a relaxation network that attempts to dynamically bind related features. Features transmit a complex-valued signal (amplitude and phase) to one another; binding can thus be represented by phase locking related features. MAGIC's training procedure is a generalization of recurrent backpropagation to complex-valued units.