such as the orientation of a line in the visual field or the location of Two main goals for reconstruction are approached in this the body in space are coded as activity levels in populations of neurons. Reconstruction or decoding is an inverse problem in which paper. The first goal is technical and is exemplified by the the physical variables are estimated from observed neural activity. population vector method applied to motor cortical activities Reconstruction is useful first in quantifying how much information during various reaching tasks (Georgopoulos et al. 1986, 1989; about the physical variables is present in the population and, second, Schwartz 1994) and the template matching method applied to in providing insight into how the brain might use distributed represen- disparity selective cells in the visual cortex (Lehky and Sejnowtations in solving related computational problems such as visual ob- ski 1990) and hippocampal place cells during rapid learning of ject recognition and spatial navigation. Two classes of reconstruction place fields in a novel environment (Wilson and McNaughton methods, namely, probabilistic or Bayesian methods and basis func- 1993). In these examples, reconstruction extracts information tion methods, are discussed. They include important existing methods from noisy neuronal population activity and transforms it to a

Coarse codes are widely used throughout the brain to encode sensory and motor variables. Methods designed to interpret these codes, such as population vector analysis, are either inefficient (the variance of the estimate is much larger than the smallest possible variance) or biologically implausible, like maximum likelihood. Moreover, these methods attempt to compute a scalar or vector estimate of the encoded variable. Neurons are faced with a similar estimation problem. They must read out the responses of the presynaptic neurons, but, by contrast, they typically encode the variable with a further population code rather than as a scalar. We show how a nonlinear recurrent network can be used to perform estimation in a near-optimal way while keeping the estimate in a coarse code format. This work suggests that lateral connections in the cortex may be involved in cleaning up uncorrelated noise among neurons representing similar variables.

A large number of human psychophysical results have been successfully explained in recent years using Bayesian models. However, the neural implementation of such mod-els remains largely unclear. In this paper, we show that a network architecture com-monly used to model the cerebral cortex can implement Bayesian inference for an arbi-trary hidden Markov model. We illustrate the approach using an orientation discrimi-nation task and a visual motion detection task. In the case of orientation discrimination, we show that the model network can infer the posterior distribution over orientations and correctly estimate stimulus orientation in the presence of significant noise. In the case of motion detection, we show that the resulting model network exhibits direction selectivity and correctly computes the posterior probabilities over motion direction and position. When used to solve the well-known random dots motion discrimination task, the model generates responses that mimic the activities of evidence-accumulating neu-rons in cortical areas LIP and FEF. The framework introduced in the paper posits a new interpretation of cortical activities in terms of log posterior probabilities of stimuli occurring in the natural world. 1 1

For a robot, an animal, and even for man, to be able to use an internal representation of the spatial layout of its environment to position itself is a very complex task, which raises numerous issues of perception, categorization and motor control that must all be solved in an integrated manner to promote survival. This point is illustrated here, within the framework of a review of localization strategies in mobile robots. The allothetic and idiothetic sensors that may be used by these robots to build internal representations of their environment, and the maps in which these representations may be instantiated, are first described. Then map-based navigation systems are categorized according to a 3-level hierarchy of localization strategies, which respectively call upon direct position inference, single-hypothesis tracking, and multiple-hypothesis tracking. The advantages and drawbacks of these strategies, notably with respect to the limitations of the sensors on which they rely, are discussed throughout the text.

Perceptual inference fundamentally involves uncertainty, arising from noise in sensation and the ill-posed nature of many perceptual problems. Accurate perception requires that this uncertainty be correctly represented, manipulated, and learned about. The choices made by subjects in various psychophysical experiments suggest that they do indeed take such uncertainty into account when making perceptual inferences, posing the question as to how uncertainty is represented in the activities of neuronal populations. Most theoretical investigations of population coding have ignored this issue altogether; the few existing proposals that address it, do so in such a way that it is fatally conflated with another facet of perceptual problems that also needs correct handling, namely multiplicity (that is, the simultaneous presence of multiple distinct stimuli). We present and validate a more powerful proposal for the way that population activity may encode uncertainty, both distinctly from, and simultaneously with, multiplicity.

We study the synthesis of neural coding, selective attention and perceptual decision making. A hierarchical neural architecture is proposed, which implements Bayesian integration of noisy sensory input and topdown attentional priors, leading to sound perceptual discrimination. The model offers an explicit explanation for the experimentally observed modulation that prior information in one stimulus feature (location) can have on an independent feature (orientation). The network’s intermediate levels of representation instantiate known physiological properties of visual cortical neurons. The model also illustrates a possible reconciliation of cortical and neuromodulatory representations of uncertainty. 1

There is growing evidence from psychophysical and neurophysiological studies that the brain utilizes Bayesian principles for inference and decision making. An important open question is how Bayesian inference for arbitrary graphical models can be implemented in networks of spiking neurons. In this paper, we show that recurrent networks of noisy integrate-and-fire neurons can perform approximate Bayesian inference for dynamic and hierarchical graphical models. The membrane potential dynamics of neurons is used to implement belief propagation in the log domain. The spiking probability of a neuron is shown to approximate the posterior probability of the preferred state encoded by the neuron, given past inputs. We illustrate the model using two examples: (1) a motion detection network in which the spiking probability of a direction-selective neuron becomes proportional to the posterior probability of motion in a preferred direction, and (2) a two-level hierarchical network that produces attentional effects similar to those observed in visual cortical areas V2 and V4. The hierarchical model offers a new Bayesian interpretation of attentional modulation in V2 and V4. 1

Don’t confuse the moon with the finger that points at it. Zen proverb iii iv This thesis introduces and explores a new type of representation for low and medium level vision operations called channel representation. The channel representation is a more general way to represent information than e.g. as numerical values, since it allows incorporation of uncertainty, and simultaneous representation of several hypotheses. More importantly it also allows the representation of “no information ” when no statement can be given. A channel representation of a scalar value is a vector of channel values, which are generated by passing the original scalar value through a set of kernel functions. The resultant representation is sparse and monopolar. The word sparse signifies that information is not necessarily

This paper describes a navigation system implemented on a real mobile robot. Using simple sonar and visual sensors, it makes possible the autonomous construction of a dense topological map representing the environment. At any time during the mapping process, this system is able to globally localize the robot, i.e. to estimate the robot's position even if the robot is passively moved from one place to another within the mapped area. This is achieved using algorithms inspired by Hidden Markov Models adapted to the on-line building of the map. Advantages and drawbacks of the system are discussed, along with its potential implications for the understanding of biological navigation systems.

Most theoretical and empirical studies of population codes make the assumption that underlying neuronal activities is a unique and unambiguous value of an encoded quantity. However, population activities can contain additional information about such things as multiple values of or uncertainty about the quantity. We have previously suggested a method to recover extra information by treating the activities of the population of cells as coding for a complete distribution over the coded quantity rather than just a single value. We now show how this approach bears on psychophysical and neurophysiological studies of population codes for motion direction in tasks involving transparent motion stimuli. We show that, unlike standard approaches, it is able to recover multiple motions from population responses, and also that its output is consistent with both correct and erroneous human performance on psychophysical tasks. A population code can be defined as a set of units whose activities collectively encode some underlying variable (or variables). The standard view is that population codes are useful for accurately encoding the underlying variable when the individual units are noisy. Current statistical approaches to interpreting population activity reflect this view, in that they determine the optimal single value that explains the observed activity pattern given a particular model of the noise (and possibly a loss function). In our work, we have pursued an alternative hypothesis, that the population encodes additional information about the underlying variable, including multiple values and uncertainty. The Distributional Population Coding (DPC) framework finds the best probability distribution across values that fits the population activity