Bayesian decoding to account for the presentation of multiple objects.

From olfaction to vision and audition, there is an increasing need, and a growing number of experiments [1]-[8] that study responses of sensory neurons to natural stimuli. Natural stimuli have specific statistical properties [9, 10], and therefore sample only a subspace of all possible spatial and temporal frequencies explored during stimulation with white noise. Observing the full dynamic range of neural responses may require using stimulus ensembles whichapproximate those occurring in nature, and it is an attractive hypothesis that the neural representation of these natural signals may be optimized in some way. Finally, some neuron responses are strongly nonlinear and adaptive, and may not be predicted from a combination of responses to simple stimuli. It has also been shown that the variability in neural response decreases substantially when dynamical, rather than static, stimuli are used [11, 12]. For all these reasons, it would be attractive to have a rigorous method of analyzing neural responses to complex, naturalistic inputs.

In Slow Feature Analysis (SFA [1]), it has been demonstrated that high-order invariant properties can be extracted by projecting inputs intoa nonlinear space and computing the slowest changing features in this space; this has been proposed as a simple general model for learning nonlinear invariances in the visual system. However, thismethod is highly constrained by the curse of dimensionality which limits it to simple theoretical simulations. This paper demonstrates that by using a different but closely-related objective function for extracting slowly varying features ([2, 3]), and then exploiting thekernel trick, this curse can be avoided. Using this new method we show that both the complex cell properties of translation invarianceand disparity coding can be learnt simultaneously from natural images when complex cells are driven by simple cells also learnt from the image. The notion of maximising an objective function based upon the temporal predictability ofoutput has been progressively applied in modelling the development of invariances in the visual system.

Cortical synaptic plasticity depends on the relative timing of pre-and postsynaptic spikes and also on the temporal pattern of presynaptic spikes and of postsynaptic spikes. We study the hypothesis that cortical synaptic plasticitydoes not associate individual spikes, but rather whole firing episodes,and depends only on when these episodes start and how long they last, but as little as possible on the timing of individual spikes. Here we present the mathematical background for such a study. Standard methodsfrom hidden Markov models are used to define what "firing episodes" are. Estimating the probability of being in such an episode requires not only the knowledge of past spikes, but also of future spikes. We show how to construct a causal learning rule, which depends only on past spikes, but associates pre-and postsynaptic firing episodes as if it also knew future spikes. We also show that this learning rule agrees with some features of synaptic plasticity in superficial layers of rat visual cortex (Froemke and Dan, Nature 416:433, 2002).

Re-mapping patterns in order to equalize their distribution may greatly simplify both the structure and the training of classifiers. Here, the properties of one such map obtained by running a few steps of discrete-time dynamical system are explored. The system is called'Digital Antennal Lobe' (DAL) because it is inspired by recent studies of the antennallobe, a structure in the olfactory system ofthe grasshopper. The pattern-spreading properties of the DAL as well as its average behavior as a function of its (few) design parametersare analyzed by extending previous results of Van Vreeswijk and Sompolinsky. Furthermore, a technique for adapting the parameters of the initial design in order to obtain opportune noise-rejection behavior is suggested.

Adaptation is a ubiquitous neural and psychological phenomenon, with a wealth of instantiations and implications. Although a basic form of plasticity, it has, bar some notable exceptions, attracted computational theory of only one main variety. In this paper, we study adaptation from the perspective of factor analysis, a paradigmatic technique of unsupervised learning.We use factor analysis to reinterpret a standard view of adaptation, and apply our new model to some recent data on adaptation in the domain of face discrimination.

We introduce the notion of Morton-style factorial coding and illustrate how it may help understand information integration and perceptual coding inthe brain. We show that by focusing on average responses one may miss the existence of factorial coding mechanisms that become only apparent when analyzing spike count histograms. We show evidence suggesting that the classical/nonclassical receptive field organization in the cortex effectively enforces the development of Morton-style factorial codes. This may provide some cues to help understand perceptual coding inthe brain and to develop new unsupervised learning algorithms. While methods like ICA (Bell & Sejnowski, 1997) develop independent codes, in Morton-style coding the goal is to make two or more external aspects of the world become independent when conditioning on internal representations.

A population of neurons typically exhibits a broad diversity of responses to sensory inputs. The intuitive notion of functional classification is that cells can be clustered so that most of the diversity is captured by the identity ofthe clusters rather than by individuals within clusters. We show how this intuition can be made precise using information theory, without anyneed to introduce a metric on the space of stimuli or responses. Applied to the retinal ganglion cells of the salamander, this approach recovers classicalresults, but also provides clear evidence for subclasses beyond those identified previously. Further, we find that each of the ganglion cellsis functionally unique, and that even within the same subclass only a few spikes are needed to reliably distinguish between cells.

Here we derive optimal gain functions for minimum mean square reconstruction fromneural rate responses subjected to Poisson noise. The shape of these functions strongly depends on the length T of the time window within which spikes are counted in order to estimate the underlying firingrate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three provided the minimum firing rate is zero. For a particular function class, we were able to prove the existence of a second-order phase transition analytically.The critical decoding time window length obtained from the analytical derivation is in precise agreement with the numerical results. We conclude that under most circumstances relevant to information processingin the brain, rate coding can be better ascribed to a binary (low-entropy) code than to the other extreme ofrich analog coding. 1 Optimal neuronal gain functions for short decoding time windows The use of action potentials (spikes) as a means of communication is the striking feature of neurons in the central nervous system.

Inner-product operators, often referred to as kernels in statistical learning, define amapping from some input space into a feature space. The focus of this paper is the construction of biologically-motivated kernels for cortical activities. Thekernels we derive, termed Spikernels, map spike count sequences into an abstract vector space in which we can perform various prediction tasks. We discuss in detail the derivation of Spikernels and describe an efficient algorithm forcomputing their value on any two sequences of neural population spike counts. We demonstrate the merits of our modeling approach using the Spikernel and various standard kernels for the task of predicting hand movement velocitiesfrom cortical recordings. In all of our experiments all the kernels we tested outperform the standard scalar product used in regression with the Spikernel consistently achieving the best performance.