Learning the higher-order structure of a natural sound

Unsupervised learning algorithms paying attention only to second-order statistics ignore the phase structure (higher-order statistics) of signals, which contains all the informative temporal and spatial coincidences which we think of as 'features'. Here we discuss how an Independent Component Analysis (ICA) algorithm may be used to elucidate the higher-order structure of natural signals, yielding their independent basis functions. This is illustrated with the ICA transform of the sound of a fingernail tapping musically on a tooth. The resulting independent basis functions look like the sounds themselves, having similar temporal envelopes and the same musical pitches. Thus they reflect both the phase and frequency information inherent in the data.     

Integrate-and-fire neurons driven by correlated stochastic input

Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron's response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times of two simple integrate-and-fire model neurons driven by a correlated binary variable that represents the total input current. Analytic expressions were obtained for the average firing rate and coefficient of variation (a measure of spike-train variability) as functions of the mean, variance, and correlation time of the stochastic input. The results of computer simulations were in excellent agreement with these expressions. In these models, an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains. However, the magnitude of the changes depends differentially on the relative values of the input mean and variance: the increase in firing rate is higher when the variance is large relative to the mean, whereas the increase in variability is higher when the variance is relatively small. In addition, the firing rate always tends to a finite limit value as the correlation time increases toward infinity, whereas the coefficient of variation typically diverges. These results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains.     

Seeing white: Qualia in the context of decoding population codes.

When the nervous system is presented with multiple simultaneous inputs of some variable, such as wavelength or disparity, they can be combined to give rise to qualitatively new percepts that cannot be produced by any single input value. For example, there is no single wavelength that appears white. Many models of decoding neural population codes have problems handling multiple inputs, either attempting to extract a single value of the input parameter or, in some cases, registering the presence of multiple inputs without synthesizing them into something new. These examples raise a more general issue regarding the interpretation of population codes. We propose that population decoding involves not the extraction of specific values of the physical inputs, but rather a transformation from the input space to some abstract representational space that is not simply related to physical parameters. As a specific example, a four-layer network is presented that implements a transformation from wavelength to a high-level hue-saturation color space.     

A model for encoding multiple object motions and self-motion in area MST of primate visual cortex

Many cells in the dorsal part of the medial superior temporal (MST) region of visual cortex respond selectively to specific combinations of expansion/contraction, translation, and rotation motions. Previous investigators have suggested that these cells may respond selectively to the flow fields generated by self-motion of an observer. These patterns can also be generated by the relative motion between an observer and a particular object. We explored a neurally constrained model based on the hypothesis that neurons in MST partially segment the motion fields generated by several independently moving objects. Inputs to the model were generated from sequences of ray-traced images that simulated realistic motion situations, combining observer motion, eye movements, and independent object motions. The input representation was based on the response properties of neurons in the middle temporal area (MT), which provides the primary input to area MST. After applying an unsupervised optimization technique, the units became tuned to patterns signaling coherent motion, matching many of the known properties of MST cells. The results of this model are consistent with recent studies indicating that MST cells primarily encode information concerning the relative three-dimensional motion between objects and the observer.     

Independent component analysis of fMRI data: examining the assumptions

Independent component analysis (ICA), which separates fMRI data into spatially independent patterns of activity, has recently been shown to be a suitable method for exploratory fMRI analysis. The validity of the assumptions of ICA, mainly that the underlying components are spatially independent and add linearly, was explored with a representative fMRI data set by calculating the log-likelihood of observing each voxel's time course conditioned on the ICA model. The probability of observing the time courses from white-matter voxels was higher compared to other observed brain regions. Regions containing blood vessels had the lowest probabilities. The statistical distribution of probabilities over all voxels did not resemble that expected for a small number of independent components mixed with Gaussian noise. These results suggest the ICA model may more accurately represent the data in specific regions of the brain, and that both the activity-dependent sources of blood flow and noise are non-Gaussian.     

Attractor reliability reveals deterministic structure in neuronal spike trains

When periodic current is injected into an integrate-and-fire model neuron, the voltage as a function of time converges from different initial conditions to an attractor that produces reproducible sequences of spikes. The attractor reliability is a measure of the stability of spike trains against intrinsic noise and is quantified here as the inverse of the number of distinct spike trains obtained in response to repeated presentations of the same stimulus. High reliability characterizes neurons that can support a spike-time code, unlike neurons with discharges forming a renewal process (such as a Poisson process). These two classes of responses cannot be distinguished using measures based on the spike-time histogram, but they can be identified by the attractor dynamics of spike trains, as shown here using a new method for calculating the attractor reliability. We applied these methods to spike trains obtained from current injection into cortical neurons recorded in vitro. These spike trains did not form a renewal process and had a higher reliability compared to renewal-like processes with the same spike-time histogram.     

Parallel Fiber Coding in the Cerebellum for Life-Long Learning

Continuous and real-time learning is a difficult problem in robotics. To learn efficiently, it is important to recognize the current situation and learn appropriately for that context. To be effective, this requires the integration of a large number of sensorimotor and cognitive signals. So far, few principles on how to perform this integration have been proposed. Another limitation is the difficulty to include the complete contextual information to avoid destructive interference while learning different tasks.We suggest that a vertebrate brain structure important for sensorimotor coordination, the cerebellum, may provide answers to these difficult problems. We investigate how learning in the input layer of the cerebellum may successfully encode contextual knowledge in a representation useful for coordination and life-long learning. We propose that a sparsely-distributed and statistically-independent representation provides a valid criterion for the self-organizing classification and integration of context signals. A biologically motivated unsupervised learning algorithm that approximate such a representation is derived from maximum likelihood. This representation is beneficial for learning in the cerebellum by simplifying the credit assignment problem between what must be learned and the relevant signals in the current context for learning it. Due to its statistical independence, this representation is also beneficial for life-long learning by reducing the destructive interference across tasks, while retaining the ability to generalize. The benefits of the learning algorithm are investigated in a spiking model that learns to generate predictive smooth pursuit eye movements to follow target trajectories.     

Generalization and multirate models of motor adaptation

When subjects adapt their reaching movements in the setting of a systematic force or visual perturbation, generalization of adaptation can be assessed psychophysically in two ways: by testing untrained locations in the work space at the end of adaptation (slow postadaptation generalization) or by determining the influence of an error on the next trial during adaptation (fast trial-by-trial generalization). These two measures of generalization have been widely used in psychophysical studies, but the reason that they might differ has not been addressed explicitly. Our goal was to develop a computational framework for determining when a two-state model is justified by the data and to explore the implications of these two types of generalization for neural representations of movements. We first investigated, for single-target learning, how well standard statistical model selection procedures can discriminate two-process models from single-process models when learning and retention coefficients were systematically varied. We then built a two-state model for multitarget learning and showed that if an adaptation process is indeed two-rate, then the postadaptation generalization approach primarily probes the slow process, whereas the trial-by-trial generalization approach is most informative about the fast process. The fast process, due to its strong sensitivity to trial error, contributes predominantly to trial-by-trial generalization, whereas the strong retention of the slow system contributes predominantly to postadaptation generalization. Thus, when adaptation can be shown to be two-rate, the two measures of generalization may probe different brain representations of movement direction.