Choice and value flexibility jointly contribute to the capacity of a subsampled quadratic classifier

Dendritic excitability controls overdispersion

The brain is an intricate assembly of intercommunicating neurons whose input-output function is only partially understood. The role of active dendrites in shaping spiking responses, in particular, is unclear. Although existing models account for active dendrites and spiking responses, they are too complex to analyze analytically and demand long stochastic simulations. Here we combine cable and renewal theory to describe how input fluctuations shape the response of neuronal ensembles with active dendrites. We found that dendritic input readily and potently controls interspike interval dispersion. This phenomenon can be understood by considering that neurons display three fundamental operating regimes: one mean-driven regime and two fluctuation-driven regimes. We show that these results are expected to appear for a wide range of dendritic properties and verify predictions of the model in experimental data. These findings have implications for the role of interspike interval dispersion in learning and for theories of attractor states.

STDP-Driven Rewiring in Spiking Neural Networks under Stimulus-Induced and Spontaneous Activity

Mathematical and computer simulation of learning in living neural networks have typically focused on changes in the efficiency of synaptic connections represented by synaptic weights in the models. Synaptic plasticity is believed to be the cellular basis for learning and memory. In spiking neural networks composed of dynamical spiking units, a biologically relevant learning rule is based on the so-called spike-timing-dependent plasticity or STDP. However, experimental data suggest that synaptic plasticity is only a part of brain circuit plasticity, which also includes homeostatic and structural plasticity. A model of structural plasticity proposed in this study is based on the activity-dependent appearance and disappearance of synaptic connections. The results of the research indicate that such adaptive rewiring enables the consolidation of the effects of STDP in response to a local external stimulation of a neural network. Subsequently, a vector field approach is used to demonstrate the successive "recording" of spike paths in both functional connectome and synaptic connectome, and finally in the anatomical connectome of the network. Moreover, the findings suggest that the adaptive rewiring could stabilize network dynamics over time in the context of activity patterns' reproducibility. A universal measure of such reproducibility introduced in this article is based on similarity between time-consequent patterns of the special vector fields characterizing both functional and anatomical connectomes.

Dendritic slow dynamics enables localized cortical activity to switch between mobile and immobile modes with noisy background input

Mounting lines of evidence suggest the significant computational ability of a single neuron empowered by active dendritic dynamics. This motivates us to study what functionality can be acquired by a network of such neurons. The present paper studies how such rich single-neuron dendritic dynamics affects the network dynamics, a question which has scarcely been specifically studied to date. We simulate neurons with active dendrites networked locally like cortical pyramidal neurons, and find that naturally arising localized activity--called a bump--can be in two distinct modes, mobile or immobile. The mode can be switched back and forth by transient input to the cortical network. Interestingly, this functionality arises only if each neuron is equipped with the observed slow dendritic dynamics and with in vivo-like noisy background input. If the bump activity is considered to indicate a point of attention in the sensory areas or to indicate a representation of memory in the storage areas of the cortex, this would imply that the flexible mode switching would be of great potential use for the brain as an information processing device. We derive these conclusions using a natural extension of the conventional field model, which is defined by combining two distinct fields, one representing the somatic population and the other representing the dendritic population. With this tool, we analyze the spatial distribution of the degree of after-spike adaptation and explain how we can understand the presence of the two distinct modes and switching between the modes. We also discuss the possible functional impact of this mode-switching ability.

Cortical rewiring and information storage

Current thinking about long-term memory in the cortex is focused on changes in the strengths of connections between neurons. But ongoing structural plasticity in the adult brain, including synapse formation/elimination and remodelling of axons and dendrites, suggests that memory could also depend on learning-induced changes in the cortical 'wiring diagram'. Given that the cortex is sparsely connected, wiring plasticity could provide a substantial boost in storage capacity, although at a cost of more elaborate biological machinery and slower learning.

Nonlinear Population Codes

Theoretical and experimental studies of distributed neuronal representations of sensory and behavioral variables usually assume that the tuning of the mean firing rates is the main source of information. However, recent theoretical studies have investigated the effect of cross-correlations in the trial-to-trial fluctuations of the neuronal responses on the accuracy of the representation. Assuming that only the first-order statistics of the neuronal responses are tuned to the stimulus, these studies have shown that n the presence of correlations, similar to those observed experimentally in cortical ensembles of neurons, the amount of information in the population is limited, yielding nonzero error levels even in the limit of infinitely large populations of neurons.

In this letter, we study correlated neuronal populations whose higher-order statistics, and in particular response variances, are also modulated by the stimulus. We ask two questions: Does the correlated noise limit the accuracy of the neuronal representation of the stimulus? and, How can a biological mechanism extract most of the information embedded in the higher-order statistics of the neuronal responses? Specifically, we address these questions in the context of a population of neurons coding an angular variable. We show that the information embedded in the variances grows linearly with the population size despite the presence of strong correlated noise. This information cannot be extracted by linear readout schemes, including the linear population vector. Instead, we propose a bilinear readout scheme that involves spatial decorrelation, quadratic nonlinearity, and population vector summation. We show that this nonlinear population vector scheme yields accurate estimates of stimulus parameters, with an efficiency that grows linearly with the population size. This code can be implemented using biologically plausible neurons.

Have we been hebbing down the wrong path?

In this issue of Neuron, Stepanyants, Hof, and Chklovskii derive a simple mathematical formula to calculate, from measurable anatomical parameters, the capacity for neuronal wiring plasticity involving local synaptic rearrangements. Their work provides a deeper understanding of the potential contribution of structural plasticity to learning and memory.

Impact of active dendrites and structural plasticity on the memory capacity of neural tissue

We consider the combined effects of active dendrites and structural plasticity on the storage capacity of neural tissue. We compare capacity for two different modes of dendritic integration: (1) linear, where synaptic inputs are summed across the entire dendritic arbor, and (2) nonlinear, where each dendritic compartment functions as a separately thresholded neuron-like summing unit. We calculate much larger storage capacities for cells with nonlinear subunits and show that this capacity is accessible to a structural learning rule that combines random synapse formation with activity-dependent stabilization/elimination. In a departure from the common view that memories are encoded in the overall connection strengths between neurons, our results suggest that long-term information storage in neural tissue could reside primarily in the selective addressing of synaptic contacts onto dendritic subunits.