Nonlinear Input Model Research Articles

Data-driven modelling of visual receptive fields: comparison between the generalized quadratic model and the nonlinear input model

Objective: Neurons in primary visual cortex (V1) display a range of sensitivity in their response to translations of their preferred visual features within their receptive field: from high specificity to a precise position through to complete invariance. This visual feature selectivity and invariance is frequently modeled by applying a selection of linear spatial filters to the input image, that define the feature selectivity, followed by a nonlinear function that combines the filter outputs, that defines the invariance, to predict the neural response. We compare two such classes of model, that are both popular and parsimonious, the generalized quadratic model (GQM) and the nonlinear input model (NIM). These two classes of model differ primarily in that the NIM can accommodate a greater diversity in the form of nonlinearity that is applied to the outputs of the filters. Approach: We compare the two model types by applying them to data from multielectrode recordings from cat primary visual cortex in response to spatially white Gaussian noise After fitting both classes of model to a database of 342 single units (SUs), we analyze the qualitative and quantitative differences in the visual feature processing performed by the two models and their ability to predict neural response. Main results: We find that the NIM predicts response rates on a held-out data at least as well as the GQM for 95% of SUs. Superior performance occurs predominantly for those units with above average spike rates and is largely due to the NIMs ability to capture aspects of the model’s nonlinear function cannot be captured with the GQM rather than differences in the visual features being processed by the two different models. Significance: These results can help guide model choice for data-driven receptive field modelling.

Characterization of extracellular spike waveforms recorded in wallaby primary visual cortex.

Extracellular recordings were made from 642 units in the primary visual cortex (V1) of a highly visual marsupial, the Tammar wallaby. The receptive field (RF) characteristics of the cells were objectively estimated using the non-linear input model (NIM), and these were correlated with spike shapes. We found that wallaby cortical units had 68% regular spiking (RS), 12% fast spiking (FS), 4% triphasic spiking (TS), 5% compound spiking (CS) and 11% positive spiking (PS). RS waveforms are most often associated with recordings from pyramidal or spiny stellate cell bodies, suggesting that recordings from these cell types dominate in the wallaby cortex. In wallaby, 70-80% of FS and RS cells had orientation selective RFs and had evenly distributed linear and nonlinear RFs. We found that 47% of wallaby PS units were non-orientation selective and they were dominated by linear RFs. Previous studies suggest that the PS units represent recordings from the axon terminals of non-orientation selective cells originating in the lateral geniculate nucleus (LGN). If this is also true in wallaby, as strongly suggested by their low response latencies and bursty spiking properties, the results suggest that significantly more neurons in wallaby LGN are already orientation selective. In wallaby, less than 10% of recorded spikes had triphasic (TS) or sluggish compound spiking (CS) waveforms. These units had a mixture of orientation selective and non-oriented properties, and their cellular origins remain difficult to classify.

Functional characterization of retinal ganglion cells using tailored nonlinear modeling

The mammalian retina encodes the visual world in action potentials generated by 20–50 functionally and anatomically-distinct types of retinal ganglion cell (RGC). Individual RGC types receive synaptic input from distinct presynaptic circuits; therefore, their responsiveness to specific features in the visual scene arises from the information encoded in synaptic input and shaped by postsynaptic signal integration and spike generation. Unfortunately, there is a dearth of tools for characterizing the computations reflected in RGC spike output. Therefore, we developed a statistical model, the separable Nonlinear Input Model, to characterize the excitatory and suppressive components of RGC receptive fields. We recorded RGC responses to a correlated noise (“cloud”) stimulus in an in vitro preparation of mouse retina and found that our model accurately predicted RGC responses at high spatiotemporal resolution. It identified multiple receptive fields reflecting the main excitatory and suppressive components of the response of each neuron. Significantly, our model accurately identified ON-OFF cells and distinguished their distinct ON and OFF receptive fields, and it demonstrated a diversity of suppressive receptive fields in the RGC population. In total, our method offers a rich description of RGC computation and sets a foundation for relating it to retinal circuitry.

Sparse Functional Identification of Complex Cells from Spike Times and the Decoding of Visual Stimuli

We investigate the sparse functional identification of complex cells and the decoding of spatio-temporal visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm is formulated as a rank minimization problem that significantly reduces the number of sampling measurements (spikes) required for decoding. We also establish the duality between sparse decoding and functional identification and provide algorithms for identification of low-rank dendritic stimulus processors. The duality enables us to efficiently evaluate our functional identification algorithms by reconstructing novel stimuli in the input space. Finally, we demonstrate that our identification algorithms substantially outperform the generalized quadratic model, the nonlinear input model, and the widely used spike-triggered covariance algorithm.

Inferring nonlinear neuronal computation based on physiologically plausible inputs.

The computation represented by a sensory neuron's response to stimuli is constructed from an array of physiological processes both belonging to that neuron and inherited from its inputs. Although many of these physiological processes are known to be nonlinear, linear approximations are commonly used to describe the stimulus selectivity of sensory neurons (i.e., linear receptive fields). Here we present an approach for modeling sensory processing, termed the Nonlinear Input Model (NIM), which is based on the hypothesis that the dominant nonlinearities imposed by physiological mechanisms arise from rectification of a neuron's inputs. Incorporating such ‘upstream nonlinearities’ within the standard linear-nonlinear (LN) cascade modeling structure implicitly allows for the identification of multiple stimulus features driving a neuron's response, which become directly interpretable as either excitatory or inhibitory. Because its form is analogous to an integrate-and-fire neuron receiving excitatory and inhibitory inputs, model fitting can be guided by prior knowledge about the inputs to a given neuron, and elements of the resulting model can often result in specific physiological predictions. Furthermore, by providing an explicit probabilistic model with a relatively simple nonlinear structure, its parameters can be efficiently optimized and appropriately regularized. Parameter estimation is robust and efficient even with large numbers of model components and in the context of high-dimensional stimuli with complex statistical structure (e.g. natural stimuli). We describe detailed methods for estimating the model parameters, and illustrate the advantages of the NIM using a range of example sensory neurons in the visual and auditory systems. We thus present a modeling framework that can capture a broad range of nonlinear response functions while providing physiologically interpretable descriptions of neural computation.

Adaptive stabilization of uncertain unified chaotic systems with nonlinear input

This paper addresses the problem of adaptive stabilization of uncertain unified chaotic systems with nonlinear input in the sector form. A novel representation of nonlinear input function, that is, a linear input with bounded time-varying coefficient, is firstly established. Then, an adaptive control scheme is proposed based on the new nonlinear input model. By using Barbalat’s lemma, the asymptotic stability of the closed-loop system is proved in spite of system uncertainties, external disturbance and input nonlinearity. One of the advantages of the proposed design method is that the prior knowledge on the plant parameter, the bound parameters of the uncertainties and the slope parameters inside the sector nonlinearity is not required. Finally, numerical simulations are performed to verify the analytical results.