Formation Of Receptive Fields Research Articles

Synapse-type-specific competitive Hebbian learning forms functional recurrent networks

Cortical networks exhibit complex stimulus-response patterns that are based on specific recurrent interactions between neurons. For example, the balance between excitatory and inhibitory currents has been identified as a central component of cortical computations. However, it remains unclear how the required synaptic connectivity can emerge in developing circuits where synapses between excitatory and inhibitory neurons are simultaneously plastic. Using theory and modeling, we propose that a wide range of cortical response properties can arise from a single plasticity paradigm that acts simultaneously at all excitatory and inhibitory connections-Hebbian learning that is stabilized by the synapse-type-specific competition for a limited supply of synaptic resources. In plastic recurrent circuits, this competition enables the formation and decorrelation of inhibition-balanced receptive fields. Networks develop an assembly structure with stronger synaptic connections between similarly tuned excitatory and inhibitory neurons and exhibit response normalization and orientation-specific center-surround suppression, reflecting the stimulus statistics during training. These results demonstrate how neurons can self-organize into functional networks and suggest an essential role for synapse-type-specific competitive learning in the development of cortical circuits.

Effective Regulation of Auditory Processing by Parvalbumin Interneurons in the Tail of the Striatum.

Parvalbumin (PV) interneurons in the auditory cortex (AC) play a crucial role in shaping auditory processing, including receptive field formation, temporal precision enhancement, and gain regulation. PV interneurons are also the primary inhibitory neurons in the tail of the striatum (TS), which is one of the major descending brain regions in the auditory nervous system. However, the specific roles of TS-PV interneurons in auditory processing remain elusive. In this study, morphological and slice recording experiments in both male and female mice revealed that TS-PV interneurons, compared with AC-PV interneurons, were present in fewer numbers but exhibited longer projection distances, which enabled them to provide sufficient inhibitory inputs to spiny projection neurons (SPNs). Furthermore, TS-PV interneurons received dense auditory input from both the AC and medial geniculate body (MGB), particularly from the MGB, which rendered their auditory responses comparable to those of AC-PV interneurons. Optogenetic manipulation experiments demonstrated that TS-PV interneurons were capable of bidirectionally regulating the auditory responses of SPNs. Our findings suggest that PV interneurons can effectively modulate auditory processing in the TS and may play a critical role in auditory-related behaviors.

Data-driven emergence of convolutional structure in neural networks

Exploiting data invariances is crucial for efficient learning in both artificial and biological neural circuits. Understanding how neural networks can discover appropriate representations capable of harnessing the underlying symmetries of their inputs is thus crucial in machine learning and neuroscience. Convolutional neural networks, for example, were designed to exploit translation symmetry, and their capabilities triggered the first wave of deep learning successes. However, learning convolutions directly from translation-invariant data with a fully connected network has so far proven elusive. Here we show how initially fully connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs, resulting in localized, space-tiling receptive fields. These receptive fields match the filters of a convolutional network trained on the same task. By carefully designing data models for the visual scene, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs, which has long been recognized as the hallmark of natural images. We provide an analytical and numerical characterization of the pattern formation mechanism responsible for this phenomenon in a simple model and find an unexpected link between receptive field formation and tensor decomposition of higher-order input correlations. These results provide a perspective on the development of low-level feature detectors in various sensory modalities and pave the way for studying the impact of higher-order statistics on learning in neural networks.

Vesicular Release of GABA by Mammalian Horizontal Cells Mediates Inhibitory Output to Photoreceptors.

Feedback inhibition by horizontal cells regulates rod and cone photoreceptor calcium channels that control their release of the neurotransmitter glutamate. This inhibition contributes to synaptic gain control and the formation of the center-surround antagonistic receptive fields passed on to all downstream neurons, which is important for contrast sensitivity and color opponency in vision. In contrast to the plasmalemmal GABA transporter found in non-mammalian horizontal cells, there is evidence that the mechanism by which mammalian horizontal cells inhibit photoreceptors involves the vesicular release of the inhibitory neurotransmitter GABA. Historically, inconsistent findings of GABA and its biosynthetic enzyme, L-glutamate decarboxylase (GAD) in horizontal cells, and the apparent lack of surround response block by GABAergic agents diminished support for GABA's role in feedback inhibition. However, the immunolocalization of the vesicular GABA transporter (VGAT) in the dendritic and axonal endings of horizontal cells that innervate photoreceptor terminals suggested GABA was released via vesicular exocytosis. To test the idea that GABA is released from vesicles, we localized GABA and GAD, multiple SNARE complex proteins, synaptic vesicle proteins, and Cav channels that mediate exocytosis to horizontal cell dendritic tips and axonal terminals. To address the perceived relative paucity of synaptic vesicles in horizontal cell endings, we used conical electron tomography on mouse and guinea pig retinas that revealed small, clear-core vesicles, along with a few clathrin-coated vesicles and endosomes in horizontal cell processes within photoreceptor terminals. Some small-diameter vesicles were adjacent to the plasma membrane and plasma membrane specializations. To assess vesicular release, a functional assay involving incubation of retinal slices in luminal VGAT-C antibodies demonstrated vesicles fused with the membrane in a depolarization- and calcium-dependent manner, and these labeled vesicles can fuse multiple times. Finally, targeted elimination of VGAT in horizontal cells resulted in a loss of tonic, autaptic GABA currents, and of inhibitory feedback modulation of the cone photoreceptor Cai, consistent with the elimination of GABA release from horizontal cell endings. These results in mammalian retina identify the central role of vesicular release of GABA from horizontal cells in the feedback inhibition of photoreceptors.

A memristive plasticity model of voltage-based STDP suitable for recurrent bidirectional neural networks in the hippocampus

Memristive systems have gained considerable attention in the field of neuromorphic engineering, because they allow the emulation of synaptic functionality in solid state nano-physical systems. In this study, we show that memristive behavior provides a broad working framework for the phenomenological modelling of cellular synaptic mechanisms. In particular, we seek to understand how close a memristive system can account for the biological realism. The basic characteristics of memristive systems, i.e. voltage and memory behavior, are used to derive a voltage-based plasticity rule. We show that this model is suitable to account for a variety of electrophysiology plasticity data. Furthermore, we incorporate the plasticity model into an all-to-all connecting network scheme. Motivated by the auto-associative CA3 network of the hippocampus, we show that the implemented network allows the discrimination and processing of mnemonic pattern information, i.e. the formation of functional bidirectional connections resulting in the formation of local receptive fields. Since the presented plasticity model can be applied to real memristive devices as well, the presented theoretical framework can support both, the design of appropriate memristive devices for neuromorphic computing and the development of complex neuromorphic networks, which account for the specific advantage of memristive devices.

Role of zero synapses in unsupervised feature learning

Synapses in real neural circuits can take discrete values including zero (silent or potential) synapses. The computational role of zero synapses in unsupervised feature learning of unlabeled noisy data is still unclear, thus it is important to understand how the sparseness of synaptic activity is shaped during learning and its relationship with receptive field formation. Here, we formulate this kind of sparse feature learning by a statistical mechanics approach. We find that learning decreases the fraction of zero synapses, and when the fraction decreases rapidly around a critical data size, an intrinsically structured receptive field starts to develop. Further increasing the data size refines the receptive field, while a very small fraction of zero synapses remain to act as contour detectors. This phenomenon is discovered not only in learning a handwritten digits dataset, but also in learning retinal neural activity measured in a natural-movie-stimuli experiment.

Versatile functional roles of horizontal cells in the retinal circuit

In the retinal circuit, environmental light signals are converted into electrical signals that can be decoded properly by the brain. At the first synapse of the visual system, information flow from photoreceptors to bipolar cells is modulated by horizontal cells (HCs), however, their functional contribution to retinal output and individual visual function is not fully understood. In the current study, we investigated functional roles for HCs in retinal ganglion cell (RGC) response properties and optokinetic responses by establishing a HC-depleted mouse line. We observed that HC depletion impairs the antagonistic center-surround receptive field formation of RGCs, supporting a previously reported HC function revealed by pharmacological approaches. In addition, we found that HC loss reduces both the ON and OFF response diversities of RGCs, impairs adjustment of the sensitivity to ambient light at the retinal output level, and alters spatial frequency tuning at an individual level. Taken together, our current study suggests multiple functional aspects of HCs crucial for visual processing.

Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.

Targeted Deletion of Vesicular GABA Transporter from Retinal Horizontal Cells Eliminates Feedback Modulation of Photoreceptor Calcium Channels.

The cellular mechanisms underlying feedback signaling from horizontal cells to photoreceptors, which are important for the formation of receptive field surrounds of early visual neurons, remain unsettled. Mammalian horizontal cells express a complement of synaptic proteins that are necessary and sufficient for calcium-dependent exocytosis of inhibitory neurotransmitters at their contacts with photoreceptor terminals, suggesting that they are capable of releasing GABA via vesicular release. To test whether horizontal cell vesicular release is involved in feedback signaling, we perturbed inhibitory neurotransmission in these cells by targeted deletion of the vesicular GABA transporter (VGAT), the protein responsible for the uptake of inhibitory transmitter by synaptic vesicles. To manipulate horizontal cells selectively, an iCre mouse line with Cre recombinase expression controlled by connexin57 (Cx57) regulatory elements was generated. In Cx57-iCre mouse retina, only horizontal cells expressed Cre protein, and its expression occurred in all retinal regions. After crossing with a VGATflox/flox mouse line, VGAT was selectively eliminated from horizontal cells, which was confirmed immunohistochemically. Voltage-gated ion channel currents in horizontal cells of Cx57-VGAT−/− mice were the same as Cx57-VGAT+/+ controls, as were the cell responses to the ionotropic glutamate receptor agonist kainate, but the response to the GABAA receptor agonist muscimol in Cx57-VGAT−/− mice was larger. In contrast, the feedback inhibition of photoreceptor calcium channels, which in control animals is induced by horizontal cell depolarization, was completely absent in Cx57-VGAT−/− mice. The results suggest that vesicular release of GABA from horizontal cells is required for feedback inhibition of photoreceptors.

Impact of noise on theta-nested gamma oscillations in a spiking continuous attractor model of grid cells

Grid cells in the medial entorhinal cortex (MEC) encode location through firing fields that form grid-like maps of the environment. At the same time network activity in the MEC is dominated by oscillations in the theta (4-12 Hz) and gamma (30-100 Hz) bands. Our recent experimental data established that feedback inhibition between excitatory stellate cells and inhibitory fast spiking interneurons dominates the synaptic connectivity in layer II of the MEC, and that continuous attractor models derived from these properties are sufficient to explain both the network oscillations and grid firing fields [1]. Here we use a spiking continuous attractor network model of layer II stellate cells and fast spiking interneurons to examine the effect of intrinsic noise on the emergence of theta nested-gamma oscillations. In this model, stellate cells connect exclusively to interneurons, while interneurons contact only stellate cells. When driven with a theta (8 Hz) modulated external input, we observed network synchronization in the gamma range during the trough of the theta signal, which depended on the amount of intrinsic Gaussian noise generated independently at each neuron. Without noise, the network exhibited aberrant hyper-synchronous firing of a subpopulation of stellate cells at the beginning of each theta cycle. The stellate cell firing resulted in a strong feedback inhibitory postsynaptic currents from fast spiking interneurons that had an additional synchronizing effect. The strong inhibitory feedback abolished nested gamma oscillations. With increasing noise, the network entered an intermediate state in which we observed theta nested-gamma oscillations [1]. When noise level was set even higher, the nested gamma oscillations disappeared without increasing the amount of inhibitory coupling. We also present the impact of noise on bump attractor formation and gridness score of the grid-like receptive fields. Together, these results show that the presence of noise may have profound implications on the stability of theta-nested gamma oscillations in attractor neural circuits with feedback inhibition.

Balanced excitation and inhibition in a spiking model of V1

Experimental studies have shown that neuronal excitation is balanced with inhibition and spikes are triggered only when that fine balance is perturbed. It is also known that inhibition is critical for receptive field tuning, yet it is not clear what role is played by different types of inhibitory interneurons and how the corresponding balanced circuitry could emerge via spike timing dependent plasticity (STDP). To study these questions we have constructed a large-scale detailed spiking model of V1 involving a variety of simulated neurons: fast-spiking (FS) interneurons, low threshold spiking (LTS) interneurons and regular spiking (RS) neurons. We modeled layer 4 and layer 2/3 of the primary visual cortex and a number of projections between cell types in agreement with anatomical data. Synaptic dynamics is governed by a set of STDP and activity dependent plasticity mechanisms for both inhibitory and excitatory synapses. The plasticity rules have been chosen to be in quantitative agreement with experiment where the data is available. For many of connections however, the data is either unavailable or noisy. In these cases plasticity rules were chosen based on a guided guess constrained by the requirement of structural stability of the system and expected response properties of cells to probing stimuli. Together, the plasticity rules lead to stable neuronal response and formation of orientation-selective receptive fields. The network learns simple and complex cells of a broad range of orientations and spatial frequencies. The model converges to a balanced neurodynamics and biologically reasonable firing rates. Our study shows that in the presence of strong thalamic drive, plastic inhibition is necessary for feature selectivity. The FS cells remove DC component of the input while firing of the LTS cells imposes sparse response and balances out feedback excitation.

Oral Proton Pump Inhibitors Disrupt Horizontal Cell-Cone Feedback and Enhance Visual Hallucinations in Macular Degeneration Patients

Visual hallucinations (VHs) occur in macular degeneration patients with poor vision but normal cognitive function. The underlying mechanisms are poorly understood. We report the identification of pharmaceutical agents that enhance VH and use these agents to examine the contribution of retinal neurons to this syndrome. We detail clinical observations on VH in five macular degeneration patients treated with proton pump inhibitors having the core structure, 2-pyridyl-methylsulfinyl-benzimidazole. We tested possible retinal mechanisms using paired whole cell recordings to examine effects of these compounds on feedback interactions between horizontal cells and cones in amphibian retina. Five patients with advanced wet macular degeneration described patterned VHs that were induced or enhanced by oral proton pump inhibitors. The abnormal images increased with light, disappeared in the dark, and originated in the retina, based on ophthalmodynamometry. Simultaneous paired whole cell recordings from amphibian cones and horizontal cells showed that 2-pyridyl-methylsulfinyl-benzimidazoles blocked the negative shift in voltage dependence and increase in amplitude of the calcium current (ICa) in cones that is induced by changes in horizontal cell membrane potential. These effects disrupt the negative feedback from horizontal cells to cones that is important for the formation of center-surround receptive fields in bipolar and ganglion cells, and thus for normal spatial and chromatic perception. Our study suggests that changes in the output of retinal neurons caused by disturbances in outer retinal feedback mechanisms can enhance patterned visual hallucinations.

Dynamic Coding of Signed Quantities in Cortical Feedback Circuits

In the early sensory and motor areas of the cortex, individual neurons transmit information about specific sensory features via a peaked response. This concept has been crystallized as “labeled lines,” to denote that axons communicate the specific properties of their sensory or motor parent cell. Such cells also can be characterized as being polarized, that is, as representing a signed quantity that is either positive or negative. We show in a model simulation that there are two important consequences when learning receptive fields using such signed codings in circuits that subtract different inputs. The first is that, in feedback circuits using labeled lines, such arithmetic operations need to be distributed across multiple distinct pathways. The second consequence is that such pathways must be necessarily dynamic, i.e., that synapses can grow and retract when forming receptive fields. The model monitors the breaking and growing of new circuit connections when their synapses need to change polarities and predicts that the rate of such changes should be inversely correlated with the progress of receptive field formation.

Presynaptic Gating of Postsynaptically Expressed Plasticity at Mature Thalamocortical Synapses

Thalamocortical (TC) projections provide the major pathway for ascending sensory information to the mammalian neocortex. Arrays of these projections form synaptic inputs on thalamorecipient neurons, thus contributing to the formation of receptive fields (RFs) in sensory cortices. Experience-dependent plasticity of RFs persists throughout an organism's life span but in adults requires activation of cholinergic inputs to the cortex. In contrast, synaptic plasticity at TC projections is limited to the early postnatal period. This disconnect led to the widespread belief that TC synapses are the principal site of RF plasticity only in neonatal sensory cortices, but that they lose this plasticity upon maturation. Here, we tested an alternative hypothesis that mature TC projections do not lose synaptic plasticity but rather acquire gating mechanisms that prevent the induction of synaptic plasticity. Using whole-cell recordings and direct measures of postsynaptic and presynaptic activity (two-photon glutamate uncaging and two-photon imaging of the FM 1-43 assay, respectively) at individual synapses in acute mouse brain slices that contain the auditory thalamus and cortex, we determined that long-term depression (LTD) persists at mature TC synapses but is gated presynaptically. Cholinergic activation releases presynaptic gating through M(1) muscarinic receptors that downregulate adenosine inhibition of neurotransmitter release acting through A(1) adenosine receptors. Once presynaptic gating is released, mature TC synapses can express LTD postsynaptically through group I metabotropic glutamate receptors. These results indicate that synaptic plasticity at TC synapses is preserved throughout the life span and, therefore, may be a cellular substrate of RF plasticity in both neonate and mature animals.

Light‐ and dopamine‐regulated receptive field plasticity in primate horizontal cells

Center-surround antagonistic receptive fields (CSARFs) are building blocks for spatial vision and contrast perception. Retinal horizontal cells (HCs) are the first lateral elements along the visual pathway, and are thought to contribute to receptive field surrounds of higher order neurons. Primate HC receptive fields have not been found to change with light, and dopaminergic modulation has not been investigated. Recording intracellularly from HCs in dark-adapted macaque retina, we found that H1-HCs had large receptive fields (λ = 1,158 ± 137 μm) that were reduced by background light (-45%), gap junction closure (-53%), and D1 dopamine receptor activation (-48%). Tracer coupling was modulated in a correlative manner, suggesting that coupling resistance plays a dominant role in receptive field formation under low light conditions. The D1 antagonist SCH23390 increased the size of receptive fields (+13%), suggesting tonic dopamine release in the dark. Because light elevates dopamine release in primate retina, our results support a dopaminergic role in post-receptoral light adaptation by decreasing HC receptive field diameters, which influences the center-surround receptive field organization of higher-order neurons and thereby spatial contrast sensitivity.

Online competitive incremental-decremental clustering with the Winner-Kill-Loser rule

Event Abstract Back to Event Online competitive incremental-decremental clustering with the Winner-Kill-Loser rule Jasmin Leveille1*, Isao Hayashi2, Kunihiko Fukushima2 and Massimiliano Versace1 1 Boston University, Center of Excellence for Learning in Education, Science, and Technology, United States 2 Kansai University, Faculty of Informatics, Japan Incremental clustering techniques are general-purpose methods for clustering where the number of cluster nodes is determined online, and in particular increased, upon presentation of training data. Examples include the Leader algorithm (Hartigan, 1975), and adaptive resonance theory (Carpenter and Grossberg, 2003). Incremental learning rules for clustering are attractive for their simplicity and ease of application, and have generally led to good results on a number of tasks. Recently, a variant of incremental learning which considers online removal of tuned nodes was proposed to train simple cells in a hierarchical network (Fukushima, 2010). The learning rule presented therein, termed winner-kill-loser (WKL), is a kind of competitive rule in which only sufficiently active units enter the competition and where the losing units are effectively removed from the network. In this work, we extend the WKL learning rule to study the structure and formation of simple cell receptive fields. We start with an analysis of the properties of the WKL rule and demonstrate that, unlike many clustering techniques, in its simplest form the learning rule does not seek to approximate maximum-likelihood estimates of the node parameters. Instead, the WKL learning rule converges asymptotically to a uniform covering of the input space, irrespective of the data probability distribution. Even in the case of a uniform data distribution, our analysis also highlights conditions for the presence of irreducible gaps in this covering. We can compute a lower bound on the size of these gaps, and show how this bound relates to clustering performance in sample simulations. In particular, we investigate through simulation whether this lower bound can account for improvements in performance reported when using the dual-threshold rule, in which the net input activation threshold for each simple cell is lowered after learning (Fukushima, 2010). Based on these results, we propose to complement the WKL learning rule by inserting activity-dependent thresholds that govern the selectivity of learned receptive fields. We show through simulation that the structure of the newly developed receptive fields approximates the input data distribution.

Normative Visual Development: efficient coding principles for adult V1 predict properties of LGN waves prior to eye opening

We present a novel approach to understanding spontaneous activity in the LGN and V1 prior to natural visual experience. Patterned, spontaneous neural activity has been measured in these areas but is poorly understood in comparison to work on retinal waves [1]. Our predictions about LGN/V1 spontaneous activity not only have implications for future experiments, but provide an additional computational-level interpretation. In the same way that V1 can be understood through neural network receptive field models (Marr's algorithmic level) as well as an efficient coding of natural images (Marr's computational level), we propose that early visual spontaneous activity can be understood not only through neural network models of receptive field and map formation, as in many previous approaches [2,3], but also by how this activity relates to the high-level coding objectives of V1. The key insight in this work is that the form of spontaneous activity in the early visual system can be constrained by these normative principles to resemble measured spontaneous activity patterns. The neural code in fully-developed adult primary visual cortex (V1) is presumed to be an efficient code; by encoding images of our natural visual environment, techniques such as sparse coding [4] and independent components analysis [5] have produced linear filters which resemble experimentally measured receptive fields in V1. Our simulations show how patterns which qualitatively resemble such activity are capable of producing these V1-like visual codes by using the same learning algorithms. The spontaneous activity model is similar to a previous abstracted version of retinal wave generation [6] with the addition of multiple eye-layers and correlated interaction between the layers as has been measured experimentally [7]. All model parameters have a direct physiological interpretation and also relate to theoretical models used in the physics of critical phenomena (e.g. percolation networks). This normative approach demonstrates that binocular disparity-selective cells can be refined by spontaneous activity in a way that promotes early stereopsis. This unique, normative approach to visual development provides a way of applying the tools of efficient coding used in the adult visual system to better understand how the how V1 refines prior to visual experience.

STDP: spiking, timing, rates and beyond

STDP: spiking, timing, rates and beyond

Constraint on the Number of Synaptic Inputs to a Visual Cortical Neuron Controls Receptive Field Formation

To date, Hebbian learning combined with some form of constraint on synaptic inputs has been demonstrated to describe well the development of neural networks. The previous models revealed mathematically the importance of synaptic constraints to reproduce orientation selectivity in the visual cortical neurons, but biological mechanisms underlying such constraints remain unclear. In this study, we addressed this issue by formulating a synaptic constraint based on activity-dependent mechanisms of synaptic changes. Particularly, considering metabotropic glutamate receptor-mediated long-term depression, we derived synaptic constraint that suppresses the number of inputs from individual presynaptic neurons. We performed computer simulations of the activity-dependent self-organization of geniculocortical inputs with the synaptic constraint and examined the formation of receptive fields (RFs) of model visual cortical neurons. When we changed the magnitude of the synaptic constraint, we found the emergence of distinct RF structures such as concentric RFs, simple-cell-like RFs, and double-oriented RFs and also a gradual transition between spatiotemporal separable and inseparable RFs. Thus, the model based on the synaptic constraint derived from biological consideration can account systematically for the repertoire of RF structures observed in the primary visual cortices of different species for the first time.

A Gamma-phase Model of Receptive Field Formation

Event Abstract Back to Event A Gamma-phase Model of Receptive Field Formation Rate coding is a ubiquitous model of cortical signaling but is it the cause of computation or a correlate? Criticisms of the causal model cite difficulties in achieving the precision and the speed of computation, but we argue that there is an additional constraint that arises from Bayesian models of RF formation3. Think of the problem representing a distribution of inputs amongst cells with overlapping RFs. When a spike sent, if it is to be included in a pool that causes the synaptic input to be modified, then it should be so classified probabilistically according to a competition between its neighbors. This is a standard feature of the Expectation Maximization algorithm. If this is not done, errors in the RF structure will result. However the accumulation of statistics in this process is slow. It might be suitable for RF formation but it is unsuitable for communicating the values of variables used in the overarching algorithm quickly. Thus it would be beneficial to somehow have two processes, one a slow one that accumulates statistics and another a fast one that signals values. This can be done if the cortex uses gamma-phase coding to signal analog values1 and spike selection to modify the RF. The gamma signal is used as a timing reference and timing delays represent numerical values, with spikes closest in time to the timing reference being the highest value. This strategy has the additional virtue of being compatible with spike-timing dependent modification of synaptic strength. However gamma-phase coding seems incompatible with a large amount of single cell recording data. If the cortex is using a timing reference2, why does the output of cells appear Poission and mimic receptive field organization? Our claim is that the probabilistic structure used to update receptive fields can be thought of as the routing used in the overlying computation. Simply, the computation being done can take alternate routes that are chosen probabilistically, but for each neuron on the route that is chosen to send a spike, the value sent can be signaled quickly and accurately using gamma-phase coding. The cells appear Poisson since they are chosen randomly and they reflect RF statistics since those statistics govern their selection. We illustrate these points using adapting the classical sparse-coding model of RF formation between LGN and striate cortex3 to use gamma phase coding. The stunning demonstration is that the representation of an image is stable even though from moment to moment alternate choices of RFs are being used to represent it. We further demonstrate that the probabilistic routing that results has the consequence that a neuron?s receptive field, when measured in the classical way with the peristimulus histogram, recapitulates the RF statistics. Finally we show that gamma-phase coding may be more ubiquitous than currently believed as it can be difficult to detect if probabilistic routing is used. Supported by NIH Grant R01RR009283