In order to record the stream of autobiographical information that defines our unique personal history, our brains must form durable memories from single brief exposures to the patterned stimuli that impinge on them continuously throughout life. However, little is known about the computational strategies or neural mechanisms that underlie the brain's ability to perform this type of "online" learning. Based on increasing evidence that dendrites act as both signaling and learning units in the brain, we developed an analytical model that relates online recognition memory capacity to roughly a dozen dendritic, network, pattern, and task-related parameters. We used the model to determine what dendrite size maximizes storage capacity under varying assumptions about pattern density and noise level. We show that over a several-fold range of both of these parameters, and over multiple orders-of-magnitude of memory size, capacity is maximized when dendrites contain a few hundred synapses-roughly the natural number found in memory-related areas of the brain. Thus, in comparison to entire neurons, dendrites increase storage capacity by providing a larger number of better-sized learning units. Our model provides the first normative theory that explains how dendrites increase the brain's capacity for online learning; predicts which combinations of parameter settings we should expect to find in the brain under normal operating conditions; leads to novel interpretations of an array of existing experimental results; and provides a tool for understanding which changes associated with neurological disorders, aging, or stress are most likely to produce memory deficits-knowledge that could eventually help in the design of improved clinical treatments for memory loss.

In pursuit of the goal to understand and eventually reproduce the diverse functions of the brain, a key challenge lies in reverse engineering the peculiar biology-based "technology" that underlies the brain's remarkable ability to process and store information. The basic building block of the nervous system is the nerve cell, or "neuron," yet after more than 100 years of neurophysiological study and 60 years of modeling, the information processing functions of individual neurons, and the parameters that allow them to engage in so many different types of computation (sensory, motor, mnemonic, executive, etc.) remain poorly understood. In this paper, we review both historical and recent findings that have led to our current understanding of the analog spatial processing capabilities of dendrites, the major input structures of neurons, with a focus on the principal cell type of the neocortex and hippocampus, the pyramidal neuron (PN). We encapsulate our current understanding of PN dendritic integration in an abstract layered model whose spatially sensitive branch-subunits compute multidimensional sigmoidal functions. Unlike the 1-D sigmoids found in conventional neural network models, multidimensional sigmoids allow the cell to implement a rich spectrum of nonlinear modulation effects directly within their dendritic trees.

Neocortical pyramidal neurons (PNs) receive thousands of excitatory synaptic contacts on their basal dendrites. Some act as classical driver inputs while others are thought to modulate PN responses based on sensory or behavioral context, but the biophysical mechanisms that mediate classical-contextual interactions in these dendrites remain poorly understood. We hypothesized that if two excitatory pathways bias their synaptic projections towards proximal vs. distal ends of the basal branches, the very different local spike thresholds and attenuation factors for inputs near and far from the soma might provide the basis for a classical-contextual functional asymmetry. Supporting this possibility, we found both in compartmental models and electrophysiological recordings in brain slices that the responses of basal dendrites to spatially separated inputs are indeed strongly asymmetric. Distal excitation lowers the local spike threshold for more proximal inputs, while having little effect on peak responses at the soma. In contrast, proximal excitation lowers the threshold, but also substantially increases the gain of distally-driven responses. Our findings support the view that PN basal dendrites possess significant analog computing capabilities, and suggest that the diverse forms of nonlinear response modulation seen in the neocortex, including uni-modal, cross-modal, and attentional effects, could depend in part on pathway-specific biases in the spatial distribution of excitatory synaptic contacts onto PN basal dendritic arbors.

Cortical computations are critically dependent on interactions between pyramidal neurons (PNs) and a menagerie of inhibitory interneuron types. A key feature distinguishing interneuron types is the spatial distribution of their synaptic contacts onto PNs, but the location-dependent effects of inhibition are mostly unknown, especially under conditions involving active dendritic responses. We studied the effect of somatic vs. dendritic inhibition on local spike generation in basal dendrites of layer 5 PNs both in neocortical slices and in simple and detailed compartmental models, with equivalent results: somatic inhibition divisively suppressed the amplitude of dendritic spikes recorded at the soma while minimally affecting dendritic spike thresholds. In contrast, distal dendritic inhibition raised dendritic spike thresholds while minimally affecting their amplitudes. On-the-path dendritic inhibition modulated both the gain and threshold of dendritic spikes depending on its distance from the spike initiation zone. Our findings suggest that cortical circuits could assign different mixtures of gain vs. threshold inhibition to different neural pathways, and thus tailor their local computations, by managing their relative activation of soma- vs. dendrite-targeting interneurons.

Compartmental models provide a major source of insight into the information processing functions of single neurons. Over the past 15 years, one of the most widely used neuronal morphologies has been the cell called "j4," a layer 5 pyramidal cell from cat visual cortex originally described in Douglas, Martin, and Whitteridge (1991). The cell has since appeared in at least 28 published compartmental modeling studies, including several in this journal. In recently examining why we could not reproduce certain in vitro data involving the attenuation of signals originating in distal basal dendrites, we discovered that pronounced fluctuations in the diameter measurements of j4 lead to a bottlenecking effect that increases distal input resistances and significantly reduces voltage transfer between distal sites and the cell body. Upon smoothing these diameter fluctuations, bringing j4 more in line with other reconstructions of layer 5 pyramidal neurons, we found that the attenuation of steady-state voltage signals traveling to the cell body V(distal)/V(soma) was reduced by 60% at some locations in some branches (corresponding to a 2.5-fold increase in the voltage response at the soma for the same distal depolarization) and by 30% on average (corresponding to a 45% increase in somatic response). Changes of this magnitude could lead to different outcomes in some types of compartmental modeling studies. A smoothed version of the j4 morphology is available online at http://lnc.usc.edu/j4-smooth/ .

Neurons in area V4 have relatively large receptive fields (RFs), so multi(cid:173) ple visual features are simultaneously "seen" by these cells. Recordings from single V 4 neurons suggest that simultaneously presented stimuli compete to set the output firing rate, and that attention acts to isolate individual features by biasing the competition in favor of the attended object. We propose that both stimulus competition and attentional bias(cid:173) ing arise from the spatial segregation of afferent synapses onto different regions of the excitable dendritic tree of V 4 neurons. The pattern of feed(cid:173) forward, stimulus-driven inputs follows from a Hebbian rule: excitatory afferents with similar RFs tend to group together on the dendritic tree, avoiding randomly located inhibitory inputs with similar RFs. The same principle guides the formation of inputs that mediate attentional mod(cid:173) ulation. Using both biophysically detailed compartmental models and simplified models of computation in single neurons, we demonstrate that such an architecture could account for the response properties and atten(cid:173) tional modulation of V 4 neurons. Our results suggest an important role for nonlinear dendritic conductances in extrastriate cortical processing.

We have studied some of the design trade-offs governing visual representations based on spatially invariant conjunctive feature detectors, with an emphasis on the susceptibility of such systems to false-positive recognition errors-Malsburg's classical binding problem. We begin by deriving an analytical model that makes explicit how recognition performance is affected by the number of objects that must be distinguished, the number of features included in the representation, the complexity of individual objects, and the clutter load, that is, the amount of visual material in the field of view in which multiple objects must be simultaneously recognized, independent of pose, and without explicit segmentation. Using the domain of text to model object recognition in cluttered scenes, we show that with corrections for the nonuniform probability and nonindependence of text features, the analytical model achieves good fits to measured recognition rates in simulations involving a wide range of clutter loads, word size, and feature counts. We then introduce a greedy algorithm for feature learning, derived from the analytical model, which grows a representation by choosing those conjunctive features that are most likely to distinguish objects from the cluttered backgrounds in which they are embedded. We show that the representations produced by this algorithm are compact, decorrelated, and heavily weighted toward features of low conjunctive order. Our results provide a more quantitative basis for understanding when spatially invariant conjunctive features can support unambiguous perception in multiobject scenes, and lead to several insights regarding the properties of visual representations optimized for specific recognition tasks.

We have studied some of the design trade-offs governing visual representations based on spatially invariant conjunctive feature detectors, with an emphasis on the susceptibility of such systems to false-positive recognition errors-Malsburg's classical binding problem. We begin by deriving an analytical model that makes explicit how recognition performance is affected by the number of objects that must be distinguished, the number of features included in the representation, the complexity of individual objects, and the clutter load, that is, the amount of visual material in the field of view in which multiple objects must be simultaneously recognized, independent of pose, and without explicit segmentation. Using the domain of text to model object recognition in cluttered scenes, we show that with corrections for the nonuniform probability and nonindependence of text features, the analytical model achieves good fits to measured recognition rates in simulations involving a wide range of clutter loads, word size, and feature counts. We then introduce a greedy algorithm for feature learning, derived from the analytical model, which grows a representation by choosing those conjunctive features that are most likely to distinguish objects from the cluttered backgrounds in which they are embedded. We show that the representations produced by this algorithm are compact, decorrelated, and heavily weighted toward features of low conjunctive order. Our results provide a more quantitative basis for understanding when spatially invariant conjunctive features can support unambiguous perception in multiobject scenes, and lead to several insights regarding the properties of visual representations optimized for specific recognition tasks.

Biophysical modeling studies have suggested that neurons with active dendrites can be viewed as linear units augmented by product terms that arise from interactions between synaptic inputs within the same dendritic subregions. However, the degree to which local nonlinear synaptic interactions could augment the memory capacity of a neuron is not known in a quantitative sense. To approach this question, we have studied the family of subsampled quadratic classifiers: linear classifiers augmented by the best k terms from the set of K = (d2 + d)/2 second-order product terms available in d dimensions. We developed an expression for the total parameter entropy, whose form shows that the capacity of an SQ classifier does not reside solely in its conventional weight values-the explicit memory used to store constant, linear, and higher-order coefficients. Rather, we identify a second type of parameter flexibility that jointly contributes to an SQ classifier's capacity: the choice as to which product terms are included in the model and which are not. We validate the form of the entropy expression using empirical studies of relative capacity within families of geometrically isomorphic SQ classifiers. Our results have direct implications for neurobiological (and other hardware) learning systems, where in the limit of high-dimensional input spaces and low-resolution synaptic weight values, this relatively little explored form of choice flexibility could constitute a major source of trainable model capacity.

Severe architectural and timing constraints within the primate visual system support the conjecture that the early phase of object recognition in the brain is based on a feedforward feature-extraction hierarchy. To assess the plausibility of this conjecture in an engineering context, a difficult three-dimensional object recognition domain was developed to challenge a pure feedforward, receptive-field-based recognition model called SEEMORE. SEEMORE is based on 102 viewpoint-invariant nonlinear filters that as a group are sensitive to contour, texture, and color cues. The visual domains consists of 100 real objects of many different types, including rigid (shovel), nonrigid (telephone cord), and statistical (maple leaf cluster) objects and photographs of complex scenes. Objects were individually presented in color video images under normal room lighting conditions. Based on 12 to 36 training views, SEEMORE was required to recognize unnormalized test views of objects that could vary in position, orientation in the image plane and in depth, and scale (factor of 2); for nonrigid objects, recognition was also tested under gross shape deformations. Correct classification performance on a test set consisting of 600 novel object views was 97 percent (chance was 1 percent) and was comparable for the subset of 15 nonrigid objects. Performance was also measured under a variety of image degradation conditions, including partial occlusion, limited clutter, color shift, and additive noise. Generalization behavior and classification errors illustrated the emergence of several striking natural shape categories that are not explicitly encoded in the dimensions of the feature space. It is concluded that in the light of the vast hardware resources available in the ventral stream of the primate visual system relative to those exercised here, the appealingly simple feature-space conjecture remains worthy of serious consideration as a neurobiological model.

A view-based, high-dimensional feature-space recognition system called SEEMORE was developed as a testbed to explore the representational trade-offs that arise when a simple feedforward neural architecture is challenged with a difficult 3D object recognition problem. Particular emphasis was placed on designing an object representation that could: 1) cope with a large number of real 3D objects of many different types; 2) operate directly on input images without shift, scale, or other object pre-normalization steps; 3) integrate multiple visual cues; and 4) recognize objects over 6 degrees of freedom of viewpoint, gross non-rigid shape distortions, and/or partial occulsion. Recognition results were obtained using a set of 102 color and shape feature channels, each designed to be invariant to image plane shifts and rotations, and only modestly sensitive to orientation in depth. In response to a test set of 600 novel test views of 100 objects presented individually in color video images, SEEMORE identified the object correctly 97% of the time using a nearest neighbour classifier. Similar levels of performance were obtained for the subset of 15 non-rigid objects.

This review considers the input-output behavior of neurons with dendritic trees, with an emphasis on questions of information processing. The parts of this review are (1) a brief history of ideas about dendritic trees, (2) a review of the complex electrophysiology of dendritic neurons, (3) an overview of conceptual tools used in dendritic modeling studies, including the cable equation and compartmental modeling techniques, and (4) a review of modeling studies that have addressed various issues relevant to dendritic information processing.

Compartmental simulations of an anatomically characterized cortical pyramidal cell were carried out to study the integrative behavior of a complex dendritic tree. Previous theoretical (Feldman and Ballard 1982; Durbin and Rumelhart 1989; Mel 1990; Mel and Koch 1990; Poggio and Girosi 1990) and compartmental modeling (Koch et al. 1983; Shepherd et al. 1985; Koch and Poggio 1987; Rall and Segev 1987; Shepherd and Brayton 1987; Shepherd et al. 1989; Brown et al. 1991) work had suggested that multiplicative interactions among groups of neighboring synapses could greatly enhance the processing power of a neuron relative to a unit with only a single global firing threshold. This issue was investigated here, with a particular focus on the role of voltage-dependent N-methyl-D-asparate (NMDA) channels in the generation of cell responses. First, it was found that when a large proportion of the excitatory synaptic input to dendritic spines is carried by NMDA channels, the pyramidal cell responds preferentially to spatially clustered, rather than random, distributions of activated synapses. Second, based on this mechanism, the NMDA-rich neuron is shown to be capable of solving a nonlinear pattern discrimination task. We propose that manipulation of the spatial ordering of afferent synaptic connections onto the dendritic arbor is a possible biological strategy for pattern information storage during learning.