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/ .

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 = ( d 2 + 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.

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 sizes, 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 sizes, 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.

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 domain 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 in dividually 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 non rigid 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 illustrate 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.

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.