Detailed Description

Anatomically, the cerebral cortex is the outermost neuronal tissue of the brain, and it is believed to play a key role in sensation, perception, higher cognitive functions, and motor control. It is a layered structure referred to as the gray matter, because it contains largely cell bodies as compared to the white matter containing largely myelinated axons. The evolutionary origin can be traced back to reptiles, but it first appeared as a uniform structure in early mammals. The increase in the size of this layered cortical sheet during evolution is believed to be crucial for the development of human cognition and ultimately human culture during human brain evolution. Even though many entries in this section on “Cortex: Models and Computation” are applicable to the [hippocampus] as well, the focus is on the phylogenetically younger six-layered neocortex.

Why is it so interesting and important to investigate the cortex using modeling? If the co-occurrence of the expansion of the neocortex during evolution of the emergence of human cognition and culture is more than a suspicious coincident, then understanding the cortex is essential to understand the human condition. Identifying brain and mind is certainly a too naïve approach, but it is now widely accepted that – whatever the relation between mind and brain is – an understanding of cortex will at least constrain theories of how the mind works. Testable theories and predictive models are needed to complement conceptual modeling and colloquial talk on that matter. Moreover, understanding how the cortex operates may help to diagnose neurological diseases earlier, to develop more efficient treatments, and to construct [brain-machine interfaces]. Models in general, and patient-specific models in particular, will be useful to link measurements of macroscopic brain activity obtained with brain imaging techniques to the underlying causes. This rather practical justification for modeling cortex is becoming even more relevant today as a “deliverable” of computational neuroscience. However, accurate and faithful modeling has to deal with the complexity of the neural circuits and the cellular and synaptic heterogeneity. Multiple large-scale initiatives currently address this by collecting massive amounts of data to facilitate the development of faithful models of the cortex. Here, the role of cortical models is in organizing and summarizing the data, and they could even be integrated into (semi)automatic data-driven modeling pipelines with little intervention of a “modeler.” I argue that modeling cortex is interesting and exciting, because despite massive amounts of available data, the activity of modeling will remain in large parts an art: Finding the right level of abstraction to arrive at insights for the question at hand can hardly be automated.

On the one hand, the neocortex is an umbrella for a set of distinct structures that differ, for example, in terms of their function, connectivity, and cytoarchitecture. On the other hand, Mountcastle (1978) suggested that similarities of these neocortical regions point to a common computational machinery in the sense that each region has the same basic architecture and operates according to the same computational principles. This is also the guiding idea of this section, without accepting it as a truism or dogma. It is indeed conceivable that different regions of the neocortex operate according to fundamentally different principles, or that conventional notions of “computation” are not suited as a metaphor to understand the cortex. The philosophy of science is not conclusive regarding a clear distinction of theory vs. model. However, as a tentative distinction for modeling cortex, we may adopt the short-hand definition that theory provides meaning to models, while models explain data. Computational principles come close to the notion of a theory. With that reading, the entries assembled in this section cover the whole spectrum between theories and models of cortex.

Robert Legenstein (“Recurrent Network Models, Reservoir Computing”) summarizes the state of the art in how artificial recurrent neural networks (RNNs) address demanding learning tasks. RNN researchers can be thought of as being in the luxurious position to investigate computations in cortex-inspired architectures without the burden to comply with all the constraints set by experimental neuroscience. The performance of these architectures and learning algorithms can serve as a yardstick for existing biologically more faithful models and as a guideline for constructing new models. Jochen Triesch’s contribution on “Cortical Function, Normative Models of” gives a bird’s eye perspective on how to derive models from computational principles. Cortical modeling involves determining model structure and parameterization, and for data-driven approaches, computational neuroscience has developed a [rich repertoire of methods]. The normative approach endorsed by Triesch is a complementary addition for doing this, which applies in particular to explaining cortical networks in terms of their genesis via [learning mechanisms]. The contributions of Sophie Deneve (“Bayesian Inference with Spiking Neurons”) and Walter Senn and Jean-Pascal Pfister (“Reinforcement Learning in Cortical Networks”) are instances of this normative approach. Deneve shows how Bayesian inference can be carried out by spiking neurons. The Bayesian approach turned out to be very fruitful for understanding computations in the cortex as evident by a whole section in this encyclopedia being dedicated to the [“Bayesian brain”]. It should be noted that both Deneve’s and Senn’s and Pfister’s entries explicitly address computation with spiking neurons and thus represent an explicit formal link between computational principles and experimentally testable predictions at the level of individual neurons. Both of these mutually compatible approaches make explicit a notion of optimality as required within the normative approach: The Bayesian approach is based on a principled way of conducing logical inference under uncertainty, whereas reinforcement learning is based on Bellman optimality, i.e., [decision making] in dynamic and often only partially observable environments.

In a similar way, Udo Ernst (“Center-Surround Processing, Computational Role of”) addresses the phenomenon of center-surround processing (CSP) from a computational point of view. Even though CSP has been investigated mainly in the visual system, where it is exemplified, e.g., by the phenomenon of end stopping already described by Hubel and Wiesen (Hubel and Wiesel 1965), it is also a candidate for a canonical cortical computation to be found in various cortical regions. Ernst links CSP to the laws formulated by Gestalt psychologists in the early twentieth century but also to modern normative approaches that utilize the statistics of natural visual scenes in explaining physiological and perceptual phenomena. He points out that CSP has been successfully implemented in [cortex-inspired artificial vision systems], where it improved object detection and recognition of natural scenes. Such real-world tests of cortical models are excellent yardsticks modelers may want to consider in addition to reproducing physiological or perceptual phenomena that are usually observed in rather artificial laboratory settings with less naturalistic stimuli. Michael Spratling (“Predictive Coding”) reviews the concept of predictive coding. This is an instance of a theory (in the sense defined above), but models derived from this theory can predict CSP as a by-product. The distinctive feature of predictive coding is that downstream areas in the hierarchically organized cortex continuously predict activity in areas at a lower level of the hierarchy. Given that downstream areas in sensory cortices integrate signals from neuronal populations with adjacent receptive fields (RFs), the predictions carry not only information about anticipated future inputs but also from the neighboring RFs as in CSP. Models derived from predictive coding are candidates for a canonical cortical computation. Applications to sensory cortices may be relatively straightforward, but the crucial test for a theory is its predictions when extrapolated beyond the postdoc explanations of already known phenomena. Let me point out three selected such extrapolations: First, it has been applied to explain mirror neuron activity as the natural consequence of predictive coding in the hierarchically organized “social brain” (Kilner et al. 2007). Second, it has been applied to interoception from which predictions about bodily self-consciousness could be derived (Seth et al. 2011). Third, it has been suggested that it may also be applicable to the [motor system] with the surprising consequence that the actual motor acts are carried out to fulfill predictions about sensory consequences of just these acts (Hawkins and Blakeslee 2004) as compared to being only the output stage of a sensory-to-motor transformation. Future experimental studies will need to further test these predictions. Interestingly, Spratling has shown that predictive coding and the concept of biased competition can be thought of as being just variants of the same mathematical model. Thus, while the interpretation of models derived from the predictive coding theory in terms of “prediction of inputs” may be unusual in some cases, as in the case of the motor system, the theory is still a rich framework to systematically derive mathematical models and testable predictions.

Computation cannot be considered in isolation. Communication engineers and designers of processors know this too well. Matthias Bethge (“Efficient Population Coding”) considers how much information is communicated by cortical networks. Bethge introduces the psychometric and neurometric functions and highlights that the information contained in the spiking activity of populations of neurons is often enough to predict the behavioral responses of the whole organisms. This is an empirical finding, but computational neuroscience also needs to ask more fundamental questions such as “how much information can be transmitted?” Only this allows for assessing how close to optimality the cortical circuits are actually operating. To address such questions, he reviews how the concepts of Fisher and Shannon’s mutual information can be applied to quantify the information content of population activity. Combining the approaches that focus on computation introduced so far with these studies of communication and information content could be a very fruitful direction for future studies, in particular when factoring in limitations due to fiber bottlenecks between cortical areas and energy expenditure.

RNNs are Turing-complete, which means that finite RNNs could, in principle, approximate any computation. However, to determine the computations actually performed by the cerebral networks, it is imperative to develop mechanistically plausible models that explicitly respect the anatomical and physiological constraints set by experimental neuroscience. Sean Hill (“Cortical Columns, Models of”) presents models of the so-called cortical column, which itself is a theoretical concept motivated by early experimental studies that showed smooth variation of functional properties tangential to the cortical surface but an invariance across cortical layers at a given position. The notion of a cortical column remains controversial, but for computational neuroscience it is certainly a goal to deliver predictive mechanistic models of signal propagation across cortical layers within an area. Probably the most prominent example of mechanistic network modeling to explain a physiologically observed phenomenon is the models for orientation tuning in primary visual cortex (V1), which are reviewed by Nicholas Priebe and Benjamin Scholl (“Emergence of Orientation Selectivity in the Cerebral Cortex, Modeling”). Hubel and Wiesel discovered orientation tuning (Hubel and Wiesel 1959) and formulated a first model, namely, that the tuning derives from the pattern of afferent connections from the thalamus onto neurons in V1. The subsequently developed models emphasized the role of intracortical connections to account for experimentally observed properties of orientation tuning such as contrast invariance. Interestingly, the original feedforward model by Hubel and Wiesel is still a guiding idea, even though it had to be refined. This highlights that such more informal and conceptual models remain valuable today, even though computational neuroscience has to show explicitly when and how models fail as reviewed by Priebe and Scholl.

In my first entrie (“Center-Surround Processing, Network Models of”), I take a similar approach and address the question of how the CSP in V1, as introduced by Ernst, may be realized by cortical circuits. More specifically, I review network models of CSP that are distinct in terms of the assumed pathways. Early models emphasized the role of long-range connections within an area, but later models came to acknowledge the role of feedback from downstream areas. The cortical operating mode in vivo is characterized by strong recurrent excitation and balanced inhibition that affect how single neurons integrate and propagate signals (reviewed in my second short contribution “Balanced State”). Interestingly, more recent modeling studies investigated the role of short-range local connections in CSP and found that the properties of strongly connected recurrent networks in a balanced state need to be considered in models of CSP. Adaptation is another phenomenon that seems to be omnipresent in the cerebral cortex. Klaus Wimmer (“Adaptation in Sensory Cortices, Models of”) reviews models of adaptation and considers both their role in perception and how plausible mechanisms such as short-term synaptic depression mediate them. Since strongly recurrent networks in a balanced state with static synaptic connections may already exhibit counterintuitive phenomena, Wimmer argues for systematic modeling studies of structured networks with adaptation mechanisms as an important approach to understand adaptation in sensory cortices.

Selected examples of higher cognitive functions are attention and working memory. Cortical models of these functions are reviewed by Philipp Schwedhelm and Stefan Treue (“Attentional Top-Down Modulation, Models of”) and Gianluigi Mongillo (“Working Memory, Models of”). Schwedhelm and Treue review models of attentional top-down modulation. They highlight how phenomenological models have guided experiments and how those fed back into refining the models. Some of the models assume the mechanism of gain modulation but remain intentionally agnostic regarding the biophysical mechanisms. This exemplifies that cortical modeling with a properly chosen level of description could be integrated closely with experimental investigations. Working memory has also been studied experimentally in great detail, but most early network models of the persistent activity that is characteristic for the physiological correlate of working memory were variants of attractor networks, where a self-sustained “bump” of activity was identified with the content of working memory. Only more recent modeling studies suggested that self-sustained activity may not be restricted to the spiking activity of groups of neurons, because the state of synapses with short-term dynamics can also be considered as an activity variable that could be exploited to store self-sustained activity. The idea that synaptic variables, which are by multiple orders of magnitude more numerous than single cell state variables, may be crucial for cerebral information processing has been around in the computational neuroscience community for a long time. However, explicit formal models need to spell this out and show the potential benefit in, for example, systematic simulation studies even if the models are speculative and experimentally very hard to test as in the case of the synaptic theory of working memory. This also applies for models of attention: Given that after 50 years of the discovery of orientation tuning in V1, there is still no agreement on network models of even such a basal response property, it may not come as a surprise that the mechanisms of attention remain elusive. While, for example, mechanistic models of top-down gain modulation via synchronizing the discharges of inhibitory interneurons may be consistent with the available anatomical, physiological, and biophysical knowledge, recording multiple identified inhibitory interneurons in vivo in attentional demanding tasks remains to be achieved.

Another currently only poorly understood phenomenon is how the so-called resting state of the brain is generated and maintained. Computational Neuroscience research has already identified the problem of explaining mechanistically the ongoing low-activity state in recurrently connected local networks (Brunel et al. 2013) and derived models to explain them as a stable attractor. Joana Cabral and Gustavo Deco (“Spontaneous Activity, Models of”) review models of the global spontaneous activity that exhibits characteristic temporal properties and is found in the so-called default mode network. This activity (and the default mode network) has been studied intensively using functional magnetic resonance imaging (fMRI), but Cabral and Deco correctly point out that a deeper analysis of the network models is still needed to provide insights into the dynamical properties of the resting state.

The entries in this section cover computation and modeling of the cortex using different approaches and models at various levels of abstraction. Certainly, the cortex cannot be considered in isolation but needs to be modeled and understood in concert with other structures, such as the [thalamus] and [basal ganglia]. Will it be possible to understand cortex without modeling the whole brain or even closed sensory-motor loops within an “enactive” approach (Noe 2006) that states that to understand the brain – in our case, only the cortex – one needs to look at more than just the brain? This is indeed an open question that is of special interest for philosophers of science and mind. However, I argue that the cortex considered as a complex and self-assembled adaptive structure will remain a challenge for any kind of modeling conducted by Computational Neuroscientists who are open to empirical findings and brave enough to ignore irrelevant details without throwing out the baby with the bath water. The reward shall be motivating: to gain an insight into how the cortex works. Relevance and irrelevance of details needs to be decided on a case-by-case basis, which also depends on the taste of the modeler (or theoretician). Unfortunately, despite a multitude of models and some promising candidates for theories of cortical function, one needs to attest that we are not yet there: A unified theory of cortical computation with associated models still needs to be derived and thoroughly tested. My own requirement for accepting such a theory is that it will cover at least the topics addressed by the entries in this section.

Cross-References