Representational geometry: integrating cognition, computation, and the brain

Nikolaus Kriegeskorte, Rogier A. Kievit
2013 Trends in Cognitive Sciences  
The cognitive concept of representation plays a key role in theories of brain information processing. However, linking neuronal activity to representational content and cognitive theory remains challenging. Recent studies have characterized the representational geometry of neural population codes by means of representational distance matrices, enabling researchers to compare representations across stages of processing and to test cognitive and computational theories. Representational geometry
more » ... ovides a useful intermediate level of description, capturing both the information represented in a neuronal population code and the format in which it is represented. We review recent insights gained with this approach in perception, memory, cognition, and action. Analyses of representational geometry can compare representations between models and the brain, and promise to explain brain computation as transformation of representational similarity structure. The representational geometry of neuronal population codes The concept of representation is central to the cognitive and brain sciences. We interpret neuronal activity as serving the function of representing content, and of transforming representations of content, with the ultimate objective to produce successful behaviors. The content could be a visual image, a sound or odor, a semantic interpretation of sensory input, a proposition, a goal, a planned action, or a motor sequence. The representational interpretation [1] provides a powerful explanatory framework that makes it easier to understand neuronal activity in the context of the overall function of the brain. Representation links cognition to brain activity and enables us to build functional theories of brain information processing [2] . Neurophysiology has long interpreted the selectivity of neurons as serving to represent various kinds of sensory and higher-level information. The population of neurons within an area is thought to jointly represent the content in what is called a neuronal population code [3] . It is the pattern of activity across neurons that represents the content. The many possible combinations of activity states of neurons provide a rich representational space. Motivated by this idea, recent analyses of neuronal recordings and functional imaging data have increasingly focused on patterns of activity across many neurons within a functional region [4] . We can think of a brain region's representation as a multidimensional space. The dimensions of the space correspond to the neurons, and a point corresponds to an activity pattern (i.e., each neuron's activity provides the coordinate value for one of the dimensions). A visually perceived object, for example, will correspond to a point in the representational space of a given visual area. The set of all possible objects (or pieces of mental content) corresponds to a vast set of points in the space. It is the geometry of these points that defines the nature of the representation. Mathematical and cognitive psychology have a long history of investigations of representational geometry on the basis of behavioral data [5] [6] [7] [8] [9] [10] . However, the notion of representational geometry has only more recently been brought into the analysis of brain-activity data [11] [12] [13] [14] [15] . To characterize the geometry of a representation, we can compare the brain-activity patterns representing a set of stimuli (or, more generally, experimental conditions) to each other. The dissimilarity of two patterns corresponds to the distance between their points in the representational space. Having measured these distances, we can construct a matrix, the representational dissimilarity matrix (RDM), in which we can look up the representational distance (or dissimilarity) for each pair of stimuli ( Figure 1) . Intuitively, the RDM tells us which distinctions between stimuli the population code honors and which distinctions it disregards. Considering RDMs makes it very easy to compare different representations (e.g., different brain regions, a region to a computational model representation, or the same region between different individuals or species) by just computing the correlation between the RDMs (Box 1). Comparing activity patterns directly, by contrast, would require us to define the correspondence mapping between, say, voxels of two regions, or between single neurons and the units of a computational network model, or between voxels of the same region in two individuals. Establishing these mappings can be difficult and generally requires a separate experimental data set [16] [17] [18] [19] . The 'representational Review 1364-6613/$ -see front matter ß
doi:10.1016/j.tics.2013.06.007 pmid:23876494 pmcid:PMC3730178 fatcat:c2swzal2pzhdljj2rliiqwzo2e