Symphony of high-dimensional brain: Reply to comments on "The unreasonable effectiveness of small neural ensembles in high-dimensional brain"

A Biomorphic Model of Cortical Column for Content-Based Image Retrieval

How do living systems process information? The search for an answer to this question is ongoing. We have developed an intelligent video analytics system. The process of the formation of detectors for content-based image retrieval aimed at detecting objects of various types simulates the operation of the structural and functional modules for image processing in living systems. The process of detector construction is, in fact, a model of the formation (or activation) of connections in the cortical column (structural and functional unit of information processing in the human and animal brain). The process of content-based image retrieval, that is, the detection of various types of images in the developed system, reproduces the process of “triggering” a model biomorphic column, i.e., a detector in which connections are formed during the learning process. The recognition process is a reaction of the receptive field of the column to the activation by a given signal. Since the learning process of the detector can be visualized, it is possible to see how a column (a detector of specific stimuli) is formed: a face, a digit, a number, etc. The created artificial cognitive system is a biomorphic model of the recognition column of living systems.

High-Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality

High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the “curse of dimensionality” states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the “blessing of dimensionality”, has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.

Lizard Brain: Tackling Locally Low-Dimensional Yet Globally Complex Organization of Multi-Dimensional Datasets

Machine learning deals with datasets characterized by high dimensionality. However, in many cases, the intrinsic dimensionality of the datasets is surprisingly low. For example, the dimensionality of a robot's perception space can be large and multi-modal but its variables can have more or less complex non-linear interdependencies. Thus multidimensional data point clouds can be effectively located in the vicinity of principal varieties possessing locally small dimensionality, but having a globally complicated organization which is sometimes difficult to represent with regular mathematical objects (such as manifolds). We review modern machine learning approaches for extracting low-dimensional geometries from multi-dimensional data and their applications in various scientific fields.