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Register a new userThe unreasonable effectiveness of small neural ensembles in high-dimensional brain
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Despite the widely-spread consensus on the brain complexity, sprouts of the single neuron revolution emerged in neuroscience in the 1970s. They brought many unexpected discoveries, including grandmother or concept cells and sparse coding of information in the brain. In machine learning for a long time, the famous curse of dimensionality seemed to be an unsolvable problem. Nevertheless, the idea of the blessing of dimensionality becomes gradually more and more popular. Ensembles of non-interacting or weakly interacting simple units prove to be an effective tool for solving essentially multidimensional problems. This approach is especially useful for one-shot (non-iterative) correction of errors in large legacy artificial intelligence systems. These simplicity revolutions in the era of complexity have deep fundamental reasons grounded in geometry of multidimensional data spaces. To explore and understand these reasons we revisit the background ideas of statistical physics. In the course of the 20th century they were developed into the concentration of measure theory. New stochastic separation theorems reveal the fine structure of the data clouds. We review and analyse biological, physical, and mathematical problems at the core of the fundamental question: how can high-dimensional brain organise reliable and fast learning in high-dimensional world of data by simple tools? Two critical applications are reviewed to exemplify the approach: one-shot correction of errors in intellectual systems and emergence of static and associative memories in ensembles of single neurons.
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Optimal transport has become part of the standard quantitative economics toolbox. It is the framework of choice to describe models of matching with transfers, but beyond that, it allows to: extend quantile regression; identify discrete choice models; provide new algorithms for computing the random coefficient logit model; and generalize the gravity model in trade. This paper offer a brief review of the basics of the theory, its applications to economics, and some extensions.
In artificial neural networks, learning from data is a computationally demanding task in which a large number of connection weights are iteratively tuned through stochastic-gradient-based heuristic processes over a cost-function. It is not well understood how learning occurs in these systems, in particular how they avoid getting trapped in configurations with poor computational performance. Here we study the difficult case of networks with discrete weights, where the optimization landscape is very rough even for simple architectures, and provide theoretical and numerical evidence of the existence of rare - but extremely dense and accessible - regions of configurations in the network weight space. We define a novel measure, which we call the robust ensemble (RE), which suppresses trapping by isolated configurations and amplifies the role of these dense regions. We analytically compute the RE in some exactly solvable models, and also provide a general algorithmic scheme which is straightforward to implement: define a cost-function given by a sum of a finite number of replicas of the original cost-function, with a constraint centering the replicas around a driving assignment. To illustrate this, we derive several powerful new algorithms, ranging from Markov Chains to message passing to gradient descent processes, where the algorithms target the robust dense states, resulting in substantial improvements in performance. The weak dependence on the number of precision bits of the weights leads us to conjecture that very similar reasoning applies to more conventional neural networks. Analogous algorithmic schemes can also be applied to other optimization problems.
This article surveys engineering and neuroscientific models of planning as a cognitive function, which is regarded as a typical function of fluid intelligence in the discussion of general intelligence. It aims to present existing planning models as references for realizing the planning function in brain-inspired AI or artificial general intelligence (AGI). It also proposes themes for the research and development of brain-inspired AI from the viewpoint of tasks and architecture.
Physical symbol systems are needed for open-ended cognition. A good way to understand physical symbol systems is by comparison of thought to chemistry. Both have systematicity, productivity and compositionality. The state of the art in cognitive architectures for open-ended cognition is critically assessed. I conclude that a cognitive architecture that evolves symbol structures in the brain is a promising candidate to explain open-ended cognition. Part 2 of the paper presents such a cognitive architecture.
Working with data in table form is usually considered a preparatory and tedious step in the sensemaking pipeline; a way of getting the data ready for more sophisticated visualization and analytical tools. But for many people, spreadsheets -- the quintessential table tool -- remain a critical part of their information ecosystem, allowing them to interact with their data in ways that are hidden or abstracted in more complex tools. This is particularly true for data workers: people who work with data as part of their job but do not identify as professional analysts or data scientists. We report on a qualitative study of how these workers interact with and reason about their data. Our findings show that data tables serve a broader purpose beyond data cleanup at the initial stage of a linear analytic flow: users want to see and get their hands on the underlying data throughout the analytics process, reshaping and augmenting it to support sensemaking. They reorganize, mark up, layer on levels of detail, and spawn alternatives within the context of the base data. These direct interactions and human-readable table representations form a rich and cognitively important part of building understanding of what the data mean and what they can do with it. We argue that interactive tables are an important visualization idiom in their own right; that the direct data interaction they afford offers a fertile design space for visual analytics; and that sense making can be enriched by more flexible human-data interaction than is currently supported in visual analytics tools.
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