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Universal Metaphysics
(2019-12-31)
The development of natural science especially physics allows us to understand to a large extent the material world. However, the world also contains a large amount of concepts that are non-material and abstract, which are ...
Double descent in the condition number
(Center for Brains, Minds and Machines (CBMM), 2019-12-04)
In solving a system of n linear equations in d variables Ax=b, the condition number of the (n,d) matrix A measures how much errors in the data b affect the solution x. Bounds of this type are important in many inverse ...
Brain Signals Localization by Alternating Projections
(Center for Brains, Minds and Machines (CBMM), arXiv, 2019-08-29)
We present a novel solution to the problem of localization of brain signals. The solution is sequential and iterative, and is based on minimizing the least-squares (LS) criterion by the alternating projection (AP) algorithm, ...
Theoretical Issues in Deep Networks
(Center for Brains, Minds and Machines (CBMM), 2019-08-17)
While deep learning is successful in a number of applications, it is not yet well understood theoretically. A theoretical characterization of deep learning should answer questions about their approximation power, the ...
An analysis of training and generalization errors in shallow and deep networks
(Center for Brains, Minds and Machines (CBMM), arXiv.org, 2019-05-30)
This paper is motivated by an open problem around deep networks, namely, the apparent absence of overfitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze ...
Hippocampal Remapping as Hidden State Inference
(Center for Brains, Minds and Machines (CBMM), bioRxiv, 2019-08-22)
Cells in the hippocampus tuned to spatial location (place cells) typically change their tuning when an animal changes context, a phenomenon known as remapping. A fundamental challenge to understanding remapping is the fact ...
Technical Report: Building a Neural Ensemble Decoder by Extracting Features Shared Across Multiple Populations
(2019-09-05)
To understand whether and how a certain population of neurons represent behavioral-relevant vari- ables, building a neural ensemble decoder has been used to extract information from the recorded activity. Among different ...