Related papers: Descriptive inner model theory
In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly…
This is a survey of Rational Homotopy Theory, intended for a Mathematical Physics readership.
This popular article provides a short summary of the progress and prospects in Weather and Climate Modelling for the benefit of high school and undergraduate college students and early career researchers. Although this is not a…
Handling trust is one of the core requirements for facilitating effective interaction between the human and the AI agent. Thus, any decision-making framework designed to work with humans must possess the ability to estimate and leverage…
This paper establishes fundamental results for statistical inference of diagnostic classification models (DCM). The results are developed at a high level of generality, applicable to essentially all diagnostic classification models. In…
A Density Matrix Functional theory is constructed semi-empirically for the two-level Lipkin model. This theory, based on natural orbitals and occupation numbers, is shown to provide a good description for the ground state energy of the…
In this paper we introduce a general framework for defining the depth of a sequence with respect to a class of observers. We show that our general framework captures all depth notions introduced in complexity theory so far. We review most…
Despite the recent progress in deep learning and reinforcement learning, transfer and generalization of skills learned on specific tasks is very limited compared to human (or animal) intelligence. The lifelong, incremental building of…
In this article we discuss a generalized Wirtinger inequality.
This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain…
Deep learning model design, development, and debugging is a process driven by best practices, guidelines, trial-and-error, and the personal experiences of model developers. At multiple stages of this process, performance and internal model…
This is a draft of an article to appear in the October 2022 issue of the Notices of the AMS. In this survey article we explore a fascinating area called descriptive combinatorics and its recently discovered connections to distributed…
The paper contained a preliminary version of a general theory of reciprocity laws on vector spaces.
A general mean field theory is presented for the construction of equilibrium coarse grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of…
This the first of a series of articles dealing with abstract classification theory. The apparatus to assign systems of cardinal invariants to models of a first order theory (or determine its impossibility) is developed in [Sh:a]. It is…
Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.
Neural abstractive summarization models are flexible and can produce coherent summaries, but they are sometimes unfaithful and can be difficult to control. While previous studies attempt to provide different types of guidance to control the…
In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the training process, hidden representations, final weights, and…
We assert that models of cognitive structure all have the same basic features. These basic features, independent of the model, have important implications for instruction and assessment. We describe the basic features of models of cognitive…
We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure…