A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
End-to-end model extracts nested terms without extra features.
An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type in terms of orbit equivalence. As…
We propose an alternative approach on the existence of affine realizations for HJM interest rate models. It is applicable to a wide class of models, and simultaneously it is conceptually rather comprehensible. We also supplement some known existence results for particular volatility structures and provide further insig…
PACE explains ViTs by modeling patch-level concept distributions, surpassing existing methods.
New model explains how concepts grow based on experience.
The cognitive framework of conceptual spaces bridges the gap between symbolic and subsymbolic AI by proposing an intermediate conceptual layer where knowledge is represented geometrically. There are two main approaches for obtaining the dimensions of this conceptual similarity space: using similarity ratings from psych…
We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the infinitesimal counterparts of multiplicative forms, multivector fields and holomorp…
Humans perceive the seemingly chaotic world in a structured and compositional way with the prerequisite of being able to segregate conceptual entities from the complex visual scenes. The mechanism of grouping basic visual elements of scenes into conceptual entities is termed as perceptual grouping. In this work, we pro…
This paper presents a computational model for conceptual shifts, based on a novelty metric applied to a vector representation generated through deep learning. This model is integrated into a co-creative design system, which enables a partnership between an AI agent and a human designer interacting through a sketching c…
We introduce a simple recurrent variational auto-encoder architecture that significantly improves image modeling. The system represents the state-of-the-art in latent variable models for both the ImageNet and Omniglot datasets. We show that it naturally separates global conceptual information from lower level details, …
Following the programme set out in Part I of this work, we develop a conceptual higher order differential calculus. The '' local linear algebra '' defined in Part I is generalized by '' higher order local linear algebra ''. The underlying combinatorial object of such higher algebra is the natural n-dimensional hyper-cu…
The Allais and Ellsberg paradoxes show that the expected utility hypothesis and Savage's Sure-Thing Principle are violated in real life decisions. The popular explanation in terms of 'ambiguity aversion' is not completely accepted. On the other hand, we have recently introduced a notion of 'contextual risk' to mathemat…
It was recently shown that there exists an explicit bound for the number of Pachner moves needed to connect any two triangulation of any Haken 3-manifold which contains no fibred sub-manifolds as strongly simple pieces of its JSJ-decomposition. In this paper we prove a generalisation of that result to all knot compleme…
Online news media provides aggregated news and stories from different sources all over the world and up-to-date news coverage. The main goal of this study is to have a solution that considered as a homogeneous source for the news and to represent the news in a new conceptual framework. Furthermore, the user can easily …
We study coordinate-invariance of some asymptotic invariants such as the ADM mass or the Chruściel-Herzlich momentum, given by an integral over a "boundary at infinity". When changing the coordinates at infinity, some terms in the change of integrand do not decay fast enough to have a vanishing integral at infinity; bu…
It is not known whether there exists a computable function bounding the number of Pachner moves needed to connect any two triangulation of a compact 3-manifold. In this paper we find an explicit bound of this kind for all Haken 3-manifolds which contain no fibred submanifolds as strongly simple pieces of their JSJ-deco…
Unsupervised method constructs knowledge graph from text and code.
Concept induction requires the extraction and naming of concepts from noisy perceptual experience. For supervised approaches, as the number of concepts grows, so does the number of required training examples. Philosophers, psychologists, and computer scientists, have long recognized that children can learn to label obj…
We present a system for identifying conceptual shifts between visual categories, which will form the basis for a co-creative drawing system to help users draw more creative sketches. The system recognizes human sketches and matches them to structurally similar sketches from categories to which they do not belong. This …
We present the general theory of curves in conformal geometry using tractor calculus. This primarily involves a tractorial determination of distinguished parametrizations and relative and absolute conformal invariants of generic curves. The absolute conformal invariants are defined via a tractor analogue of the classic…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can be used to create more interpretable machine learning models. By proposing a nove…
We review two strands of conceptual approaches to the formal representation of a decision maker's non-knowledge at the initial stage of a static one-person, one-shot decision problem in economic theory. One focuses on representations of non-knowledge in terms of probability measures over sets of mutually exclusive and …
Simplifies noisy convex optimization with a new algorithm.
'Ergodicity economics' is criticized as pseudoscience.
Frolicher and Nijenhuis recognized well in the middle of the previous century that the Lie bracket and its Jacobi identity could and should exist beyond Lie algebras. Nevertheless the conceptual meaning of their discovery has been obscured by the messy techniques they exploited. The principal objective in this paper is…
We show how supersymmetry conditions for flux compactifications of supergravity and string theory can be described in terms of a flat subalgebra of the Kahler-Atiyah algebra of the compactification space, a description which has wide-ranging applications. As a motivating example, we consider the most general M-theory c…
VALC provides concept-level interpretations of FLMs, overcoming word-level limitations.
In this paper we develop a general conceptual approach to the problem of existence of action-angle variables for dynamical systems, which establishes and uses the fundamental conservation property of associated torus actions: anything which is preserved by the system is also preserved by the associated torus actions. T…
We introduce new aspects in conformal geometry of some very natural second-order differential operators. These operators are termed shift operators. In the flat space, they are intertwining operators which are closely related to symmetry breaking differential operators. In the curved case, they are closely connected wi…
At the heart of convex geometry lies the observation that the volume of convex bodies behaves as a polynomial. Many geometric inequalities may be expressed in terms of the coefficients of this polynomial, called mixed volumes. Among the deepest results of this theory is the Alexandrov-Fenchel inequality, which subsumes…
This paper is an exposition of the relationship between Witten's Chern-Simons functional integral and the theory of Vassiliev Invariants of knots and links in three dimensional space. We conceptualize the functional integral in terms of equivalence classes of functionals of gauge fields and we do not use measure theory…
Defines Lie and Courant algebroids over Lie groupoids using homological vector fields.
Hybrid model learns novel handwritten characters better than neural or symbolic models alone.
Harmonic gauge simplifies geometric analysis of Riemannian metrics.
We address the problem of maintaining high voltage power transmission networks in security at all time, namely anticipating exceeding of thermal limit for eventual single line disconnection (whatever its cause may be) by running slow, but accurate, physical grid simulators. New conceptual frameworks are calling for a p…
The fragmentation of production across countries has become an important feature of the globalization in recent decades and is often conceptualized by the term, global value chains (GVCs). When empirically investigating the GVCs, previous studies are mainly interested in knowing how global the GVCs are rather than how …
We view strict ring spectra as generalized rings. The study of their algebraic K-theory is motivated by its applications to the automorphism groups of compact manifolds. Partial calculations of algebraic K-theory for the sphere spectrum are available at regular primes, but we seek more conceptual answers in terms of lo…
We propose and analyze a constrained level-set method for semi-automatic image segmentation. Our level-set model with constraints on the level-set function enables us to specify which parts of the image lie inside respectively outside the segmented objects. Such a-priori information can be expressed in terms of upper a…
One of the defining characteristics of human creativity is the ability to make conceptual leaps, creating something surprising from typical knowledge. In comparison, deep neural networks often struggle to handle cases outside of their training data, which is especially problematic for problems with limited training dat…
The exploding and vanishing gradient problem has been the major conceptual principle behind most architecture and training improvements in recurrent neural networks (RNNs) during the last decade. In this paper, we argue that this principle, while powerful, might need some refinement to explain recent developments. We r…
We provide a new, self-contained and more conceptual proof of the result that an almost contact metric manifold of dimension greater than 5 is Sasakian if and only if it is nearly Sasakian.
The study develops a logic reasoner to verify MS case management specifications.
Field canals improvement projects (FCIPs) are one of the ambitious projects constructed to save fresh water. To finance this project, Conceptual cost models are important to accurately predict preliminary costs at the early stages of the project. The first step is to develop a conceptual cost model to identify key cost…
Develops a parameter-free SGD algorithm with optimal convergence rate.
We provide an explicit upper bound on the number of Reidemeister moves required to pass between two diagrams of the same link. This leads to a conceptually simple solution to the equivalence problem for links.
Enhances CNN feature extractors' separation capacity analysis.
Factorization homology theories of topological manifolds, after Beilinson, Drinfeld and Lurie, are homology-type theories for topological -manifolds whose coefficient systems are -disk algebras or -disk stacks. In this work we prove a precise formulation of this idea, giving an axiomatic characterization of fa…
Explanation in machine learning and related fields such as artificial intelligence aims at making machine learning models and their decisions understandable to humans. Existing work suggests that personalizing explanations might help to improve understandability. In this work, we derive a conceptualization of personali…