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.
Combines psychological ratings with machine learning to map images to psychological similarity spaces.
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…
Deep learning model for AI co-creativity boosts design creativity.
New model explains how concepts grow based on experience.
This study creates a new conceptual framework for news aggregation.
In this work we analyze the behavior of Massey products of closed manifolds under the blow-up construction. The results obtained in the article are applied to the problem of constructing closed symplectic non-formal manifolds. The proofs use Thom spaces as an important technical tool. This application of Thom spaces is…
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, …
Measures neural network complexity using tangent space diversity.
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…
We give a conceptual proof of the fact that if M is a complete submanifold of a space form, then the maximal integral manifolds of the nullity distribution of its second fundamental form through points of minimal index of nullity are complete.
System identifies shifts in sketches for creative drawing.
Research connects Lie algebras to configuration space (co)homology.
Children learn concepts without explicit teaching by aligning internal systems.
New model discovers complex structures without explicit forms.
Unsupervised method constructs knowledge graph from text and code.
Sacks-Uhlenbeck's result on metric spaces expanded.
Develops a conceptual approach to action-angle variables.
The paper introduces a new framework for off-policy reinforcement learning.
Study the stability of Einstein metrics on homogeneous spaces.
We give a short, simple and conceptual proof, based on spin structures, of sphere eversion: an embedded 2-sphere in can be turned inside out by regular homotopy. Ingredients of this eversion are seamlessly connected. We also give the mathematical origins of the proof: the Hopf fibration, and the topological struc…
We discuss the Ribaucour transformation of Legendre maps in Lie sphere geometry. In this context, we give a simple conceptual proof of Bianchi's original Permutability Theorem and its generalisation by Dajczer--Tojeiro. We go on to formulate and prove a higher dimensional version of the Permutability Theorem. It is sho…
New approach combines neural networks for creative problem-solving.
New methods identify concepts in trained embeddings reliably without human labels.
'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 demonstrate that it is conceptually and computationally favorable to regard spin-weighted spherical harmonics as vector valued functions on the total space of the Hopf bundle, satisfying a covariance condition with respect to the gauge group of this bundle. A key role is played by the invariant connec…
VALC provides concept-level interpretations of FLMs, overcoming word-level limitations.
PACE explains ViTs by modeling patch-level concept distributions, surpassing existing methods.
New approach to deep learning for domain adaptation.
A conceptual framework for cluster analysis from the viewpoint of p-adic geometry is introduced by describing the space of all dendrograms for n datapoints and relating it to the moduli space of p-adic Riemannian spheres with punctures using a method recently applied by Murtagh (2004b). This method embeds a dendrogram …
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…
We give conceptual proofs of some well known results concerning compact non-positively curved locally symmetric spaces. We discuss vanishing and non-vanishing of Pontrjagin numbers and Euler characteristics for these locally symmetric spaces. We also establish vanishing results for Stiefel-Whitney numbers of (finite co…
Characterizes Alexandrov spaces with Cohen-Macaulay actions.
A general theory of quantum spinor structures on quantum spaces is presented, within the conceptual framework of the formalism of quantum principal bundles. Quantum analogs of all basic objects of the classical theory are constructed and analyzed. This includes Laplace and Dirac operators, quantum versions of Clifford …
New proof shows L-space knots are fibered and have specific properties.
The article discusses new horizons in black hole physics.
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology of both the commutative and Lie types in computations of the cohomology of the ou…
Gradient-based MCMC for discrete spaces improves sampling performance.
End-to-end model extracts nested terms without extra features.
New method adapts neural networks without losing prior knowledge.
Hybrid model learns novel handwritten characters better than neural or symbolic models alone.
We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as degenerate hermitian metrics that satisfy a certain curvature equation. Using this view…
Quantum blockchain uses entangled photon states over time.
The Schroedinger operator on the Newtonian space-time is defined in a way which is independent on the class of inertial observers. In this picture the Schroedinger operator acts not on functions on the space-time but on sections of certain one-dimensional complex vector bundle over space-time. This bundle, constructed …
Study shows mapping class group actions on configuration spaces are trivial for specific stages.
HyperML boosts recommender systems by learning in hyperbolic space.
We consider natural algebraic differential operations acting on geometric quantities over smooth manifolds. We introduce a method of study and classification of such operations, called IT-reduction. It reduces the study of natural operations to the study of polynomial maps between (vector) spaces of jets which are equi…
The study develops a logic reasoner to verify MS case management specifications.