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.
The paper explores new learning principles based on least cognitive action.
Geodesics on Kähler manifold potentials are paths of least action.
Paper proposes a new learning principle based on least cognitive action.
Study introduces constrained neural units over time for learning problems.
New neural network theory mimics physics laws, making computations more plausible.
In a strengthening of the G-Signature Theorem of Atiyah and Singer, we compute, at least in principle (modulo certain torsion of exponent dividing a power of the order of G), the class in equivariant K-homology of the signature operator on a G-manifold, localized at a prime idea of R(G), in terms of the classes in non-…
How do organisms recognize their environment by acquiring knowledge about the world, and what actions do they take based on this knowledge? This article examines hypotheses about organisms' adaptation to the environment from machine learning, information-theoretic, and thermodynamic perspectives. We start with construc…
We give a proof, using harmonic maps from disks to real trees, of Skora's theorem (Morgan-Otal (1993), Skora (1990), originally conjectured by Shalen): if G is the fundamental group of a surface of genus at least 2, then any small minimal G-action on a real tree is dual to the lift of a measured foliation. Analytic too…
The algebra of transactions as fundamental measurements is constructed on the basis of the analysis of their properties and represents an expansion of the Boolean algebra. The notion of the generalized economic measurements of the economic quantity and quality of objects of transactions is introduced. It has been shown…
Reduction principles for proper actions on smooth manifolds.
The thesis optimizes quantum state exploration using bandit algorithms.
Study optimal offline RL with uncertainty sets and distribution shifts.
The importance of Einstein's geometrization philosophy, as an alternative to the least action principle, in constructing general relativity (GR), is illuminated. The role of differential identities in this philosophy is clarified. The use of Bianchi identity to write the field equations of GR is shown. Another similar …
Holographic principle matches deformed Liouville theory action.
Local-to-global principle for Morse actions on symmetric spaces.
We show an equivariant bordism principle for constructing metrics of positive scalar curvature that are invariant under a given group action. Furthermore, we develop a new codimension-2 surgery technique which removes singular strata from fixed point free -manifolds while preserving equivariant positive scalar cur…
General Relativity can be reformulated as a diffeomorphism invariant SU(2) gauge theory. A new action principle for this "pure connection" formulation of GR is described.
Least symmetry breaking principle explains SGD's local minima in shallow ReLU networks.
Paper presents an action principle for Einstein-Weyl equations in 3D.
Geometric derivation of Einstein equations from causal fermion systems.
We derive a consistent differential representation for the dynamics of a self-financing portfolio for different hedging strategies. In the basis of the derivation there is the so called "retarded action principle", which represents the causality in the evolution of dependent stochastic variables. We demonstrate this pr…
We show that all vector bundles over CP^2 which are not spin admit a complete metric with nonnegative sectional curvature. In the proof we construct a nonnegatively curved metric on the corresponding principle bundle by showing that it admits a cohomogeneity one action with singular orbits of codimension 2. This is clo…
New algorithms reduce contextual bandits' regret without knowing reward noise variances.
Reduces proper actions to simpler core actions for analysis.
UCBVI-γ algorithm minimizes regret in discounted MDPs.
Let G be a connected semisimple Lie group without compact factors whose real rank is at least 2, and let Γ\subset G be an irreducible lattice. We provide a C^\infty classification for volume-preserving Cartan actions of Γand G. Also, if G has real rank at least 3, we provide a C^\infty classification for volume-preserv…
The paper proposes a principle for dynamically adjusting the granularity of reinforcement learning abstractions.
We prove that for each integer k of at least 2, there is an open neigborhood ν_k of the identity map of the 2-sphere S^2, in C^1-topology such that: if G is a nilpotent subgroup of Diff^1(S^2) with length k of nilpotency, generated by elements in ν_k, then the natural action on S^2 has non-empty fixed point set. Moreov…
CLWF improves time series imputation speed and accuracy.
Study nonrigid dynamics of unitary groups on Lie groups via kinetic energy metrics.
Proposes a Gaussian process model for constrained dynamics learning.
Curves in Carnot groups avoid compact sets, growing at least .
Paper finds at least 6 fixed points for a specific circle action on a 10D manifold.
New Einstein manifolds split into symmetric and compact parts.
We classify symplectic actions of 2-tori on compact, connected symplectic 4-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants, which are invariants of the topology of the manifold, of th…
We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on compact symmetric spaces.
The paper finds infinite families of exotic spheres with free actions.
The biggest problem with the methods of machine learning used today in business analytics is that they do not generalize well and often fail when applied to new data. One of the possible approaches to this problem is to enrich these methods (which are almost exclusively based on statistical algorithms) with some intrin…
New method QMLE performs well in complex action spaces without policy gradients.
New principle optimizes bandit decisions with context.
We construct new families of quasimorphisms on many groups acting on CAT(0) cube complexes. These quasimorphisms have a uniformly bounded defect of 12, and they "see" all elements that act hyperbolically on the cube complex. We deduce that all such elements have stable commutator length at least 1/24. The group actions…
In this paper we show that the Seiberg--Witten invariant is zero for all smooth 4--manifolds with which admit circle actions that have at least one fixed point. Furthermore, we show that all symplectic 4--manifolds which admit circle actions with fixed points are rational or ruled, and thus admit a symplectic…
There is a well known link between (maximal) polar representations and isotropy representations of symmetric spaces provided by Dadok. Moreover, the theory by Tits and Burns-Spatzier provides a link between irreducible symmetric spaces of non-compact type of rank at least three and irreducible topological spherical bui…
Minimum attention improves reinforcement learning performance in high-dimensional dynamics.
Starting from the Fermat's principle of least action, which governs classical and quantum mechanics and from the theory of exterior differential forms, which governs the geometry of curved manifolds, we show how to derive the equations governing neural networks in an intrinsic, coordinate invariant way, where the loss …
Internal Lagrangians derived from variational principles.
We consider a natural mechanical system on a Finsler manifold and study its \emph{curvature} using the intrinsic Jacobi equations (called \emph{Jacobi curves}) along the extremals of the least action of the system. The curvature for such a system is expressed in terms of the Riemann curvature and the Chern curvature (i…
Paper introduces probabilistic digital twins for optimal decision making under uncertainty.