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.
Reduction principles for proper actions on smooth manifolds.
Holographic principle matches deformed Liouville theory action.
Local-to-global principle for Morse actions on symmetric spaces.
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.
Paper presents an action principle for Einstein-Weyl equations in 3D.
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…
Geometric derivation of Einstein equations from causal fermion systems.
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…
Reduces proper actions to simpler core actions for analysis.
Machine Learning algorithms are typically regarded as appropriate optimization schemes for minimizing risk functions that are constructed on the training set, which conveys statistical flavor to the corresponding learning problem. When the focus is shifted on perception, which is inherently interwound with time, recent…
The paper proposes a principle for dynamically adjusting the granularity of reinforcement learning abstractions.
New Einstein manifolds split into symmetric and compact parts.
New method QMLE performs well in complex action spaces without policy gradients.
New principle optimizes bandit decisions with context.
Internal Lagrangians derived from variational principles.
There are three quite distinct ways to train a machine learning model on recommender system logs. The first method is to model the reward prediction for each possible recommendation to the user, at the scoring time the best recommendation is found by computing an argmax over the personalized recommendations. This metho…
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…
Extending our reduction construction in \cite{Hu} to the Hamiltonian action of a Poisson Lie group, we show that generalized Kähler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show that the constructions in string theory of the (geometrical) -dua…
The paper examines how risk reduction and insurance choices interact under convex premium principles.
Geodesics on Kähler manifold potentials are paths of least action.
We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of elliptic elements to the classical Liouville action is derived in terms of the Bloch-Wigner functions. We prove the first and second variation formulas for the cla…
Symmetric Positive Definite (SPD) matrices have been widely used in medical data analysis and a number of different Riemannian met-rics were proposed to compute with them. However, there are very few methodological principles guiding the choice of one particular metric for a given application. Invariance under the acti…
Paradan and Vergne generalised the quantisation commutes with reduction principle of Guillemin and Sternberg from symplectic to Spin-manifolds. We extend their result to noncompact groups and manifolds. This leads to a result for cocompact actions, and a result for non-cocompact actions for reduction at zero. The r…
Differential K-theory gets a -ring structure.
We formulate a quantization commutes with reduction principle in the setting where the Lie group , the symplectic manifold it acts on, and the orbit space of the action may all be noncompact. It is assumed that the action is proper, and the zero set of a deformation vector field, associated to the momentum map and a…
New principle for supersymmetric localization on Lie groups.
For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy le…
This paper is devoted to a systematic study of the geometry of nondegenerate $\bbR^n$-actions on -manifolds. The motivations for this study come from both dynamics, where these actions form a special class of integrable dynamical systems and the understanding of their nature is important for the study of other Hamil…
Low precision networks in the reinforcement learning (RL) setting are relatively unexplored because of the limitations of binary activations for function approximation. Here, in the discrete action ATARI domain, we demonstrate, for the first time, that low precision policy distillation from a high precision network pro…
Study optimal offline RL with uncertainty sets and distribution shifts.
New definition of interpretability makes model design more actionable.
We rigorously define the Liouville action functional for finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that the classical action - the critical point of the Liouville action functional, considered as a funct…
We enhance conformal prediction for risk-averse decisions with action-conditional guarantees.
This paper explores the possibility that asset prices, especially those traded in large volume on public exchanges, might comply with specific physical laws of motion and probability. The paper first examines the basic dynamics of asset price displacement and finds one can model this dynamic as a harmonic oscillator at…
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…
The thesis optimizes quantum state exploration using bandit algorithms.
Paper tackles reinforcement learning generalization through invariant policy optimization.
From a young age humans learn to use grammatical principles to hierarchically combine words into sentences. Action grammars is the parallel idea, that there is an underlying set of rules (a "grammar") that govern how we hierarchically combine actions to form new, more complex actions. We introduce the Action Grammar Re…
This paper applies machine learning techniques to student modeling. It presents a method for discovering high-level student behaviors from a very large set of low-level traces corresponding to problem-solving actions in a learning environment. Basic actions are encoded into sets of domain-dependent attribute-value patt…
Study manifolds with positive intermediate Ricci curvature and large symmetry rank.
Interactive machine learning improves learning efficiency with user input.
The paper studies differential operator invariants and equivalence under Lie pseudogroups.
AI system narrows human decision options for better outcomes.
The paper improves Q-learning by incorporating pessimism for better sample efficiency.
Latent variable models improve RL by facilitating efficient learning and exploration.
We study the rigidity of polyhedral surfaces using variational principle. The action functionals are derived from the cosine laws. The main focus of this paper is on the cosine law for a non-triangular region bounded by three possibly disjoint geodesics. Several of these cosine laws were first discovered and used by Fe…
Identifies latent actions and dynamics from offline data with diverse demonstrators.
We consider intersecting hypersurfaces in curved spacetime with gravity governed by a class of actions which are topological invariants in lower dimensionality. Along with the Chern-Simons boundary terms there is a sequence of intersection terms that should be added in the action functional for a well defined variation…