arXiv research

Generally accepted depreciation methods do not compute the intrinsic value of an asset, as they do not factor for the Time Value of Money, a key principle within financial theory. This is disadvantageous, as knowing the intrinsic value of an asset can assist with making effective purchase and sale decisions. By applyin…

Develops intrinsic Gaussian process regression for manifold-valued data.

Study uniformly differentiable graphs in Carnot groups, proving area formulas.

Learning goal-directed behavior in environments with sparse feedback is a major challenge for reinforcement learning algorithms. The primary difficulty arises due to insufficient exploration, resulting in an agent being unable to learn robust value functions. Intrinsically motivated agents can explore new behavior for …

AutoDIME automates design of multi-agent environments for RL.

Geometrically reformulates elasticity theory using exterior calculus.

eDCF estimates intrinsic dimension using local connectivity.

A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the non-convex optimization problem as transformations of Euclidean conditional expectation. …

New risk measures for financial networks avoid external capital, reducing systemic risk.

A new method calculates intrinsic effective sample size for manifold-valued data.

The article presents a new entropy model for assessing stock market interest.

We use the theory of rectifiable metric spaces to define a Dirichlet energy of Lipschitz functions defined on the support of integral currents. This energy is obtained by integration of the square of the norm of the tangential derivative, or equivalently of the approximate local dilatation, of the Lipschitz functions. …

Characterizes density-valued symplectic forms on multisymplectic manifolds.

Proves compactness for timed-metric spaces using new distance and maps.

Monetary risk measures are usually interpreted as the smallest amount of external capital that must be added to a financial position to make it acceptable. We propose a new concept: intrinsic risk measures and argue that this approach provides a direct path from unacceptable positions towards the acceptance set. Intrin…

This study examines how ChiNext IPOs' initial returns are influenced by regulation regime changes.

Hadwiger's Theorem states that Euclidean-invariant convex-continuous valuations of definable sets are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable real-valued functions on n-dimensional Euclidean space. This generalizes intrinsic vol…

For any closed smooth Riemannian manifold H. Weyl has defined a sequence of numbers called today intrinsic volumes. They include volume, Euler characteristic, and integral of the scalar curvature. We conjecture that absolute values of all intrinsic volumes are bounded by a constant depending only on the dimension of th…

Introduces intrinsic Riemannian cross-covariance for manifold-valued random objects.

Learning about many things can provide numerous benefits to a reinforcement learning system. For example, learning many auxiliary value functions, in addition to optimizing the environmental reward, appears to improve both exploration and representation learning. The question we tackle in this paper is how to sculpt th…

New RL approach uses future state and action visitation measures for better exploration.

Minimal surfaces' area bounds proven equivalent, extending known results.

A new measure of causal influence quantifies intrinsic contributions in DAGs.

Study shows one-dimensional location-scale-shape models are flat in Wasserstein geometry.

Researchers classify and decompose valuations on convex functions.

The intrinsic entropy model accurately estimates stock market volatility.

A new multi-objective RL framework improves intrinsic exploration performance.

This paper presents the Homeo-Heterostatic Value Gradients (HHVG) algorithm as a formal account on the constructive interplay between boredom and curiosity which gives rise to effective exploration and superior forward model learning. We envisaged actions as instrumental in agent's own epistemic disclosure. This motiva…

We introduce novel equations, in the spirit of rough path theory, that parametrize level sets of intrinsically regular maps on the Heisenberg group with values in $\mathbb{R}^2$. These equations can be seen as a sub-Riemannian counterpart to classical ODEs arising from the implicit function theorem. We show that they e…

This paper constructs a function on Gromov-Hausdorff limits of 2-surfaces with curvature constraints.

This paper introduces a new method to compare collections of distributions on manifolds and graphs.

The paper introduces novel Gaussian process models for vector-valued signals on manifolds.

We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measu…

Defines tensor eigenvalues and singular values without basis, simplifying analysis.

We define the notion of characteristic classes for supermanifolds endowed with a homological vector field $Q$. These take values in the cohomology of the Lie derivative operator $L_Q$ acting on arbitrary tensor fields. We formulate a classification theorem for intrinsic characteristic classes and give their explicit de…

In this paper we establish the basic tools to develop the "Calculus" associated with group-valued continuously Pansu differentiable mappings. We develop the technical machinery on which all of our results rely. In particular, the linearization of addends appearing in the Baker-Campbell-Hausdorff formula is one of the m…

Study on predicting sequences with Gaussian constraints, linking to intrinsic volumes and metric complexity.

The paper analyzes profitable bidding strategies for BESS in day-ahead and intraday markets.

We establish formulas that give the intrinsic volumes, or curvature measures, of sublevel sets of functions defined on Riemannian manifolds as integrals of functionals of the function and its derivatives. For instance, in the Euclidean case, if $f \in \mathcal{C}^3(\mathbb{R}^n, \mathbb{R})$ and 0 is a regular value of…

In [7] Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. In this paper, we extend the hyperboloidal method from Minkowski space to Lorentzian spacetimes. This approach is developed in [14] for proving, under the ma…

Introduces intrinsic Hopf-Lax semigroup linking to intrinsic slope.

The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise strategy. We show how the solution depends on different constraint types including carr…

In distributional reinforcement learning (RL), the estimated distribution of value function models both the parametric and intrinsic uncertainties. We propose a novel and efficient exploration method for deep RL that has two components. The first is a decaying schedule to suppress the intrinsic uncertainty. The second …

Three training regimes found for scale-invariant neural networks on the sphere.

We use splines and the Sasaki metric to analyze and compare manifold-valued trajectories.

New tensors capture intrinsic embedding data of conformal hypersurfaces.

Intrinsically motivated reinforcement learning aims to address the exploration challenge for sparse-reward tasks. However, the study of exploration methods in transition-dependent multi-agent settings is largely absent from the literature. We aim to take a step towards solving this problem. We present two exploration m…

Paper introduces CSIE for estimating stock market volatility.