arXiv research

Entropy data replaces classical charts for smooth manifolds.

Characterizes pseudo-Anosov mapping classes using cluster algebra techniques.

New algorithms accelerate MAP inference in Markov fields with faster convergence.

A discrete diffusion model learns denoising, scoring, and bridging in different coordinates.

New sampling and identity-testing methods for mixtures of distributions that don't satisfy approximate tensorization of entropy.

The paper proves lower bounds for Gaussian-weighted curvature integrals of self-shrinkers.

Researchers calculate entropy of heat kernel on manifolds for very small times.

Paper optimizes approximating high-dimensional diffusions by independent coordinates.

Geometric study of thermodynamics using cotangent bundles.

New framework for multi-agent reinforcement learning improves coordination and efficiency.

CAVI converges for log-concave measures via optimal transport.

We introduce a new algorithm, called CDER, for supervised machine learning that merges the multi-scale geometric properties of Cover Trees with the information-theoretic properties of entropy. CDER applies to a training set of labeled pointclouds embedded in a common Euclidean space. If typical pointclouds correspondin…

AI learns to classify and represent univariate distributions in a 2D latent space.

Improved regret bounds for Thompson Sampling in combinatorial settings.

Modified Gibbs-Helmholtz equation geometric models for thermodynamics.

Collective behaviours taking place in financial markets reveal strongly correlated states especially during a crisis period. A natural hypothesis is that trend reversals are also driven by mutual influences between the different stock exchanges. Using a maximum entropy approach, we find coordinated behaviour during tre…

The aim of this short note is to produce new examples of geometrical flows associated to a given Riemannian flow $g(t)$. The considered flow in covariant symmetric $2$-tensor fields will be called Ricci-Yamabe map since it involves a scalar combination of Ricci tensor and scalar curvature of $g(t)$. Due to the signs of…

Develops variable-lag Granger causality and Transfer Entropy for time series analysis.

Study risk-sensitive market making with entropy regularization for better quote control.

Study predicts configurational energy of high entropy alloys using Bayesian methods.

We describe society as a nonequilibrium probabilistic system: N individuals occupy W resource states in it and produce entropy S over definite time periods. Resulting thermodynamics is however unusual because a second entropy, H, measures a typically social feature, inequality or diversity in the distribution of availa…

Generative networks are analyzed using spline operators to understand their properties and limitations.

Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex co…

We introduce a new algorithm for reinforcement learning called Maximum aposteriori Policy Optimisation (MPO) based on coordinate ascent on a relative entropy objective. We show that several existing methods can directly be related to our derivation. We develop two off-policy algorithms and demonstrate that they are com…

This paper proposes a new method for efficient data compression using Bayesian neural networks.

Using the work of Bonahon-Dreyer and Fock-Goncharov, one can construct a real-analytic parameterization for the PSL(n,R) Hitchin component of a surface S, that is explicitly analogous to the Fenchel-Nielsen coordinates on the Teichmuller space of S. Given a Hitchin representation, we give a lower bound on the "length" …

Investor flows in Korean equity market transmit shared information, not private signals.

Novel method uses information theory to measure causal influences during transient neural events.

Proposes an active RBI framework using Rényi information measures for more informed decision-making.

01 loss neural network improves adversarial robustness on CIFAR10.

New methods optimize sums of bivariate functions on finite domains.

A new method solves the projection robust Wasserstein distance problem efficiently.

Support vector machines (SVMs) naturally embody sparseness due to their use of hinge loss functions. However, SVMs can not directly estimate conditional class probabilities. In this paper we propose and study a family of coherence functions, which are convex and differentiable, as surrogates of the hinge function. The …

Stochastic gradient descent converges to universal limits in high dimensions.

This paper is a sequel of arxiv:1709.09045 and deals with privileged coordinates and nilpotent approximation of Carnot manifolds. By a Carnot manifold it is meant a manifold equipped with a filtration by subbundles of the tangent bundle which is compatible with the Lie bracket of vector fields. In this paper, we single…

Enhances RL by controlling policy stochasticity through trajectory entropy constraints.

Coordinate descent methods usually minimize a cost function by updating a random decision variable (corresponding to one coordinate) at a time. Ideally, we would update the decision variable that yields the largest decrease in the cost function. However, finding this coordinate would require checking all of them, which…

The paper calculates bounds for risk metrics and entropies under partial information constraints.

The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.

COIN++ compresses multiple data types efficiently.

Entropy measures geodesic flow complexity.

New findings on Kähler manifolds restrict orthogonal coordinates existence.

Defines Fenchel-Nielsen coordinates for SL(3,C) representations.

Entropy for uniform hypergraphs defined via tensor theory.

Submanifolds of coordinate finite-type were introduced in HV1. A submanifold of a Euclidean space is called a coordinate finite-type submanifold if its coordinate functions are eigenfunctions of Δ. In the present study we consider coordinate finite-type surfaces in E^4. We give necessary and sufficient conditions for g…

HCLM framework uses entropy regularization for open learning systems.

We consider complex Fenchel-Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra's plumbing construction and are related to earthquakes on Teichmueller space. They also allow us to interpolate between two coordinate systems on Teichmueller space, namely…

Dynnikov system maps Teichmüller space boundary, aiding pseudo-Anosov braid study.