arXiv research

Extended characterization of RAAGs with zero minimal volume entropy.

Minimal volume entropy vanishes for mapping tori over 3-manifolds.

Study shows rigidity for entropy minimizers in non-monotone cases.

Entropy-minimal measure calculated for a stochastic volatility model.

We compute the Minimal Entropy of every closed, orientable $3$-manifold, showing that its cube equals the sum of the cubes of the minimal entropies of each hyperbolic component arising from the $JSJ$ decomposition of each prime summand. As a consequence we show that the cube of the Minimal Entropy is additive with resp…

Constructs entropy-minimizing pseudo-Anosov diffeomorphisms on K3 surfaces.

The entropy of minimal surfaces is minimized in hyperbolic manifolds.

Study minimal surfaces in complex hyperbolic space, linking entropy and volume.

Minimal volume entropy vanishes or is positive under certain fiber growth conditions.

We show vanishing results about the infimum of the topological entropy of the geodesic flow of homogeneous smooth four manifolds. We prove that any closed oriented geometric four manifold has zero minimal entropy if and only if it has zero simplicial volume. We also show that if a four manifold M admits a geometric dec…

The study examines conditions for minimal volume entropy of simplicial complexes.

Study minimal volume entropy for free-by-cyclic groups and 2D right-angled Artin groups.

Entropy minimization has been widely used in unsupervised domain adaptation (UDA). However, existing works reveal that entropy minimization only may result into collapsed trivial solutions. In this paper, we propose to avoid trivial solutions by further introducing diversity maximization. In order to achieve the possib…

We consider the minimal entropy problem, namely the question of whether there exists a smooth metric of minimal entropy, for certain classes of 3-manifolds. Among other resulsts, we show that if M is a closed, orientable, geometrizable 3-manifold with zero simplicial volume, then the minimal entropy can be solved for M…

The paper studies minimal surface entropy on hyperbolic 3-manifolds and compares it to the hyperbolic case.

We prove minimal entropy rigidity for complete, finite volume manifolds locally isometric to a product of rank one symmetric spaces of dimension at least 3: the locally symmetric metric uniquely minimizes (normalized) entropy among all Riemannian metrics. The corresponding theorem is true for maps into these spaces as …

We establish isosystolic inequalities for a class of manifolds which includes the aspherical manifolds. In particular, we relate the systolic volume of aspherical manifolds first to their minimal entropy, then to the algebraic entropy of their fundamental groups.

We show that the minimal volume entropy of closed manifolds remains unaffected when nonessential manifolds are added in a connected sum. We combine this result with the stable cohomotopy invariant of Bauer-Furuta in order to present an infinite family of four-manifolds with the following properties: 1) They have positi…

Entropy asymmetry affects regularization in ERM, leading to biased solutions.

The study proves compactness and existence of entropy minimizers for self-shrinking surfaces.

We introduce on any smooth oriented minimal surface in Euclidean $3$-space a meromorphic quadratic differential, $P$, which we call the entropy differential. This differential arises naturally in a number of different contexts. Of particular interest is the realization of its real part as a conservation law for a natur…

Let (M,g) be a compact Riemannian manifold of hyperbolic type, i.e M is a manifold admitting another metric of strictly negative curvature. In this paper we study the geodesic flow restricted to the set of geodesics which are minimal on the universal covering. In particular for surfaces we show that the topological ent…

New regularization method reduces support of empirical risk minimization solutions.

The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.

The Cayley hyperbolic space minimizes volume entropy among finite-volume metrics.

Low-entropy surfaces can be flowed into spheres and cylinders.

Cross-entropy loss linked to metric learning, outperforming complex pairwise losses.

We prove that, among metrics on a compact quotient of $\left(\mathbb{H}^2\right)^n$ (product of hyperbolic planes) of prescribed total volume, the product of hyperbolic metrics has minimal volume entropy.

COME replaces entropy minimization to prevent model collapse.

Tent adapts models during testing by minimizing entropy of predictions.

Study simplicial volume for fixed fundamental groups, finding gaps.

Study finds optimal martingale coupling between two distributions with minimal entropy.

Quantum machine learning uses quantum cross entropy to minimize loss, but measurement loss affects this process.

Minimal surfaces and average area ratio found to be maximized by hyperbolic metrics.

Let (T^2, g) be a two-dimensional Riemannian torus. In this paper we prove that the topological entropy of the geodesic flow restricted to the set of initial conditions of minimal geodesics vanishes, independent of the choice of the Riemannian metric.

As we have proved in [L], the geodesic flows associated with the flat metrics on T^2 minimize the polynomial entropy. In this paper, we show that, among the geodesic flows that are Bott integrable and dynamically coherent, the geodesic flows associated to flat metrics are local strict minima for the polynomial entropy.…

We show that if a closed manifold M admits an F-structure (possibly of rank 0) then its minimal entropy vanishes. In particular, this is the case if M admits a non-trivial circle action. As a corollary we obtain that the simplicial volume of a colsed manifold admitting an F-structure is zero. We also show that if M adm…

In this paper, we propose a general framework to learn a robust large-margin binary classifier when corrupt measurements, called anomalies, caused by sensor failure might be present in the training set. The goal is to minimize the generalization error of the classifier on non-corrupted measurements while controlling th…

AdaDEM decouples EM into two parts to improve class overlap and uncertainty.

We determine the minimal entropy martingale measure for a general class of stochastic volatility models where both price process and volatility process contain jump terms which are correlated. This generalizes previous studies which have treated either the geometric Lévy case or continuous price processes with an ortho…

In this short note, we analyze geometric properties of orbit spaces of certain involutions in dimensions four, five, and six. We consider constructions of $\mathcal{F}$-structures on manifolds of dimension at least four that allows us to study minimal entropy, minimal volume, collapse with bounded curvature, and sign o…

PAC-Bayesian bounds for MLPs with cross entropy loss validated.

Study of focal-entropy for class-imbalanced classification.

Paper proves Jeffrey's update rule minimizes relative entropy.

New method detects changes by maximizing cross-entropy, outperforming existing techniques.

Study on entropy stability in product spaces of negatively curved symmetric spaces.

We study the problem of existence of F-structures on compact complex surfaces, giving a complete classification modulo the gap in the classification of surfaces of class VII. We then use these results to study the minimal entropy problem for compact complex surfaces. For instance we prove that compact Kahler surfaces o…

In [5], Colding-Ilmanen-Minicozzi-White showed that within the class of closed smooth self-shrinkers in $\mathbb{R}^{n+1}$, the entropy is uniquely minimized at the round sphere. They conjectured that, for $2\leq n\leq 6$, the round sphere minimizes the entropy among all closed smooth hypersurfaces. Using an appropriat…