arXiv research

This work shows MLPs can approximate monotonic functions without bounded activations.

The paper is motivated by a problem concerning the monotonicity of insurance premiums with respect to their loading parameter: the larger the parameter, the larger the insurance premium is expected to be. This property, usually called loading monotonicity, is satisfied by premiums that appear in the literature. The inc…

The paper proves weighted monotonicity theorems in various spaces and applies them to minimal surfaces.

New formulas derived for scalar curvature in generalized Ricci flow.

Study finds formulas for minimal submanifolds using Möbius transformations.

Paper characterizes monotonic mean-deviation risk measures.

The paper examines the unexpected losses and risk ratios for co-monotonic alternatives in large portfolios.

Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.

Let $M$ be an $n$-dimensional closed Riemannian manifold with metric $g$, $dμ=e^{-φ(x)}dν$ be the weighted measure and $Δ_{p,φ}$ be the weighted $p$-Laplacian. In this article we will investigate monotonicity for the first eigenvalue problem of the weighted $p$-Laplace operator acting on the space of functions along th…

We give a family of monotone quantities along smooth solutions to the inverse curvature flows in Euclidean spaces. We also derive a related geometric inequality for closed hypersurfaces with positive k-th mean curvature.

Study online monotone density estimation with expert aggregation and log-optimal calibration.

The paper addresses estimating long-term treatment effects with monotone missing data.

Monotone neural networks can approximate and interpolate functions efficiently.

Paper tackles ranking items with a semi-random comparison graph and a monotone adversary.

Proves volume comparison and monotonicity for Bakry-Émery Ricci curvature.

Develops tropical geometry for weighted Hurwitz numbers, generalizing previous results.

We find a new monotone increasing quantity along smooth solutions to the inverse mean curvature flow in $\mathbb R^n$. As an application, we derive a sharp geometric inequality for mean convex, star-shaped hypersurfaces which relates the volume enclosed by a hypersurface to a weighted total mean curvature of the hypers…

By means of a space-time Wasserstein control, we show the monotonicity of the W-entropy functional in time along heat flows on possibly singular metric measure spaces with non-negative Ricci curvature and a finite upper bound of dimension in an appropriate sense. The associated rigidity result on the rate of dissipatio…

In the article, we generalize some recent results of Colding and Minicozzi on generic singularities of mean curvature flow to curved ambient spaces. To do so, we make use of a weighted monotonicity formula to derive an "almost monotonicity" for the entropy upon embedding into $\R^\ell$. We are also lead to study the co…

Monotonic neural networks have recently been proposed as a way to define invertible transformations. These transformations can be combined into powerful autoregressive flows that have been shown to be universal approximators of continuous probability distributions. Architectures that ensure monotonicity typically enfor…

Study on manifolds with density using modified Hessians for curvature comparison.

In this paper, we first introduce the weighted forward reduced volume of Ricci flow. The weighted forward reduced volume, which related to expanders of Ricci flow, is well-defined on noncompact manifolds and monotone non-increasing under Ricci flow. Moreover, we show that, just the same as the Perelman's reduced volume…

Diffusion models optimize objectives similar to ELBO with Gaussian noise augmentation.

Monotonic Linear Interpolation property in neural networks persists despite non-convexity.

New insights into variational inference using Monte Carlo estimates.

New, shorter proofs for varifolds and flows with improved decay of flatness.

Introduces nondecreasing rank for matrices and tensors, developing methods and applications.

Study non-monotonic loss functions in CRC, achieving valid risk control with large calibration samples.

The paper extends spin geometry to weighted manifolds and defines a new mass for Ricci flow.

Efficient algorithms find optimal monotone transforms for calibration under strictly convex losses.

New rigidity results for scalar curvature with stabilized conditions.

In the multiple linear regression setting, we propose a general framework, termed weighted orthogonal components regression (WOCR), which encompasses many known methods as special cases, including ridge regression and principal components regression. WOCR makes use of the monotonicity inherent in orthogonal components …

Monotonicity of normalized implied-volatility coordinates under no-arbitrage

Improved Q-learning for multi-agent reinforcement learning by weighting joint action values.

The monotonic linear interpolation in deep networks often leads to plateaus, revealing biases in optimization.

Using the monotonicity formulas of Colding and Minicozzi, we prove that on any complete, non-parabolic Riemannian manifold $(M^3, g)$ with non-negative Ricci curvature, the asymptotic weighted scaling invariant integral of scalar curvature has an explicit bound in form of asymptotic volume ratio.

New method makes CP intervals locally adaptive using trainable transformations.

We study deep neural networks with polynomial activations, particularly their expressive power. For a fixed architecture and activation degree, a polynomial neural network defines an algebraic map from weights to polynomials. The image of this map is the functional space associated to the network, and it is an irreduci…

New method for optimizing risk in financial models using Fourier transforms.

We consider two natural Lagrangian intersection problems in the context of symplectic toric manifolds: displaceability of torus orbits and of a torus orbit with the real part of the toric manifold. Our remarks address the fact that one can use simple cartesian product and symplectic reduction considerations to go from …

New lower bounds for combinatorial multi-armed bandits for general reward functions.

A mathematical analysis of the distribution of voting power in the Council of the European Union operating according to the Treaty of Lisbon is presented. We study the effects of Brexit on the voting power of the remaining members, measured by the Penrose--Banzhaf Index. We note that the effects in question are non-mon…

Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete bipartite graph where each vertex corresponds to a word in the two input senten…

We present a fast and scalable algorithm to induce non-monotonic logic programs from statistical learning models. We reduce the problem of search for best clauses to instances of the High-Utility Itemset Mining (HUIM) problem. In the HUIM problem, feature values and their importance are treated as transactions and util…

As surrogate functions of $L_0$-norm, many nonconvex penalty functions have been proposed to enhance the sparse vector recovery. It is easy to extend these nonconvex penalty functions on singular values of a matrix to enhance low-rank matrix recovery. However, different from convex optimization, solving the nonconvex l…

There is a growing body of literature showing that deep neural networks are vulnerable to adversarial input modification. Recently this work has been extended from image classification to malware classification over boolean features. In this paper we present several new methods for training restricted networks in this …

QMIX combines per-agent values to create decentralised policies.

Graphons connect graph structures to manifold properties.