arXiv research

New algorithm proves most inflexible manifolds are not strongly inflexible.

We prove hyperbolic 3-manifolds are geometrically inflexible: a unit quasiconformal deformation of a Kleinian group extends to an equivariant bi-Lipschitz diffeomorphism between quotients whose pointwise bi-Lipschitz constant decays exponentially in the distance form the boundary of the convex core for points in the th…

We prove 3-dimensional hyperbolic cone-manifolds are geometrically inflexible: a cone-deformation of a hyperbolic cone-manifold determines a bi-Lipschitz diffeomorphism between initial and terminal manifolds in the deformation in the complement of a standard tubular neighborhood of the cone-locus whose pointwise bi-Lip…

In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also exploited to provide highly connected inflexible and strongly chiral manifolds.

A recent preprint of S. Kojima and G. McShane [KM] observes a beautiful explicit connection between Teichmüller translation distance and hyperbolic volume. It relies on a key estimate which we supply here: using geometric inflexibility of hyperbolic 3-manifolds, we show that for $S$ a closed surface, and $ψ\in \text{Mo…

In this paper we prove new embedding results for compactly supported deformations of $CR$ submanifolds of $\mathbb{C}^{n+d}$: We show that if $M$ is a $2$-pseudoconcave $CR$ submanifold of type $(n,d)$ in $\mathbb{C}^{n+d}$, then any compactly supported $CR$ deformation stays in the space of globally $CR$ embeddable in…

The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models th…

Learning algorithms need bias to generalize and perform better than random guessing. We examine the flexibility (expressivity) of biased algorithms. An expressive algorithm can adapt to changing training data, altering its outcome based on changes in its input. We measure expressivity by using an information-theoretic …

In this paper we propose a class of prior distributions on decomposable graphs, allowing for improved modeling flexibility. While existing methods solely penalize the number of edges, the proposed work empowers practitioners to control clustering, level of separation, and other features of the graph. Emphasis is placed…

This paper solves hedging in incomplete markets using neural networks.

Most neural network designs for FPGAs are inflexible. In this paper, we propose a flexible VHDL structure that would allow any neural network to be implemented on multiple FPGAs. Moreover, the VHDL structure allows for testing as well as training multiple neural networks. The VHDL design consists of multiple processor …

This paper develops, in a Brownian information setting, an approach for analyzing the preference for information, a question that motivates the stochastic differential utility (SDU) due to Duffie and Epstein [Econometrica 60 (1992) 353-394]. For a class of backward stochastic differential equations (BSDEs) including th…

The paper studies circle packings using renormalization and subdivision rules.

Semi-supervised learning (SSL) provides a powerful framework for leveraging unlabeled data when labels are limited or expensive to obtain. SSL algorithms based on deep neural networks have recently proven successful on standard benchmark tasks. However, many of them have thus far been either inflexible, inefficient or …

Every closed oriented manifold $M$ is associated with a set of integers $D(M)$, the set of self-mapping degrees of $M$. In this paper we investigate whether a product $M\times N$ admits a self-map of degree $d$, when neither $D(M)$ nor $D(N)$ contains $d$. We find sufficient conditions so that $D(M\times N)$ contains e…

A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing maps in homology. Functorial semi-norms can be used to give constraints on the possible mapping degrees of maps between oriented manifolds. …

Learn to automatically plug domain-specific modules into a common network.

Recent work has shown that Field-Programmable Gate Arrays (FPGAs) play an important role in the acceleration of Machine Learning applications. Initial specification of machine learning applications are often done using a high-level Python-oriented framework such as Tensorflow, followed by a manual translation to either…

A new method for learning gradient flows from population dynamics.

Gaussian processes are the leading class of distributions on random functions, but they suffer from well known issues including difficulty scaling and inflexibility with respect to certain shape constraints (such as nonnegativity). Here we propose Deep Random Splines, a flexible class of random functions obtained by tr…

A new method for efficient BNC parameter estimation outperforms HDP smoothing.

LI-ITR combines flexible ML with interpretable approximations for personalized treatment rules.

Improves Bayesian neural networks inference efficiency and accuracy.

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent trajectories. However, simple state transition structures, linear embedding assumpti…

Frugal Flows learn complex data and infer marginal causal effects.

Simformer uses transformer models to perform flexible Bayesian inference.

gKRLS accelerates KRLS estimation for complex models.

Artifical Neural Networks are a particular class of learning systems modeled after biological neural functions with an interesting penchant for Hebbian learning, that is "neurons that wire together, fire together". However, unlike their natural counterparts, artificial neural networks have a close and stringent couplin…

The NNGP kernel's predictions closely match those of the Matern kernel under certain conditions.

New method robustly discovers causal relationships from imperfect data.

A new method learns DAG structures from data without false edges.

Study uses reinforcement learning to optimize metachronal paddling at low Reynolds number.

A new ML framework for RF fingerprinting across various applications.

AlphaForge mines and dynamically combines alpha factors for better investment performance.

Proposes a new method to optimize graph neural network architectures on heterogeneous information networks.

Modeling European spot power markets with game theory for Nash equilibria.

It was not until the beginning of the 1990s that the effects of information and communication technology on economic growth as well as on the profitability of enterprises raised the interest of researchers. After giving a general description on the relationship between a more intense use of ICT devices and dynamic econ…

PRESTO improves rare event prediction by shrinking towards proportional odds model.

New method for interpreting non-linear models using forward marginal effects.

Study compares two market clearing methods for European power markets.

It is well established that humans decision making and instrumental control uses multiple systems, some which use habitual action selection and some which require deliberate planning. Deliberate planning systems use predictions of action-outcomes using an internal model of the agent's environment, while habitual action…

This work explores Target Networks and Functional Regularization in deep Reinforcement Learning.

PushNet efficiently and adaptively pushes messages in neural networks, improving performance.

Reducing user attrition, i.e. churn, is a broad challenge faced by several industries. In mobile social games, decreasing churn is decisive to increase player retention and rise revenues. Churn prediction models allow to understand player loyalty and to anticipate when they will stop playing a game. Thanks to these pre…

Lock-in, the escalating commitment of decision-makers to an ineffective course of action, has the potential to explain the large cost overruns in large scale transportation infrastructure projects. Lock-in can occur both at the decision-making level (before the decision to build) and at the project level (after the dec…

Nonnegative Matrix Factorization (NMF) aims to factorize a matrix into two optimized nonnegative matrices appropriate for the intended applications. The method has been widely used for unsupervised learning tasks, including recommender systems (rating matrix of users by items) and document clustering (weighting matrix …

PSEUDo learns patterns in multivariate time series with locality-sensitive hashing and relevance feedback.