arXiv research

Adversarial policies beat superhuman Go AI systems.

A new unbiased Hessian estimator for expectation-based objectives.

A geodesic orbit manifold (GO manifold) is a Riemannian manifold (M,g) with the property that any geodesic in M is an orbit of a one-parameter subgroup of a group G of isometries of (M,g). The metric g is then called a G-GO metric in M. For an arbitrary compact homogeneous manifold M=G/H, we simplify the general proble…

Paper examines Go AI robustness against adversarial attacks.

A grand challenge in reinforcement learning is intelligent exploration, especially when rewards are sparse or deceptive. Two Atari games serve as benchmarks for such hard-exploration domains: Montezuma's Revenge and Pitfall. On both games, current RL algorithms perform poorly, even those with intrinsic motivation, whic…

Optimizes identifying the best arm with fixed samples.

Within many machine learning algorithms, a fundamental problem concerns efficient calculation of an unbiased gradient wrt parameters $\gammav$ for expectation-based objectives $\Ebb_{q_{\gammav} (\yv)} [f(\yv)]$. Most existing methods either (i) suffer from high variance, seeking help from (often) complicated variance-…

New families of non-singular geodesic orbit nilmanifolds discovered.

GO-OED maximizes predictive information gain on nonlinear QoIs.

PolicySynth improves synthetic data alignment with real data for better campaign decisions.

A new method for experimental design focuses on predicting downstream quantities of interest.

GO-CBED optimizes experiments for specific causal queries, improving efficiency.

Consider two families of closed oriented curves in a d-manifold. At each point of intersecction of a curve of one family with a curve of the other family, form a new closed curve by going around the first curve and then going around the second. Typically, an i-dimensional family and a j-dimensional family will produce …

MuZero learns models to master complex games without domain knowledge.

By introducing several improvements to the AlphaZero process and architecture, we greatly accelerate self-play learning in Go, achieving a 50x reduction in computation over comparable methods. Like AlphaZero and replications such as ELF OpenGo and Leela Zero, our bot KataGo only learns from neural-net-guided Monte Carl…

We applied machine learning to predict whether a gene is involved in axon regeneration. We extracted 31 features from different databases and trained five machine learning models. Our optimal model, a Random Forest Classifier with 50 submodels, yielded a test score of 85.71%, which is 4.1% higher than the baseline scor…

Investigates optimal pension policies in PAYG systems with forward utility and ageing population.

Undirected graphical models encode in a graph $G$ the dependency structure of a random vector $Y$. In many applications, it is of interest to model $Y$ given another random vector $X$ as input. We refer to the problem of estimating the graph $G(x)$ of $Y$ conditioned on $X=x$ as ``graph-valued regression.'' In this pap…

Study of mean curvature flows on graphs in warped product manifolds, focusing on behavior at infinity.

Internal crossing of trades between multiple alpha streams results in portfolio turnover reduction. Turnover reduction can be modeled using the correlation structure of the alpha streams. As more and more alphas are added, generally turnover reduces. In this note we use a factor model approach to address the question o…

This research presents an analysis of the demographic risk related to future membership patterns in pension funds with restricted entrance, financed under a pay-as-you-go scheme. The paper, therefore, proposes a stochastic model for investigating the behaviour of the demographic variable "new entrants" and the influenc…

Study on curves around a Whitney umbrella focusing on geodesic and normal curvatures.

LDA-GO improves LDA for high-dimensional data via gradient optimization.

We first show that every quasisimple sporadic group possesses an unmixed strongly real Beauville structure aside from the Mathieu groups M11 and M23 (and possibly 2B and M). We go on to show that no almost simple sporadic group possesses a mixed Beauville structure. We then go on to use the exceptional nature of the al…

A homogeneous Riemannian space $(M= G/H,g)$ is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group $G$. We study the structure of compact GO-spaces and give some sufficient conditions for existence and non-existence of an invariant metric $g$ wit…

A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat co…

We study horospheres in hyperbolic 3-manifolds $M$ all whose ends are degenerate. Towards this, we study which almost minimizing geodesics in $M$ go through arbitrarily thin parts.

Recently Brendle-Huisken introduced a fully nonlinear flow $G$. Their aim was to extend the surgery algorithm of Huisken-Sinestrari, into the Riemannian setting. The aim of this paper is to go through the details on how to perform neck detection for a closed, embedded hypersurface $M_0$ in $\mathbb{R}^{n+1}$ undergoing…

Backdoor attacks on DRL-based traffic controllers cause stop-and-go waves or crashes.

We propose a novel method to forecast the future from the present using time-reversed data.

This note explains how to transform Heegaard diagrams into framed link diagrams.

The instability of historical risk factor correlations renders their use in estimating portfolio risk extremely questionable. In periods of market stress correlations of risk factors have a tendency to quickly go well beyond estimated values. For instance, in times of severe market stress, one would expect with certain…

Different models of capital exchange among economic agents have been proposed recently trying to explain the emergence of Pareto's wealth power law distribution. One important factor to be considered is the existence of risk aversion. In this paper we study a model where agents posses different levels of risk aversion,…

ReRe detects anomalies in real-time for time series data.

The study examines the long-term behavior of mean curvature flows in closed 3-manifolds.

In the present work we are going to give a formal exposition of the ribbon graphs topic based on notes of Labourie \cite{Lab}, since is difficult to find as such in the literature.

GOTabPFN improves tabular model performance with compact tokenization for HDLSS data.

In this short note, we show that the negative curvature is preserved in the deformation of hyperbolic warped product metrics under Ricci flow. It is also showed that the flow converges to a flat metric as time going to infinity.

Monte-Carlo Tree Search (MCTS) methods are drawing great interest after yielding breakthrough results in computer Go. This paper proposes a Bayesian approach to MCTS that is inspired by distributionfree approaches such as UCT [13], yet significantly differs in important respects. The Bayesian framework allows potential…

The AlphaGo, AlphaGo Zero, and AlphaZero series of algorithms are remarkable demonstrations of deep reinforcement learning's capabilities, achieving superhuman performance in the complex game of Go with progressively increasing autonomy. However, many obstacles remain in the understanding of and usability of these prom…

In this paper, we consider a CscK metric defined away from divisor and with metric upper bound and lower bound going to zero in certain rate. And we'll prove that this "nicely" behaved metric is a smooth CscK metric across the divisor.

In Finsler geometry, we use calculus to study the geometry of regular inner metric spaces. In this note I will briefly discuss various curvatures and their geometric meanings from the metric geometry point of view, without going into the forest of tensors.

It is known that every infinite index quasi-convex subgroup $H$ of a non-elementary hyperbolic group $G$ is a free factor in a larger quasi-convex subgroup of $G$. We give a probabilistic generalization of this result. That is, we show that when $R$ is a subgroup generated by independent random walks in $G$, then $\lan…

Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the option price function and three significant results are deduced. The first is the …

The financial market entropy is modeled using open quantum systems.

Growth rate of the world Growth Domestic Product (GDP) is analysed to determine possible pathways of the future economic growth. The analysis is based on using the latest data of the World Bank and it reveals that the growth rate between 1960 and 2014 was following a trajectory approaching asymptotically a constant val…

We study the explicit calculation of the set of superhedging portfolios of contingent claims in a discrete-time market model for d assets with proportional transaction costs. The set of superhedging portfolios can be obtained by a recursive construction involving set operations, going backward in the event tree. We ref…

This paper analyzes the direction of the causality between crude oil, gold and stock markets for the largest economy in the world with respect to such markets, the US. To do so, we apply non-linear Granger causality tests. We find a nonlinear causal relationship among the three markets considered, with the causality go…