arXiv research

WideBNet learns inverse scattering from wide-band data efficiently and stably.

We give an explicit handy (and cocycle-free) description of the groupoid of weak maps between two crossed-modules in terms of certain digrams of groups which we we call a {\em butterflies}. We define composition of butterflies and this way find a bicategory that is naturally biequivalent to the 2-category of pointed ho…

Sparse butterfly network replaces dense layers in neural networks, improving expressibility and performance.

Deep networks, especially convolutional neural networks (CNNs), have been successfully applied in various areas of machine learning as well as to challenging problems in other scientific and engineering fields. This paper introduces Butterfly-Net, a low-complexity CNN with structured and sparse cross-channel connection…

In unsupervised domain adaptation (UDA), classifiers for the target domain (TD) are trained with clean labeled data from the source domain (SD) and unlabeled data from TD. However, in the wild, it is difficult to acquire a large amount of perfectly clean labeled data in SD given limited budget. Hence, we consider a new…

ButterflyFlow uses butterfly matrices for efficient invertible layers in normalizing flows.

Characterizes no Butterfly arbitrage in SVI model parameters.

Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and inline with the conventional CNN. Moreover, a Fourier transform i…

We show how to integrate a weak morphism of Lie algebra crossed-modules to a weak morphism of Lie 2-groups. To do so we develop a theory of butterflies for 2-term L_infty algebras. In particular, we obtain a new description of the bicategory of 2-term L_infty algebras. We use butterflies to give a functorial constructi…

Study on 2-bridge knots, proving equivariant concordance order is infinite.

Unified 3D R-matrices from quantum cluster algebra.

Support Vector Regression (SVR) has achieved high performance on forecasting future behavior of random systems. However, the performance of SVR models highly depends upon the appropriate choice of SVR parameters. In this study, a novel BOA-SVR model based on Butterfly Optimization Algorithm (BOA) is presented. The perf…

In this paper we test for the sensitive dependence on initial conditions (the so called "butterfly effect") of energy futures time series (heating oil, natural gas), and thus the determinism of those series. This paper is distinguished from previous studies in the following points: first, we reread existent works in th…

The Runge-Kutta-Legendre scheme improves pricing American options and other derivatives.

We study surfaces of constant positive Gauss curvature in Euclidean 3-space via the harmonicity of the Gauss map. Using the loop group representation, we solve the regular and the singular geometric Cauchy problems for these surfaces, and use these solutions to compute several new examples. We give the criteria on the …

The study classifies points on ruled surfaces in 4-space based on geometric properties.

Characterizes smiles in delta satisfying specific conditions.

Paper studies singularities of timelike minimal surfaces in Minkowski 3-space.

Investment strategies derived from commodity futures curves exploit dynamics in price movements.

Unified market making controls risk, arbitrage, and volatility surfaces.

Traditional anatomical analyses captured only a fraction of real phenomic information. Here, we apply deep learning to quantify total phenotypic similarity across 2468 butterfly photographs, covering 38 subspecies from the polymorphic mimicry complex of $\textit{Heliconius erato}$ and $\textit{Heliconius melpomene}$. E…

We investigate singularities of all parallel surfaces to a given regular surface. In generic context, the types of singularities of parallel surfaces are cuspidal edge, swallowtail, cuspidal lips, cuspidal beaks, cuspidal butterfly and 3-dimensional $D_4^\pm$ singularities. We give criteria for these singularities type…

Graev's nerve implies invariant Einstein metrics on homogeneous spaces.

Study geometric singular solutions of generalized Monge-Ampère equations.

Many neural speech enhancement and source separation systems operate in the time-frequency domain. Such models often benefit from making their Short-Time Fourier Transform (STFT) front-ends trainable. In current literature, these are implemented as large Discrete Fourier Transform matrices; which are prohibitively inef…

We simplify SVI volatility smile constraints for three sub-SVIs without numerical methods.

We describe a robust calibration algorithm of a set of SSVI slices (i.e. a set of 3 SSVI parameters $θ, ρ, \varphi$ attached to each option maturity available on the market), which grants that these slices are free of Butterfly and Calendar-Spread arbitrage. Given such a set of consistent SSVI parameters, we show that …

Fast linear transforms are ubiquitous in machine learning, including the discrete Fourier transform, discrete cosine transform, and other structured transformations such as convolutions. All of these transforms can be represented by dense matrix-vector multiplication, yet each has a specialized and highly efficient (su…

There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strateg…

Proposes a method to construct risk-neutral marginals from arbitrage-free option prices.

We introduce the Schubert form a $3$-bridge link diagram, as a generalization of the Schubert normal form of a $3$-bridge link. It consists of a set of six positive integers, written as $\left( p/n,q/m,s/l\right)$, with some conditions and it is based on the concept of $3$-butterfly. Using the Schubert normal form of …

Model quantifies uncertainty's impact on European option prices.

This paper studies the valuation of European contingent claims with short selling bans under the equal risk pricing (ERP) framework proposed in Guo and Zhu (2017) where analytical pricing formulae were derived in the case of monotonic payoffs under risk-neutral measures. We establish a unified framework for this new pr…

New method reconstructs Black-Scholes option prices from current profiles.

This paper is devoted to the application of an $l_1$ -minimisation technique to construct an arbitrage-free call-option surface. We propose a nononparametric approach to obtaining model-free call option surfaces that are perfectly consistent with market quotes and free of static arbitrage. The approach is inspired from…

We proposed a new Portfolio Management method termed as Robust Log-Optimal Strategy (RLOS), which ameliorates the General Log-Optimal Strategy (GLOS) by approximating the traditional objective function with quadratic Taylor expansion. It avoids GLOS's complex CDF estimation process,hence resists the "Butterfly Effect" …

This paper proposes a new algorithm for controlling classification results by generating a small additive perturbation without changing the classifier network. Our work is inspired by existing works generating adversarial perturbation that worsens classification performance. In contrast to the existing methods, our wor…

For a smooth (locally trivial) principal bundle in Ehresmann's sense, the relation between the commuting vertical and horizontal actions of the structural Lie group and the structural Lie groupoid (isomorphisms between vertical fibers) is regarded as a special case of a symmetrical concept of conjugation between "princ…

Unified framework for inference in complex nonlinear processes.

ARBITER learns SPX-VIX term structures without arbitrage constraints.

The paper generalizes envelope constructions for chords in circles, revealing complex singularities.

LOFT separates subspace rotation and transformation for orthogonal fine-tuning.

Deep learning solves wave-based inverse problems, including super-resolution imaging.

Behavior cloning training instabilities amplified by SGD noise over long horizons.

Investigate the local geometry of smooth surfaces in 4-space via contact with 2-planes and apparent contours.

A hybrid Convolutional VAE predicts crypto volatility surfaces, outperforming single-symbol approaches.

Develops a deep multi-factor model for factor investing with clear financial insights.

Factor Engine simplifies financial factor computation and analysis in Python.