This paper tests for chaos in energy futures markets using the butterfly effect.
problem Determining chaos in energy futures time series.
method Reread existing literature on energy markets, introduced a coefficient to measure determinism and reliability.
result Maximum reliability level was approximately 56%, not strong evidence of chaos.
Butterfly-Net improves CNN performance with structured connections and initialization.
problem Improving the performance of convolutional neural networks (CNNs).
method Butterfly-Net introduces structured and sparse cross-channel connections, and Butterfly initialization strategy.
result Butterfly-Net approximates Fourier representations with exponentially decaying error as depth increases.
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.
problem Improving expressibility and performance of neural networks with dense layers.
method Replacing dense layers with a butterfly network architecture.
result The proposed architecture significantly reduces the number of weights from quadratic to nearly linear, with comparable or better performance.
Butterfly tackles wild unsupervised domain adaptation with noisy labeled data.
problem Training classifiers with noisy labeled data from source domain and unlabeled data from target domain.
method Butterfly framework, maintaining four deep networks for simultaneous adaptations.
result Butterfly significantly outperforms existing methods in wild unsupervised domain adaptation.
Efficient trainable front-end for neural speech enhancement.
problem Inefficient STFT front-ends in neural speech enhancement models.
method Butterfly mechanism for Fast Fourier Transform, trainable STFT window.
result Accuracy and efficiency improvements for low-compute systems.
ButterflyFlow uses butterfly matrices for efficient invertible layers in normalizing flows.
problem Building efficient invertible layers for complex probability distributions.
method Proposes butterfly layers for invertible linear layers, leveraging their ability to capture complex structures.
result ButterflyFlow achieves strong density estimation and significantly better log-likelihoods on various datasets.
Characterizes no Butterfly arbitrage in SVI model parameters.
problem No Butterfly arbitrage in SVI implied total variance formula.
method Characterization using intermediary condition from Fukasawa (2012) and rescaling of SVI parameters.
result Simple range conditions on SVI parameters ensure no Butterfly arbitrage.
Simplified Butterfly-Net2 improves CNN efficiency in solving PDEs and signal processing tasks.
problem Improving CNN efficiency in solving PDEs and signal processing tasks.
method Introducing BNet2, a simplified Butterfly-Net, and Fourier transform initialization.
result BNet2 achieves similar accuracy as CNN but with fewer parameters and improves accuracy over randomly initialized CNN.
Deep learning quantifies butterfly phenotypes, validating evolutionary theory.
problem Capturing comprehensive phenotypic information of butterflies.
method Deep convolutional triplet network for phenotypic distance calculation.
result Euclidean phenotypic distances support classical mimicry theory.
WideBNet learns inverse scattering from wide-band data efficiently and stably.
problem Learning the inverse scattering map from wide-band scattering data.
method Combines butterfly factorization, FFT, and deep learning.
result WideBNet requires fewer training points and has stable training dynamics.
BOA-SVR model improves SVR performance in stock market forecasting.
problem Optimizing SVR parameters for better stock market forecasting accuracy.
method A novel BOA-SVR model using Butterfly Optimization Algorithm.
result The BOA-SVR model outperforms other meta-heuristic algorithms in stock market forecasting.
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.
problem Equivariant concordance of 2-bridge knots.
method Formula for butterfly polynomial, two proofs of non-equivariant sliceness, new invariant for strongly invertible knots.
result Equivariant concordance order of 2-bridge knots is infinite.
Unified 3D R-matrices from quantum cluster algebra.
problem Constructing new solutions to the tetrahedron equation.
method Symmetric butterfly quiver, quantum cluster algebra, quantum dilogarithms, q-Weyl algebra.
result Unified 3D R-matrices from various sources.
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.
problem Characterizing points on smooth ruled surfaces in 4-space.
method Contact with transverse planes, binary differential equations, and projective transformations.
result Parabolic points on ruled surfaces in 4-space can be classified as butterfly hyperbolic, parabolic, or elliptic based on the discriminant of a binary differential equation.
Characterizes smiles in delta satisfying specific conditions.
problem Characterizing no butterfly arbitrage smiles in delta.
method Using parametrization of the smile in delta, we characterize the set of smiles.
result Obtained a parametrization of the set via one real number and three positive functions.
Paper studies singularities of timelike minimal surfaces in Minkowski 3-space.
problem Exploring singularities of timelike minimal surfaces in Minkowski 3-space.
method Existence and non-existence theorems, criteria for specific singularities.
result Various singularities unique to timelike minimal surfaces, including cuspidal butterfly and (2,5)-cuspidal edge. Unified market making controls risk, arbitrage, and volatility surfaces.
problem Market making risk, arbitrage, and volatility surface consistency.
method Constrained RL and stochastic control for risk-sensitive execution and hedging.
result Agent achieves positive P&L with zero calendar and butterfly violations.
Introduces Schubert normal form for 3-bridge links and presents their groups.
problem Representing and understanding 3-bridge link groups.
method Develops Schubert normal form and uses it to present 3-bridge link groups.
result Two presentations of 3-bridge link groups based on Schubert normal form.
Algorithm calibrates SSVI slices to prevent arbitrage and interpolate volatility surfaces.
problem Preventing arbitrage in SSVI slices for volatility surface interpolation.
method Robust calibration algorithm for SSVI slices, ensuring no Butterfly or Calendar-Spread arbitrage.
result Interpolated SSVI parameters create an arbitrage-free volatility surface.
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 D4± singularities. We give criteria for these singularities type…
Model quantifies uncertainty's impact on European option prices.
problem Uncertainty in market volatility risk affects option pricing.
method Hamilton-Jacobi-Bellman framework and finite element method.
result Dependence of Delta on uncertainty is nonlinear and varied.
Graev's nerve implies invariant Einstein metrics on homogeneous spaces.
problem Existence of invariant Einstein metrics on homogeneous spaces.
method Lie-theoretic definition of Graev's nerve and curvature estimates.
result Detailed description of Graev's work and curvature estimates.
Behavior cloning training instabilities amplified by SGD noise over long horizons.
problem Training instabilities in behavior cloning with deep neural networks.
method Empirical dissection of minibatch SGD updates and their effects on long-horizon rewards.
result Exponential moving average (EMA) of iterates effectively mitigates gradient variance amplification (GVA).
Study geometric singular solutions of generalized Monge-Ampère equations.
problem Solving generalized Monge-Ampère equations on a plane.
method Using exterior differential systems and Cauchy characteristics.
result Criteria for geometric singular solutions to be equivalent to specific types.
Enhances classification performance with small, additive perturbations.
problem Improving classification performance using small, additive perturbations.
method Proposes a perturbation generation network (PGN) based on adversarial learning to enhance classifier performance.
result Demonstrates that PGN can enhance overall classification performance without altering the target classifier network.
RLOSRL improves portfolio management by combining RL with a robust strategy.
problem Portfolio optimization and resilience to estimation errors.
method Combining RL with RLOS, approximating objective function with Taylor expansion.
result RLOSRL outperforms traditional strategies in back tests.
We simplify SVI volatility smile constraints for three sub-SVIs without numerical methods.
problem No arbitrage constraints for SVI volatility smiles.
method Explicit domain derivation for sub-SVIs without numerical procedures.
result Explicit no arbitrage domains for Symmetric SVI, Vanishing Upward/Downward SVI, and SSVI.
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.
problem Lack of risk-neutral marginals that are free of arbitrage and easy to use.
method Explicit construction of risk-neutral marginals from discrete arbitrage-free option prices.
result Explicit construction guarantees risk-neutral marginals free of butterfly and calendar arbitrage.
Unified theory of volatility surfaces developed in this paper.
problem Developing a comprehensive mathematical theory for volatility surfaces.
method Unified mathematical theory, topology, tangent geometry, and topology of arbitrage set.
result Exact modal reduction and closed-form truncation error for dynamics.
Investment strategies derived from commodity futures curves exploit dynamics in price movements.
problem Modeling and predicting the term structure of commodity futures prices.
method Employed the Nelson-Siegel framework to model term structure, and developed investment strategies based on changes in slope and curvature parameters.
result Significant profits generated from systematic strategies based on the change in slope, unrelated to risk factors and robust to transaction costs.
This paper is devoted to the application of an l1 -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…
The Runge-Kutta-Legendre scheme improves pricing American options and other derivatives.
problem Pricing American options and other derivatives with improved accuracy and stability.
method Runge-Kutta-Legendre finite difference scheme applied to Black-Scholes and Heston models.
result Improved convergence and stability compared to existing schemes.
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…
The paper extends ERP framework to non-monotonic payoffs and short selling bans.
problem Valuation of contingent claims with short selling bans under ERP framework.
method Unified framework for ERP pricing, extending to non-monotonic payoffs, and comparing with Black-Scholes.
result Equal-risk prices differ from Black-Scholes prices under short selling bans.
Unified framework for inference in complex nonlinear processes.
problem Challenges in inferring nonlinear continuous stochastic processes with sparse observations and complex topologies.
method Neural Backward Filtering Forward Guiding (NBFFG) framework that constructs a variational posterior using a proxy linear-Gaussian process.
result Empirical results show NBFFG outperforms baselines on synthetic benchmarks and high-dimensional phylogenetic analysis tasks.
ARBITER learns SPX-VIX term structures without arbitrage constraints.
problem Arbitrage-free modeling of SPX-VIX term structures.
method Risk-neutral neural operator mapping market states to operator outputs enforcing static arbitrage constraints.
result ARBITER outperforms other models in derivatives term structure evaluation metrics.
The paper generalizes envelope constructions for chords in circles, revealing complex singularities.
problem Understanding envelopes of chords in circles with varying parameters and configurations.
method Generalizing the embroidery method to rational and concentric circles, breaking symmetry to reveal higher singularities.
result Higher singularities like swallowtails and butterflies can be unfolded, revealing their structure.
New method reconstructs Black-Scholes option prices from current profiles.
problem Reconstructing Black-Scholes prices from current profiles, dealing with ill-posedness.
method Price-dimensional reduction using Legendre polynomials, Tikhonov regularization.
result Reconstructs Black-Scholes prices from noisy initial data, stabilizing the solution.
A new method generates implied volatility surfaces without arbitrage issues.
problem Generating volatility surfaces without financial arbitrage constraints.
method Variational autoencoder with flow-matching for latent space learning.
result Model closely reproduces empirical distribution and satisfies no-arbitrage conditions.
LOFT separates subspace rotation and transformation for orthogonal fine-tuning.
problem Conflating subspace rotation and transformation in orthogonal fine-tuning.
method LOFT explicitly separates subspace rotation and transformation, using task-aware support selection.
result LOFT recovers principal-subspace orthogonal adaptation and improves efficiency-performance trade-off.
Deep learning solves wave-based inverse problems, including super-resolution imaging.
problem Solving inverse wave scattering problems across all length scales.
method Wide-band butterfly network coupled with dynamic noise injection.
result Framework successfully solves super-resolution imaging problems.
Automatically learns efficient algorithms for structured transforms like FFT.
problem Efficient algorithms for structured linear transforms.
method Generic parameterization of divide-and-conquer methods.
result Reproduces Cooley-Tukey FFT algorithm to machine precision.
Investigate the local geometry of smooth surfaces in 4-space via contact with 2-planes and apparent contours.
problem Local geometry of smooth surfaces in 4-space
method Contact with 2-planes and apparent contour
result Prove connections between singularities of parallel projections, orthogonal projections, and height functions.
A hybrid Convolutional VAE predicts crypto volatility surfaces, outperforming single-symbol approaches.
problem Predicting crypto volatility surfaces
method Convolutional VAE with hybrid predictor
result Model achieves 0.94-1.56 vol-point RMSE across BTC and ETH markets