Paper extends known α-minimizing hypercones using polynomial analysis.
problem Limitations in the class of known α-minimizing hypercones. method Sub-calibration methods and analysis of cubic and quartic polynomials.
result Significantly extended class of α-minimizing hypercones. Characterizes harmonic morphisms preserving minimal submanifolds and finds novel area-minimising hypercones.
problem Understanding harmonic morphisms and their relationship to minimal submanifolds.
method Characterization of harmonic morphisms as weakly horizontally conformal maps preserving minimal submanifold equations, derivation of reduction properties for other co-dimensions, application to find novel area-minimising hypercones.
result Novel family of degree 4 area-minimising hypercones in R^m, m≥32.
We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces (classified by Lawlor) following Lawson's original idea in his 72' Trans. A.M.S. paper "The equivariant Plateau problem and interior regularity". Moreover, each of them enjoys (coflat) calibrations singular only at th…
The study proves that certain stable minimal hypersurfaces must be cylindrical.
problem Characterizing stable minimal hypersurfaces in Euclidean space.
method Analyzing the density at infinity and using stable area minimizing hypercone properties.
result Stable minimal hypersurfaces with specific conditions are cylindrical.
Extends isoparametric foliations and area-minimizing cones in product manifolds.
problem Generalizing isoparametric foliations and area-minimizing cones in SnimesSn. method Analyzes isoparametric foliations and area-minimizing cones, extending known results.
result Extends known area-minimizing cones to codimension-two cases, yielding infinitely many families of area-minimizing subcones.
Study compares nodal sets of solutions to the Allen-Cahn equation.
problem Comparing nodal sets of solutions to the Allen-Cahn equation with conical asymptotics.
method Maximum principle for linearized operator on unbounded domains.
result Positive phase uniquely determines the solution and enforces global ordering.
We show that every area-minimizing hypercone and every oriented Lawlor cone in [Law91] can be realized as a tangent cone at a point of some homologically area-minimizing singular compact submanifold. In particular this generalizes the result of N. Smale [Sma99].
Rectifying curves on hypercones are geodesics, characterized in higher dimensions.
problem Characterizing rectifying curves in higher-dimensional spaces.
method Extending results from Chen (2017) to higher dimensions, using hypercones and hyperplanes.
result Rectifying curves on hypercones are geodesics, and these curves can be mapped to spherical curves in higher dimensions.
Smooths out complex shapes into simpler forms.
problem Transforming complex shapes into simpler, smooth forms.
method Perturbing minimizing hypercones and viscosity mean convex cones into smooth, properly embedded hypersurfaces.
result Properly embedded smooth minimizing hypersurfaces and self-expanders are achieved.
The paper evaluates biased methods for alpha-divergence minimization.
problem The impact of bias on solutions found for alpha-divergence minimization.
method Empirical evaluation of biased methods for alpha-divergence minimization, focusing on bias effects and dimensionality.
result Solutions are biased towards KL-divergence minimizers and require impractical computation in high dimensions to minimize alpha-divergence.
We prove that the density of a topologically nontrivial, area-minimizing hypercone with an isolated singularity must be greater than the square root of 2. The Simons' cones show that this is the best possible constant. If one of the components of the complement of the cone has nontrivial kth homotopy group, we prove a …
Paper constructs flows converging to cones and foliations.
problem Understanding mean curvature flow convergence to cones and foliations.
method Constructs a family of mean curvature flows converging to cones and foliations under specific conditions.
result Flow converges to area minimizing, strictly stable hypercone and Hardt-Simon foliation of the cone.
Unbiased methods for alpha-divergence minimization struggle in high dimensions.
problem The difficulty of unbiased alpha-divergence minimization in high dimensions.
method Signal-to-Noise Ratio (SNR) analysis of gradient estimators.
result The SNR of the gradient estimator worsens exponentially with dimensionality.
Construct locally minimizing (1,2)-clusters with prescribed asymptotic geometry.
problem Minimizing clusters with prescribed asymptotic geometry.
method Develop a refined construction using the Hardt-Simon foliation.
result Produce a countably infinite family of distinct locally minimizing clusters asymptotic to a singular area-minimizing hypercone.
This paper explores portfolio management strategies to maximize alpha and minimize beta.
problem Maximizing returns while minimizing risk in investment portfolios.
method Examines asset allocation, diversification, active management, and risk management strategies.
result Combining these strategies optimizes portfolio performance.
Extends a Liouville theorem for stable minimal hypersurfaces.
problem Stable minimal hypersurfaces in cylindrical cones.
method Analyzes the density and foliation of minimal hypersurfaces.
result Shows that stable minimal hypersurfaces are cylindrical.
Unified convergence analysis of alpha-SVRG under strong convexity.
problem Analyzing the convergence of alpha-SVRG in strongly convex environments.
method Unified convergence rate expression for alpha-SVRG under fixed learning rate, demonstrating faster convergence than SGD and SVRG.
result alpha-SVRG has a faster convergence rate compared to SGD and SVRG under suitable choice of alpha.
The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.
problem Characterizing canal hypersurfaces in Lorentz-Minkowski 4-space.
method Analyzing geometric invariants and conditions for canal hypersurfaces.
result Characterizations of canal hypersurfaces, including flatness and minimality conditions.
We describe the underlying probabilistic interpretation of alpha and beta divergences. We first show that beta divergences are inherently tied to Tweedie distributions, a particular type of exponential family, known as exponential dispersion models. Starting from the variance function of a Tweedie model, we outline how…
Paper proves minimal surfaces near quadratic cones have specific smooth structure.
problem Characterize minimal surfaces near quadratic cones.
method Analyzes n-varifolds in the unit ball close to a minimizing quadratic cone. result Singularities modeled on these cones determine the local structure of nearby minimal surfaces.
The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on H_{n-1}(M,R) is a homogenized version of the Riemannian (n-1)-volume. We study…
Paper proposes a new REINFORCE algorithm for mining formulaic alpha factors with reduced variance.
problem Mining formulaic alpha factors with interpretability and robustness in volatile markets.
method Developed a novel REINFORCE algorithm with a dedicated baseline and reward shaping.
result Boosts correlation with returns by 3.83% and enhances excess returns compared to existing methods.
A surface is called a tube if its level-sets with respect to some coordinate function (the axis of the surface) are compact. Any tube of zero mean curvature has an invariant, the so-called flow vector. We study how the geometry of the Gaussian image of a higher-dimensional minimal tube M is controlled by the angle alph…
The study characterizes canal hypersurfaces in Euclidean spaces and their curvature properties.
problem Characterizing canal hypersurfaces in Euclidean spaces.
method Analyzing canal hypersurfaces in Euclidean n-space, focusing on E4, computing curvature properties, and proving specific cases.
result Flat canal hypersurfaces in Euclidean 4-space are only circular hypercylinders or circular hypercones, and minimal canal hypersurfaces are only generalized catenoids.
Alpha2 discovers logical formulaic alphas using deep reinforcement learning.
problem Discovering interpretable formulaic alphas for better trading strategies.
method Formulating alpha discovery as program construction, using deep reinforcement learning to navigate the search space.
result Empirical experiments show Alpha2 identifies diverse, logical, and effective alphas improving trading strategy performance.
Alpha-GPT mines new trading signals with human-AI interaction.
problem Mining new alphas for effective trading signals.
method Human-AI interaction and prompt engineering algorithmic framework.
result Demonstrates Alpha-GPT's effectiveness in generating creative, insightful, and effective alphas.
We give an explicit algorithm and source code for extracting expected returns for stocks from expected returns for alphas. Our algorithm altogether bypasses combining alphas with weights into "alpha combos". Simply put, we have developed a new method for trading alphas which does not involve combining them. This yields…
A study on α-GANs proving convergence and estimation guarantees.
problem Analyzing the convergence and estimation guarantees of α-GANs. method Proved a correspondence between α-GANs and f-divergences, and provided estimation bounds. result Estimation bounds indicate diverse GAN behavior as a function of α. Paper proposes a new framework to mine synergistic formulaic alphas for better stock trend forecasting.
problem Mining alphas separately ignores their combined performance, leading to suboptimal models.
method Proposes a reinforcement learning-based framework that optimizes the mining of synergistic formulaic alpha sets.
result Demonstrates higher returns in stock trend forecasting compared to previous approaches.
Alpha-R1 uses LLMs to reason about economic factors and news for better alpha screening.
problem Challenges in data-driven investment strategies due to signal decay and regime shifts.
method Reinforcement learning trained on 8B parameters to evaluate alpha relevance under changing market conditions.
result Empirically outperforms benchmark strategies and shows improved robustness to alpha decay.
We propose a framework for constructing factor models for alpha streams. Our motivation is threefold. 1) When the number of alphas is large, the sample covariance matrix is singular. 2) Its out-of-sample stability is challenging. 3) Optimization of investment allocation into alpha streams can be tractable for a factor …
We compute the analytic expression of the probability distributions F{FTSE100,+} and F{FTSE100,-} of the normalized positive and negative FTSE100 (UK) index daily returns r(t). Furthermore, we define the alpha re-scaled FTSE100 daily index positive returns r(t)^alpha and negative returns (-r(t))^alpha that we call, aft…
The paper studies stability and minimizing properties of higher codimensional surfaces in Euclidean space.
problem Stability and minimizing properties of higher codimensional surfaces in Euclidean space.
method Analyzes surfaces associated with the weighted area-functional and proves stability and minimization properties under specific conditions.
result Minimal cones with globally flat normal bundles are f-stable, and highly singular determinantal varieties and Pfaffian varieties are f-minimizing. In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the alpha re-scaled DAX daily index positive returns r(t)^alpha and negative returns (-…
Alpha-GPT 2.0 integrates human insights into AI-driven investment research.
problem Efficiency and precision in quantitative investment research.
method Iterative Human-AI interaction using large language models.
result Enhanced efficiency and precision in quantitative investment research.
It is well known that combining multiple hedge fund alpha streams yields diversification benefits to the resultant portfolio. Additionally, crossing trades between different alpha streams reduces transaction costs. As the number of alpha streams increases, the relative turnover of the portfolio decreases as more trades…
RiskMiner discovers formulaic alphas using MCTS for better performance.
problem Mining formulaic alphas without considering structural information and alpha correlations.
method Formulates alpha mining as an MDP and solves it with a risk-seeking MCTS.
result Our method outperforms state-of-the-art benchmarks and achieves the most profitable results.
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…
Enhances genetic programming for stock alpha discovery with warm start and structural constraints.
problem Overwhelming search space and computational burden in traditional genetic programming for alpha factor discovery.
method Proposes a new GP framework with warm start and structural constraints to enhance search performance and interpretability.
result Superior out-of-sample prediction results and higher portfolio returns compared to benchmarks.
We give an explicit algorithm and source code for combining alpha streams via bounded regression. In practical applications typically there is insufficient history to compute a sample covariance matrix (SCM) for a large number of alphas. To compute alpha allocation weights, one then resorts to (weighted) regression ove…
We prove that a stable minimal hypersurface of an open ball having a singular set of locally finite codimension 2 Hausdorff measure which is weakly close to a multiplicity 2 hyperplane is a 2-valued C^{1, alpha} graph in the interior. Applications including a compactness theorem for a class of immersed stable minimal h…
AI-driven investment strategies self-defeat at scale due to signal crowding and erosion.
problem Excess returns from AI-driven investment strategies diminish at scale due to signal crowding and erosion.
method Theoretical model and empirical validation using SEC Form 13F filings and hedge fund return dynamics.
result The alpha half-life of signals decreases significantly with AI adoption, leading to diminishing returns.
Paper formalizes and analyzes a new bound for variational inference.
problem Lack of theoretical guarantees in variational algorithms.
method Introduces VR-IWAE bound, a generalization of IWAE.
result VR-IWAE bound leads to unbiased gradient estimators.
AlphaEval evaluates alpha mining models efficiently and comprehensively.
problem Lack of systematic evaluation for alpha mining models.
method Unified, parallelizable evaluation framework assessing predictive power, stability, robustness, financial logic, and diversity.
result AlphaEval achieves evaluation consistency comparable to comprehensive backtesting, providing more comprehensive insights and higher efficiency.
New methods for tuning alpha in Gibbs posteriors improve speed and accuracy.
problem Inconsistency in Bayesian inference and lack of fast tuning methods for alpha.
method Proposed two data-driven methods: sample-splitting and bootstrapping. Formulated alpha-posteriors for three models.
result Sample-splitting outperforms SafeBayes in speed and accuracy, especially in complex models.
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha > alpha_0, where 0 < alpha_0 < 1 is of the order 1/k. This suggests that the flow…
The weak variance-alpha-gamma process is a multivariate Lévy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibrati…
Researchers calculate alpha invariant for certain complex projective spaces.
problem Computing alpha invariant for specific types of complex projective spaces.
method Computed alpha invariant using total degree and Pontryagin classes.
result Alpha invariant depends only on total degree and Pontryagin classes.