Proposes a new framework for invariant quadratic P&L predictions in option books.
problem Inconsistent second-order P&L predictions across different factor parameterizations.
method Local, model-agnostic framework using covariant Hessian defined by an affine connection.
result Coordinate-invariant quadratic P&L predictions that match desk targets.
The paper studies optimal transport in linear quadratic systems and derives interpolation inequalities.
problem Optimal transport problem in Linear Quadratic optimal control systems.
method Well-posedness of the Monge problem, regularity of optimal transport map, displacement interpolation of measures.
result Derivation of general interpolation inequalities for entropy functionals.
The paper models asset pricing in a partially observed market using mean field game theory and exponential quadratic Gaussian framework.
problem Asset pricing in a market with partial observation and heterogeneous agents.
method Mean field game theory, exponential quadratic Gaussian framework, Kalman-Bucy filtering theory.
result Characterization of equilibrium risk premium through mean field BSDE and construction of unobservable risk premium process.
We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of st…
We consider the problem of high-dimensional classification between the two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on original data, with the subsequent application of quadr…
Paper connects MoE and self-attention, proposing active-attention.
problem Improving efficiency and performance of self-attention mechanisms.
method Established connection between MoE and self-attention, analyzed quadratic gating functions, proposed active-attention mechanism.
result Active-attention outperforms standard self-attention in various tasks.
A Gaussian Process Ordinary Differential Equation framework for large continuous dynamical systems
problem Forecasting complex dynamical systems
method Kernel autonomous ODE approach based on Gaussian Processes and Quadratic Order Model Reduction
result Full model outperforms ROM methods in terms of accuracy or computational costs
This paper develops a new method for eliciting more flexible metrics, improving fairness and applicability.
problem Limited flexibility in existing metric elicitation strategies for reflecting user preferences.
method Develops a strategy for eliciting quadratic metrics based on predictive rates, requiring only relative preference feedback.
result Achieves near-optimal query complexity and broadens the use cases for metric elicitation.
Develops a control framework for systemic risk under uncertainty.
problem Systemic risk under model uncertainty.
method Linear-quadratic mean-field control framework with viscosity solutions and verification theorems.
result Explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability.
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and noisy data, the quadratic error functionals demonstrated many weaknesses including…
This paper optimizes portfolio selection for multivariate affine and quadratic Volterra models with rough volatilities.
problem Optimizing portfolio selection for multivariate models with rough volatilities and stochastic correlations.
method Investigates continuous-time Markowitz mean-variance problem for multivariate affine and quadratic Volterra models using Riccati backward stochastic differential equations (BSDEs).
result Derives explicit solutions for BSDEs in affine Volterra models and new analytic formulae for quadratic models.
A quadratic point on a surface in RP3 is a point at which the surface can be approximated by a quadric abnormally well (up to order 3). We conjecture that the least number of quadratic points on a generic compact non-degenerate hyperbolic surface is 8; the relation between this and the classic Carathéodory conjectur…
The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. \cite{AIS}, and Arai …
Gradient model for memristive systems in neurophysiology and neuromorphic circuits.
problem Understanding and modeling memristive systems.
method Introducing a gradient modeling framework based on Chua's definition of memristive elements.
result Gradient properties of memristive systems have implications for neuromorphic circuit analysis and design.
Gradient descent dynamics in quadratic regression models are analyzed, revealing five phases: monotonic, catapult, periodic, chaotic, and divergent.
problem Analyzing the dynamics of gradient descent in quadratic regression models.
method Fine-grained bifurcation analysis of gradient descent dynamics using a cubic map parameterized by the step-size.
result Gradient descent dynamics in quadratic regression models exhibit five distinct phases: monotonic, catapult, periodic, chaotic, and divergent.
FedExProx's performance is no better than GD for quadratic optimization.
problem Improving convergence of parallel proximal algorithms.
method Developed a novel analysis framework to establish tighter convergence rates.
result FedExProx can outperform GD in non-strongly convex quadratic problems.
In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our …
Extends trading framework to incorporate real-world constraints.
problem Trading strategies in multi-player non-cooperative games with constraints.
method Re-framed as quadratic programming problem, constraints readily incorporated.
result Two-trader equilibria calculated dynamically.
Proof of wall-crossing formula using spectral networks.
problem Proving the Kontsevich-Soibelman wall-crossing formula.
method Path-lifting rules for spectral networks, convergence justification.
result Definition and justification of path lifting rules for spectral networks.
Extends QHawkes to MQHawkes for analyzing financial co-jumps.
problem Capturing endogenous co-jumps in financial markets.
method Develops MQHawkes process with quadratic kernels, investigates stationarity, and derives Yule-Walker equations.
result Volatility distribution exhibits power-law behavior with computable exponents.
Turbo-Aggregate reduces secure aggregation time from quadratic to nearly linear.
problem Quadratic overhead in secure model aggregation for federated learning.
method Multi-group circular strategy, additive secret sharing, and coding techniques.
result Achieves O(NlogN) overhead, compared to O(N2), for up to 50% user dropout. Estimates manifold dimension using local graph structure.
problem Estimating the intrinsic dimension of manifolds from data.
method Regression on local PCA coordinates, focusing on local graph structure.
result Proposed QE and TLS estimators outperform existing methods.
Investment strategy optimization from discrete to continuous models.
problem Optimizing investment strategies and stopping times in both continuous and discrete settings.
method Characterized value functions via quadratic reflected BSDEs for continuous case, discretized BSDEs for discrete case, and derived uniform convergence rates.
result Uniform convergence and rate from discrete to continuous quadratic reflected BSDEs.
A key issue in the estimation of energy hedges is the hedgers' attitude towards risk which is encapsulated in the form of the hedgers' utility function. However, the literature typically uses only one form of utility function such as the quadratic when estimating hedges. This paper addresses this issue by estimating an…
New method solves nonseparable stochastic control problems.
problem Nonseparable and non-monotonic stochastic control problems.
method Scenario-decomposition solution framework using progressive hedging algorithm.
result Extends reach of stochastic optimal control.
In this paper, we study the problem of escaping from saddle points in smooth nonconvex optimization problems subject to a convex set C. We propose a generic framework that yields convergence to a second-order stationary point of the problem, if the convex set C is simple for a quadratic objectiv…
Paper solves time-inconsistent control problems with BSDEs.
problem Time-inconsistent stochastic control in continuous time.
method Probabilistic representation via BSDEs.
result Equilibrium value function resolved for inconsistent cases.
Quadratic discriminant analysis (QDA) is a standard tool for classification due to its simplicity and flexibility. Because the number of its parameters scales quadratically with the number of the variables, QDA is not practical, however, when the dimensionality is relatively large. To address this, we propose a novel p…
Novel method solves group synchronization with robust corruption tolerance.
problem Group synchronization with high corruption tolerance.
method Quadratic programming formulation exploiting cycle consistency.
result Global minimum recovers corruption levels under mild conditions.
Estimates parameters in max-linear Bayesian networks with noise.
problem Causal inference in extreme-value settings with noise parameters.
method Max-plus algebra and logarithm transformation, normal distribution estimation, EM algorithm and quadratic optimization.
result An estimator of a parameter for each edge in a DAG is normally distributed.
We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered when the quadratic kern…
Gaussian equivalence fails for simple polynomial embeddings in quadratic scaling RF models.
problem Failure of Gaussian equivalence in polynomial feature embeddings under quadratic scaling.
method Introduced Conditional Gaussian Equivalent (CGE) model to capture non-Gaussian behavior.
result Correct asymptotics derived for training and test errors in CGE model.
Paper uses Koopman operator and Nyström method for efficient nonlinear control.
problem Control of nonlinear dynamical systems.
method Combines Koopman operator framework with Nyström approximation for kernel methods.
result Theoretical guarantees on the convergence rates of the approximated Riccati operator and regulator objective.
Skeinformer accelerates self-attention for long sequences with linear complexity.
problem Efficiency of Transformer models in processing long sequences.
method Matrix sketching and column sampling to reduce quadratic complexity to linear.
result Skeinformer outperforms alternatives with smaller time/space footprint.
Study solves HJB equations for time-inconsistent control problems.
problem Time-inconsistent deterministic linear quadratic control problems.
method Characterized solutions using Riccati equations with integral terms, proving uniqueness.
result Uniqueness of solutions to equilibrium HJB equations proved.
The paper studies new curvature properties in Finsler geometry.
problem Properties of projectively equivalent Finsler metrics and their curvature structures.
method Introducing new characterizations of quadratic curvature properties in Finsler manifolds.
result Novel insights into curvature behavior under generalized projective sprays.
Paper solves Gromov-Wasserstein for point clouds efficiently.
problem Quantifying similarity between two formations or shapes.
method Reformulates QAP as low-rank concave quadratic optimization problem.
result Global solution for large-scale problems with thousands of points.
Individuals, or organizations, cooperate with or compete against one another in a wide range of practical situations. Such strategic interactions are often modeled as games played on networks, where an individual's payoff depends not only on her action but also on that of her neighbors. The current literature has large…
Unified analysis of first-order methods for smooth games using IQCs.
problem Certify convergence rates of first-order methods for smooth and strongly-monotone games.
method Adapted integral quadratic constraints (IQCs) to study first-order methods and derive tight upper bounds of convergence rates.
result First global convergence rate for the negative momentum method with O(κ1.5) iteration complexity. Efficient sparse modern Hopfield models are introduced for memory retrieval and learning tasks.
problem Efficient modern Hopfield models for memory retrieval and learning tasks.
method Nonparametric interpretation of Hopfield models as a regression problem.
result Sparse-structured modern Hopfield models with sub-quadratic complexity.
Study uses G-BSDEs to decompose pricing kernels under robust G-expectation.
problem Long-term decomposition of robust pricing kernels under G-expectation.
method Proposes and analyzes three types of quadratic G-BSDEs to decompose pricing kernels.
result Pricing kernels decomposed into four components: discounting, transitory, symmetric martingale, and volatility uncertainty.
Optimizes dividends with stability for risky businesses.
problem Maximizing dividends with stability in risky businesses.
method Linear-quadratic optimization for a general Lévy process.
result Derives optimal affine dividend strategies with stability.
New framework for RL with linear-convex models reduces performance gap.
problem Continuous-time episodic reinforcement learning with unknown coefficients and convex objectives.
method Probabilistic framework and phase-based learning algorithm for optimal exploration-exploitation trade-off.
result Sublinear regrets achieved, matching best possible results in literature.
We construct a finitely presented group G with non-quadratic Dehn function f majorizable by a quadratic function on arbitrary long intervals.
Unified framework for fast large-scale portfolio optimization.
problem Efficient portfolio optimization for large-scale financial data.
method Incorporates shrinkage and regularization techniques, addressing multiple objectives.
result AP-Trees and PCA-based factor models consistently outperform other approaches in out-of-sample portfolio performance.
The paper classifies biharmonic quadratic maps between spheres, proving their energy density properties.
problem Classifying non-harmonic biharmonic quadratic forms between spheres.
method Proving non-harmonic biharmonic quadratic forms have constant energy density and classifying them.
result Non-harmonic biharmonic quadratic forms have constant energy density (m+1)/2. This work establishes safe reinforcement learning for LQR with nonlinear baselines.
problem Safe reinforcement learning in LQR with unknown dynamics and safety constraints.
method General framework for nonlinear baselines, focusing on 1D spaces.
result Achieves optimal regret bounds for constrained reinforcement learning.
Recently, deep learning has achieved huge successes in many important applications. In our previous studies, we proposed quadratic/second-order neurons and deep quadratic neural networks. In a quadratic neuron, the inner product of a vector of data and the corresponding weights in a conventional neuron is replaced with…