Paper develops a continuous-time framework for financial markets without stochastic calculus.
problem Developing continuous-time financial models without stochastic calculus.
method A general framework using conditional topologies and pseudo-distance topologies.
result No-arbitrage conditions hold in continuous time if and only if they hold in discrete time.
New method improves continual learning by generating samples and labels together.
problem Improving continual learning in complex classification tasks.
method Conditional replay generates samples and labels together, reducing label inference error.
result Conditional replay outperforms marginal replay and EWC on benchmarks.
We study the stability of several no-arbitrage conditions with respect to absolutely continuous, but not necessarily equivalent, changes of measure. We first consider models based on continuous semimartingales and show that no-arbitrage conditions weaker than NA and NFLVR are always stable. Then, in the context of gene…
Proves conditions for Fourier transforms in rank 1 symmetric spaces.
problem Understanding Fourier transform bounds in symmetric spaces.
method Proves sufficient and necessary conditions using Lipschitz and Fourier type integral conditions.
result Establishes bounds for Fourier transforms in rank 1 symmetric spaces with specific moduli of continuity.
Working in a continuous time setting, we extend to the general case of dynamic risk measures continuous from above the characterization of time consistency in terms of ``cocycle condition'' of the minimal penalty function. We prove also the supermartingale property for general time consistent dynamic risk measures. Whe…
Monotone aggregation of dependent random vectors has an absolutely continuous distribution under certain conditions.
problem Monotone aggregation of dependent random vectors
method Coordinatewise monotonicity and uniform lower-increment conditions
result One-dimensional push-forwards of dependent random vectors have an absolutely continuous distribution
Infinite Lie groups meet continuity conditions.
problem Continuity conditions for Lie groups.
method Analyzing locally μ-convex Lie groups. result Infinite dimensional Lie groups have the strong Trotter property.
CcGAN tackles conditional image generation for continuous labels.
problem Mathematical challenges in conditioning on continuous, scalar labels.
method Proposes novel empirical losses and label input methods for continuous conditional GANs.
result CcGAN generates diverse, high-quality images from continuous labels.
Paper identifies and estimates CAPCEs in continuous treatment settings.
problem Estimating heterogeneous causal effects of continuous treatments.
method Instrumental variable approach to identify CAPCEs under weaker conditions.
result Developed three families of CAPCE estimators with statistical properties analyzed.
Sufficient condition for log-continuity of complex Monge-Ampère solutions.
problem Ensuring log-continuity of solutions to complex Monge-Ampère equations.
method Analyzing compact Kähler manifolds and line bundles, providing sufficient conditions for log-continuity.
result Log-continuity of solutions to complex Monge-Ampère equations with Lp right-hand sides. Extends neural network approximations to guarantee continuity of real-world learning tasks.
problem Guaranteeing continuity of real-world learning tasks given by conditional expectations.
method Establishing conditions on learning tasks that guarantee their continuity under a factorization of the data-generating process.
result Conditions guaranteeing the continuity of practically any derived learning task.
CANDI solves the gap between continuous and discrete diffusion models for text generation.
problem Underperformance of continuous diffusion models in discrete data domains.
method Introduces token identifiability and a hybrid framework (CANDI) to decouple discrete and continuous corruption.
result CANDI successfully avoids temporal dissonance, enabling continuous diffusion benefits for discrete spaces.
Continuous-time SGD converges under certain conditions, useful for deep learning.
problem Minimizing population expected loss in learning problems.
method Continuous-time approximation of stochastic gradient descent.
result Establishes sufficient conditions for convergence, applicable to overparametrized neural networks.
ORDisCo learns from unlabeled data to improve semi-supervised continual learning.
problem Lack of effective use of unlabeled data in semi-supervised continual learning.
method Deep Online Replay with Discriminator Consistency (ORDisCo) that continually passes the learned data distribution to a classifier and selectively stabilizes discriminator parameters.
result Significant performance improvement on various semi-supervised learning benchmark datasets.
Root's barrier is continuous and finite under certain conditions.
problem Continuity of the root barrier function.
method Analyzing Skorokhod embedding problem and properties of target measures.
result The barrier function is continuous and finite under specified conditions.
Researchers find a timing error in Black-Scholes-Merton option pricing model.
problem Timing error in Black-Scholes-Merton option pricing model.
method Discovered a timing mistake in Merton's 1971 model and showed misspecification in continuous and discrete time.
result Invalidates seminal contributions to the literature including Black-Scholes (1973) and Merton (1971).
Proposes Mv-TCNN for continual learning without known tasks in advance.
problem Catastrophic forgetting in continual learning.
method Multi-view Task Conditional Neural Networks (Mv-TCNN).
result Outperforms state-of-the-art continual learning models.
We propose a unified analysis of a whole spectrum of no-arbitrage conditions for financial market models based on continuous semimartingales. In particular, we focus on no-arbitrage conditions weaker than the classical notions of No Arbitrage and No Free Lunch with Vanishing Risk. We provide a complete characterisation…
Study of affine processes without stochastic continuity assumption.
problem Time-inhomogeneous affine processes with unpredictable jumps.
method Developed a general theory of finite dimensional affine semimartingales under weak assumptions.
result Affine form of semimartingale characteristics and solutions to Riccati equations.
New RBF networks can approximate any continuous function.
problem Approximating any continuous function on a compact subset.
method Replacing smoothing factors with shifts in RBF networks and proving approximation under certain conditions.
result RBF networks can approximate any continuous function on any compact subset.
The study finds continuous solutions to complex Hessian equations on compact Hermitian manifolds.
problem Finding continuous solutions to complex Hessian equations on compact Hermitian manifolds.
method Deriving an L∞-estimate for bounded solutions to the complex m-th Hessian equations on compact Hermitian manifolds, assuming a positive right-hand side in the Orlicz space Lmn(logL)n(h∘log∘logL)n. result Establishing the existence of continuous solutions to the complex Hessian equation under the prescribed assumptions.
The paper explores how Lipschitz-continuity improves GAN training stability and quality.
problem Failure and instability in GAN training due to unreliable gradient from optimal discriminative function.
method Investigates the property of optimal discriminative function and proves Lipschitz-continuity is a solution.
result Lipschitz-continuity condition ensures convergence and leads to more stable and higher quality generated samples.
Injective maps between manifolds are continuous under specific conditions.
problem Continuity of injective maps between manifolds.
method Conditions on connected subsets and manifold dimensions.
result Partial answer to a problem posed by Willie Wong.
Study on existence and properties of continuous solutions to complex Hessian equations.
problem Existence and properties of continuous solutions to complex Hessian equations.
method Established new capacity estimates and weak stability estimates for the m-Hessian measure. result Existence of continuous solutions to the complex Hessian equation under certain conditions.
Proves Hölder continuity of complex Monge-Ampère solutions.
problem Global Hölder continuity of solutions to complex Monge-Ampère equation.
method Analyzes Dirichlet problem on strictly pseudoconvex domains or Hermitian manifolds.
result Proves global Hölder continuity of solutions under given conditions.
SplineNets improve CNNs by using continuous functions that can be conditioned on inputs.
problem Efficiency and accuracy trade-offs in CNNs.
method Continuous generalization of neural decision graphs using B-splines.
result SplineNets can significantly increase accuracy with minimal runtime cost.
Method discovers local independence in systems with continuous variables.
problem Applying Context-Specific Independence (CSI) to continuous variables is impractical.
method Neural contextual decomposition (NCD) learns partition of joint outcome space.
result NCD successfully discovers local independence in synthetic and real-world systems.
Let M be a complete Riemannian manifold possessing a strictly convex Lipschitz continuous exhaustion function. We show that the isoperimetric profile of M is a continuous and non-decreasing function. Particular cases are Hadamard manifolds and complete non-compact manifolds with strictly positive sectional curvatur…
Private CI tests for continuous Z with privacy constraints.
problem Testing conditional independence under differential privacy constraints.
method Developed two private CI testing procedures based on generalized covariance and conditional randomization tests.
result First private CI tests with rigorous theoretical guarantees for continuous Z.
We show that a trader, who starts with no initial wealth and is not allowed to borrow money or short sell assets, is theoretically able to attain positive wealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be…
The article examines entropy-information inequalities for continuous-time Markov chains under curvature-dimension conditions.
problem Proving Li-Yau inequalities and modified logarithmic Sobolev inequalities for reversible Markov chains.
method Introducing the CDΥ(κ,F) condition and deriving entropy-information inequalities. result Derives functional inequalities relating entropy to Fisher information.
A new method for continual learning in GANs learns new modes with limited data.
problem Learning new target modes with limited samples while preserving previously learned ones.
method Mode-affinity score for generative modeling, generator replay, and weighted label generation.
result Gains over state-of-the-art methods, even with fewer training samples.
In this note we continue the analysis of metric measure space with variable ricci curvature bounds. First, we study (κ,N)-convex functions on metric spaces where κ is a lower semi-continuous function, and gradient flow curves in the sense of a new evolution variational inequality that captures the information that …
Neural Jump ODE improves continuous-time prediction and filtering of irregularly sampled time series.
problem Theoretical guarantees for continuous-time prediction and filtering of irregularly observed time series.
method Introducing Neural Jump ODE (NJ-ODE) that models conditional expectation between observations with neural ODEs and jumps.
result Theoretical guarantees for the L2-optimal prediction are provided, showing convergence of model output to optimal prediction. We present sufficient conditions for topological stability of continuous functions f:R→R having finitely many local extrema with respect to averagings by discrete measures with finite supports.
Proposes a new model for predicting chronic conditions over time.
problem Predicting complex relationships between multiple chronic conditions.
method Continuous time Bayesian network with adaptive regularization for structure and parameter learning.
result Proposed model provides sparse, intuitive representation of chronic condition relationships.
Neural framework for conditional OT maps learns from categorical and continuous variables.
problem Learning conditional optimal transport maps between complex distributions.
method Hypernetwork generates adaptive transport layer parameters based on conditioning variables.
result Our method outperforms simpler conditioning methods in comprehensive ablation studies.
Ricci flow stability proven, extending convergence results.
problem Stability of Ricci flow solutions near initial conditions.
method Continuous dependence on initial conditions, stability of fixed points.
result Ricci flow solutions converge to stable fixed points near initial conditions.
Higher-order optimization problems naturally appear when investigating the effects of a patent with finite length, as in the pioneering work of Futagami and Iwaisako (2007). In this paper, we establish the Euler equations and transversality conditions necessary for analyzing such higher-order optimization problems. We …
Study on scalar-flat Kahler 4-manifolds with a continuous symmetry.
problem Understanding scalar-flat Kahler 4-manifolds with a Killing field.
method Analysis of manifolds with a Killing field and asymptotic conditions.
result Rigidity results that restrict the behavior of scalar-flat Kahler manifolds at infinity.
Paper defines conditions for limit sets of Anosov representations to be smooth submanifolds.
problem Understanding the smoothness of limit sets of Anosov representations.
method Established conditions for limit sets to be differentiable submanifolds and calculated optimal Holder constants.
result Limit sets of projective Anosov representations are differentiable submanifolds with Holder continuous derivatives.
Partition Tree estimates conditional densities for mixed continuous and categorical variables.
problem Estimating conditional densities for mixed data types.
method Tree-based framework modeling conditional distributions as piecewise-constant densities on adaptive partitions, minimizing conditional negative log-likelihood.
result Improved probabilistic prediction compared to CART-style trees and state-of-the-art methods.
Paper introduces CRLMaze, a new benchmark for continual reinforcement learning in 3D non-stationary environments.
problem Challenges of training reinforcement learning agents in high-dimensional, always-changing environments.
method End-to-end model-free continual reinforcement learning strategy.
result Competitive results in a complex 3D non-stationary task, outperforming four baselines.
Researchers find continuous solutions to minimizers in weighted least gradient problems.
problem Existence and regularity of minimizers to weighted least gradient problems.
method Constructing continuous solutions using Sternberg-Williams-Ziemer technique extended to inhomogeneous variations.
result Continuous solutions constructed for minimizers in any dimension n≥2, with level sets being minimal surfaces in a conformal metric.
This work proposes a method to integrate algorithms into neural networks using continuous relaxation.
problem Training neural networks with new forms of supervision like ordering constraints.
method Relaxing discrete conditions in control structures like conditional statements, loops, and indexing to make them differentiable.
result The proposed method can keep up with relaxations designed for specific tasks, showing general applicability.
Classifies Tk-manifolds with continuous sections.
problem Classifying Tk-manifolds with specific properties. method Uses continuous sections to orbit map for classification.
result Classifies Tk-manifolds up to equivariant diffeomorphism. Introduces a Boltzmann machine with Riemann-Theta functions for continuous and discrete states.
problem Modeling continuous and discrete states in neural networks.
method Develops a Boltzmann machine with continuous visible and discrete hidden states, solving probability density and conditional expectation analytically.
result Derives a novel parametric density function involving Riemann-Theta functions and uses it as an activation function in a feedforward neural network.
Counterexamples to continuity of optimal transportation on Riemannian manifolds with everywhere positive sectional curvature are provided. These examples show that the condition A3w of Ma, Trudinger, & Wang is not guaranteed by positivity of sectional curvature.