NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes

arXiv:2607.14361 · math.PR, cs.LG, q-fin.CP, stat.ML · Submitted 2026-07-15 · Read on arXiv

Anastasis Kratsios, Giulia Livieri, Philipp Schmocker

math.PR, cs.LG, q-fin.CP, stat.ML

Submitted: 2026-07-15

Code: https://github.com/AnastasisKratsios/CausalTransformer

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Calibration — 8× in this paper · explained in 9 episodes
• Localization — 8× in this paper · explained in 2 episodes
• Accuracy — 7× in this paper · explained in 1 episode
• Lasso — 5× in this paper · explained in 2 episodes
• Hilbert Space — 4× in this paper · explained in 2 episodes
• Neural Operators — 4× in this paper · explained in 2 episodes
• ReLU Network — 4× in this paper · explained in 2 episodes
• Reinforcement Learning — 4× in this paper · explained in 4 episodes
• Universality — 4× in this paper · explained in 2 episodes
• Orthogonal Projection — 3× in this paper · explained in 2 episodes
• Augmentation — 2× in this paper · explained in 2 episodes
• Composition — 2× in this paper · explained in 2 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Curse of Dimensionality — 2× in this paper · explained in 6 episodes
• Generator — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 3 episodes
• Clarity — 1× in this paper · explained in 3 episodes
• Expressivity — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 14 episodes
• Inverse Problem — 1× in this paper · explained in 2 episodes
• Parameterization — 1× in this paper · explained in 2 episodes
• Q-learning — 1× in this paper · explained in 3 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Sparsity — 1× in this paper · explained in 5 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• SANOS Smooth strictly Arbitrage-free Non-parametric Option Surfaces
• A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration
• Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs
• One model to solve them all: 2BSDE families via neural operators
• Bridging the Gap Between Approximation and Learning via Optimal Approximation by ReLU MLPs of Maximal Regularity
• Deep Signature Approach for McKean-Vlasov FBSDEs in a Random Environment
• Adam: A Method for Stochastic Optimization
• Neural Operators Which Certifiably Simultaneously Solve Infinitely Many Convex Programs using Logarithmic Rank and Linear Complexity
• Universal approximation property of neural stochastic differential equations
• Solving stochastic partial differential equations using neural networks in the Wiener chaos expansion
• Mathematical theory of deep learning
• Autonomous-Flow-Based Generation
• Weighted universal approximation of differentiable maps on infinite-dimensional manifolds
• Nearly optimal bounds on the Fourier sampling numbers of Besov spaces
• Deep-learning based numerical BSDE method for barrier options
• ADADELTA: An Adaptive Learning Rate Method

Related papers

• Sharp Deviations Bounds for Dirichlet Weighted Sums with Application to analysis of Bayesian algorithms
• Subspace Uncertainty and Sharp Sampling Thresholds on the Boolean Cube
• Local Anticoncentration for Gaussian Boson Sampling via Conditional Wishart Geometry
• Beyond the Semicircle: Free Diffusion Models with Prescribed Equilibria
• Explicit Steady-State Approximations for Parallel Server Systems with Heterogeneous Servers
• A New Bound on the Cumulant Generating Function of Dirichlet Processes