Controller stabilizes spherical robot's position and line-of-sight.
problem Stabilizing a spherical robot's position and line-of-sight.
method Geometric control law with feedforward and proportional-derivative control.
result Controller performance validated through simulations.
Paper formulates EnKF as optimal transport problem for unique control law.
problem Unique control law for EnKF algorithms.
method Formulated as optimal transportation problem, derived explicit control law.
result Mean squared error converges to zero with finite particles.
Nonparametric adaptive robust control tackles model uncertainty in stochastic processes.
problem Model uncertainty in stochastic processes.
method Adaptive robust control methodology using online learning and uncertainty reduction, empirical distribution, and Lagrangian duality.
result Nonparametric adaptive robust control approach is preferable to traditional robust frameworks.
The paper uses information theory to find limits of feedback control systems.
problem Fundamental performance limitations of feedback control systems.
method Utilizes information theory to derive Lp bounds on control error. result Bounds are characterized by the conditional entropy of the disturbance.
We show that Masur's logarithmic law of geodesics in the moduli space of translation surfaces does not imply unique ergodicity of the translation flow, but that a similar law involving the flat systole of a Teichmüller geodesic does imply unique ergodicity. It shows that the flat geometry has a better control on ergodi…
This work explains scaling laws as redundancy laws in deep learning.
problem The mathematical origins of scaling laws in deep learning models remain unclear.
method Kernel regression and analysis of data covariance spectra.
result Scaling laws can be explained as redundancy laws, revealing the learning curve's slope depends on data redundancy.
The paper explores symmetries and conservation laws in Hamiltonian systems.
problem Understanding symmetries and conservation laws in Hamiltonian systems.
method Using dynamical covariant derivative and Jacobi endomorphism, the paper finds invariant equations of symmetries and proves the canonical nonlinear connection can be determined by these symmetries.
result The canonical nonlinear connection can be determined by infinitesimal symmetries and Newtonoid vector fields.
Unified theory for neural scaling laws in hierarchically compositional data.
problem Understanding neural scaling laws in hierarchically compositional data.
method Probabilistic context-free grammars and power-law distributed production rules.
result Unified learning curve behavior for classification and next-token prediction tasks.
A new method steers Gaussian distributions with minimal effort.
problem Steering high-dimensional Gaussian distributions efficiently.
method Sliced feedback controller using one-dimensional projections and averaging.
result The method steers Gaussian distributions to targets efficiently.
Optimizes consumption, investment, and healthcare spending for aging populations.
problem Maximizing utility in an aging population with changing mortality rates.
method Solves an optimal stochastic control problem using a novel version of Perron's method.
result Endogenous mortality law that is asymptotically exponential in the old-age limit.
Fault diagnosis method for refrigerant leaks using scaling law.
problem Difficulty in improving fault-detection model generalization due to complex system configuration and insufficient data.
method Derive a scaling law based on physical modeling and control mechanism, apply to other systems without modification.
result Scaling exponents of different air-conditioning systems are equivalent, indicating the proposed method's applicability.
The paper challenges the assumption that majority voting rights equate to 'effective control' in foreign ownership regulations.
problem The assumption that majority voting rights determine 'effective control' in foreign ownership regulations is flawed.
method The paper proposes and demonstrates a method for calculating 'effective control' based on voting thresholds and weights.
result The 'effective control' of a foreign minority stockholder can be higher than their shareholding size, challenging the assumption that majority voting rights equate to 'effective control'.
The paper proves geometric and spectral alignment for deep neural networks.
problem Understanding the singular spectra of deep neural network layers.
method Proves deterministic quotient-geometric estimates for singular spectra of Frobenius-normalized layer factors.
result Exact power-law spectra form a trace-normalized Cartan orbit under Frobenius normalization.
Framework learns stochastic dynamics from endpoint and intermediate distributions using soft energy constraints.
problem Learning stochastic dynamics from endpoint and intermediate distributional observations.
method Formulates generation as a McKean-Vlasov control problem with soft energy constraints, solving it through FBSDE.
result Model learns coherent stochastic trajectories matching prescribed marginal laws.
The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integra…
Proposes deep optimal feedback control for continuous-time systems with action constraints.
problem Learning optimal feedback control laws for robotic applications.
method Exploits Hamilton-Jacobi-Bellman equation and deep differential networks to learn optimal value function and feedback policy.
result Enables learning an optimal feedback control law that generates an optimal trajectory from any point in state-space without replanning.
Hybrid method uses GP models to control robot trajectories.
problem Minimizing unmodeled dynamics in robot motion.
method Embeds non-parametric statistical models (GPs) for feedback control.
result Proposed method avoids complex analysis for wide trajectory classes.
We study how the presence of correlations in physical variables contributes to the form of probability distributions. We investigate a process with correlations in the variance generated by (i) a Gaussian or (ii) a truncated Lévy distribution. For both (i) and (ii), we find that due to the correlations in the variance,…
New algorithm achieves logarithmic regret for adversarial online control.
problem Online linear-quadratic control in systems with adversarial disturbances.
method Characterization of optimal offline control law, reduced to online learning with approximate advantage functions.
result First algorithm with logarithmic regret for arbitrary adversarial disturbance sequences.
A simple model explains inference scaling in neural models.
problem Understanding how model performance improves with repeated inference attempts.
method A statistical ansatz based on memorization to study inference scaling laws.
result Inference loss exhibits a power law decay with increasing trials.
New method uses neural nets to control systems safely with disturbances.
problem Designing safe control laws for systems with disturbances.
method Imitation learning to train neural network controllers that satisfy CBF constraints.
result Demonstrated on a unicycle model with external disturbances.
Study uses OT to simulate markets, revealing power-law returns are driven by informational effect.
problem Reproduce power-law returns in financial markets using realistic simulations.
method Constructed artificial markets, used optimal transport (OT) to measure similarity, incrementally introduced behavioral components.
result Informational effect of prices is dominant in reproducing power-law returns, and multiple components interact synergistically.
Develops control and observer methods for complex systems.
problem Controlling and observing infinite-dimensional systems with boundary actuation.
method Energy-Casimir method and port-Hamiltonian system representation.
result Control law and observer designed for Kirchhoff-Love plate example.
We discover scaling laws for kernel regression loss under various learning rate schedules.
problem Understanding loss dynamics and learning rate schedules in kernel regression.
method Theoretical analysis of stochastic gradient descent on a power-law kernel regression model.
result Established a Functional Scaling Law (FSL) capturing the full loss trajectory under arbitrary learning rate schedules.
Formula adjusts steady-state models for control confounding.
problem Learning steady-state models from operational data can be flawed due to control confounding.
method Derives a formula to adjust for control confounding using structural dynamical causal models.
result Estimates a causal steady-state model from closed-loop operational data.
Paper tackles non-Markovian control problems with new learning methods.
problem Non-Markovian stochastic control problems with unknown parameters.
method Off-model training and importance sampling for deep neural network approximation.
result Quantitative error bounds for adaptive learning under model uncertainty.
Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision mak- ing and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, o…
Exact results on power-law distributions in systems with resets.
problem Understanding power-law distributions in systems with resets.
method Exact mathematical analysis of multiplicative processes with resets.
result Power-law distributions are built up over time and their moments behave quantitatively determined by parameters.
Study how generalization scales with model size and data in quadratic neural networks.
problem Understanding how generalization scales with model size and data in quadratic neural networks.
method Analyzed ℓ2-regularized empirical test error minimization in a quadratic two-layer network with finite-sample setting and structured data. result Revealed a phase diagram with distinct scaling regimes as the number of parameters varies, showing data-dependent power laws controlled by spectral structure of the target.
This paper first describes a class of uncertain stochastic control systems with Markovian switching, and derives an Itô-Liu formula for Markov-modulated processes. And we characterize an optimal control law, which satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching. Then, by using …
This study reveals statistical patterns in ERC20 token transactions on Ethereum blockchain.
problem Understanding transactional dynamics in decentralized systems.
method Examined over 44 million ERC20 token transfers, categorized by address type (EOA or SC), and analyzed using scaling laws.
result EOA-driven transactions exhibit consistent statistical behavior, while SC-driven activity displays sublinear scaling and bursty activity.
Taylor's law of temporal fluctuation scaling, variance ∼ a(mean)b, is ubiquitous in natural and social sciences. We report for the first time convincing evidence of a solid temporal fluctuation scaling law in stock illiquidity by investigating the mean-variance relationship of the high-frequency illiquidity o…
A theory of exceptional extreme events, characterized by their abnormal sizes compared with the rest of the distribution, is presented. Such outliers, called "dragon-kings", have been reported in the distribution of financial drawdowns, city-size distributions (e.g., Paris in France and London in the UK), in material f…
The paper proves local laws for non-separable sample covariance matrices.
problem Analyzing non-separable sample covariance matrices with dependent or nonlinearly transformed data.
method Tensor network framework for analyzing fluctuation averaging in the presence of higher-order cumulant structure.
result Optimal averaged local law and full anisotropic local law for non-separable sample covariance matrices.
Reinforcement Learning optimizes low-thrust interplanetary trajectories under disturbances.
problem Designing robust interplanetary trajectories in the presence of disturbances.
method Reformulated as a Markov Decision Process, RL algorithm Proximal Policy Optimization trained on a deep neural network.
result Deep neural network provides robust nominal trajectory and guidance law.
Study Transformer layers under cross-entropy training using mean field control.
problem Understanding the behavior of Transformer layers in cross-entropy training.
method Continuous-depth mean field control analysis, treating depth as time and layer parameters as controls.
result Derivation of a Pontryagin condition for the limiting population problem, involving the softmax residual.
We use a control framework to analyze the digital vendor's profit maximization problem. The vendor captures market share by focusing costly effort on post-launch product maintenance, which influences user perception of the product and drives a revenue stream associated with product use. Our theoretical results show nec…
Robust Q-learning for mean-field control under Wasserstein uncertainty
problem Mean-field control under Wasserstein uncertainty
method Quantization-and-projection scheme with Wasserstein dual reformulation
result Convergence and finite-time iteration bounds
For controlled discrete-time stochastic processes we introduce a new class of dynamic risk measures, which we call process-based. Their main features are that they measure risk of processes that are functions of the history of a base process. We introduce a new concept of conditional stochastic time consistency and we …
AntLer anticipates future learning to improve control performance.
problem Improving control performance through online learning is not well understood.
method AntLer uses a probabilistic model to anticipate future learning and optimize control parameters.
result AntLer approximates optimal solutions with high probability.
New models explain heavy-tailed behavior in neural networks.
problem Heavy-tailed spectral densities in neural networks.
method High-temperature Marchenko-Pastur (HTMP) ensemble models.
result Heavy-tailed behavior arises from three factors: data structure, training temperature, and eigenvector entropy.
Develops a new approach to optimal control of stochastic systems.
problem Optimal control of stochastic nonlinear dynamical systems is challenging.
method Formulates optimal control as input estimation, using probabilistic inference and Expectation Maximization.
result Extracts time-varying linear Gaussian feedback controllers from the joint state-action distribution.
The paper synthesizes the mathematics of modeling the future.
problem Modeling the future
method Unified mathematical synthesis
result Explicit connection of classical objects into a unified forecasting calculus
Gaussian Process improves tracking control for unknown systems.
problem Challenges in perfect tracking control for real-world Euler-Lagrange systems.
method Employing Gaussian Process regression for data-driven model of unknown dynamics and adaptive feedback gains.
result Guaranteed globally bounded tracking error with specific probability.
This paper uses a kinetic approach to model financial agents and their impact on stock prices and wealth distribution.
problem Understanding power-laws in financial data and the causes behind them.
method A kinetic approach inspired by the Levy-Levy-Solomon model, incorporating model predictive control (MPC) for optimization.
result The stock price distribution exhibits power-law behavior for high-frequency traders and lognormal for long-term investors.
Study dynamic risk measures with distributional uncertainty using optimal transport.
problem Risk robustification under distributional uncertainty in Markovian models.
method Characterize risk measures via convex monotone semigroups and optimal transport costs.
result Identify generator and correction terms for dynamic risk measures under different scaling regimes.
Tools of the theory of critical phenomena, namely the scaling analysis and universality, are argued to be applicable to large complex web-like network structures. Using a detailed analysis of the real data of the International Trade Network we argue that the scaled link weight distribution has an approximate log-normal…
An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control term representing the local environmental pressure which avoids an exponential gro…