arXiv research

New loss function helps learn unstable dynamical systems.

The complete invariant for gradient like Morse-Smale dynamical systems (vector fields and diffeomorphisms) on closed 4-manifolds are constructed. It is same as Kirby diagram in a case of polar vector field without fixed points of index 3.

GFM models neural network training as a dynamical system to forecast final weights.

Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.

Optimizes basis functions for learning dynamical systems from data.

Reinforcement learning is a promising approach to learning robotics controllers. It has recently been shown that algorithms based on finite-difference estimates of the policy gradient are competitive with algorithms based on the policy gradient theorem. We propose a theoretical framework for understanding this phenomen…

Weak correlations explain linear dynamics in deep learning models.

We prove that stochastic gradient descent efficiently converges to the global optimizer of the maximum likelihood objective of an unknown linear time-invariant dynamical system from a sequence of noisy observations generated by the system. Even though the objective function is non-convex, we provide polynomial running …

KSOS improves kernel learning for dynamical systems via global optimization.

Gradient Starvation causes neural networks to focus on a subset of features, leading to imbalance.

The topological classification of gradient like Morse-Smale vector fields and diffeomorphisms on 3-manifolds was obtained.

The paper presents a model-free method for stabilizing unknown control systems.

Equivalence of convex optimization, saddle-point problems, and variational inequalities is a well-established concept. The variational inequality (VI) is a static problem which is studied under dynamical settings using a framework called the projected dynamical system, whose stationary points coincide with the static s…

Study on dynamic curves with elastic energy and spontaneous curvature.

New framework for online control in evolving populations.

The Volterra lattice is considered. New gradient interpretation for this dynamical system is proposed. This interpretation seems to be more natural than existing ones.

This paper learns state, dynamics, and filtering algorithms together for data assimilation.

We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations which do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world and the reservation prices …

Greedy policy maximizes information in unknown linear systems.

We consider the problem of learning stabilizable systems governed by nonlinear state equation $h_{t+1}=φ(h_t,u_t;θ)+w_t$. Here $θ$ is the unknown system dynamics, $h_t$ is the state, $u_t$ is the input and $w_t$ is the additive noise vector. We study gradient based algorithms to learn the system dynamics $θ$ from samp…

We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.

Faster policy learning via continuous-time gradients.

AdaptOn achieves logarithmic regret in adaptive control of unknown partially observable linear systems.

LEM efficiently models long-term sequences with gradients.

A new DDR framework learns low-dimensional data representations using dynamical systems.

New algorithm converges to optimal filter for predicting linear dynamical systems.

Gradient flow solves optimal mass transport for covariance matrices.

BLADE uses Bayesian methods to discover complex systems from scarce data.

Recent research on accelerated gradient methods of use in optimization has demonstrated that these methods can be derived as discretizations of dynamical systems. This, in turn, has provided a basis for more systematic investigations, especially into the geometric structure of those dynamical systems and their structur…

A method uses non-autonomous equations to classify time signals efficiently.

New model-free algorithm achieves similar LQR regret guarantees.

Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical integration. However, for many real-world applications, only sparse observations are avail…

RNNs struggle with chaotic dynamics due to exploding gradients, but we found a way to optimize training.

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computationa…

Gradient-free framework for Bayesian experimental design in complex systems.

This work learns models for population dynamics using variational methods and higher-order quadrature.

We study the dynamics of the vector field on an open surface given by the gradient of a Green's function. This dynamical approach enables us to show that this field induces an invariant decomposition of the surface as the union of a disk and a 1-skeleton that encodes the topology of the surface. We analyze the structur…

Policy gradient methods converge for LQR problems with noisy state dynamics.

The linear quadratic regulator (LQR) problem has reemerged as an important theoretical benchmark for reinforcement learning-based control of complex dynamical systems with continuous state and action spaces. In contrast with nearly all recent work in this area, we consider multiplicative noise models, which are increas…

The extended Kalman filter is perhaps the most standard tool to estimate in real time the state of a dynamical system from noisy measurements of some function of the system, with extensive practical applications (such as position tracking via GPS). While the plain Kalman filter for linear systems is well-understood, th…

NOHD optimizes multi-agent systems by decomposing dynamics into irrotational and solenoidal components.

The paper studies a gradient system on a beta statistical manifold, proving integrability and deriving explicit expressions.

We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient descent, coordinate gradient descent, proximal coordinate gradient, and Newton's …

Study local convergence of GDA for training GANs with kernel-based discriminators.

Many recent Markov chain Monte Carlo (MCMC) samplers leverage continuous dynamics to define a transition kernel that efficiently explores a target distribution. In tandem, a focus has been on devising scalable variants that subsample the data and use stochastic gradients in place of full-data gradients in the dynamic s…

We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow entropies", they describe the polynomial growth rate of the number of balls (fo…

A dynamical neural network consists of a set of interconnected neurons that interact over time continuously. It can exhibit computational properties in the sense that the dynamical system's evolution and/or limit points in the associated state space can correspond to numerical solutions to certain mathematical optimiza…

New method reconstructs non-equilibrium stochastic systems from data.