Related papers: Exact Fixed-Point Constraints in Neural-ODEs with …
We propose a novel second-order ODE as the continuous-time limit of a Riemannian accelerated gradient-based method on a manifold with curvature bounded from below. This ODE can be seen as a generalization of the ODE derived for Euclidean…
Is there any theoretical guarantee for the approximation ability of neural networks? The answer to this question is the "Universal Approximation Theorem for Neural Networks". This theorem states that a neural network is dense in a certain…
This study develops a fixed-time convergent saddle point dynamical system for solving min-max problems under a relaxation of standard convexity-concavity assumption. In particular, it is shown that by leveraging the dynamical systems…
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that…
Embedding nonlinear dynamical systems into artificial neural networks is a powerful new formalism for machine learning. By parameterizing ordinary differential equations (ODEs) as neural network layers, these Neural ODEs are…
State-of-the-art object pose estimation handles multiple instances in a test image by using multi-model formulations: detection as a first stage and then separately trained networks per object for 2D-3D geometric correspondence prediction…
This paper considers the fixed point problem for a nonexpansive mapping on a real Hilbert space and proposes novel line search fixed point algorithms to accelerate the search. The termination conditions for the line search are based on the…
Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…
Machine learning models can assign fixed predictions that preclude individuals from changing their outcome. Existing approaches to audit fixed predictions do so on a pointwise basis, which requires access to an existing dataset of…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
Neural ODE Processes approach the problem of meta-learning for dynamics using a latent variable model, which permits a flexible aggregation of contextual information. This flexibility is inherited from the Neural Process framework and…
We introduce a large scale analogue of the classical fixed-point property for continuous maps, which shall apply to coarse maps. We also develop a coarse version of degree for coarse maps on Euclidean spaces. Then, applying a coarse…
A new computationally simple method of imposing hard convex constraints on the neural network output values is proposed. The key idea behind the method is to map a vector of hidden parameters of the network to a point that is guaranteed to…
We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…
Global localisation from visual data is a challenging problem applicable to many robotics domains. Prior works have shown that neural networks can be trained to map images of an environment to absolute camera pose within that environment,…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
Learning neural implicit fields of 3D shapes is a rapidly emerging field that enables shape representation at arbitrary resolutions. Due to the flexibility, neural implicit fields have succeeded in many research areas, including shape…
Planning collision-free motions for robots with many degrees of freedom is challenging in environments with complex obstacle geometries. Recent work introduced the idea of speeding up the planning by encoding prior experience of successful…
Forward invariance is a long-studied property in control theory that is used to certify that a dynamical system stays within some pre-specified set of states for all time, and also admits robustness guarantees (e.g., the certificate holds…
We use fixed point theory to analyze nonnegative neural networks, which we define as neural networks that map nonnegative vectors to nonnegative vectors. We first show that nonnegative neural networks with nonnegative weights and biases can…