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Found 39 papers, 11 papers with code
Computing committor functions for the study of rare events using deep learning with importance sampling
The committor function is a central object of study in understanding transitions between metastable states in complex systems.
A Brief Survey on the Approximation Theory for Sequence Modelling
We survey current developments in the approximation theory of sequence modelling in machine learning.
On the Universal Approximation Property of Deep Fully Convolutional Neural Networks
We study the approximation of shift-invariant or equivariant functions by deep fully convolutional networks from the dynamical systems perspective.
A Recursively Recurrent Neural Network (R2N2) Architecture for Learning Iterative Algorithms
Meta-learning of numerical algorithms for a given task consist of the data-driven identification and adaptation of an algorithmic structure and the associated hyperparameters.
Fast Bayesian Optimization of Needle-in-a-Haystack Problems using Zooming Memory-Based Initialization (ZoMBI)
Needle-in-a-Haystack problems exist across a wide range of applications including rare disease prediction, ecological resource management, fraud detection, and material property optimization.
Deep Neural Network Approximation of Invariant Functions through Dynamical Systems
We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems.
Self-Healing Robust Neural Networks via Closed-Loop Control
While numerous attack and defense techniques have been developed, this work investigates the robustness issue from a new angle: can we design a self-healing neural network that can automatically detect and fix the vulnerability issue by itself?
Principled Acceleration of Iterative Numerical Methods Using Machine Learning
Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them.
Tackling Data Scarcity with Transfer Learning: A Case Study of Thickness Characterization from Optical Spectra of Perovskite Thin Films
Transfer learning increasingly becomes an important tool in handling data scarcity often encountered in machine learning.
From Optimization Dynamics to Generalization Bounds via Łojasiewicz Gradient Inequality
Optimization and generalization are two essential aspects of statistical machine learning.
Computing the Invariant Distribution of Randomly Perturbed Dynamical Systems Using Deep Learning
The potential component of the decomposition gives the generalized potential.
On the approximation properties of recurrent encoder-decoder architectures
Our results provide the theoretical understanding of approximation properties of the recurrent encoder-decoder architecture, which characterises, in the considered setting, the types of temporal relationships that can be efficiently learned.
Gradient-based Meta-solving and Its Applications to Iterative Methods for Solving Differential Equations
In science and engineering applications, it is often required to solve similar computational problems repeatedly.
Short optimization paths lead to good generalization
Through our approach, we show that, with a proper initialization, gradient flow converges following a short path with an explicit length estimate.
Unraveling Model-Agnostic Meta-Learning via The Adaptation Learning Rate
In this paper, we study the effect of the adaptation learning rate in meta-learning with mixed linear regression.
Approximation Theory of Convolutional Architectures for Time Series Modelling
We study the approximation properties of convolutional architectures applied to time series modelling, which can be formulated mathematically as a functional approximation problem.
Adversarial Invariant Learning
To the best of our knowledge, this is one of the first to adopt differentiable environment splitting method to enable stable predictions across environments without environment index information, which achieves the state-of-the-art performance on datasets with strong spurious correlation, such as Colored MNIST.
Personalized Algorithm Generation: A Case Study in Learning ODE Integrators
As a case study, we develop a machine learning approach that automatically learns effective solvers for initial value problems in the form of ordinary differential equations (ODEs), based on the Runge-Kutta (RK) integrator architecture.
QROSS: QUBO Relaxation Parameter Optimisation via Learning Solver Surrogates
In this way, we are able capture the common structure of the instances and their interactions with the solver, and produce good choices of penalty parameters with fewer number of calls to the QUBO solver.
Towards Robust Neural Networks via Close-loop Control
We connect the robustness of neural networks with optimal control using the geometrical information of underlying data to design the control objective.
Amata: An Annealing Mechanism for Adversarial Training Acceleration
However, conducting adversarial training brings much computational overhead compared with standard training.
A Data Driven Method for Computing Quasipotentials
The quasipotential is a natural generalization of the concept of energy functions to non-equilibrium systems.
Optimising Stochastic Routing for Taxi Fleets with Model Enhanced Reinforcement Learning
The future of mobility-as-a-Service (Maas)should embrace an integrated system of ride-hailing, street-hailing and ride-sharing with optimised intelligent vehicle routing in response to a real-time, stochastic demand pattern.
On the Curse of Memory in Recurrent Neural Networks: Approximation and Optimization Analysis
We study the approximation properties and optimization dynamics of recurrent neural networks (RNNs) when applied to learn input-output relationships in temporal data.
OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle
We further apply this method to study Rayleigh-Benard convection and learn Lorenz-like low dimensional autonomous reduced order models that capture both qualitative and quantitative properties of the underlying dynamics.
An invertible crystallographic representation for general inverse design of inorganic crystals with targeted properties
Realizing general inverse design could greatly accelerate the discovery of new materials with user-defined properties.
Optimization in Machine Learning: A Distribution Space Approach
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.
Collaborative Inference for Efficient Remote Monitoring
While current machine learning models have impressive performance over a wide range of applications, their large size and complexity render them unsuitable for tasks such as remote monitoring on edge devices with limited storage and computational power.
Embedding physics domain knowledge into a Bayesian network enables layer-by-layer process innovation for photovoltaics
Process optimization of photovoltaic devices is a time-intensive, trial-and-error endeavor, which lacks full transparency of the underlying physics and relies on user-imposed constraints that may or may not lead to a global optimum.
Deep Learning via Dynamical Systems: An Approximation Perspective
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective.
Computing Committor Functions for the Study of Rare Events Using Deep Learning
The committor function is a central object of study in understanding transitions between metastable states in complex systems.
Distributed Optimization for Over-Parameterized Learning
Moreover, we show that the more local updating can reduce the overall communication, even for an infinity number of steps where each node is free to update its local model to near-optimality before exchanging information.
On the Convergence and Robustness of Batch Normalization
Despite its empirical success, the theoretical underpinnings of the stability, convergence and acceleration properties of batch normalization (BN) remain elusive.
Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations
We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with small noise parameters.
A Quantitative Analysis of the Effect of Batch Normalization on Gradient Descent
Despite its empirical success and recent theoretical progress, there generally lacks a quantitative analysis of the effect of batch normalization (BN) on the convergence and stability of gradient descent.
A Mean-Field Optimal Control Formulation of Deep Learning
This paper introduces the mathematical formulation of the population risk minimization problem in deep learning as a mean-field optimal control problem.
An Optimal Control Approach to Deep Learning and Applications to Discrete-Weight Neural Networks
Deep learning is formulated as a discrete-time optimal control problem.
Maximum Principle Based Algorithms for Deep Learning
The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms.
Stochastic modified equations and adaptive stochastic gradient algorithms
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations.
