Related papers: Discovering conservation laws from trajectories vi…

In this document, a neural network is employed in order to estimate the solution of the initial value problem in the context of non linear trajectories. Such trajectories can be subject to gravity, thrust, drag, centrifugal force,…

We assume that a sufficiently large database is available, where a physical property of interest and a number of associated ruling primitive variables or observables are stored. We introduce and test two machine learning approaches to…

Understanding and following directions provided by humans can enable robots to navigate effectively in unknown situations. We present FollowNet, an end-to-end differentiable neural architecture for learning multi-modal navigation policies.…

Energy conservation is a basic physics principle, the breakdown of which often implies new physics. This paper presents a method for data-driven "new physics" discovery. Specifically, given a trajectory governed by unknown forces, our…

We develop an analytical framework for understanding how the generated distribution evolves during diffusion model training. Leveraging a Gaussian-equivalence principle, we solve the full-batch gradient-flow dynamics of linear and…

We present a new approach and a novel architecture, termed WSNet, for learning compact and efficient deep neural networks. Existing approaches conventionally learn full model parameters independently and then compress them via ad hoc…

Traditional algorithms for compressive sensing recovery are computationally expensive and are ineffective at low measurement rates. In this work, we propose a data driven non-iterative algorithm to overcome the shortcomings of earlier…

Magnetic-anomaly navigation, leveraging small-scale variations in the Earth's magnetic field, is a promising alternative when GPS is unavailable or compromised. Airborne systems face a key challenge in extracting geomagnetic field data: the…

Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…

Matching images and sentences demands a fine understanding of both modalities. In this paper, we propose a new system to discriminatively embed the image and text to a shared visual-textual space. In this field, most existing works apply…

Practitioners often face the challenge of deploying prediction models in new environments with shifted distributions of covariates and responses. With observational data, such shifts are often driven by unobserved confounding, and can in…

In this paper, we provide an overview of a common phenomenon, condensation, observed during the nonlinear training of neural networks: During the nonlinear training of neural networks, neurons in the same layer tend to condense into groups…

The modeling of realistic magnetic materials requires the inclusion of defects. Based on the pseudospectral Landau-Lifshitz description of magnetisation dynamics, we propose a statistical model that takes into account defects, specifically…

Inspired by the ConvNets with structured hidden representations, we propose a Tensor-based Neural Network, TCNN. Different from ConvNets, TCNNs are composed of structured neurons rather than scalar neurons, and the basic operation is neuron…

Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of…

This paper presents an end-to-end approach for tracking static and dynamic objects for an autonomous vehicle driving through crowded urban environments. Unlike traditional approaches to tracking, this method is learned end-to-end, and is…

Latent dynamics discovery is challenging in extracting complex dynamics from high-dimensional noisy neural data. Many dimensionality reduction methods have been widely adopted to extract low-dimensional, smooth and time-evolving latent…

Transformation groups, such as translations or rotations, effectively express part of the variability observed in many recognition problems. The group structure enables the construction of invariant signal representations with appealing…