arXiv research

Algorithm improves wildlife protection patrols.

Deep learning system speeds up wildlife species identification from camera trap images.

We are losing biodiversity at an unprecedented scale and in many cases, we do not even know the basic data for the species. Traditional methods for wildlife monitoring are inadequate. Development of new computer vision tools enables the use of images as the source of information about wildlife. Social media is the rich…

StatEcoNet models species distribution using neural networks to correct observation errors.

Algorithm learns to play against unknown opponents in sequential games.

WILDS 2.0 expands benchmark datasets for unsupervised adaptation.

Theoretical analysis confirms non-conservative algorithms can converge to optimal policies.

Study finds conserved quantities for two types of curves on conformal sphere.

Survey on conservation laws for geometric PDEs.

The article discusses conservation laws for polyharmonic maps and their applications.

Paper presents a reduction-based framework for conservative bandits and RL with improved lower and upper bounds.

I consider the existence and structure of conservation laws for the general class of evolutionary scalar second-order differential equations with parabolic symbol. First I calculate the linearized characteristic cohomology for such equations. This provides an auxiliary differential equation satisfied by the conservatio…

Non-trivial conservation law found for a specific system.

This work connects symmetries and conserved quantities in machine learning.

Proposes a conservative exploration method for RL agents.

The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation law has a unique representative. The structure of this subspace naturally gives …

Conservation law for weakly harmonic mappings in high dimensions.

Given a vector field on a manifold M, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitable submanifolds are constant under time evolution, the Kelvin circulation theorem being a well-known special case. More generally, conserved…

We study higher-order conservation laws of the non-linearizable elliptic Poisson equation $\frac{{\partial}^2 u}{\partial z \partial \bar{z}} = -f(u)$ as elements of the characteristic cohomology of the associated exterior differential system. The theory of characteristic cohomology determines a normal form for diffe…

New conservation laws found for polyharmonic maps in critical dimension.

A challenging problem in complex networks is the network reconstruction problem from data. This work deals with a class of networks denoted as conserved networks, in which a flow associated with every edge and the flows are conserved at all non-source and non-sink nodes. We propose a novel polynomial time algorithm to …

MC-LSTM extends LSTM to conserve mass in neural networks.

We propose a generalization of the best arm identification problem in stochastic multi-armed bandits (MAB) to the setting where every pull of an arm is associated with delayed feedback. The delay in feedback increases the effective sample complexity of standard algorithms, but can be offset if we have access to partial…

The paper studies symmetries and conservation laws of non-diagonalisable hydrodynamic systems.

We present a connection between the Killing fields that arise in the loop-group approach to integrable systems and conservation laws viewed as elements of the characteristic cohomology. We use the connection to generate the complete set of conservation laws (as elements of the characteristic cohomology) for the Tzitzei…

A new algorithm balances exploration and exploitation in online decision-making.

We obtain necessary and sufficient conditions for the existence of "conservation laws" on null hypersurfaces for the wave equation on general four-dimensional Lorentzian manifolds. Examples of null hypersurfaces exhibiting such conservation laws include the standard null cones of Minkowski spacetime and the degenerate …

New neural network enforces mass conservation for better ice flow predictions.

The study finds resonance points in polarised curves with polynomial conserved quantities.

Following an approach of the second author for conformally invariant variational problems in two dimensions, we show in four dimensions the existence of a conservation law for fourth order systems, which includes both intrinsic and extrinsic biharmonic maps. With the help of this conservation law we prove the continuit…

There is a well-known example of integrable conservative system on $S^2$, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev proposed a one-parameter family of examples of conservative systems on $S^2$ possessing an integral of fourth degree in moment…

Data symmetries in neural networks can generate conserved quantities.

RORL improves offline RL robustness with conservative smoothing.

We propose a dynamical model for business cycle based on an optimal DI model. In the model there exists a conserved quantity, which corresponds to the total energy in a dynamical system. We found that the business cycle with the period 6 or 7 years is nicely reproduced, since the model predicts a periodic motion in the…

New definitions of conserved quantities at null infinity resolve ambiguities in general relativity.

This work extends balancing to various simulation-based inference algorithms for more conservative posterior approximations.

Discover conservation laws from trajectories using a neural network.

Study connects surface classes to conservation laws.

New framework models non-conservative stochastic processes without energy conservation constraints.

A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.

Noether's First Theorem yields conservation laws for Lagrangians with a variational symmetry group. The explicit formulae for the laws are well known and the symmetry group is known to act on the linear space generated by the conservation laws. In recent work the authors showed the mathematical structure behind both th…

Dan Reznik discovered conserved quantities for ellipses using billiard maps.

Framework infers conservation laws from trained neural networks.

For one-dimensional systems of conservation laws admitting two additional conservation laws we assign a ruled surface of codimension two in projective space. We call two such systems dual if the corresponding ruled surfaces are dual. We show that a Hamiltonian system is autodual, its ruled surface sits in some quadric,…

A new algorithm for contextual combinatorial bandits reduces regret.

StepMix algorithm ensures safe exploration in reinforcement learning with near-optimal performance.

In the classical Lagrangian approach to conservation laws of gauge-natural field theories a suitable (vector) density is known to generate the so--called {\em conserved Noether currents}. It turns out that along any section of the relevant gauge--natural bundle this density is the divergence of a skew--symmetric (tenso…

Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a peculiarity, namely, the closed inexact exterior forms are obtained from that. The closur…