In Hamiltonian mechanics, a (continuous) symmetry leads to conserved quantity, which is a function on (extended) phase space. In Nambu mechanics, a straightforward consequence of symmetry is just a relative integral invariant, a differential form which only upon integration over a cycle provides a conserved real number…
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48 results for “relevance conservation”
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…
MambaLRP enhances Mamba models' explainability and performance.
problem Lack of transparency in Mamba models for real-world applications.
method Layer-wise Relevance Propagation (LRP) with relevance conservation axioms.
result MambaLRP provides stable and reliable explanations for Mamba models.
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…
A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a variational sequence such that the generalized Jacobi morphism is naturally self-ad…
The statistical mechanics approach to wealth distribution is based on the conservative kinetic multi-agent model for money exchange, where the local interaction rule between the agents is analogous to the elastic particle scattering process. Here, we discuss the role of a class of conservative local operators, and we s…
Study maps research streams in biodiversity finance, identifies key areas.
problem Biodiversity loss and need for finance to reverse trends.
method Quantitative bibliometric analysis of 189,456 references.
result Identifies eight primary research streams in biodiversity finance.
Proposes a method to improve few-shot transfer in off-dynamics RL.
problem Traditional RL struggles with transferring policies between environments with different dynamics.
method Introduces a penalty to regulate source-trained policies in target environments with limited data.
result Improves performance in various off-dynamics RL scenarios compared to existing methods.
We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first chapter contains an introduction of the classical Poincare-Cartan form in the context of EDS, follow…
The purpose of this paper is to identify a relevant statistical correlation between rate of default, RD, and loss given default, LGD, in a major Brazilian financial institution Retail Home Equity exposure rated using the IRB approach, so that we may find a causal relationship between the two risk parameters. Therefore,…
Algorithm learns latent variables for thermodynamically-consistent deep neural networks.
problem Predicting time evolution of large-scale physical systems with thermodynamic consistency.
method Sparse autoencoders and structure-preserving neural networks.
result Method conserves total energy and entropy inequality for both conservative and dissipative systems.
Theoretical analysis confirms non-conservative algorithms can converge to optimal policies.
problem Theoretical guarantees for non-conservative reinforcement learning algorithms.
method Theoretical analysis of Peng's Q() algorithm.
result Peng's Q() converges to an optimal policy under certain conditions.
Study finds conserved quantities for two types of curves on conformal sphere.
problem Identifying conserved quantities for specific types of curves on a conformal sphere.
method Used parallel tractor and Lagrangian formalism to compute conserved quantities.
result Found relation between conserved quantities of two curve types.
Survey on conservation laws for geometric PDEs.
problem Modeling polyharmonic maps.
method Conservation law approach.
result Overview of conservation laws in geometric PDEs.
The article discusses conservation laws for polyharmonic maps and their applications.
problem Understanding conservation laws for polyharmonic maps.
method Recalling the stress-energy tensor and showing conservation laws with Killing vector fields.
result 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.
problem Conservative bandits and reinforcement learning problems.
method Reduction technique to calculate necessary and sufficient budget from baseline policy.
result Improved lower and upper bounds for various conservative settings.
Paper proves impossible for large language models to control hallucinations without sacrificing other properties.
problem Achieving truthful knowledge representation, semantic information conservation, and knowledge-constrained optimality simultaneously in large language models.
method Modeling inference as an auction of ideas, using mechanism design, proper scoring rules, and transformer architecture analysis.
result No LLM can simultaneously achieve all four essential properties without violating at least one.
Geometry and Conservation Laws for a Class of Second-Order Parabolic Equations II: Conservation Lawsmath.AP
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.
problem Conservation law for a specific system with a vanishing characteristic.
method Analyzing overdetermined system with given characteristics.
result Non-trivial conservation law despite vanishing characteristic.
Contact Lie systemsmath-ph
Contact Lie systems analyze integral curves of Hamiltonian vector fields.
problem Analyzing integral curves of Hamiltonian vector fields.
method Define and study contact Lie systems, including conservative systems.
result Develop Liouville theorems, contact reductions, and Gromov non-squeezing theorems.
This work connects symmetries and conserved quantities in machine learning.
problem Improving machine learning models by learning conserved quantities.
method Using Noether's theorem, learn symmetries and conserved quantities directly from data.
result Correctly identifies conserved quantities and improves model performance.
Proposes a conservative exploration method for RL agents.
problem Guaranteeing performance of exploratory policies in RL.
method Importance sampling for off-policy policy evaluation.
result Derives a regret bound ensuring no conservative constraint violation.
Conservation law for weakly harmonic mappings in high dimensions.
problem Conservation law for harmonic mappings in supercritical dimensions.
method Partial extension of Rivière's conservation law with Lorentz integrability condition.
result Conservation law for weakly harmonic mappings in supercritical dimensions.
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 …
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 introduce a new elliptic operator on null hypersurfaces of four-dimensional Lorentzian manifolds. This operator depends on the first and second fundamental forms of the sections of a foliation of the null hypersurface and its novelty originates from its covariant transformation under change of foliation. It thus pro…
Higher-order conservation laws for the non-linear Poisson equation via the characteristic cohomologymath.DG
We study higher-order conservation laws of the non-linearizable elliptic Poisson equation as elements of the characteristic cohomology of the associated exterior differential system. The theory of characteristic cohomology determines a normal form for diffe…
Rethinking Financial Contagionq-fin.RM
How, and to what extent, does an interconnected financial system endogenously amplify external shocks? This paper attempts to reconcile some apparently different views emerged after the 2008 crisis regarding the nature and the relevance of contagion in financial networks. We develop a common framework encompassing seve…
Conservation laws for even order elliptic systems in the critical dimension -- a new approachmath.AP
New conservation laws found for polyharmonic maps in critical dimension.
problem Existence of conservation laws for polyharmonic maps in critical dimension.
method Small perturbation of Uhlenbeck's gauge fixing matrix.
result Existence of conservation laws for elliptic systems of even order 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.
problem Conservation laws in real-world systems.
method Extending LSTM's inductive bias to conserve mass.
result MC-LSTM sets new state-of-the-art for predicting peak flows.
The paper studies symmetries and conservation laws of non-diagonalisable hydrodynamic systems.
problem Integrating non-diagonalisable hydrodynamic systems of partial differential equations.
method Analysis of gl-regular Nijenhuis operators, splitting Theorem for symmetries and conservation laws, relationship between symmetries and conservation laws.
result The system of partial differential equations is integrable in quadratures.
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.
problem Balancing exploration and exploitation in online decision-making.
method Proposed -UCB algorithm incorporating conservative mechanism.
result Proved n-step upper regret bound for two situations.
The characteristic gluing problem and conservation laws for the wave equation on null hypersurfacesgr-qc
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 …
Mass Conservation on Rails -- Rethinking Physics-Informed Learning of Ice Flow Vector Fieldsphysics.ao-ph
New neural network enforces mass conservation for better ice flow predictions.
problem Reliably project future sea level rise by improving ice sheet model inputs.
method Proposes divergence-free neural networks (dfNNs) enforcing local mass conservation.
result dfNNs yield more reliable ice flux estimates compared to other models.
Proposes a new feature selection method integrating feature relationships.
problem Feature selection in machine learning models.
method Integrates feature-feature and feature-target relationships via penalized mRMR.
result Correctly identifies inactive features, reducing false discoveries.
The study finds resonance points in polarised curves with polynomial conserved quantities.
problem Finding resonance points in polarised curves with polynomial conserved quantities.
method Using the non-orthogonality assumption on the conserved quantity, the study deduces the existence of resonance points.
result Every finite type polarised curve in the conformal 2-sphere with a polynomial conserved quantity admits a resonance point.
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…
The paper tackles causal rule discovery from observational data.
problem Challenges in inferring causal effects from observational data due to confounding factors and high variance.
method Measures causal effect from observational data, providing graphical criteria and a conservative estimator.
result Proposes an efficient algorithm that maximises the estimator and discovers meaningful causal rules.
There is a well-known example of integrable conservative system on , 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 possessing an integral of fourth degree in moment…
Data symmetries in neural networks can generate conserved quantities.
problem Conservation laws in neural networks
method Using tensorizable networks
result Data augmentation can induce conserved quantities
Developing tools for computing string amplitudes with hyperbolic vertices.
problem Computing off-shell string amplitudes with new vertices.
method Constructing local coordinates and investigating limits for hyperbolic three-string vertex.
result Derived conservation laws and performed sample computations.
RORL improves offline RL robustness with conservative smoothing.
problem Distribution shift and robustness issues in offline RL.
method RORL introduces regularization and conservative smoothing for robustness.
result RORL achieves state-of-the-art performance and robustness to adversarial perturbations.
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.
problem Ambiguities in defining conserved quantities like angular momentum at null infinity.
method New definitions based on Chen-Wang-Yau quasilocal conserved quantities and optimal isometric embedding theory.
result These new definitions are free of supertranslation ambiguity and limit to classical Bondi mass.
This work extends balancing to various simulation-based inference algorithms for more conservative posterior approximations.
problem Overconfident posterior approximations in simulation-based inference.
method Introduces a balanced version of neural posterior estimation and contrastive neural ratio estimation.
result Balanced versions tend to produce conservative posterior approximations on various benchmarks.
Discover conservation laws from trajectories using a neural network.
problem Finding invariants and conservation laws from large-scale data without prior knowledge.
method ConservNet, a neural network trained with noise-variance loss to discover hidden invariants in grouped multi-dimensional observables.
result Successfully discovers underlying invariants from simulated and real-world systems.