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
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48 results for “conservative inputs”
We consider the problem of estimating the set of all inputs that leads a system to some particular behavior. The system is modeled by an expensive-to-evaluate function, such as a computer experiment, and we are interested in its excursion set, i.e. the set of points where the function takes values above or below some p…
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.
Paper proposes COM-QEL to avoid overoptimistic solutions in offline optimization.
problem Incorrect extrapolation of objective values in unexplored regions.
method Integrates quantum extremal learning with conservative objective models.
result COM-QEL finds higher true objective values compared to QEL.
Conservative objective models are a special kind of contrastive divergence-based energy modelstat.ML
Theoretical proof shows COMs are a type of contrastive divergence model with improved sampling.
problem Improving sampling quality in offline model-based optimization.
method Showed COMs are contrastive divergence models, proposed Langevin MCMC sampler, and decoupled model.
result Improved sampling quality achieved by decoupling model and using Langevin MCMC.
Unified routing and arbitrage with concave continuation.
problem Combining routing and arbitrage in financial markets.
method Extending AMM trade functions to negative inputs via concave continuation.
result Unified approach unifies routing and arbitrage.
We investigate the effects of the unsupervised pre-training method under the perspective of information theory. If the input distribution displays multiple views of the supervision, then unsupervised pre-training allows to learn hierarchical representation which communicates these views across layers, while disentangli…
Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how fast the energy contained in the propagated signals (a.k.a. feature maps) decays across laye…
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.
Safe exploration method for RL under disturbance ensures safety with probabilistic guarantees.
problem Safe reinforcement learning in real environments with disturbance.
method Uses partial prior knowledge and conservative inputs to ensure state constraint satisfaction.
result Guaranteed safety with pre-specified probability in the presence of stochastic disturbance.
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.
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.
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…
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…
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 …
We introduce Minimal Achievable Sufficient Statistic (MASS) Learning, a training method for machine learning models that attempts to produce minimal sufficient statistics with respect to a class of functions (e.g. deep networks) being optimized over. In deriving MASS Learning, we also introduce Conserved Differential I…
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…
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…
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…
Conformal prediction is a technique for constructing prediction intervals that attain valid coverage in finite samples, without making distributional assumptions. Despite this appeal, existing conformal methods can be unnecessarily conservative because they form intervals of constant or weakly varying length across the…
Paper extends Bayes Theorem for interval probability estimates.
problem Real-world input probabilities are often interval estimates, not precise.
method Developed IT2 version of Bayes Theorem and a novel algorithm for encoding intervals.
result Conservative method avoids invalid output results from inconsistent input.
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.
Study connects surface classes to conservation laws.
problem Understanding CMC surfaces in space forms.
method Relates moment class to cohomology class, shows variational origin.
result Both classes have a variational origin as Noether currents.
New framework models non-conservative stochastic processes without energy conservation constraints.
problem Existing Schrödinger Bridge methods are limited by energy-conservation assumptions.
method Introduces non-conservative generalized Schrödinger bridge (NCGSB) based on contact Hamiltonian mechanics.
result Contact Wasserstein geodesic (CWG) provides a broader class of real-world stochastic processes.
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…
A new AI optimization method uses energy-conserving dynamics inspired by Born-Infeld theory.
problem Optimization challenges in non-convex loss functions and machine learning tasks.
method Discretization of Born-Infeld dynamics for energy-conserving Hamiltonian optimization.
result The method avoids high local minima and outperforms traditional methods in shallow valleys.
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,…
StepMix algorithm ensures safe exploration in reinforcement learning with near-optimal performance.
problem Conservative exploration in reinforcement learning under episode-wise constraints.
method StepMix algorithm balances exploitation and exploration while ensuring episode-wise conservative constraint.
result StepMix achieves near-optimal regret order as in the constraint-free setting.
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…