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.
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
The paper tackles safe exploration in RL by a conservative safety critic.
problem Safe exploration in reinforcement learning (RL) when partially trained policies are deployed.
method Learning a conservative safety estimate through a critic, provably bounding catastrophic failures.
result The approach provably converges to competitive task performance with significantly lower catastrophic failure rates.
Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a reduced model of such complex systems on the basis of insights alone. We propose a nov…
Conservation laws improve diffusion model training by optimizing likelihood.
problem Training diffusion models with denoising objectives.
method Developed conservation laws based on GEXIT functions for memoryless noise processes.
result Unified characterization of diffusion model likelihood, reducing training to learning marginal posteriors.
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.
Enhances HNNs for conservative systems with noisy data.
problem Modeling conservative systems with neural networks.
method Proposes a deep hidden physics model for continuous-time trajectory estimation.
result Integration scheme works well for HNNs, especially with low sampling rates.
Higher conservative training increases reward-hacking in reasoning models.
problem Reward hacking during online adaptation in reasoning models.
method Conservative offline training with varying levels of conservatism (β) was applied to a Qwen3-14B policy, and online adaptation was measured against a reward ensemble.
result Higher conservatism (β) increases reward-hacking damage, measured by the Goodhart gap and AUGC.
VaR-CPO optimizes VaR-constrained RL problems with conservative policy updates.
problem Optimizing VaR-constrained reinforcement learning problems.
method Combines Cantelli's inequality and trust-region framework for efficient and conservative optimization.
result Achieves zero constraint violations during training in feasible environments.
Analyzes symmetries in neural networks to predict learning dynamics.
problem Understanding the dynamics of neural network parameters during training.
method Unified theoretical framework based on symmetries and conservation laws.
result Symmetries impose geometric constraints on gradients and Hessians, leading to conservation laws.
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…
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.
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(λ) algorithm. result Peng's Q(λ) 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.
Unified neural network framework for context-aware Gaussian overbounds in uncertainty propagation.
problem Uncertainty quantification in safety-critical settings requires conservative bounds, but existing methods often fail to compose and are overly conservative.
method Proposes a learning framework that trains neural networks to produce context-aware Gaussian overbounds with provable conservatism.
result The method yields tighter bounds while maintaining conservatism on the enforced grid and in experiments.
Canary optimizes VaR-constrained RL problems with a conservative bound using Cantelli's inequality.
problem Optimizing reinforcement learning policies under VaR constraints in dense cost regimes.
method Employing Cantelli's inequality to create a conservative and smooth bound on VaR constraints based on moments of cost returns. Extending trust-region framework for worst-case bounds on policy improvement and constraint violation.
result Canary reliably satisfies VaR constraints with fewest violations and earliest permanent satisfaction, while maintaining reward competitiveness.
CQL learns conservative Q-functions to improve offline RL performance.
problem Leveraging large, static datasets in reinforcement learning without further interaction.
method Conservative Q-learning (CQL) which learns a conservative Q-function to lower-bound policy values.
result CQL substantially outperforms existing offline RL methods, often achieving 2-5 times higher final returns.
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.
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…
SBMs learn manifold-like structures by mixing samples with a non-conservative field.
problem How SBMs learn data distributions on low-dimensional manifolds.
method Investigating linear approximations and subspaces of local feature vectors during diffusion.
result SBMs mix samples by a non-conservative field within the manifold, maintaining manifold-like structure.
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.
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 study higher-order conservation laws of the non-linearizable elliptic Poisson equation ∂z∂zˉ∂2u=−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.
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.
Bayesian deep ensembles improve prediction accuracy in various settings.
problem Improving prediction accuracy of deep ensembles in out-of-distribution settings.
method Introducing a randomised, untrainable function to each ensemble member, enabling a posterior predictive distribution interpretation.
result Bayesian deep ensembles make more conservative predictions and outperform standard ensembles in various tasks.
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.
Gradient descent dynamics studied for DEQs in linear and single-index models.
problem Understanding gradient descent dynamics for DEQs.
method Rigorously studied gradient descent dynamics for DEQs in linear and single-index models.
result Gradient descent converges to a global minimizer for linear DEQs and single-index models.
BRAID fine-tunes diffusion models to optimize reward models in offline scenarios.
problem Combining generative modeling and model-based optimization in offline scenarios.
method Conservative fine-tuning of diffusion models using RL to optimize reward models.
result BRAID outperforms existing methods in offline data, avoiding invalid designs.
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…
Paper presents a deep reinforcement learning algorithm for online trading without offline training.
problem Developing a fully online trading algorithm without offline training.
method Double Deep Q-learning with Fast Learning Networks, defining terminal states for money conservation. result The algorithm outperforms random action trading and captures different market trends.
A new algorithm balances exploration and exploitation in online decision-making.
problem Balancing exploration and exploitation in online decision-making.
method Proposed C4-UCB algorithm incorporating conservative mechanism. result Proved n-step upper regret bound for two situations.
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.
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.
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…
Novel loss functions improve decision tree learning from noisy data.
problem Training decision trees with noisy labels.
method Introducing distribution losses and a new negative exponential loss.
result The negative exponential loss leads to efficient and robust decision tree learning.
There is a well-known example of integrable conservative system on S2, 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 S2 possessing an integral of fourth degree in moment…
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.
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.