Unified q-learning for mean-field jump-diffusion models with unobservable population distribution.
problem Continuous-time q-learning in mean-field jump-diffusion models with unobservable population distribution.
method Proposed decoupled Iq-function for unified policy evaluation in MFG and MFC problems; unified q-learning algorithm based on test policies and averaged martingale orthogonality condition.
result Unified policy evaluation rule for MFG and MFC problems based on decoupled Iq-function.
The paper extends macroscopic market making to stochastic games, revealing properties and solving equations.
problem Price competition among market makers in a stochastic game setting.
method Extension of macroscopic market making framework to stochastic games, introducing multidimensional characteristic equations.
result New well-posedness results for forward-backward stochastic differential equations.
New equations simplify gauge-theoretic Khovanov homology solutions.
problem Solving the Haydys-Witten equations for Khovanov homology.
method Introduced decoupled version of Haydys-Witten equations; investigated asymptotic behavior.
result Decoupled equations simplify analysis of full equations on manifolds with ends and boundaries.
New algorithms for interpreting complex multivariate functions.
problem Hard interpretation of multivariate functions due to many parameters.
method Filtered tensor decompositions of derivative information.
result Nonparametric estimates of smooth decoupled functions.
Study shows how large neural networks avoid overfitting through decoupling of feature learning and complexity growth.
problem Understanding inductive bias and generalization in large neural networks.
method Dynamical mean field theory applied to large two-layer networks.
result Training dynamics of large networks exhibit a separation of timescales, decoupling feature learning and overfitting.
Capacity analysis has been recently introduced as a way to analyze how linear models distribute their modelling capacity across the input space. In this paper, we extend the notion of capacity allocation to the case of neural networks with non-linear layers. We show that under some hypotheses the problem is equivalent …
Inner product-based convolution has been a central component of convolutional neural networks (CNNs) and the key to learning visual representations. Inspired by the observation that CNN-learned features are naturally decoupled with the norm of features corresponding to the intra-class variation and the angle correspond…
Decouples moduli groups in heterotic string theory cohomology.
problem Decomposing moduli groups in heterotic string theory cohomology.
method Computing cohomology groups at the standard embedding and showing their direct sum decomposition.
result Decomposes moduli groups into a direct sum of cohomologies at the standard embedding.
We present two instances, L-GAE and L-VGAE, of the variational graph auto-encoding family (VGAE) based on separating feature propagation operations from graph convolution layers typically found in graph learning methods to a single linear matrix computation made prior to input in standard auto-encoder architectures. Th…
In this paper we consider the field equations for linearized gravity and other integer spin fields on the Kerr spacetime, and more generally on spacetimes of Petrov type D. We give a derivation, using the GHP formalism, of decoupled field equations for the linearized Weyl scalars for all spin weights and identify the g…
We construct a geometric structure on deformed supermanifolds as a certain subalgebra of the vector fields. In the classical limit we obtain a decoupling of the infinitesimal odd and even transformations, whereas in the semiclassical limit the result is a representation of the supersymmetry algebra. In the case of mass…
Constructs coordinates to diagonalize Toda flow on matrices with simple spectrum.
problem Diagonalizing the Toda flow on matrices with simple spectrum.
method Lie theoretic methods applied to complex semisimple Lie algebras and their real forms.
result Decouples the Toda vector field into simpler components.
A close relationship between the classical Hamilton-Jacobi theory and the kinematic reduction of control systems by decoupling vector fields is shown in this paper. The geometric interpretation of this relationship relies on new mathematical techniques for mechanics defined on a skew-symmetric algebroid. This geometric…
We investigate finite-time decoupled convergence in nonlinear two-time-scale stochastic approximation.
problem Achieving decoupled convergence in nonlinear two-time-scale stochastic approximation.
method Nested local linearity assumption, suitable step size selection, convergence analysis of matrix cross term, fourth-order moment convergence rates.
result Finite-time decoupled convergence rates can be achieved in nonlinear two-time-scale stochastic approximation with proper step size selection.
Spectral decoupling improves neural network generalization in medical imaging.
problem Poor generalization of neural networks trained on medical imaging data.
method Spectral decoupling, a regularization technique that encourages learning more features.
result Spectral decoupling increases network robustness and performance on external datasets.
VecMol generates 3D molecules as continuous vector fields, overcoming modality and geometry constraints.
problem Challenges in generating 3D molecules, especially in drug discovery and materials science.
method VecMol reimagines molecular representation by modeling 3D molecules as continuous vector fields over Euclidean space, parameterized by a neural field and generated using a latent diffusion model.
result Vector-field-based representations show promise for 3D molecular generation, validated on benchmarks.
Decoupled GCN is shown to be equivalent to label propagation.
problem Improving semi-supervised node classification in graph learning.
method The paper proves the equivalence of decoupled GCN and label propagation, and proposes a new method named PTA.
result Decoupled GCN is equivalent to two-step label propagation and can automatically assign weights to pseudo-labels.
In the artificial intelligence field, learning often corresponds to changing the parameters of a parameterized function. A learning rule is an algorithm or mathematical expression that specifies precisely how the parameters should be changed. When creating an artificial intelligence system, we must make two decisions: …
Bayesian ODEs with Gaussian processes infer unknown dynamics from data.
problem Estimating unknown continuous-time system dynamics from data.
method Bayesian nonparametric model using Gaussian processes, sparse variational inference, probabilistic shooting.
result Posterior predictive uncertainty scores outperform alternative methods on multiple ODE learning tasks.
Improved sampling from mean-field stationary distributions.
problem Sampling from the stationary distribution of mean-field SDEs.
method Decoupling the problem into two aspects: approximation of mean-field SDE and sampling from finite-particle distribution.
result Improved guarantees in various settings, including optimizing neural networks.
Compositional diffusion models simulate coupled PDEs efficiently.
problem Efficiently simulating long-horizon coupled PDE systems.
method Diffusion models trained on decoupled data are composed at inference time.
result Compositional diffusion models recover coupled trajectories with low error.
Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
problem Proving convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.
method Differentiation-based approach to handle Z process, uniformly controlling Lipschitz continuity of decoupling fields.
result Proves convergence of Markovian iteration method for FBSDEs with fully coupled drift and Z process.
We consider a class of participation rights, i.e. obligations issued by a company to investors who are interested in performance-based compensation. Albeit having desirable economic properties equity-based debt obligations (EbDO) pose challenges in accounting and contract pricing. We formulate and solve the associated …
A new framework for generative modeling using controlled vector fields.
problem Expressive modeling with limited parameters.
method Continuous-time modeling with modulated fixed vector fields and learned scalar controls.
result Expressive transport achieved with a small number of learned control channels.
We investigate probabilistic decoupling of labels supplied for training, from the underlying classes for prediction. Decoupling enables an inference scheme general enough to implement many classification problems, including supervised, semi-supervised, positive-unlabelled, noisy-label and suggests a general solution to…
The paper proposes a decoupled approach to efficiently estimate CoVaR, a measure of systemic financial risk.
problem Estimating CoVaR, a measure of systemic financial risk, is challenging due to zero-probability events and portfolio repricing.
method The paper introduces a decoupled approach using smoothing techniques and a functional perspective to model CoVaR.
result The decoupled estimator achieves a rate of convergence of approximately OmP(Γ−1/2). This paper investigates the effectiveness of decoupled weight decay at the start of training.
problem The traditional approach to weight decay is not effective throughout training.
method The authors investigate decoupled weight decay, applying it only at the start of training.
result Applying weight decay only at the start of training stabilizes network weights and improves performance.
Clarifies method of phase synchronization for decoupling linear differential equations.
problem Velocity-dependent transformations in linear second-order differential equations.
method Linear transformation of coordinates and velocities.
result Velocity-dependent transformations do not preserve second-order character and define their own system.
Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.
problem Separate Earth's magnetic field from vehicle's magnetic field for accurate magnetic navigation.
method Use machine learning (ML) and integrate physics of magnetic navigation (SciML) to remove aircraft magnetic field from total magnetic field.
result A model can be constructed to effectively remove aircraft magnetic field from the dataset.
Kahler geometry explains decoupling of Kerr perturbations.
problem Decoupling of curvature scalars in Kerr spacetime.
method Hidden Kahler structure in Kerr spacetime, showing decoupling as a consequence of Kahler geometry.
result Decoupling of Teukolsky equations on Kahler background.
AdaDEM decouples EM into two parts to improve class overlap and uncertainty.
problem Improper EM limits its effectiveness in various machine learning tasks.
method Decouple EM into CADF and GMC, and AdaDEM normalizes CADF reward and uses MEC.
result AdaDEM outperforms classical EM and improves performance in noisy and dynamic environments.
In three dimensions, a `master theory' for all Thurston geometries requires imaginary flux. However, these geometries can be obtained from physical three-dimensional theories with various additional scalar fields, which can be interpreted as moduli in various compactifications of a higher-dimensional `master theory'. T…
Recent variants improve knowledge distillation performance.
problem Improving the performance of knowledge distillation.
method Introducing additional components or changing the learning process.
result These variants have shown promising results.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
We establish decoupled functional CLTs for two-time-scale stochastic approximation.
problem Understanding the asymptotic behavior of two-time-scale stochastic approximation.
method Martingale problem approach and auxiliary sequence.
result The limiting dynamics of two-time-scale SA are independent of each other.
Current reinforcement learning (RL) methods can successfully learn single tasks but often generalize poorly to modest perturbations in task domain or training procedure. In this work, we present a decoupled learning strategy for RL that creates a shared representation space where knowledge can be robustly transferred. …
Stylized facts can be regarded as constraints for any modeling attempt of price dynamics on a financial market, in that an empirically reasonable model has to reproduce these stylized facts at least qualitatively. The dynamics of market prices is modeled on a macro-level as the result of the dynamic coupling of two dyn…
This research highlights the secrecy potential of nonlinear generative models and their all-or-nothing phase transition.
problem Secrecy potential of nonlinear generative models in statistical learning.
method Replica method to derive asymptotic normalized cross entropy and statistical decoupling of Bayesian estimator.
result Strictly nonlinear models exhibit an all-or-nothing phase transition, leading to perfect secrecy.
Market equilibrium price proven in a large-agent model.
problem Proving market equilibrium in a large-agent setting.
method Proved existence of equilibrium price in a complete, continuous time market with infinite agents.
result The equilibrium price dynamics decouple as the number of agents increases.
Backpropagation algorithm is indispensable for the training of feedforward neural networks. It requires propagating error gradients sequentially from the output layer all the way back to the input layer. The backward locking in backpropagation algorithm constrains us from updating network layers in parallel and fully l…
A new model decouples global and local image representations without supervision.
problem Learning decoupled global and local image representations without supervision.
method Variational auto-encoding framework with invertible generative flow.
result The model effectively learns decoupled representations of images.
Decoupled PFNs improve sequential decision-making by separating epistemic and aleatoric uncertainties.
problem Sequential decision-making requires distinguishing between epistemic uncertainty about latent signals and irreducible aleatoric observation noise.
method Developed a decoupled PFN architecture that uses query-level labels to train separate heads for latent signal and aleatoric noise.
result Empirically, decoupled PFNs mitigate the failure mode of total-variance exploration in noisy and heteroscedastic settings.
Novel Adam-family method with decoupled weight decay for training neural networks.
problem Training nonsmooth neural networks with weight decay.
method Proposes a novel Adam-family method with decoupled weight decay, establishing convergence properties and demonstrating superior performance.
result Asymptotically approximates SGD and enhances generalization performance.
DAPS++ improves diffusion-based image restoration by decoupling prior and likelihood.
problem Decoupling prior and likelihood in diffusion-based inverse problems for better performance.
method Introducing DAPS++, which separates diffusion initialization from likelihood refinement.
result DAPS++ achieves high computational efficiency and robust reconstruction performance.
New method uses diffusion models for Bayesian inverse problems.
problem Solving Bayesian inverse problems with linear-Gaussian models.
method Decoupled Diffusion Sequential Monte Carlo (DDSMC) method.
result Asymptotically exact solution demonstrated on various data types.
Method combines deep learning and elicitability for solving complex stochastic equations.
problem Solving McKean-Vlasov FBSDEs with common noise.
method Combines Picard iterations, elicitability, and deep learning.
result Validated on systemic-risk model and extended to quantile-mediated interactions.
We investigate the convergence and stability properties of the decoupled extended Kalman filter learning algorithm (DEKF) within the long-short term memory network (LSTM) based online learning framework. For this purpose, we model DEKF as a perturbed extended Kalman filter and derive sufficient conditions for its stabi…
DAPS++ improves diffusion-based image restoration by decoupling prior and likelihood.
problem Decoupling prior and likelihood in diffusion-based inverse problems.
method Introducing DAPS++, which fully decouples diffusion-based initialization from likelihood-driven refinement.
result Achieves high computational efficiency and robust reconstruction performance.