Forward-Euler fails for simulating Wasserstein gradient flows with KL divergence.
problem Simulating Wasserstein gradient flows with forward-Euler discretization fails for KL divergence.
method Forward-Euler discretization for Wasserstein gradient flows with KL divergence.
result Forward-Euler discretization can be incorrect for Wasserstein gradient flows with KL divergence.
Proposes a new learning method for RBMs that combines strengths of forward and reverse KLD.
problem Underfitting and mode-collapse issues in RBM learning.
method Ratio divergence learning using target energy.
result Significantly outperforms other learning methods in energy function fitting, mode-covering, and stability.
SRFE clarifies KL divergences without unifying learning frameworks.
problem Inductive biases of KL divergences and their limitations.
method Introducing SRFE, a log-moment-based functional of the likelihood ratio.
result SRFE recovers KL divergences as limits and reveals a mean-variance tradeoff.
Improved KL divergence estimators for normalizing flows lead to faster convergence and better approximations.
problem Estimating KL divergences for normalizing flows efficiently and accurately.
method Path-gradient estimators for reverse and forward KL divergences.
result Path-gradient estimators lead to faster convergence and better approximation results.
A new VIS approach improves log-likelihood estimation in latent variable models.
problem Challenges in achieving high log-likelihood with VI for complex posterior distributions.
method Uses forward χ2 divergence to optimize proposal distribution for better log-likelihood estimation. result Consistently outperforms state-of-the-art baselines in log-likelihood and parameter estimation.
Paper proposes f-DPG for aligning language models with preferences.
problem Aligning language models with user preferences.
method Uses f-divergence to approximate target distributions and minimizes a forward KL from it using DPG.
result Jensen-Shannon divergence often outperforms forward KL divergence, leading to significant improvements.
Variational inference improves training of generative flow networks.
problem Training generative flow networks efficiently and accurately.
method Define variational objectives in terms of KL divergences and optimize convex combinations.
result Variational inference methods can reduce the variance of gradients in training generative flow networks.
New methods minimize GFlowNet training divergences for better sampling.
problem Training GFlowNets with KL divergence leads to biased and high-variance estimators.
method Design and implement efficient estimators for four divergence measures.
result Properly minimizing these divergences yields a provably correct and effective training scheme.
New findings show score matching's accuracy doesn't ensure numerical stability in diffusion sampling.
problem Numerical stability issues in diffusion sampling despite small forward-marginal error.
method Constructing a smooth score field with arbitrarily small forward-marginal L2 error, showing nonexplosive behavior and moments of every order. result Euler--Maruyama discretizations can converge in probability even when moments diverge, demonstrating failure of weak convergence.
Push-forward models struggle to fit multimodal distributions due to high Lipschitz constants.
problem Expressivity of push-forward generative models in fitting multimodal distributions.
method Analyzing the Lipschitz constant and its relation to the total variation distance and Kullback-Leibler divergence.
result Push-forward models require high Lipschitz constants to approximate multimodal distributions, leading to a trade-off between expressivity and stability.
Beta diffusion generates bounded data using multiplicative transitions.
problem Generating data within specific ranges.
method Integrates demasking and denoising with scaled and shifted beta distributions.
result KLUBs are more effective for optimizing beta diffusion compared to negative ELBOs.
We show that the strong asymptotic class of Weil-Petersson (WP) geodesics with narrow end invariant and bounded annular coefficients is determined by the forward ending lamination. This generalizes the Recurrent Ending Lamination Theorem of Brock-Masur-Minsky. As an application we provide a symbolic condition for diver…
A new method combines VI and IS to improve Bayesian inference accuracy.
problem Bayesian inference often underestimates posterior tails, leading to miscalibration and degeneracy.
method Proposes a novel combination of optimization and sampling techniques using the forward KL divergence.
result The method guarantees asymptotic consistency and fast convergence to optimal IS and variational approximations.
This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, an…
We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and α-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper …
DAIS minimizes symmetrized KL divergence between initial and target distributions.
problem Optimizing over initial distributions in importance sampling.
method Differentiable annealed importance sampling (DAIS) minimizing symmetrized KL divergence.
result DAIS minimizes symmetrized KL divergence between initial and target distributions.
Introduces a new divergence measure for optimal transport.
problem Optimal transport distances and information divergences.
method Infimal convolution formulation of proximal optimal transport divergence.
result Establishes connections to dynamic formulations and partial differential equations.
This work develops a unified framework for RLHF with general f-divergence regularization.
problem Theoretical understanding of general f-divergence regularization in RLHF. method Holistic approach across f-divergence class, two algorithms based on distinct sampling principles. result Provably efficient algorithms with O(logT) regret and O(1/T) sub-optimality gap. This paper introduces f-DPO, a generalized approach to Direct Preference Optimization using diverse divergence constraints.
problem Aligning large language models with human preferences while mitigating safety risks.
method Incorporates diverse divergence constraints to simplify the relationship between reward and optimal policy, eliminating the need for estimating the normalizing constant.
result Optimizes LLMs to align with human preferences more efficiently and under a broader set of divergence constraints.
SGD converges with perturbed forward-backward passes, explained by geometric amplification.
problem Analyzing convergence of SGD with perturbed forward-backward passes in composite optimization.
method Characterized propagation and amplification of perturbations, derived convergence guarantees for non-convex and PL objectives.
result Perturbations cascade through the computational graph, affecting convergence order under specific conditions.
The paper introduces a new divergence measure for variational autoencoders to improve reconstruction and generation.
problem Balancing reconstruction and generalizability in latent space of variational autoencoders.
method Presented a regularisation mechanism based on skew-geometric Jensen-Shannon divergence.
result The skew-geometric Jensen-Shannon divergence leads to better reconstruction and generation in variational autoencoders.
Preconditioned NFs speed up sampling from complex posterior distributions in inverse problems.
problem Sampling from posterior distributions of inverse problems with expensive forward operators.
method Preconditioning a conditional normalizing flow (NF) to speed up training.
result Significant speed-ups achieved compared to training NFs from scratch.
New guarantees for VI in symmetric cases, extending previous results.
problem Symmetry in variational inference for complex distributions.
method Analysis of f-divergences and their stationary points under symmetry. result Symmetry-matching principles ensure recovery of mean and correlation matrix.
This work improves understanding of symmetrizing Bregman divergences on positive definite matrices.
problem Understanding which mean to use for symmetrizing Bregman divergences on positive definite matrices.
method Axiomatic definition of mean functionals and variational principles over the cone of positive definite matrices.
result The arithmetic mean is canonical for forward symmetrization, and the arithmetic, log-Euclidean, and harmonic means for reverse symmetrization.
In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of eith…
Cryo-EM reconstruction is reformulated as a stochastic inverse problem to handle structural heterogeneity.
problem Handling structural heterogeneity in cryo-EM 3D reconstruction.
method Formulated as a stochastic inverse problem over probability measures, using variational discrepancy and Wasserstein gradient flow.
result Validated approach using synthetic examples, demonstrating recovery of continuous structural distributions.
Unified framework for unlearning in diffusion models using KL divergence and likelihood constraints.
problem Removing undesirable data or concepts while preserving utility of pretrained models.
method Constrained optimization framework based on reverse and forward KL divergences, and likelihood constraints.
result Our KL-constrained approach achieves superior retention-unlearning tradeoffs compared to weight-based baselines.
The paper improves guarantees for VI in symmetric cases.
problem Approximating intractable densities via VI with misspecified families.
method Extends previous robust VI results to wider divergences and non-log-concave targets.
result Guarantees for exact recovery of target mean and correlation matrix under various conditions.
Develops a method for learning proposals in nested importance samplers.
problem Improving sampling quality in complex distributions.
method Nested Variational Inference (NVI) using forward or reverse KL divergence.
result Optimizing nested objectives leads to improved sample quality.
This paper bridges variational inference and Wasserstein gradient flows.
problem Combining variational inference and Wasserstein gradient flows for more efficient approximations.
method Recasting Bures-Wasserstein gradient flow as a Euclidean gradient flow and using path-derivative gradient estimator.
result A new gradient estimator for f-divergences that can be implemented using machine learning libraries. A new algorithm for training generative models using Sinkhorn divergence.
problem Training generative adversarial networks (GANs).
method Sinkhorn Natural Gradient (SiNG) algorithm for steepest descent on probability space.
result Explicit expression and efficient evaluation of the Sinkhorn information matrix (SIM).
Improved UIVI method shows better performance than state-of-the-art SIVI methods.
problem Estimating the likelihood of samples from complex distributions in high dimensions.
method Replaced the inner MCMC loop of UIVI with importance sampling and learned the optimal proposal distribution.
result The refined UIVI approach demonstrates superior performance or parity with state-of-the-art methods.
Improved analysis for diffusion models reduces KL divergence error dependence on data dimension and discretization step size.
problem Analyze the convergence of diffusion-based generative models under minimal assumptions.
method Model the generation process as a composition of reverse ODE and noising steps, leveraging Wasserstein-type error control and noise addition.
result Achieved a linear dependence on data dimension and improved dependence on discretization step size for KL divergence error.
New method uses neural networks to solve complex PDEs from optimal control theory.
problem Solving high-dimensional Hamilton-Jacobi-Bellman PDEs.
method Iterative diffusion optimization techniques, focusing on path measures and divergences.
result Favourable properties of log-variance divergence for Monte Carlo estimators.
Generative Adversarial Networks (GANs) have become a widely popular framework for generative modelling of high-dimensional datasets. However their training is well-known to be difficult. This work presents a rigorous statistical analysis of GANs providing straight-forward explanations for common training pathologies su…
The paper proves learning-curve monotonicity for maximum likelihood estimators in various parametric settings.
problem Establishing monotonicity guarantees for maximum likelihood estimators.
method Variants of GPT-5.2 Pro were used to derive the results.
result The paper proves monotonicity for maximum likelihood estimators in Gaussian and Gamma variables.
New method improves variational inference for better posterior approximation.
problem Challenges in minimizing inclusive KL divergence for amortized variational inference.
method Likelihood-tempered sequential Monte Carlo samplers to estimate inclusive KL gradient.
result SMC-Wake method fits variational distributions more accurately than existing methods.
This paper improves SGMs by using a predictor-corrector scheme to converge faster.
problem Theoretical and practical limitations of existing SGMs when T1o∞. method Integrates a predictor-corrector scheme after the forward process to converge in finite time.
result Convergence guarantees for SGMs require only a fixed finite time T1. The coefficient of determination, known as R2, is commonly used as a goodness-of-fit criterion for fitting linear models. R2 is somewhat controversial when fitting nonlinear models, although it may be generalised on a case-by-case basis to deal with specific models such as the logistic model. Assume we are fittin…
Index tracking is a popular form of asset management. Typically, a quadratic function is used to define the tracking error of a portfolio and the look back approach is applied to solve the index tracking problem. We argue that a forward looking approach is more suitable, whereby the tracking error is expressed as expec…
Diffusion models reveal latent hierarchical structure in data.
problem Quantitative measurement of data's hierarchical structure.
method Forward-backward experiments in diffusion models.
result Changes in latent variables manifest as correlated chunks in data.
New insights into how large learning rates affect transformer training dynamics.
problem Understanding how large learning rates impact the training of transformer models.
method Analyzing a simplified linear transformer model with a two-factor product map.
result Large learning rates can lead to various training outcomes including cycles, chaos, or divergence.
Generative flows learn distributions on low-dimensional manifolds robustly via Wasserstein proximals.
problem Learning distributions supported on low-dimensional manifolds robustly.
method Combining Wasserstein-1 and Wasserstein-2 proximal operators to formulate well-posed continuous-time generative flows.
result The combination of Wasserstein-1 and Wasserstein-2 proximals ensures the well-posedness of generative flows, leading to unique and robust learning.
Discrete diffusion models improve data generation for discrete data like language and graphs.
problem Adapting diffusion models to discrete state spaces for better data generation.
method Formulated as CTMCs, used uniformization of continuous Markov chains for sampling.
result Derive guarantees for sampling from any distribution on a hypercube, aligning with state-of-the-art achievements.
In this work, a novel sequential Monte Carlo filter is introduced which aims at efficient sampling of high-dimensional state spaces with a limited number of particles. Particles are pushed forward from the prior to the posterior density using a sequence of mappings that minimizes the Kullback-Leibler divergence between…
Proximal Diffusion Models improve generative model efficiency.
problem Improving generative model efficiency and accuracy.
method Developed Proximal Diffusion Models using proximal maps instead of scores.
result Proximal Diffusion Models achieve faster convergence and higher accuracy.
Statistical finite elements use Langevin dynamics to efficiently handle uncertainty quantification.
problem Uncertainty quantification in finite element models with observed data.
method Langevin dynamics, unadjusted Langevin algorithm (ULA), for sampling posterior distributions.
result ULA provides a scalable and efficient method for characterizing the posterior distribution of statFEM models.
VT-DIS improves sampling from Boltzmann distributions with minimal overhead.
problem Bias in Monte Carlo estimates from score-based diffusion models.
method Variance-Tuned Diffusion Importance Sampling (VT-DIS) adapts noise covariance to correct bias.
result VT-DIS achieves effective sample sizes of 80%, 35%, and 3.5% on benchmarks, using less computational budget.