Author name cluster

Hanlin Yu

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7 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Connecting Neural Models Latent Geometries with Relative Geodesic Representations

Hanlin Yu
Berfin Inal
Georgios Arvanitidis
Søren Hauberg
Francesco Locatello
Marco Fumero

Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different representations, even when learning the same task on the same data. However, it has recently been shown that when a latent structure is shared between distinct latent spaces, relative distances between representations can be preserved, up to distortions. Building on this idea, we demonstrate that exploiting the differential-geometric structure of latent spaces of neural models, it is possible to capture precisely the transformations between representational spaces trained on similar data distributions. Specifically, we assume that distinct neural models parametrize approximately the same underlying manifold, and introduce a representation based on the pullback metric that captures the intrinsic structure of the latent space, while scaling efficiently to large models. We validate experimentally our method on model stitching and retrieval tasks, covering autoencoders and vision foundation discriminative models, across diverse architectures, datasets, pretraining schemes and modalities. Code is available at the following link.

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ICML Conference 2025 Conference Paper

Density Ratio Estimation with Conditional Probability Paths

Hanlin Yu
Arto Klami
Aapo Hyvärinen
Anna Korba
Omar Chehab

Density ratio estimation in high dimensions can be reframed as integrating a certain quantity, the time score, over probability paths which interpolate between the two densities. In practice, the time score has to be estimated based on samples from the two densities. However, existing methods for this problem remain computationally expensive and can yield inaccurate estimates. Inspired by recent advances in generative modeling, we introduce a novel framework for time score estimation, based on a conditioning variable. Choosing the conditioning variable judiciously enables a closed-form objective function. We demonstrate that, compared to previous approaches, our approach results in faster learning of the time score and competitive or better estimation accuracies of the density ratio on challenging tasks. Furthermore, we establish theoretical guarantees on the error of the estimated density ratio.

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EAAI Journal 2025 Journal Article

Efficient safe learning for controller tuning with experimental validation

Marta Zagorowska
Christopher König
Hanlin Yu
Efe C. Balta
Alisa Rupenyan
John Lygeros

Optimization-based controller tuning is challenging because it requires formulating optimization problems explicitly as functions of controller parameters. Safe learning algorithms overcome the challenge by creating surrogate models from measured data. To ensure safety, such data-driven algorithms often rely on exhaustive grid search, which is computationally inefficient. In this paper, we propose a novel approach to safe learning by formulating a series of optimization problems instead of a grid search. We also develop a method for initializing the optimization problems to guarantee feasibility while using numerical solvers. The performance of the new method is first validated in a simulated precision motion system, demonstrating improved computational efficiency, and illustrating the role of exploiting numerical solvers to reach the desired precision. Experimental validation on an industrial-grade precision motion system confirms that the proposed algorithm achieves 30% better tracking at sub-micrometer precision as a state-of-the-art safe learning algorithm, improves the default auto-tuning solution, and reduces the computational cost seven times compared to learning algorithms based on exhaustive search.

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UAI Conference 2025 Conference Paper

Geodesic Slice Sampler for Multimodal Distributions with Strong Curvature

Bernardo Williams
Hanlin Yu
Hoang Phuc Hau Luu
Georgios Arvanitidis
Arto Klami

Traditional Markov Chain Monte Carlo sampling methods often struggle with sharp curvatures, intricate geometries, and multimodal distributions. Slice sampling can resolve local exploration inefficiency issues, and Riemannian geometries help with sharp curvatures. Recent extensions enable slice sampling on Riemannian manifolds, but they are restricted to cases where geodesics are available in a closed form. We propose a method that generalizes Hit-and-Run slice sampling to more general geometries tailored to the target distribution, by approximating geodesics as solutions to differential equations. Our approach enables the exploration of the regions with strong curvature and rapid transitions between modes in multimodal distributions. We demonstrate the advantages of the approach over challenging sampling problems.

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ICLR Conference 2025 Conference Paper

Stochastic variance-reduced Gaussian variational inference on the Bures-Wasserstein manifold

Hoang Phuc Hau Luu
Hanlin Yu
Bernardo Williams
Marcelo Hartmann
Arto Klami

Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function of Kullback–Leibler divergence can be written as the sum of the negative entropy and the potential energy, making forward-backward Euler the method of choice. Notably, the backward step admits a closed-form solution in this case, facilitating the practicality of the scheme. However, the forward step is not exact since the Bures-Wasserstein gradient of the potential energy involves "intractable" expectations. Recent approaches propose using the Monte Carlo method -- in practice a single-sample estimator -- to approximate these terms, resulting in high variance and poor performance. We propose a novel variance-reduced estimator based on the principle of control variates. We theoretically show that this estimator has a smaller variance than the Monte-Carlo estimator in scenarios of interest. We also prove that variance reduction helps improve the optimization bounds of the current analysis. We demonstrate that the proposed estimator gains order-of-magnitude improvements over the previous Bures-Wasserstein methods.

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NeurIPS Conference 2024 Conference Paper

Non-geodesically-convex optimization in the Wasserstein space

Hoang Phuc Hau Luu
Hanlin Yu
Bernardo Williams
Petrus Mikkola
Marcelo Hartmann
Kai Puolamäki
Arto Klami

We study a class of optimization problems in the Wasserstein space (the space of probability measures) where the objective function is nonconvex along generalized geodesics. Specifically, the objective exhibits some difference-of-convex structure along these geodesics. The setting also encompasses sampling problems where the logarithm of the target distribution is difference-of-convex. We derive multiple convergence insights for a novel semi Forward-Backward Euler scheme under several nonconvex (and possibly nonsmooth) regimes. Notably, the semi Forward-Backward Euler is just a slight modification of the Forward-Backward Euler whose convergence is---to our knowledge---still unknown in our very general non-geodesically-convex setting.

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TMLR Journal 2023 Journal Article

Scalable Stochastic Gradient Riemannian Langevin Dynamics in Non-Diagonal Metrics

Hanlin Yu
Marcelo Hartmann
Bernardo Williams
Arto Klami

Stochastic-gradient sampling methods are often used to perform Bayesian inference on neural networks. It has been observed that the methods in which notions of differential geometry are included tend to have better performances, with the Riemannian metric improving posterior exploration by accounting for the local curvature. However, the existing methods often resort to simple diagonal metrics to remain computationally efficient. This loses some of the gains. We propose two non-diagonal metrics that can be used in stochastic-gradient samplers to improve convergence and exploration but have only a minor computational overhead over diagonal metrics. We show that for fully connected neural networks (NNs) with sparsity-inducing priors and convolutional NNs with correlated priors, using these metrics can provide improvements. For some other choices the posterior is sufficiently easy also for the simpler metrics.

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