Çağatay Yıldız

Çağatay Yıldız, Melih Kandemir, Barbara Rakitsch

We study time uncertainty-aware modeling of continuous-time dynamics of interacting objects. We introduce a new model that decomposes independent dynamics of single objects accurately from their interactions. By employing latent Gaussian process ordinary differential equations, our model infers both independent dynamics and their interactions with reliable uncertainty estimates. In our formulation, each object is represented as a graph node and interactions are modeled by accumulating the messages coming from neighboring objects. We show that efficient inference of such a complex network of variables is possible with modern variational sparse Gaussian process inference techniques. We empirically demonstrate that our model improves the reliability of long-term predictions over neural network based alternatives and it successfully handles missing dynamic or static information. Furthermore, we observe that only our model can successfully encapsulate independent dynamics and interaction information in distinct functions and show the benefit from this disentanglement in extrapolation scenarios.

David Leeftink, Çağatay Yıldız, Steffen Ridderbusch et al.

Without exact knowledge of the true system dynamics, optimal control of non-linear continuous-time systems requires careful treatment under epistemic uncertainty. In this work, we translate a probabilistic interpretation of the Pontryagin maximum principle to the challenge of optimal control with learned probabilistic dynamics models. Our framework provides a principled treatment of epistemic uncertainty by minimizing the mean Hamiltonian with respect to a posterior distribution over the system dynamics. We propose a multiple shooting numerical method that leverages mean Hamiltonian minimization and is scalable to large-scale probabilistic dynamics models, including ensemble neural ordinary differential equations. Comparisons against other baselines in online and offline model-based reinforcement learning tasks show that our probabilistic Hamiltonian approach leads to reduced trial costs in offline settings and achieves competitive performance in online scenarios. By bridging optimal control and reinforcement learning, our approach offers a principled and practical framework for controlling uncertain systems with learned dynamics.

Çağlar Hızlı, Çağatay Yıldız, Pekka Marttinen

State-of-the-art vision pretraining methods rely on image-level self-distillation from object-centric datasets such as ImageNet, implicitly assuming each image contains a single object. This assumption does not always hold: many ImageNet images already contain multiple objects. Further, it limits scalability to scene-centric datasets that better mirror real-world complexity. We address these challenges by introducing Object-level Self-DIStillation (ODIS), a pretraining approach that shifts the self-distillation granularity from whole images to individual objects. Using object-aware cropping and masked attention, ODIS isolates object-specific regions, guiding the transformer toward semantically meaningful content and transforming a noisy, scene-level task into simpler object-level sub-tasks. We show that this approach improves visual representations both at the image and patch levels. Using masks at inference time, our method achieves an impressive $82.6\%$ $k$-NN accuracy on ImageNet1k with ViT-Large.

Çağlar Hızlı, Çağatay Yıldız, Matthias Bethge et al.

This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the realm of dynamical systems focused on the latent states, possibly with linear transition approximations. As such, they cannot identify nonlinear transition dynamics, and hence fail to reliably predict complex future behavior. Inspired by the advances in nonlinear ICA, we propose a state-space modeling framework in which we can identify not just the latent states but also the unknown transition function that maps the past states to the present. We introduce a practical algorithm based on variational auto-encoders and empirically demonstrate in realistic synthetic settings that we can (i) recover latent state dynamics with high accuracy, (ii) correspondingly achieve high future prediction accuracy, and (iii) adapt fast to new environments.

Çağatay Yıldız, Markus Heinonen, Harri Lähdesmäki

Model-based reinforcement learning (MBRL) approaches rely on discrete-time state transition models whereas physical systems and the vast majority of control tasks operate in continuous-time. To avoid time-discretization approximation of the underlying process, we propose a continuous-time MBRL framework based on a novel actor-critic method. Our approach also infers the unknown state evolution differentials with Bayesian neural ordinary differential equations (ODE) to account for epistemic uncertainty. We implement and test our method on a new ODE-RL suite that explicitly solves continuous-time control systems. Our experiments illustrate that the model is robust against irregular and noisy data, is sample-efficient, and can solve control problems which pose challenges to discrete-time MBRL methods.

Çağatay Yıldız, Markus Heinonen, Harri Lähdesmäki

We present Ordinary Differential Equation Variational Auto-Encoder (ODE$^2$VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE$^2$VAE can simultaneously learn the embedding of high dimensional trajectories and infer arbitrarily complex continuous-time latent dynamics. Our model explicitly decomposes the latent space into momentum and position components and solves a second order ODE system, which is in contrast to recurrent neural network (RNN) based time series models and recently proposed black-box ODE techniques. In order to account for uncertainty, we propose probabilistic latent ODE dynamics parameterized by deep Bayesian neural networks. We demonstrate our approach on motion capture, image rotation and bouncing balls datasets. We achieve state-of-the-art performance in long term motion prediction and imputation tasks.

Umut Şimşekli, Çağatay Yıldız, Thanh Huy Nguyen et al.

Recent studies have illustrated that stochastic gradient Markov Chain Monte Carlo techniques have a strong potential in non-convex optimization, where local and global convergence guarantees can be shown under certain conditions. By building up on this recent theory, in this study, we develop an asynchronous-parallel stochastic L-BFGS algorithm for non-convex optimization. The proposed algorithm is suitable for both distributed and shared-memory settings. We provide formal theoretical analysis and show that the proposed method achieves an ergodic convergence rate of ${\cal O}(1/\sqrt{N})$ ($N$ being the total number of iterations) and it can achieve a linear speedup under certain conditions. We perform several experiments on both synthetic and real datasets. The results support our theory and show that the proposed algorithm provides a significant speedup over the recently proposed synchronous distributed L-BFGS algorithm.

Markus Heinonen, Cagatay Yildiz, Henrik Mannerström et al.

In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the underlying dynamics. In these settings, parametric ODE model cannot be formulated. Here, we overcome this issue by introducing a novel paradigm of nonparametric ODE modelling that can learn the underlying dynamics of arbitrary continuous-time systems without prior knowledge. We propose to learn non-linear, unknown differential functions from state observations using Gaussian process vector fields within the exact ODE formalism. We demonstrate the model's capabilities to infer dynamics from sparse data and to simulate the system forward into future.