Çağatay Yıldız

Ilze Amanda Auzina, Çağatay Yıldız, Sara Magliacane et al.

Neural ordinary differential equations (NODEs) have been proven useful for learning non-linear dynamics of arbitrary trajectories. However, current NODE methods capture variations across trajectories only via the initial state value or by auto-regressive encoder updates. In this work, we introduce Modulated Neural ODEs (MoNODEs), a novel framework that sets apart dynamics states from underlying static factors of variation and improves the existing NODE methods. In particular, we introduce $\textit{time-invariant modulator variables}$ that are learned from the data. We incorporate our proposed framework into four existing NODE variants. We test MoNODE on oscillating systems, videos and human walking trajectories, where each trajectory has trajectory-specific modulation. Our framework consistently improves the existing model ability to generalize to new dynamic parameterizations and to perform far-horizon forecasting. In addition, we verify that the proposed modulator variables are informative of the true unknown factors of variation as measured by $R^2$ scores.

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.

Çağatay Yıldız, Nishaanth Kanna Ravichandran, Nitin Sharma et al.

Continual learning (CL) in large language models (LLMs) is an evolving domain that focuses on developing efficient and sustainable training strategies to adapt models to emerging knowledge and achieve robustness in dynamic environments. Our primary emphasis is on continual domain-adaptive pretraining, a process designed to equip LLMs with the ability to integrate new information from various domains while retaining previously learned knowledge. Since existing works concentrate mostly on continual fine-tuning for a limited selection of downstream tasks or training domains, we introduce a new benchmark designed to measure the adaptability of LLMs to changing pretraining data landscapes. We further examine the impact of model size on learning efficacy and forgetting, as well as how the progression and similarity of emerging domains affect the knowledge transfer within these models. Our findings uncover several key insights: (i) continual pretraining consistently improves <1.5B models studied in this work and is also superior to domain adaptation, (ii) larger models always achieve better perplexity than smaller ones when continually pretrained on the same corpus, (iii) smaller models are particularly sensitive to continual pretraining, showing the most significant rates of both learning and forgetting, (iv) continual pretraining boosts downstream task performance of GPT-2 family, (v) continual pretraining enables LLMs to specialize better when the sequence of domains shows semantic similarity while randomizing training domains leads to better transfer and final performance otherwise. We posit that our research establishes a new benchmark for CL in LLMs, providing a more realistic evaluation of knowledge retention and transfer across diverse domains.

Sebastian Dziadzio, Çağatay Yıldız, Gido M. van de Ven et al.

The ability of machine learning systems to learn continually is hindered by catastrophic forgetting, the tendency of neural networks to overwrite previously acquired knowledge when learning a new task. Existing methods mitigate this problem through regularization, parameter isolation, or rehearsal, but they are typically evaluated on benchmarks comprising only a handful of tasks. In contrast, humans are able to learn over long time horizons in dynamic, open-world environments, effortlessly memorizing unfamiliar objects and reliably recognizing them under various transformations. To make progress towards closing this gap, we introduce Infinite dSprites, a parsimonious tool for creating continual classification and disentanglement benchmarks of arbitrary length and with full control over generative factors. We show that over a sufficiently long time horizon, the performance of all major types of continual learning methods deteriorates on this simple benchmark. This result highlights an important and previously overlooked aspect of continual learning: given a finite modelling capacity and an arbitrarily long learning horizon, efficient learning requires memorizing class-specific information and accumulating knowledge about general mechanisms. In a simple setting with direct supervision on the generative factors, we show how learning class-agnostic transformations offers a way to circumvent catastrophic forgetting and improve classification accuracy over time. Our approach sets the stage for continual learning over hundreds of tasks with explicit control over memorization and forgetting, emphasizing open-set classification and one-shot generalization.

Atahan Özer, Çağatay Yıldız

Large language models (LLMs) exhibit remarkable capabilities in question answering and reasoning thanks to their extensive parametric memory. However, their knowledge is inherently limited by the scope of their pre-training data, while real-world information evolves continuously. Updating this knowledge typically requires costly and brittle re-training, or in-context learning (ICL), which becomes impractical at scale given the volume and volatility of modern information. Motivated by these limitations, we investigate how LLMs perform when exposed to temporal text corpora, or documents that reflect evolving knowledge over time, such as sports biographies where facts like a player's "current team" change year by year. To this end, we introduce two new benchmarks: Temporal Wiki, which captures factual drift across historical Wikipedia snapshots, and Unified Clark, which aggregates timestamped news articles to simulate real-world information accumulation. Our analysis reveals that LLMs often struggle to reconcile conflicting or outdated facts and can be misled when multiple versions of a fact appear in context. To address these issues, we propose a lightweight, agentic framework that incrementally builds a structured, external memory from source documents without requiring re-training. This knowledge organization strategy enables models to retrieve and reason over temporally filtered, relevant information at inference time. Empirically, our method outperforms ICL and RAG baselines across both benchmarks, especially on questions requiring more complex reasoning or integration of conflicting facts.

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.

Nitin Sharma, Thomas Wolfers, Çağatay Yıldız

The paper addresses two critical challenges in language model (LM) evaluation: creating reliable domain-specific benchmarks and understanding knowledge representation during domain adaptation. We introduce a deterministic pipeline that converts raw domain corpora into completion-type benchmarks without relying on LMs or human curation, eliminating benchmark contamination issues while enabling evaluation on the latest domain data. Our approach generates domain-specific keywords and related word lists using TF and Term TF-IDF methods and constructs prompt-target pairs. We evaluate models by measuring their ability to complete these prompts with the correct domain-specific targets, providing a direct assessment of domain knowledge with low computational cost. Through comprehensive experiments across multiple models (GPT-2 medium/XL, Llama-2/3.1, OLMo-2, Qwen-2, Mistral) and domains, we demonstrate that our benchmark strongly correlates with expert-generated benchmarks while providing a more accurate measure of domain knowledge than traditional perplexity metrics. We reveal that domain adaptation happens rapidly in smaller models (within 500 steps) and illustrate a new approach to domain knowledge evaluation in base models during training for early stopping. By extending mechanistic analysis to domain adaptation, we discover that initial-to-mid layers are primarily responsible for attribute extraction, while later layers focus on next token prediction. Furthermore, we show that during adaptation, forgetting begins in the middle layers, where attribute extraction happens and is amplified in later layers. Our work provides both a practical evaluation methodology for domain-specific LMs and novel insights into knowledge representation during adaptation, with implications for more efficient fine-tuning strategies and targeted approaches to mitigate catastrophic forgetting.

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.

Karahan Sarıtaş, Çağatay Yıldız

In this reproduction study, we revisit recent claims that self-attention implements kernel principal component analysis (KPCA) (Teo et al., 2024), positing that (i) value vectors $V$ capture the eigenvectors of the Gram matrix of the keys, and (ii) that self-attention projects queries onto the principal component axes of the key matrix $K$ in a feature space. Our analysis reveals three critical inconsistencies: (1) No alignment exists between learned self-attention value vectors and what is proposed in the KPCA perspective, with average similarity metrics (optimal cosine similarity $\leq 0.32$, linear CKA (Centered Kernel Alignment) $\leq 0.11$, kernel CKA $\leq 0.32$) indicating negligible correspondence; (2) Reported decreases in reconstruction loss $J_\text{proj}$, arguably justifying the claim that the self-attention minimizes the projection error of KPCA, are misinterpreted, as the quantities involved differ by orders of magnitude ($\sim\!10^3$); (3) Gram matrix eigenvalue statistics, introduced to justify that $V$ captures the eigenvector of the gram matrix, are irreproducible without undocumented implementation-specific adjustments. Across 10 transformer architectures, we conclude that the KPCA interpretation of self-attention lacks empirical support.

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.

Pashupati Hegde, Çağatay Yıldız, Harri Lähdesmäki et al.

Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel Bayesian nonparametric model that uses Gaussian processes to infer posteriors of unknown ODE systems directly from data. We derive sparse variational inference with decoupled functional sampling to represent vector field posteriors. We also introduce a probabilistic shooting augmentation to enable efficient inference from arbitrarily long trajectories. The method demonstrates the benefit of computing vector field posteriors, with predictive uncertainty scores outperforming alternative methods on multiple ODE learning tasks.

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.