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This work aims to recover the underlying states and their time evolution in a latent dynamical system from high-dimensional sensory measurements. Previous works on identifiable representation learning in dynamical systems focused on identifying the latent states, often 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. Our identifiability theory relies on two key assumptions: (i) sufficient variability in the latent noise, and (ii) the bijectivity of the augmented transition function. Drawing from this theory, we introduce a practical algorithm based on variational auto-encoders. We empirically demonstrate that it improves generalization and interpretability of target dynamical systems by (i) recovering latent state dynamics with high accuracy, (ii) correspondingly achieving high future prediction accuracy, and (iii) adapting fast to new environments. Additionally, for complex real-world dynamics, (iv) it produces state-of the-art future prediction results for long horizons, highlighting its usefulness for practical scenarios.

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.

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.

Accurate domain-specific benchmarking of LLMs is essential, specifically in domains with direct implications for humans, such as law, healthcare, and education. However, existing benchmarks are documented to be contaminated and are based on multiple-choice questions, which suffer from inherent biases. To measure domain-specific knowledge in LLMs, we present a deterministic pipeline that transforms raw domain corpora into completion-style benchmarks without relying on other LLMs or costly human annotation. Our approach first extracts domain-specific keywords and related target vocabulary from an input corpus. It then constructs prompt-target pairs where domain-specific words serve as prediction targets. By measuring LLMs’ ability to complete these prompts, we provide a direct assessment of domain knowledge at low computational cost. Our pipeline avoids benchmark contamination, enables automated updates with new domain data, and facilitates fair comparisons between base and instruction-tuned (chat) models. We validate our approach by showing that model performances on our benchmark significantly correlate with those on an expert-curated benchmark. We then demonstrate how our benchmark provides insights into knowledge acquisition in domain-adaptive, continual, and general pretraining. Finally, we examine the effects of instruction fine-tuning by comparing base and chat models within our unified evaluation framework. In conclusion, our pipeline enables scalable, domain-specific, LLM-independent, and unbiased evaluation of both base and chat models.

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.

We investigate why further training on pretrained language models sometimes backfires. Our key finding is that training a model on a text domain could degrade its perplexity on the test portion of the same domain. We discover that this performance degradation is positively correlated with the similarity between the additional and the original pretraining dataset of the LLM, and stems from a small set of uninformative tokens. Our work aims to clarify when model adaptation helps versus when foundational capabilities should be preserved.

The ability of machine learning systems to learn continually is hindered by catastrophic forgetting, the tendency of neural networks to overwrite existing knowledge when learning a new task. Continual learning methods alleviate 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 continually in dynamic, open-world environments, effortlessly achieving one-shot memorization of 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. Thus, Infinite dSprites highlights an important aspect of continual learning that has not received enough attention so far: 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.

Latent neural ordinary differential equations have been proven useful for learning non-linear dynamics of arbitrary sequences. In contrast with their mechanistic counterparts, the predictive accuracy of neural ODEs decreases over longer prediction horizons (Rubanova et al., 2019). To mitigate this issue, we propose disentangling dynamic states from time-invariant variables in a completely data-driven way, enabling robust neural ODE models that can generalize across different settings. We show that such variables can control the latent differential function and/or parameterize the mapping from latent variables to observations. By explicitly modeling the time-invariant variables, our framework enables the use of recent advances in representation learning. We demonstrate this by introducing a straightforward self-supervised objective that enhances the learning of these variables. The experiments on low-dimensional oscillating systems and video sequences reveal that our disentangled model achieves improved longterm predictions, when the training data involve sequence-specific factors of variation such as different rotational speeds, calligraphic styles, and friction constants.

Training dynamic models, such as neural ODEs, on long trajectories is a hard problem that requires using various tricks, such as trajectory splitting, to make model training work in practice. These methods are often heuristics with poor theoretical justifications, and require iterative manual tuning. We propose a principled multiple shooting technique for neural ODEs that splits the trajectories into manageable short segments, which are optimised in parallel, while ensuring probabilistic control on continuity over consecutive segments. We derive variational inference for our shooting-based latent neural ODE models and propose amortized encodings of irregularly sampled trajectories with a transformer-based recognition network with temporal attention and relative positional encoding. We demonstrate efficient and stable training, and state-of-the-art performance on multiple large-scale benchmark datasets.

We study 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.

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.

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.

We present Ordinary Differential Equation Variational Auto-Encoder (ODE2VAE), a latent second order ODE model for high-dimensional sequential data. Leveraging the advances in deep generative models, ODE2VAE 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.

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.

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 O(1/\sqrtN) (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.