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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.

This paper studies the evolving domain of Continual Learning (CL) in large language models (LLMs), with a focus on developing strategies for efficient and sustainable training. 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 and enhancing cross-domain knowledge transfer without relying on domain-specific identification. Unlike previous studies, which mostly concentrate on a limited selection of tasks or domains and primarily aim to address the issue of forgetting, our research evaluates the adaptability and capabilities of LLMs to changing data landscapes in practical scenarios. To this end, we introduce a new benchmark designed to measure the adaptability of LLMs to these evolving data environments, offering a comprehensive framework for evaluation. We 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) when the sequence of domains shows semantic similarity, continual pretraining enables LLMs to better specialize in the current domain compared to stand-alone fine-tuning, (ii) training across a diverse range of domains enhances both backward and forward knowledge transfer, and (iii) smaller models are particularly sensitive to continual pretraining, showing the most significant rates of both forgetting and learning. We posit that our research marks a shift towards establishing a more realistic benchmark for investigating CL in LLMs, and has the potential to play a key role in guiding the direction of future research in the field.

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.