Towards Foundational Models for Dynamical System Reconstruction: Hierarchical Meta-Learning via Mixture of Experts

• URL: http://arxiv.org/abs/2502.05335v1
• Date: Fri, 07 Feb 2025 21:16:43 GMT
• Title: Towards Foundational Models for Dynamical System Reconstruction: Hierarchical Meta-Learning via Mixture of Experts
• Authors: Roussel Desmond Nzoyem, David A. W. Barton, Tom Deakin,
• Abstract summary: We introduce MixER: Mixture of Expert Reconstructors, a novel sparse top-1 MoE layer employing a custom gating update algorithm based on $K$-means and least squares. Experiments validate MixER's capabilities, demonstrating efficient training and scalability to systems of up to ten ordinary parametric differential equations. Our layer underperforms state-of-the-art meta-learners in high-data regimes, particularly when each expert is constrained to process only a fraction of a dataset composed of highly related data points.
• Score: 0.7373617024876724
• License:
• Abstract: As foundational models reshape scientific discovery, a bottleneck persists in dynamical system reconstruction (DSR): the ability to learn across system hierarchies. Many meta-learning approaches have been applied successfully to single systems, but falter when confronted with sparse, loosely related datasets requiring multiple hierarchies to be learned. Mixture of Experts (MoE) offers a natural paradigm to address these challenges. Despite their potential, we demonstrate that naive MoEs are inadequate for the nuanced demands of hierarchical DSR, largely due to their gradient descent-based gating update mechanism which leads to slow updates and conflicted routing during training. To overcome this limitation, we introduce MixER: Mixture of Expert Reconstructors, a novel sparse top-1 MoE layer employing a custom gating update algorithm based on $K$-means and least squares. Extensive experiments validate MixER's capabilities, demonstrating efficient training and scalability to systems of up to ten parametric ordinary differential equations. However, our layer underperforms state-of-the-art meta-learners in high-data regimes, particularly when each expert is constrained to process only a fraction of a dataset composed of highly related data points. Further analysis with synthetic and neuroscientific time series suggests that the quality of the contextual representations generated by MixER is closely linked to the presence of hierarchical structure in the data.

Related papers

• DSMoE: Matrix-Partitioned Experts with Dynamic Routing for Computation-Efficient Dense LLMs [70.91804882618243]
  This paper proposes DSMoE, a novel approach that achieves sparsification by partitioning pre-trained FFN layers into computational blocks. We implement adaptive expert routing using sigmoid activation and straight-through estimators, enabling tokens to flexibly access different aspects of model knowledge. Experiments on LLaMA models demonstrate that under equivalent computational constraints, DSMoE achieves superior performance compared to existing pruning and MoE approaches.
  arXiv  Detail & Related papers  (2025-02-18T02:37:26Z)
• LayerMix: Enhanced Data Augmentation through Fractal Integration for Robust Deep Learning [1.786053901581251]
  Deep learning models often struggle to maintain consistent performance when confronted with Out-of-Distribution (OOD) samples. We introduce LayerMix, an innovative data augmentation approach that systematically enhances model robustness. Our method generates semantically consistent synthetic samples that significantly improve neural network generalization capabilities.
  arXiv  Detail & Related papers  (2025-01-08T22:22:44Z)
• Learning Hierarchical Features with Joint Latent Space Energy-Based Prior [44.4434704520236]
  We study the fundamental problem of multi-layer generator models in learning hierarchical representations. We propose a joint latent space EBM prior model with multi-layer latent variables for effective hierarchical representation learning.
  arXiv  Detail & Related papers  (2023-10-14T15:44:14Z)
• Spintronics for image recognition: performance benchmarking via ultrafast data-driven simulations [4.2412715094420665]
  We present a demonstration of image classification using an echo-state network (ESN) relying on a single simulated spintronic nanostructure. We employ an ultrafast data-driven simulation framework called the data-driven Thiele equation approach to simulate the STVO dynamics. We showcase the versatility of our solution by successfully applying it to solve classification challenges with the MNIST, EMNIST-letters and Fashion MNIST datasets.
  arXiv  Detail & Related papers  (2023-08-10T18:09:44Z)
• Dynamic Mixed Membership Stochastic Block Model for Weighted Labeled Networks [3.5450828190071655]
  A new family of Mixed Membership Block Models (MMSBM) allows to model static labeled networks under the assumption of mixed-membership clustering. We show that our method significantly differs from existing approaches, and allows to model more complex systems --dynamic labeled networks.
  arXiv  Detail & Related papers  (2023-04-12T15:01:03Z)
• Integrating Multimodal Data for Joint Generative Modeling of Complex Dynamics [6.848555909346641]
  We provide an efficient framework to combine various sources of information for optimal reconstruction. Our framework is fully textitgenerative, producing, after training, trajectories with the same geometrical and temporal structure as those of the ground truth system.
  arXiv  Detail & Related papers  (2022-12-15T15:21:28Z)
• Towards Understanding Mixture of Experts in Deep Learning [95.27215939891511]
  We study how the MoE layer improves the performance of neural network learning. Our results suggest that the cluster structure of the underlying problem and the non-linearity of the expert are pivotal to the success of MoE.
  arXiv  Detail & Related papers  (2022-08-04T17:59:10Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)
• Model-Based Deep Learning [155.063817656602]
  Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance. We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
  arXiv  Detail & Related papers  (2020-12-15T16:29:49Z)
• Understanding Self-supervised Learning with Dual Deep Networks [74.92916579635336]
  We propose a novel framework to understand contrastive self-supervised learning (SSL) methods that employ dual pairs of deep ReLU networks. We prove that in each SGD update of SimCLR with various loss functions, the weights at each layer are updated by a emphcovariance operator. To further study what role the covariance operator plays and which features are learned in such a process, we model data generation and augmentation processes through a emphhierarchical latent tree model (HLTM)
  arXiv  Detail & Related papers  (2020-10-01T17:51:49Z)
• Kernel and Rich Regimes in Overparametrized Models [69.40899443842443]
  We show that gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. We also demonstrate this transition empirically for more complex matrix factorization models and multilayer non-linear networks.
  arXiv  Detail & Related papers  (2020-02-20T15:43:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.