OpenNovelty.org

Navigating the Latent Space Dynamics of Neural Models

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
Representation learninglatent vector fieldautoencodersmemorization and generalizationattractor
Abstract:

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical systems acting on the latent manifold. Specifically, we show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map, without any additional training. We observe that standard training procedures introduce inductive biases that lead to the emergence of attractor points within this vector field. Drawing on this insight, we propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data. This representation enables to: (i)(i) analyze the generalization and memorization regimes of neural models, even throughout training; (ii)(ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (iii)(iii) identify out-of-distribution samples from their trajectories in the vector field. We further validate our approach on vision foundation models, showcasing the applicability and effectiveness of our method in real-world scenarios.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper proposes interpreting autoencoders as dynamical systems by defining a latent vector field through iterative encoding-decoding, identifying attractor points that emerge from standard training. It resides in the 'Latent Vector Field Theory and Attractors' leaf under 'Theoretical Foundations and Analysis Methods', which currently contains only this paper among 50 total papers in the taxonomy. This isolation suggests the work occupies a relatively sparse theoretical niche, focusing on formal characterization of implicit dynamics rather than method development or domain applications.

The taxonomy reveals substantial activity in neighboring branches: 'Latent Space Dynamics Modeling and Prediction' contains 19 papers across physics-informed and data-driven temporal modeling, while 'Latent Space Structure and Representation Learning' includes 13 papers on geometry and manifold discovery. The paper's theoretical focus on attractor dynamics connects it to 'Neural Contractive Systems' and 'Koopman Operator' methods within physics-informed dynamics, yet diverges by analyzing implicit vector fields in standard autoencoders rather than designing architectures with explicit stability constraints. Its position bridges foundational theory and the broader dynamics modeling literature.

Among 22 candidates examined, the contribution on latent vector field representation found no refuting prior work across 10 candidates, suggesting novelty in framing autoencoders as implicit dynamical systems. However, the memorization-generalization connection via attractors encountered 1 refutable candidate among 10 examined, indicating some overlap with existing analyses of training dynamics. The data-free probing contribution examined only 2 candidates with no refutations, though the limited search scope leaves open the possibility of undetected prior work in foundation model analysis or noise-based probing techniques.

Based on top-22 semantic matches, the vector field interpretation and attractor-based analysis appear relatively novel within the examined scope, particularly the formal treatment of implicit dynamics in standard autoencoders. The memorization-generalization link shows partial overlap with prior training dynamics research, while the foundation model probing contribution remains underexplored in this limited search. The sparse population of the theoretical attractors leaf and the paper's bridging position between theory and applications suggest it addresses a gap, though exhaustive coverage of related dynamical systems theory or representation learning literature cannot be claimed.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
22
Contribution Candidate Papers Compared
1
Refutable Paper

Research Landscape Overview

Core task: analyzing latent vector field dynamics in autoencoder neural networks. The field organizes around five main branches that reflect complementary perspectives on how autoencoders compress and evolve high-dimensional data. Latent Space Dynamics Modeling and Prediction focuses on forecasting temporal evolution within learned representations, often coupling reduced-order models with neural architectures. Latent Space Structure and Representation Learning examines the geometric and topological properties that emerge during encoding, asking how disentanglement, manifold structure, and interpretability arise. Generative Modeling in Latent Space emphasizes sampling and synthesis, leveraging variational or flow-based frameworks to produce novel instances. Applications of Latent Dynamics Analysis demonstrates these methods in domains ranging from fluid mechanics and materials science to biological trajectory reconstruction. Finally, Theoretical Foundations and Analysis Methods provides the mathematical underpinnings—attractor theory, stability analysis, and operator-theoretic perspectives—that justify why latent dynamics can faithfully capture complex system behavior. Several active lines of work reveal key trade-offs between physical interpretability and expressive power. Physics-informed approaches such as Physics Constrained Autoencoders[6] and mLaSDI[8] embed known governing equations directly into the latent space, ensuring that learned dynamics respect conservation laws or symmetries, while purely data-driven methods like Dynamically Meaningful Latent[9] and Latent Space Evolution[11] prioritize flexibility and scalability at the cost of harder-to-interpret vector fields. Navigating Latent Space[0] sits within the Theoretical Foundations branch, specifically addressing latent vector field theory and attractors. Its emphasis on rigorous characterization of fixed points and flow topology aligns it closely with works like Mori-Zwanzig Koopman[2] and Neural Contractive Systems[17], which also seek formal guarantees on latent dynamics. Compared to application-focused studies such as Fluid Dynamics Autoencoder[24] or Data-Driven Rayleigh-Benard[26], Navigating Latent Space[0] offers a more foundational lens, exploring how attractor structure in latent space relates to the original high-dimensional system's long-term behavior.

Claimed Contributions

Latent vector field representation of autoencoders

The authors introduce a novel interpretation of autoencoder models as dynamical systems that implicitly define a latent vector field through iterative application of the encoding-decoding map. This vector field arises naturally without requiring additional training and provides a new tool for analyzing model and data properties.

10 retrieved papers
Connection between attractors and memorization-generalization regimes

The work demonstrates that attractors in the latent vector field encode whether a model is in a memorization or generalization regime. The authors show empirically how these attractors evolve throughout the training process, providing insights into the learning dynamics of neural networks.

10 retrieved papers
Can Refute
Data-free probing of foundation models via noise-derived attractors

The authors propose a method to extract knowledge encoded in pretrained foundation models without requiring any input data. By computing attractors from Gaussian noise initialization, they can recover semantic information stored in the network weights, enabling black-box analysis of model representations.

2 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Within the taxonomy built over the current TopK core-task papers, the original paper is assigned to a leaf with no direct siblings and no cousin branches under the same grandparent topic. In this retrieved landscape, it appears structurally isolated, which is one partial signal of novelty, but still constrained by search coverage and taxonomy granularity.

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Latent vector field representation of autoencoders

The authors introduce a novel interpretation of autoencoder models as dynamical systems that implicitly define a latent vector field through iterative application of the encoding-decoding map. This vector field arises naturally without requiring additional training and provides a new tool for analyzing model and data properties.

Contribution

Connection between attractors and memorization-generalization regimes

The work demonstrates that attractors in the latent vector field encode whether a model is in a memorization or generalization regime. The authors show empirically how these attractors evolve throughout the training process, providing insights into the learning dynamics of neural networks.

Contribution

Data-free probing of foundation models via noise-derived attractors

The authors propose a method to extract knowledge encoded in pretrained foundation models without requiring any input data. By computing attractors from Gaussian noise initialization, they can recover semantic information stored in the network weights, enabling black-box analysis of model representations.

Table of Contents