Navigating the Latent Space Dynamics of Neural Models

2025-05-28

AI Summary

This paper addresses the poorly understood dynamical mechanisms underlying neural network latent spaces. We model post-trained networks as dynamical systems defined on latent manifolds and, for the first time, analytically derive a data-agnostic, training-free implicit vector field directly from model parameters. Methodologically, we derive the latent flow field via iterative encoder-decoder mappings and combine attractor detection with trajectory evolution analysis to uncover the intrinsic dynamical origins of generalization and memorization. Our key contributions are: (1) establishing the first zero-shot prior knowledge extraction paradigm grounded in manifold dynamics; (2) enabling interpretable, step-by-step analysis of generalization and memorization mechanisms throughout the entire training process; and (3) achieving high-accuracy out-of-distribution (OOD) sample detection on vision foundation models—without additional training or labeled data.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Large Vision Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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) analyze the generalization and memorization regimes of neural models, even throughout training; (ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (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.

Problem

• Interpreting neural models as dynamical systems on latent manifolds
• Analyzing generalization and memorization via latent vector fields
• Extracting prior knowledge from attractors without input data

Innovation

• Interprets neural models as dynamical systems
• Leverages latent vector field for analysis
• Extracts prior knowledge from attractor points