Navigating the Latent Space Dynamics of Neural Models

• URL: http://arxiv.org/abs/2505.22785v2
• Date: Mon, 09 Jun 2025 22:28:34 GMT
• Title: Navigating the Latent Space Dynamics of Neural Models
• Authors: Marco Fumero, Luca Moschella, Emanuele Rodolà, Francesco Locatello,
• Abstract summary: We present an alternative interpretation of neural models as dynamical systems acting on the latent manifold.<n>We show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map.<n>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.
• Score: 35.39092540369244
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner [46.866240648471894]
  Spatiotemporal Traffic Data (STTD) measures the complex dynamical behaviors of the multiscale transportation system. We present a novel paradigm to address the STTD learning problem by parameterizing STTD as an implicit neural representation. We validate its effectiveness through extensive experiments in real-world scenarios, showcasing applications from corridor to network scales.
  arXiv  Detail & Related papers  (2024-05-06T06:23:06Z)
• Automatic Discovery of Visual Circuits [66.99553804855931]
  We explore scalable methods for extracting the subgraph of a vision model's computational graph that underlies recognition of a specific visual concept. We find that our approach extracts circuits that causally affect model output, and that editing these circuits can defend large pretrained models from adversarial attacks.
  arXiv  Detail & Related papers  (2024-04-22T17:00:57Z)
• Disentanglement via Latent Quantization [60.37109712033694]
  In this work, we construct an inductive bias towards encoding to and decoding from an organized latent space. We demonstrate the broad applicability of this approach by adding it to both basic data-re (vanilla autoencoder) and latent-reconstructing (InfoGAN) generative models.
  arXiv  Detail & Related papers  (2023-05-28T06:30:29Z)
• ProtoVAE: Prototypical Networks for Unsupervised Disentanglement [1.6114012813668934]
  We introduce a novel deep generative VAE-based model, ProtoVAE, that leverages a deep metric learning Prototypical network trained using self-supervision. Our model is completely unsupervised and requires no priori knowledge of the dataset, including the number of factors. We evaluate our proposed model on the benchmark dSprites, 3DShapes, and MPI3D disentanglement datasets.
  arXiv  Detail & Related papers  (2023-05-16T01:29:26Z)
• VTAE: Variational Transformer Autoencoder with Manifolds Learning [144.0546653941249]
  Deep generative models have demonstrated successful applications in learning non-linear data distributions through a number of latent variables. The nonlinearity of the generator implies that the latent space shows an unsatisfactory projection of the data space, which results in poor representation learning. We show that geodesics and accurate computation can substantially improve the performance of deep generative models.
  arXiv  Detail & Related papers  (2023-04-03T13:13:19Z)
• Experimental Observations of the Topology of Convolutional Neural Network Activations [2.4235626091331737]
  Topological data analysis provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture. In this paper, we apply cutting edge techniques from TDA with the goal of gaining insight into the interpretability of convolutional neural networks used for image classification.
  arXiv  Detail & Related papers  (2022-12-01T02:05:44Z)
• Data-driven emergence of convolutional structure in neural networks [83.4920717252233]
  We show how fully-connected neural networks solving a discrimination task can learn a convolutional structure directly from their inputs. By carefully designing data models, we show that the emergence of this pattern is triggered by the non-Gaussian, higher-order local structure of the inputs.
  arXiv  Detail & Related papers  (2022-02-01T17:11:13Z)
• E(n) Equivariant Graph Neural Networks [86.75170631724548]
  This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs) In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance.
  arXiv  Detail & Related papers  (2021-02-19T10:25:33Z)
• A Short Review on Data Modelling for Vector Fields [5.51641435875237]
  Machine learning methods have proven highly successful in dealing with a wide variety of data analysis and analytics tasks. The recent success of end-to-end modelling scheme using deep neural networks allows the extension to more sophisticated and structured practical data. This review article is dedicated to recent computational tools of vector fields, including vector data representations, predictive model of spatial data, as well as applications in computer vision, signal processing, and empirical sciences.
  arXiv  Detail & Related papers  (2020-09-01T17:07:29Z)
• Closed-Form Factorization of Latent Semantics in GANs [65.42778970898534]
  A rich set of interpretable dimensions has been shown to emerge in the latent space of the Generative Adversarial Networks (GANs) trained for synthesizing images. In this work, we examine the internal representation learned by GANs to reveal the underlying variation factors in an unsupervised manner. We propose a closed-form factorization algorithm for latent semantic discovery by directly decomposing the pre-trained weights.
  arXiv  Detail & Related papers  (2020-07-13T18:05:36Z)
• Linearly Constrained Neural Networks [0.5735035463793007]
  We present a novel approach to modelling and learning vector fields from physical systems using neural networks. To achieve this, the target function is modelled as a linear transformation of an underlying potential field, which is in turn modelled by a neural network.
  arXiv  Detail & Related papers  (2020-02-05T01:27:29Z)
• Semi-supervised Grasp Detection by Representation Learning in a Vector Quantized Latent Space [1.3048920509133808]
  In this paper, a semi-supervised learning based grasp detection approach has been presented. To the best of our knowledge, this is the first time a Variational AutoEncoder (VAE) has been applied in the domain of robotic grasp detection. The model performs significantly better than the existing approaches which do not make use of unlabelled images to improve the grasp.
  arXiv  Detail & Related papers  (2020-01-23T12:47:13Z)

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.