Discovering and decoding latent mean-field structure with variational autoencoders

• URL: http://arxiv.org/abs/2606.08694v1
• Date: Sun, 07 Jun 2026 15:48:50 GMT
• Title: Discovering and decoding latent mean-field structure with variational autoencoders
• Abstract summary: We establish an intuitive criterion that quantifies the capacity of a variational autoencoder (VAE) to faithfully reconstruct the joint probability distribution of a many body system.<n>We show that the conditionally independent decoder of any successful VAE is structurally identical to a finite-size mean-field factorization.<n>We validate these conclusions on a hierarchy of solvable models with scalar (Curie-Weiss), vector (Hopfield) and tensor (Maier-Saupe) order parameters.
• Score: 25.443969857579074
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Generative models are increasingly used to capture correlations in many-body systems, but the representations they learn remain largely opaque to physical interpretation. Here, we establish an intuitive criterion that quantifies the capacity of a variational autoencoder (VAE) to faithfully reconstruct the joint probability distribution of a many body system. In a nutshell, a bound on the VAE capacity is obtained by comparing the rate of the latent channel to the bipartite mutual information of the data. Using this bound, we show that the conditionally independent decoder of any successful VAE is structurally identical to a finite-size mean-field factorization. Hence, a successful reconstruction is direct evidence for a latent mean-field theory and the microscopic parameters of that theory can be read off the trained decoder. We validate these conclusions on a hierarchy of solvable models with scalar (Curie-Weiss), vector (Hopfield) and tensor (Maier-Saupe) order parameters, recovering the full Hopfield pattern matrix from equilibrium samples alone. We find that, when applied to Salamander retinal recordings, a two-latent VAE reproduces the population statistics with only two effective collective variables allowing us to recover the `stored patterns' of the neural population and write a generalized Hopfield model which correctly models the experimental data.

Related papers

• Disentangled representations via score-based variational autoencoders [21.955536401578616]
  We present the Score-based Autoencoder for Multiscale Inference (SAMI)<n>SAMI formulates a principled objective that learns representations through score-based guidance of the underlying diffusion process.<n>It can extract useful representations from pre-trained diffusion models with minimal additional training.
  arXiv  Detail & Related papers  (2025-12-18T23:42:10Z)
• Every Step Counts: Decoding Trajectories as Authorship Fingerprints of dLLMs [63.82840470917859]
  We show that the decoding mechanism of dLLMs can be used as a powerful tool for model attribution.<n>We propose a novel information extraction scheme called the Directed Decoding Map (DDM), which captures structural relationships between decoding steps and better reveals model-specific behaviors.
  arXiv  Detail & Related papers  (2025-10-02T06:25:10Z)
• Multi-modal Gaussian Process Variational Autoencoders for Neural and Behavioral Data [0.9622208190558754]
  We propose an unsupervised latent variable model which extracts temporally evolving shared and independent latents for distinct, simultaneously recorded experimental modalities. We validate our model on simulated multi-modal data consisting of Poisson spike counts and MNIST images that scale and rotate smoothly over time. We show that the multi-modal GP-VAE is able to not only identify the shared and independent latent structure across modalities accurately, but provides good reconstructions of both images and neural rates on held-out trials.
  arXiv  Detail & Related papers  (2023-10-04T19:04:55Z)
• Symmetric Equilibrium Learning of VAEs [56.56929742714685]
  We view variational autoencoders (VAEs) as decoder-encoder pairs, which map distributions in the data space to distributions in the latent space and vice versa. We propose a Nash equilibrium learning approach, which is symmetric with respect to the encoder and decoder and allows learning VAEs in situations where both the data and the latent distributions are accessible only by sampling.
  arXiv  Detail & Related papers  (2023-07-19T10:27:34Z)
• 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)
• Language as a Latent Sequence: deep latent variable models for semi-supervised paraphrase generation [47.33223015862104]
  We present a novel unsupervised model named variational sequence auto-encoding reconstruction (VSAR), which performs latent sequence inference given an observed text. To leverage information from text pairs, we additionally introduce a novel supervised model we call dual directional learning (DDL), which is designed to integrate with our proposed VSAR model. Our empirical evaluations suggest that the combined model yields competitive performance against the state-of-the-art supervised baselines on complete data.
  arXiv  Detail & Related papers  (2023-01-05T19:35:30Z)
• Posterior Collapse and Latent Variable Non-identifiability [54.842098835445]
  We propose a class of latent-identifiable variational autoencoders, deep generative models which enforce identifiability without sacrificing flexibility. Across synthetic and real datasets, latent-identifiable variational autoencoders outperform existing methods in mitigating posterior collapse and providing meaningful representations of the data.
  arXiv  Detail & Related papers  (2023-01-02T06:16:56Z)
• Attribute Graphs Underlying Molecular Generative Models: Path to Learning with Limited Data [42.517927809224275]
  We provide an algorithm that relies on perturbation experiments on latent codes of a pre-trained generative autoencoder to uncover an attribute graph. We show that one can fit an effective graphical model that models a structural equation model between latent codes. Using a pre-trained generative autoencoder trained on a large dataset of small molecules, we demonstrate that the graphical model can be used to predict a specific property.
  arXiv  Detail & Related papers  (2022-07-14T19:20:30Z)
• Autoencoding Variational Autoencoder [56.05008520271406]
  We study the implications of this behaviour on the learned representations and also the consequences of fixing it by introducing a notion of self consistency. We show that encoders trained with our self-consistency approach lead to representations that are robust (insensitive) to perturbations in the input introduced by adversarial attacks.
  arXiv  Detail & Related papers  (2020-12-07T14:16:14Z)
• Learning Disentangled Latent Factors from Paired Data in Cross-Modal Retrieval: An Implicit Identifiable VAE Approach [33.61751393224223]
  We deal with the problem of learning the underlying disentangled latent factors that are shared between the paired bi-modal data in cross-modal retrieval. We propose a novel idea of the implicit decoder, which completely removes the ambient data decoding module from a latent variable model. Our model is shown to identify the factors accurately, significantly outperforming conventional encoder-decoder latent variable models.
  arXiv  Detail & Related papers  (2020-12-01T17:47:50Z)
• Robust Finite Mixture Regression for Heterogeneous Targets [70.19798470463378]
  We propose an FMR model that finds sample clusters and jointly models multiple incomplete mixed-type targets simultaneously. We provide non-asymptotic oracle performance bounds for our model under a high-dimensional learning framework. The results show that our model can achieve state-of-the-art performance.
  arXiv  Detail & Related papers  (2020-10-12T03:27:07Z)

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.