Geometric Constraints in Probabilistic Manifolds: A Bridge from Molecular Dynamics to Structured Diffusion Processes

• URL: http://arxiv.org/abs/2307.04493v1
• Date: Mon, 10 Jul 2023 11:31:15 GMT
• Title: Geometric Constraints in Probabilistic Manifolds: A Bridge from Molecular Dynamics to Structured Diffusion Processes
• Authors: Justin Diamond, Markus Lill
• Abstract summary: We propose a method that enables sampling from distributions that rigorously adhere to arbitrary sets of geometric constraints in Euclidean spaces. This is achieved by integrating a constraint projection operator within the well-regarded architecture of Denoising Diffusion Probabilistic Models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding the macroscopic characteristics of biological complexes demands precision and specificity in statistical ensemble modeling. One of the primary challenges in this domain lies in sampling from particular subsets of the state-space, driven either by existing structural knowledge or specific areas of interest within the state-space. We propose a method that enables sampling from distributions that rigorously adhere to arbitrary sets of geometric constraints in Euclidean spaces. This is achieved by integrating a constraint projection operator within the well-regarded architecture of Denoising Diffusion Probabilistic Models, a framework founded in generative modeling and probabilistic inference. The significance of this work becomes apparent, for instance, in the context of deep learning-based drug design, where it is imperative to maintain specific molecular profile interactions to realize the desired therapeutic outcomes and guarantee safety.

Related papers

• Model-free Estimation of Latent Structure via Multiscale Nonparametric Maximum Likelihood [13.175343048302697]
  We propose a model-free approach for estimating such latent structures whenever they are present, without assuming they exist a priori. As an application, we design a clustering algorithm based on the proposed procedure and demonstrate its effectiveness in capturing a wide range of latent structures.
  arXiv  Detail & Related papers  (2024-10-29T17:11:33Z)
• Spatial embedding promotes a specific form of modularity with low entropy and heterogeneous spectral dynamics [0.0]
  Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined structural and functional organisation of networks over learning. We show that it is possible to study these restrictions through entropic measures of the neural weights and eigenspectrum, across both rate and spiking neural networks. This work deepens our understanding of constrained learning in neural networks, across coding schemes and tasks, where solutions to simultaneous structural and functional objectives must be accomplished in tandem.
  arXiv  Detail & Related papers  (2024-09-26T10:00:05Z)
• Compositional Structures in Neural Embedding and Interaction Decompositions [101.40245125955306]
  We describe a basic correspondence between linear algebraic structures within vector embeddings in artificial neural networks. We introduce a characterization of compositional structures in terms of "interaction decompositions" We establish necessary and sufficient conditions for the presence of such structures within the representations of a model.
  arXiv  Detail & Related papers  (2024-07-12T02:39:50Z)
• Seeing Unseen: Discover Novel Biomedical Concepts via Geometry-Constrained Probabilistic Modeling [53.7117640028211]
  We present a geometry-constrained probabilistic modeling treatment to resolve the identified issues. We incorporate a suite of critical geometric properties to impose proper constraints on the layout of constructed embedding space. A spectral graph-theoretic method is devised to estimate the number of potential novel classes.
  arXiv  Detail & Related papers  (2024-03-02T00:56:05Z)
• Bayesian Semi-structured Subspace Inference [0.0]
  Semi-structured regression models enable the joint modeling of interpretable structured and complex unstructured feature effects. We present a Bayesian approximation for semi-structured regression models using subspace inference. Our approach exhibits competitive predictive performance across simulated and real-world datasets.
  arXiv  Detail & Related papers  (2024-01-23T18:15:58Z)
• Diffusion-Driven Generative Framework for Molecular Conformation Prediction [0.66567375919026]
  The rapid advancement of machine learning has revolutionized the precision of predictive modeling in this context. This research introduces a cutting-edge generative framework named method. Method views atoms as discrete entities and excels in guiding the reversal of diffusion.
  arXiv  Detail & Related papers  (2023-12-22T11:49:39Z)
• Validation Diagnostics for SBI algorithms based on Normalizing Flows [55.41644538483948]
  This work proposes easy to interpret validation diagnostics for multi-dimensional conditional (posterior) density estimators based on NF. It also offers theoretical guarantees based on results of local consistency. This work should help the design of better specified models or drive the development of novel SBI-algorithms.
  arXiv  Detail & Related papers  (2022-11-17T15:48:06Z)
• Measure-Theoretic Probability of Complex Co-occurrence and E-Integral [15.263586201516159]
  The behavior of a class of natural integrals called E-integrals is investigated based on the defined conditional probability of co-occurrence. The paper offers a novel measure-theoretic framework where E-integral as a basic measure-theoretic concept can be the starting point.
  arXiv  Detail & Related papers  (2022-10-18T14:52:23Z)
• Discovering Latent Causal Variables via Mechanism Sparsity: A New Principle for Nonlinear ICA [81.4991350761909]
  Independent component analysis (ICA) refers to an ensemble of methods which formalize this goal and provide estimation procedure for practical application. We show that the latent variables can be recovered up to a permutation if one regularizes the latent mechanisms to be sparse.
  arXiv  Detail & Related papers  (2021-07-21T14:22:14Z)
• 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)
• Invariant Causal Prediction for Block MDPs [106.63346115341862]
  Generalization across environments is critical to the successful application of reinforcement learning algorithms to real-world challenges. We propose a method of invariant prediction to learn model-irrelevance state abstractions (MISA) that generalize to novel observations in the multi-environment setting.
  arXiv  Detail & Related papers  (2020-03-12T21:03:01Z)

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.