ReLU Networks as Random Functions: Their Distribution in Probability Space

• URL: http://arxiv.org/abs/2503.22082v1
• Date: Fri, 28 Mar 2025 01:58:40 GMT
• Title: ReLU Networks as Random Functions: Their Distribution in Probability Space
• Authors: Shreyas Chaudhari, José M. F. Moura,
• Abstract summary: This paper presents a novel framework for understanding trained ReLU networks as random, affine functions.<n>We derive the discrete probability distribution over the affine functions realizable by the network.<n>Our work provides a framework for understanding the behavior and performance of ReLU networks.
• Score: 13.408904884821903
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper presents a novel framework for understanding trained ReLU networks as random, affine functions, where the randomness is induced by the distribution over the inputs. By characterizing the probability distribution of the network's activation patterns, we derive the discrete probability distribution over the affine functions realizable by the network. We extend this analysis to describe the probability distribution of the network's outputs. Our approach provides explicit, numerically tractable expressions for these distributions in terms of Gaussian orthant probabilities. Additionally, we develop approximation techniques to identify the support of affine functions a trained ReLU network can realize for a given distribution of inputs. Our work provides a framework for understanding the behavior and performance of ReLU networks corresponding to stochastic inputs, paving the way for more interpretable and reliable models.

Related papers

• Generative Assignment Flows for Representing and Learning Joint Distributions of Discrete Data [2.6499018693213316]
  We introduce a novel generative model for the representation of joint probability distributions of discrete random variables.<n>The approach uses measure transport by randomized assignment flows on the statistical submanifold of factorizing distributions.
  arXiv  Detail & Related papers  (2024-06-06T21:58:33Z)
• Uncertainty Quantification via Stable Distribution Propagation [60.065272548502]
  We propose a new approach for propagating stable probability distributions through neural networks. Our method is based on local linearization, which we show to be an optimal approximation in terms of total variation distance for the ReLU non-linearity.
  arXiv  Detail & Related papers  (2024-02-13T09:40:19Z)
• Distributional GFlowNets with Quantile Flows [73.73721901056662]
  Generative Flow Networks (GFlowNets) are a new family of probabilistic samplers where an agent learns a policy for generating complex structure through a series of decision-making steps. In this work, we adopt a distributional paradigm for GFlowNets, turning each flow function into a distribution, thus providing more informative learning signals during training. Our proposed textitquantile matching GFlowNet learning algorithm is able to learn a risk-sensitive policy, an essential component for handling scenarios with risk uncertainty.
  arXiv  Detail & Related papers  (2023-02-11T22:06:17Z)
• Probabilistic Verification of ReLU Neural Networks via Characteristic Functions [11.489187712465325]
  We use ideas from probability theory in the frequency domain to provide probabilistic verification guarantees for ReLU neural networks. We interpret a (deep) feedforward neural network as a discrete dynamical system over a finite horizon. We obtain the corresponding cumulative distribution function of the output set, which can be used to check if the network is performing as expected.
  arXiv  Detail & Related papers  (2022-12-03T05:53:57Z)
• Learning Structured Gaussians to Approximate Deep Ensembles [10.055143995729415]
  This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approxorimator for dense image prediction tasks. We capture the uncertainty and structured correlations in the predictions explicitly in a formal distribution, rather than implicitly through sampling alone. We demonstrate the merits of our approach on monocular depth estimation and show that the advantages of our approach are obtained with comparable quantitative performance.
  arXiv  Detail & Related papers  (2022-03-29T12:34:43Z)
• Robust Estimation for Nonparametric Families via Generative Adversarial Networks [92.64483100338724]
  We provide a framework for designing Generative Adversarial Networks (GANs) to solve high dimensional robust statistics problems. Our work extend these to robust mean estimation, second moment estimation, and robust linear regression. In terms of techniques, our proposed GAN losses can be viewed as a smoothed and generalized Kolmogorov-Smirnov distance.
  arXiv  Detail & Related papers  (2022-02-02T20:11:33Z)
• GFlowNet Foundations [66.69854262276391]
  Generative Flow Networks (GFlowNets) have been introduced as a method to sample a diverse set of candidates in an active learning context. We show a number of additional theoretical properties of GFlowNets.
  arXiv  Detail & Related papers  (2021-11-17T17:59:54Z)
• Goal-oriented adaptive sampling under random field modelling of response probability distributions [0.6445605125467573]
  We consider cases where the spatial variation of response distributions does not only concern their mean and/or variance but also other features including for instance shape or uni-modality versus multi-modality. Our contributions build upon a non-parametric Bayesian approach to modelling the thereby induced fields of probability distributions.
  arXiv  Detail & Related papers  (2021-02-15T15:55:23Z)
• Implicit Distributional Reinforcement Learning [61.166030238490634]
  implicit distributional actor-critic (IDAC) built on two deep generator networks (DGNs) Semi-implicit actor (SIA) powered by a flexible policy distribution. We observe IDAC outperforms state-of-the-art algorithms on representative OpenAI Gym environments.
  arXiv  Detail & Related papers  (2020-07-13T02:52:18Z)
• A Distributional Analysis of Sampling-Based Reinforcement Learning Algorithms [67.67377846416106]
  We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We show that value-based methods such as TD($lambda$) and $Q$-Learning have update rules which are contractive in the space of distributions of functions.
  arXiv  Detail & Related papers  (2020-03-27T05:13:29Z)

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.