Constrained Empirical Risk Minimization: Theory and Practice

• URL: http://arxiv.org/abs/2302.04729v1
• Date: Thu, 9 Feb 2023 16:11:58 GMT
• Title: Constrained Empirical Risk Minimization: Theory and Practice
• Authors: Eric Marcus, Ray Sheombarsing, Jan-Jakob Sonke, Jonas Teuwen
• Abstract summary: We present a framework that allows the exact enforcement of constraints on parameterized sets of functions such as Deep Neural Networks (DNNs) We focus on constraints that are outside the scope of equivariant networks used in Geometric Deep Learning. As a major example of the framework, we restrict filters of a Convolutional Neural Network (CNN) to be wavelets, and apply these wavelet networks to the task of contour prediction in the medical domain.
• Score: 2.4934936799100034
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep Neural Networks (DNNs) are widely used for their ability to effectively approximate large classes of functions. This flexibility, however, makes the strict enforcement of constraints on DNNs an open problem. Here we present a framework that, under mild assumptions, allows the exact enforcement of constraints on parameterized sets of functions such as DNNs. Instead of imposing "soft'' constraints via additional terms in the loss, we restrict (a subset of) the DNN parameters to a submanifold on which the constraints are satisfied exactly throughout the entire training procedure. We focus on constraints that are outside the scope of equivariant networks used in Geometric Deep Learning. As a major example of the framework, we restrict filters of a Convolutional Neural Network (CNN) to be wavelets, and apply these wavelet networks to the task of contour prediction in the medical domain.

Related papers

• Deep Neural Network for Constraint Acquisition through Tailored Loss Function [0.0]
  The significance of learning constraints from data is underscored by its potential applications in real-world problem-solving. This work introduces a novel approach grounded in Deep Neural Network (DNN) based on Symbolic Regression.
  arXiv  Detail & Related papers  (2024-03-04T13:47:33Z)
• Robust Stochastically-Descending Unrolled Networks [85.6993263983062]
  Deep unrolling is an emerging learning-to-optimize method that unrolls a truncated iterative algorithm in the layers of a trainable neural network. We show that convergence guarantees and generalizability of the unrolled networks are still open theoretical problems. We numerically assess unrolled architectures trained under the proposed constraints in two different applications.
  arXiv  Detail & Related papers  (2023-12-25T18:51:23Z)
• From NeurODEs to AutoencODEs: a mean-field control framework for width-varying Neural Networks [68.8204255655161]
  We propose a new type of continuous-time control system, called AutoencODE, based on a controlled field that drives dynamics. We show that many architectures can be recovered in regions where the loss function is locally convex.
  arXiv  Detail & Related papers  (2023-07-05T13:26:17Z)
• Neural Fields with Hard Constraints of Arbitrary Differential Order [61.49418682745144]
  We develop a series of approaches for enforcing hard constraints on neural fields. The constraints can be specified as a linear operator applied to the neural field and its derivatives. Our approaches are demonstrated in a wide range of real-world applications.
  arXiv  Detail & Related papers  (2023-06-15T08:33:52Z)
• DeepSaDe: Learning Neural Networks that Guarantee Domain Constraint Satisfaction [8.29487992932196]
  We present an approach to train neural networks which can enforce a wide variety of constraints and guarantee that the constraint is satisfied by all possible predictions. Our approach is flexible enough to enforce a wide variety of domain constraints and is able to guarantee them in neural networks.
  arXiv  Detail & Related papers  (2023-03-02T10:40:50Z)
• POLICE: Provably Optimal Linear Constraint Enforcement for Deep Neural Networks [19.587273175563745]
  We propose the first provable affine constraint enforcement method for Deep Neural Networks (DNNs) Our method does not require any sampling and provably ensures that the DNN fulfills the affine constraint on a given input space's region at any point during training, and testing.
  arXiv  Detail & Related papers  (2022-11-02T17:48:52Z)
• Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks [64.23331120621118]
  We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs) INNs are a class of implicit learning models that use implicit equations as layers. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs.
  arXiv  Detail & Related papers  (2022-04-01T03:31:27Z)
• Neural network training under semidefinite constraints [0.0]
  This paper is concerned with the training of neural networks (NNs) under semidefinite constraints. Semidefinite constraints can be used to verify interesting properties for NNs. In experiments, we demonstrate the superior efficiency of our training method over previous approaches.
  arXiv  Detail & Related papers  (2022-01-03T13:10:49Z)
• Chance-Constrained Control with Lexicographic Deep Reinforcement Learning [77.34726150561087]
  This paper proposes a lexicographic Deep Reinforcement Learning (DeepRL)-based approach to chance-constrained Markov Decision Processes. A lexicographic version of the well-known DeepRL algorithm DQN is also proposed and validated via simulations.
  arXiv  Detail & Related papers  (2020-10-19T13:09:14Z)
• Modeling from Features: a Mean-field Framework for Over-parameterized Deep Neural Networks [54.27962244835622]
  This paper proposes a new mean-field framework for over- parameterized deep neural networks (DNNs) In this framework, a DNN is represented by probability measures and functions over its features in the continuous limit. We illustrate the framework via the standard DNN and the Residual Network (Res-Net) architectures.
  arXiv  Detail & Related papers  (2020-07-03T01:37:16Z)

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.