A Mathematical Certification for Positivity Conditions in Neural Networks with Applications to Partial Monotonicity and Ethical AI

• URL: http://arxiv.org/abs/2406.08525v1
• Date: Wed, 12 Jun 2024 07:33:38 GMT
• Title: A Mathematical Certification for Positivity Conditions in Neural Networks with Applications to Partial Monotonicity and Ethical AI
• Authors: Alejandro Polo-Molina, David Alfaya, Jose Portela,
• Abstract summary: LipVor is an algorithm that certifies if a black-box model, such as an ANN, is positive based on a finite number of evaluations. Our approach is able to mathematically certify if an ANN is partially monotonic without needing constrained ANN's architectures or piece-wise linear activation functions.
• Score: 48.623199394622546
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Artificial Neural Networks (ANNs) have become a powerful tool for modeling complex relationships in large-scale datasets. However, their black-box nature poses ethical challenges. In certain situations, ensuring ethical predictions might require following specific partial monotonic constraints. However, certifying if an already-trained ANN is partially monotonic is challenging. Therefore, ANNs are often disregarded in some critical applications, such as credit scoring, where partial monotonicity is required. To address this challenge, this paper presents a novel algorithm (LipVor) that certifies if a black-box model, such as an ANN, is positive based on a finite number of evaluations. Therefore, as partial monotonicity can be stated as a positivity condition of the partial derivatives, the LipVor Algorithm can certify whether an already trained ANN is partially monotonic. To do so, for every positively evaluated point, the Lipschitzianity of the black-box model is used to construct a specific neighborhood where the function remains positive. Next, based on the Voronoi diagram of the evaluated points, a sufficient condition is stated to certify if the function is positive in the domain. Compared to prior methods, our approach is able to mathematically certify if an ANN is partially monotonic without needing constrained ANN's architectures or piece-wise linear activation functions. Therefore, LipVor could open up the possibility of using unconstrained ANN in some critical fields. Moreover, some other properties of an ANN, such as convexity, can be posed as positivity conditions, and therefore, LipVor could also be applied.

Related papers

• MonoKAN: Certified Monotonic Kolmogorov-Arnold Network [48.623199394622546]
  In certain applications, model predictions must align with expert-imposed requirements, sometimes exemplified by partial monotonicity constraints. We introduce a novel ANN architecture called MonoKAN, based on the KAN architecture and achieves certified partial monotonicity while enhancing interpretability. Our experiments demonstrate that MonoKAN not only enhances interpretability but also improves predictive performance across the majority of benchmarks, outperforming state-of-the-art monotonic approaches.
  arXiv  Detail & Related papers  (2024-09-17T11:10:59Z)
• Efficient Link Prediction via GNN Layers Induced by Negative Sampling [92.05291395292537]
  Graph neural networks (GNNs) for link prediction can loosely be divided into two broad categories. First, emphnode-wise architectures pre-compute individual embeddings for each node that are later combined by a simple decoder to make predictions. Second, emphedge-wise methods rely on the formation of edge-specific subgraph embeddings to enrich the representation of pair-wise relationships.
  arXiv  Detail & Related papers  (2023-10-14T07:02:54Z)
• A Unified Algebraic Perspective on Lipschitz Neural Networks [88.14073994459586]
  This paper introduces a novel perspective unifying various types of 1-Lipschitz neural networks. We show that many existing techniques can be derived and generalized via finding analytical solutions of a common semidefinite programming (SDP) condition. Our approach, called SDP-based Lipschitz Layers (SLL), allows us to design non-trivial yet efficient generalization of convex potential layers.
  arXiv  Detail & Related papers  (2023-03-06T14:31:09Z)
• Constrained Monotonic Neural Networks [0.685316573653194]
  Wider adoption of neural networks in many critical domains such as finance and healthcare is being hindered by the need to explain their predictions. Monotonicity constraint is one of the most requested properties in real-world scenarios. We show it can approximate any continuous monotone function on a compact subset of $mathbbRn$.
  arXiv  Detail & Related papers  (2022-05-24T04:26:10Z)
• Learning Smooth Neural Functions via Lipschitz Regularization [92.42667575719048]
  We introduce a novel regularization designed to encourage smooth latent spaces in neural fields. Compared with prior Lipschitz regularized networks, ours is computationally fast and can be implemented in four lines of code.
  arXiv  Detail & Related papers  (2022-02-16T21:24:54Z)
• Learning a Single Neuron for Non-monotonic Activation Functions [3.890410443467757]
  Non-monotonic activation functions outperform the traditional monotonic ones in many applications. We show that mild conditions on $sigma$ are sufficient to guarantee the learnability in samples time. We also discuss how our positive results are related to existing negative results on training two-layer neural networks.
  arXiv  Detail & Related papers  (2022-02-16T13:44:25Z)
• Robust Implicit Networks via Non-Euclidean Contractions [63.91638306025768]
  Implicit neural networks show improved accuracy and significant reduction in memory consumption. They can suffer from ill-posedness and convergence instability. This paper provides a new framework to design well-posed and robust implicit neural networks.
  arXiv  Detail & Related papers  (2021-06-06T18:05:02Z)
• Counterexample-Guided Learning of Monotonic Neural Networks [32.73558242733049]
  We focus on monotonicity constraints, which are common and require that the function's output increases with increasing values of specific input features. We develop a counterexample-guided technique to provably enforce monotonicity constraints at prediction time. We also propose a technique to use monotonicity as an inductive bias for deep learning.
  arXiv  Detail & Related papers  (2020-06-16T01:04:26Z)
• What needles do sparse neural networks find in nonlinear haystacks [0.0]
  A sparsity inducing penalty in artificial neural networks (ANNs) avoids over-fitting, especially in situations where noise is high and the training set is small. For linear models, such an approach provably also recovers the important features with high probability in regimes for a well-chosen penalty parameter. We perform a set of comprehensive Monte Carlo simulations on a simple model, and the numerical results show the effectiveness of the proposed approach.
  arXiv  Detail & Related papers  (2020-06-07T04:46:55Z)

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.