Related papers: SPINE: Soft Piecewise Interpretable Neural Equatio…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
The lack of interpretability is an inevitable problem when using neural network models in real applications. In this paper, an explainable neural network based on generalized additive models with structured interactions (GAMI-Net) is…
Piecewise affine neural networks (PANNs) provide a principled geometric perspective on neural network expressivity by characterizing the input--output map as a continuous piecewise affine (CPA) function whose complexity is governed by the…
In spite of several claims stating that some models are more interpretable than others -- e.g., "linear models are more interpretable than deep neural networks" -- we still lack a principled notion of interpretability to formally compare…
Neural Networks (NN) with ReLU activation functions are used to model multiparametric quadratic optimization problems (mp-QP) in diverse engineering applications. Researchers have suggested leveraging the piecewise affine property of deep…
Function plays an important role in mathematics and many science branches. As the fast development of computer technology, more and more study on computational function analysis, e.g., Fast Fourier Transform, Wavelet Transform, Curve…
Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…
In this paper, we propose a unified energy minimization model for the segmentation of non-smooth image structures. The energy of piecewise linear patch reconstruction is considered as an objective measure of the quality of the segmentation…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
Although artificial neural networks have shown great promise in applications including computer vision and speech recognition, there remains considerable practical and theoretical difficulty in optimizing their parameters. The seemingly…
Capsule Networks (CapsNets) have been re-introduced as a more compact and interpretable alternative to standard deep neural networks. While recent efforts have proved their compression capabilities, to date, their interpretability…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
This paper studies the approximation property of ReLU neural networks (NNs) to piecewise constant functions with unknown interfaces in bounded regions in $\mathbb{R}^d$. Under the assumption that the discontinuity interface $\Gamma$ may be…
Traditional neural networks have an impressive classification performance, but what they learn cannot be inspected, verified or extracted. Neural Logic Networks on the other hand have an interpretable structure that enables them to learn a…
PieceWise Affine (PWA) approximations for nonlinear functions have been extensively used for tractable, computationally efficient control of nonlinear systems. However, reaching a desired approximation accuracy without prior information…
Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
Strong intelligent machines powered by deep neural networks are increasingly deployed as black boxes to make decisions in risk-sensitive domains, such as finance and medical. To reduce potential risk and build trust with users, it is…
As a powerful modelling method, PieceWise Linear Neural Networks (PWLNNs) have proven successful in various fields, most recently in deep learning. To apply PWLNN methods, both the representation and the learning have long been studied. In…
Mechanistic interpretability (MI) is an emerging framework for interpreting neural networks. Given a task and model, MI aims to discover a succinct algorithmic process, an interpretation, that explains the model's decision process on that…