Injecting structure into neural networks enables learning functions that satisfy invariances with respect to subsets of inputs. For instance, when learning generative models using neural networks, it is advantageous to encode the conditional independence structure of observed variables, often in the form of Bayesian networks. We propose the Structured Neural Network (StrNN), which injects structure through masking pathways in a neural network. The masks are designed via a novel relationship we explore between neural network architectures and binary matrix factorization, to ensure that the desired independencies are respected. We devise and study practical algorithms for this otherwise NP-hard design problem based on novel objectives that control the model architecture. We demonstrate the utility of StrNN in three applications: (1) binary and Gaussian density estimation with StrNN, (2) real-valued density estimation with Structured Autoregressive Flows (StrAFs) and Structured Continuous Normalizing Flows (StrCNF), and (3) interventional and counterfactual analysis with StrAFs for causal inference. Our work opens up new avenues for learning neural networks that enable data-efficient generative modeling and the use of normalizing flows for causal effect estimation.

Injecting structure into neural networks enables learning functions that satisfy invariances with respect to subsets of inputs.

Injecting structure into neural networks enables learning functions that satisfy invariances with respect to subsets of inputs. For instance, when learning generative models using neural networks, it is advantageous to encode the conditional independence structure of observed variables, often in the form of Bayesian networks. We propose the Structured Neural Network (StrNN), which injects structure through masking pathways in a neural network. The masks are designed via a novel relationship we explore between neural network architectures and binary matrix factorization, to ensure that the desired independencies are respected. We devise and study practical algorithms for this otherwise NP-hard design problem based on novel objectives that control the model architecture.

Injecting structure into neural networks enables learning functions that satisfy invariances with respect to subsets of inputs. For instance, when learning generative models using neural networks, it is advantageous to encode the conditional independence structure of observed variables, often in the form of Bayesian networks. We propose the Structured Neural Network (StrNN), which injects structure through masking pathways in a neural network. The masks are designed via a novel relationship we explore between neural network architectures and binary matrix factorization, to ensure that the desired independencies are respected. We devise and study practical algorithms for this otherwise NP-hard design problem based on novel objectives that control the model architecture.

Injecting structure into neural networks enables learning functions that satisfy invariances with respect to subsets of inputs. For instance, when learning generative models using neural networks, it is advantageous to encode the conditional independence structure of observed variables, often in the form of Bayesian networks. We propose the Structured Neural Network (StrNN), which injects structure through masking pathways in a neural network. The masks are designed via a novel relationship we explore between neural network architectures and binary matrix factorization, to ensure that the desired independencies are respected. We devise and study practical algorithms for this otherwise NP-hard design problem based on novel objectives that control the model architecture. We demonstrate the utility of StrNN in three applications: (1) binary and Gaussian density estimation with StrNN, (2) real-valued density estimation with Structured Autoregressive Flows (StrAFs) and Structured Continuous Normalizing Flows (StrCNF), and (3) interventional and counterfactual analysis with StrAFs for causal inference. Our work opens up new avenues for learning neural networks that enable data-efficient generative modeling and the use of normalizing flows for causal effect estimation.

Recently, Strength-based Argumentation Frameworks (StrAFs) have been proposed to model situations where some quantitative strength is associated with arguments. In this setting, the notion of accrual corresponds to sets of arguments that collectively attack an argument. Some semantics have already been defined, which are sensitive to the existence of accruals that collectively defeat their target, while their individual elements cannot. However, until now, only the surface of this framework and semantics have been studied. Indeed, the existing literature focuses on the adaptation of the stable semantics to StrAFs. In this paper, we push forward the study and investigate the adaptation of admissibility-based semantics. Especially, we show that the strong admissibility defined in the literature does not satisfy a desirable property, namely Dung's fundamental lemma. We therefore propose an alternative definition that induces semantics that behave as expected. We then study computational issues for these new semantics, in particular we show that complexity of reasoning is similar to the complexity of the corresponding decision problems for standard argumentation frameworks in almost all cases. We then propose a translation in pseudo-Boolean constraints for computing (strong and weak) extensions. We conclude with an experimental evaluation of our approach which shows in particular that it scales up well for solving the problem of providing one extension as well as enumerating them all.