Search for: All records

Normalizing flows map an independent set of latent variables to their samples using a bijective transformation. Despite the exact correspondence between samples and latent variables, their high level relationship is not well understood. In this paper we characterize the geometric structure of flows using principal manifolds and understand the relationship between latent variables and samples using contours. We introduce a novel class of normalizing flows, called principal component flows (PCF), whose contours are its principal manifolds, and a variant for injective flows (iPCF) that is more efficient to train than regular injective flows. PCFs can be constructed using any flow architecture, are trained with a regularized maximum likelihood objective and can perform density estimation on all of their principal manifolds. In our experiments we show that PCFs and iPCFs are able to learn the principal manifolds over a variety of datasets. Additionally, we show that PCFs can perform density estimation on data that lie on a manifold with variable dimensionality, which is not possible with existing normalizing flows. 

Deep neural networks (DNNs) have achieved near-human level accuracy on many datasets across different domains. But they are known to produce incorrect predictions with high confidence on inputs far from the training distribution. This challenge of lack of calibration of DNNs has limited the adoption of deep learning models in high-assurance systems such as autonomous driving, air traffic management, cybersecurity, and medical diagnosis. The problem of detecting when an input is outside the training distribution of a machine learning model, and hence, its prediction on this input cannot be trusted, has received significant attention recently. Several techniques based on statistical, geometric, topological, or relational signatures have been developed to detect the out-of-distribution (OOD) or novel inputs. In this paper, we present a runtime monitor based on predictive processing and dual process theory. We posit that the bottom-up deep neural networks can be monitored using top-down context models comprising two layers. The first layer is a feature density model that learns the joint distribution of the original DNN’s inputs, outputs, and the model’s explanation for its decisions. The second layer is a graph Markov neural network that captures an even broader context. We demonstrate the efficacy of our monitoring architecture in recognizing out-of-distribution and out-of-context inputs on the image classification and object detection tasks.