Visual sense of number vs. sense of magnitude in humans and machines

Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representations; others argue that visual numerosity is estimated using continuous magnitudes, such as density or area, which usually co-vary with number. Here we reconcile these contrasting perspectives by testing deep neural networks on the same numerosity comparison task that was administered to human participants, using a stimulus space that allows the precise measurement of the contribution of non-numerical features. Our model accurately simulates the psychophysics of numerosity perception and the associated developmental changes: discrimination is driven by numerosity, but non-numerical features also have a significant impact, especially early during development. Representational similarity analysis further highlights that both numerosity and continuous magnitudes are spontaneously encoded in deep networks even when no task has to be carried out, suggesting that numerosity is a major, salient property of our visual environment

DeepSaucer: Unified Environment for Verifying Deep Neural Networks

In recent years, a number of methods for verifying DNNs have been developed. Because the approaches of the methods differ and have their own limitations, we think that a number of verification methods should be applied to a developed DNN. To apply a number of methods to the DNN, it is necessary to translate either the implementation of the DNN or the verification method so that one runs in the same environment as the other. Since those translations are time-consuming, a utility tool, named DeepSaucer, which helps to retain and reuse implementations of DNNs, verification methods, and their environments, is proposed. In DeepSaucer, code snippets of loading DNNs, running verification methods, and creating their environments are retained and reused as software assets in order to reduce cost of verifying DNNs. The feasibility of DeepSaucer is confirmed by implementing it on the basis of Anaconda, which provides virtual environment for loading a DNN and running a verification method. In addition, the effectiveness of DeepSaucer is demonstrated by usecase examples

DeepGauge: Multi-Granularity Testing Criteria for Deep Learning Systems

Deep learning (DL) defines a new data-driven programming paradigm that constructs the internal system logic of a crafted neuron network through a set of training data. We have seen wide adoption of DL in many safety-critical scenarios. However, a plethora of studies have shown that the state-of-the-art DL systems suffer from various vulnerabilities which can lead to severe consequences when applied to real-world applications. Currently, the testing adequacy of a DL system is usually measured by the accuracy of test data. Considering the limitation of accessible high quality test data, good accuracy performance on test data can hardly provide confidence to the testing adequacy and generality of DL systems. Unlike traditional software systems that have clear and controllable logic and functionality, the lack of interpretability in a DL system makes system analysis and defect detection difficult, which could potentially hinder its real-world deployment. In this paper, we propose DeepGauge, a set of multi-granularity testing criteria for DL systems, which aims at rendering a multi-faceted portrayal of the testbed. The in-depth evaluation of our proposed testing criteria is demonstrated on two well-known datasets, five DL systems, and with four state-of-the-art adversarial attack techniques against DL. The potential usefulness of DeepGauge sheds light on the construction of more generic and robust DL systems.Comment: The 33rd IEEE/ACM International Conference on Automated Software Engineering (ASE 2018