Towards Global Neural Network Abstractions with Locally-Exact Reconstruction

Neural networks are a powerful class of non-linear functions. However, their black-box nature makes it difficult to explain their behaviour and certify their safety. Abstraction techniques address this challenge by transforming the neural network into a simpler, over-approximated function. Unfortunately, existing abstraction techniques are slack, which limits their applicability to small local regions of the input domain. In this paper, we propose Global Interval Neural Network Abstractions with Center-Exact Reconstruction (GINNACER). Our novel abstraction technique produces sound over-approximation bounds over the whole input domain while guaranteeing exact reconstructions for any given local input. Our experiments show that GINNACER is several orders of magnitude tighter than state-of-the-art global abstraction techniques, while being competitive with local ones.Comment: Under submission to the Neural Networks Journal (revised version). Sections 2, 4.7, 5.4, Appendix A and B have been adde

Montague semantics and modifier consistency measurement in neural language models

In recent years, distributional language representation models have demonstrated great practical success. At the same time, the need for interpretability has elicited questions on their intrinsic properties and capabilities. Crucially, distributional models are often inconsistent when dealing with compositional phenomena in natural language, which has significant implications for their safety and fairness. Despite this, most current research on compositionality is directed towards improving their performance on similarity tasks only. This work takes a different approach, and proposes a methodology for measuring compositional behavior in contemporary language models. Specifically, we focus on adjectival modifier phenomena in adjective-noun phrases. We introduce three novel tests of compositional behavior inspired by Montague semantics. Our experimental results indicate that current neural language models behave according to the expected linguistic theories to a limited extent only. This raises the question of whether these language models are not able to capture the semantic properties we evaluated, or whether linguistic theories from Montagovian tradition would not match the expected capabilities of distributional models

On the efficiency of data collection and aggregation for the combination of multiple classifiers

Many classification problems are solved by combining the output of a group of distinct predictors. Whether it is voting, consulting domain experts, training an ensemble method or crowdsourcing, the collective consensus we reach is typically more robust and accurate than the decisions of an individual predictor alone. However, aggregating the predictors’ output efficiently is not a trivial endeavour. Furthermore, when we need to solve not just one but multiple classification problems at the same time, the question of how to allocate the limited pool of available predictors arises. These two questions of collecting and aggregating the data from multiple predictors have been addressed to various extents in the existing literature. On the one hand, aggregation algorithms are numerous but are mostly designed for predictive accuracy alone. Achieving state-of-the-art accuracy in a computationally efficient way is currently an open question. On the other hand, empirical studies show that the collection policies we use to allocate the available pool of predictors have a strong impact on the performance of the system. However, to date there is little theoretical understanding of this phenomenon. In this thesis, we tackle these research questions from both a theoretical and an algorithmic angle. First, we develop the theoretical tools to uncover the link between the predictive accuracy of the system and its causal factors: the quality of the predictors, their number and the algorithms we use. We do so by representing the data collection process as a random walk in the posterior probability space, and deriving upper and lower bounds on the expected accuracy. These bounds reveal that the tradeoff between number of predictors and accuracy is always exponential, and allow us to quantify its coefficient. With these tools, we provide the first theoretical explanation of the accuracy gap between different data collection policies. Namely, we prove that the probability of error of adaptive policies decays at more than double the exponential rate of non-adaptive ones. Likewise, we prove that the two most popular adaptive policies, uncertainty sampling and information gain maximisation, are mathematically equivalent. Furthermore, our iv analysis holds both in the case where we know the accuracy of each individual predictor exactly, and in the case where we only have access to some noisy estimate of it. Finally, we revisit the problem of aggregating the predictors’ output by proposing two novel algorithms. The first, Mirror Gibbs, is a refinement of traditional Monte Carlo sampling and achieves better than state-of-the-art accuracy with fewer samples. The second, Streaming Bayesian Inference for Crowdsourcing (SBIC), is based on variational inference and comes in two variants: Fast SBIC is designed for computational speed, while Sorted SBIC is designed for predictive accuracy. Both deliver state-of-the-art accuracy, and feature provable asymptotic guarantees

On the efficiency of data collection for multiple Naïve Bayes classifiers

Many classification problems are solved by aggregating the output of a group of distinct predictors. In this respect, a popular choice is to assume independence and employ a Naïve Bayes classifier. When we have not just one but multiple classification problems at the same time, the question of how to assign the limited pool of available predictors to the individual classification problems arises. Empirical studies show that the policies we use to perform such assignments have a strong impact on the accuracy of the system. However, to date there is little theoretical understanding of this phenomenon. To help rectify this, in this paper we provide the first theoretical explanation of the accuracy gap between the most popular policies: the non-adaptive uniform allocation, and the adaptive allocation schemes based on uncertainty sampling and information gain maximisation. To do so, we propose a novel representation of the data collection process in terms of random walks. Then, we use this tool to derive new lower and upper bounds on the accuracy of the policies. These bounds reveal that the tradeoff between the number of available predictors and the accuracy has a different exponential rate depending on the policy used. By comparing them, we are able to quantify the advantage that the two adaptive policies have over the non-adaptive one for the first time, and prove that the probability of error of the former decays at more than double the exponential rate of the latter. Furthermore, we show in our analysis that this result holds both in the case where we know the accuracy of each individual predictor, and in the case where we only have access to a noisy estimate of it

Streaming Bayesian inference for crowdsourced classification

A key challenge in crowdsourcing is inferring the ground truth from noisy and unreliable data. To do so, existing approaches rely on collecting redundant information from the crowd, and aggregating it with some probabilistic method. However, oftentimes such methods are computationally inefficient, are restricted to some specific settings, or lack theoretical guarantees. In this paper, we revisit the problem of binary classification from crowdsourced data. Specifically we propose Streaming Bayesian Inference for Crowdsourcing (SBIC), a new algorithm that does not suffer from any of these limitations. First, SBIC has low complexity and can be used in a real-time online setting. Second, SBIC has the same accuracy as the best state-of-the-art algorithms in all settings. Third, SBIC has provable asymptotic guarantees both in the online and offline settings. <br/

Influencing the dynamics of correlated opinions in the voter model on multiplex networks

Processes of opinion formation have found much attention in the recent literature on complex systems and networks [2]. Whereas many studies have considered the spread of opinions on a single network, recognition of, in particular, the multi-relational structure of online activities [6] has led to an increased interest in spreading processes on multi-layer networks, where ignoring the existence of different types of connections can have important consequences for our ability to model such systems [7, 5]. Here, building on previous work on opinion propagation in the voting dynamics [4, 8] we are interested in maximizing influence on a multi-layer network. Different to previous work [9], we study influence maximization for multiple correlated opinions, where opinions about different issues spread on different layers of a multiplex network. As an example, consider how people discuss different topics with their friends in offline and online social networks. Yet, holding a particular opinion about one topic may change the individuals’ susceptibility to adopt opinions about other topics, thus effectively coupling different network layers through opinion correlations. Studying influence maximization in such settings allows for a gradual control of the population, as has been observed in real-world scenarios [3]. For instance, we can first prime a population by spreading a particular attitude, which then allows for an easier propagation of our desired opinion. In this paper we formalize a model of such correlated opinion dynamics on multiplex networks, develop an algorithm for optimizing influence on controlled opinions, and provide analysis of different scenarios of optimal control in the presence of an adversary.<br/