A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement, system combination and expectations as linear algebra operations. This paper explores how density matrices can be used as a building block to build machine learning models exploiting their ability to straightforwardly combine linear algebra and probability. One of the main results of the paper is to show that density matrices coupled with random Fourier features could approximate arbitrary probability distributions over $\mathbb{R}^n$. Based on this finding the paper builds different models for density estimation, classification and regression. These models are differentiable, so it is possible to integrate them with other differentiable components, such as deep learning architectures and to learn their parameters using gradient-based optimization. In addition, the paper presents optimization-less training strategies based on estimation and model averaging. The models are evaluated in benchmark tasks and the results are reported and discussed.

Modern streaming services are increasingly labeling videos based on their visual or audio content. This typically augments the use of technologies such as AI and ML by allowing to use natural speech for searching by keywords and video descriptions. Prior research has successfully provided a number of solutions for speech to text, in the case of a human speech, but this article aims to investigate possible solutions to retrieve sound events based on a natural language query, and estimate how effective and accurate they are. In this study, we specifically focus on the YamNet, AlexNet, and ResNet-50 pre-trained models to automatically classify audio samples using their respective melspectrograms into a number of predefined classes. The predefined classes can represent sounds associated with actions within a video fragment. Two tests are conducted to evaluate the performance of the models on two separate problems: audio classification and intervals retrieval based on a natural language query. Results show that the benchmarked models are comparable in terms of performance, with YamNet slightly outperforming the other two models. YamNet was able to classify single fixed-size audio samples with 92.7% accuracy and 68.75% precision while its average accuracy on intervals retrieval was 71.62% and precision was 41.95%. The investigated method may be embedded into an automated event marking architecture for streaming services.

While there has been an increasing focus on the use of game theoretic models for autonomous driving, empirical evidence shows that there are still open questions around dealing with the challenges of common knowledge assumptions as well as modeling bounded rationality. To address some of these practical challenges, we develop a framework of generalized dynamic cognitive hierarchy for both modelling naturalistic human driving behavior as well as behavior planning for autonomous vehicles (AV). This framework is built upon a rich model of level-0 behavior through the use of automata strategies, an interpretable notion of bounded rationality through safety and maneuver satisficing, and a robust response for planning. Based on evaluation on two large naturalistic datasets as well as simulation of critical traffic scenarios, we show that i) automata strategies are well suited for level-0 behavior in a dynamic level-k framework, and ii) the proposed robust response to a heterogeneous population of strategic and non-strategic reasoners can be an effective approach for game theoretic planning in AV.

In neural Information Retrieval (IR), ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning \emph{sparse} representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. Introduced recently, the SPLADE model provides highly sparse representations and competitive results with respect to state-of-the-art dense and sparse approaches. In this paper, we build on SPLADE and propose several significant improvements in terms of effectiveness and/or efficiency. More specifically, we modify the pooling mechanism, benchmark a model solely based on document expansion, and introduce models trained with distillation. We also report results on the BEIR benchmark. Overall, SPLADE is considerably improved with more than $9$\% gains on NDCG@10 on TREC DL 2019, leading to state-of-the-art results on the BEIR benchmark.

Deep learning has transformed the way we think of software and what it can do. But deep neural networks are fragile and their behaviors are often surprising. In many settings, we need to provide formal guarantees on the safety, security, correctness, or robustness of neural networks. This book covers foundational ideas from formal verification and their adaptation to reasoning about neural networks and deep learning.

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