In this paper we try to find a computational interpretation for a strong form of extensionality, which we call ``converse extensionality''. These converse extensionality principles, which arise as the Dialectica interpretation of the axiom of extensionality, were first studied by Howard. In order to give a computational interpretation to these principles, we reconsider Brouwer's apartness relation, a strong constructive form of inequality. Formally, we provide a categorical construction to endow every typed combinatory algebra with an apartness relation. We then exploit that functions reflect apartness, in addition to preserving equality, to prove that the resulting categories of assemblies model a converse extensionality principle.
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The cumulative distribution or probability density of a random variable, which is itself a function of a high number of independent real-valued random variables, can be formulated as high-dimensional integrals of an indicator or a Dirac $\delta$ function, respectively. To approximate the distribution or density at a point, we carry out preintegration with respect to one suitably chosen variable, then apply a Quasi-Monte Carlo method to compute the integral of the resulting smoother function. Interpolation is then used to reconstruct the distribution or density on an interval. We provide rigorous regularity and error analysis for the preintegrated function to show that our estimators achieve nearly first order convergence. Numerical results support the theory.
Similarity search is a key operation in multimedia retrieval systems and recommender systems, and it will play an important role also for future machine learning and augmented reality applications. When these systems need to serve large objects with tight delay constraints, edge servers close to the end-user can operate as similarity caches to speed up the retrieval. In this paper we present A\c{C}AI, a new similarity caching policy which improves on the state of the art by using (i) an (approximate) index for the whole catalog to decide which objects to serve locally and which to retrieve from the remote server, and (ii) a mirror ascent algorithm to update the set of local objects with strong guarantees even when the request process does not exhibit any statistical regularity.
We show that Gottesman's semantics (GROUP22, 1998) for Clifford circuits based on the Heisenberg representation can be treated as a type system that can efficiently characterize a common subset of quantum programs. Our applications include (i) certifying whether auxiliary qubits can be safely disposed of, (ii) determining if a system is separable across a given bi-partition, (iii) checking the transversality of a gate with respect to a given stabilizer code, and (iv) typing post-measurement states for computational basis measurements. Further, this type system is extended to accommodate universal quantum computing by deriving types for the $T$-gate, multiply-controlled unitaries such as the Toffoli gate, and some gate injection circuits that use associated magic states. These types allow us to prove a lower bound on the number of $T$ gates necessary to perform a multiply-controlled $Z$ gate.
Conversational question answering (CQA) systems aim to provide natural-language answers to users in information-seeking conversations. Existing CQA benchmarks compare models with pre-collected human-human conversations, using ground-truth answers provided in conversational history. It remains unclear whether we can rely on this static evaluation for model development and whether current systems can well generalize to real-world human-machine conversations. In this work, we conduct the first large-scale human evaluation of state-of-the-art CQA systems, where human evaluators converse with models and judge the correctness of their answers. We find that the distribution of human-machine conversations differs drastically from that of human-human conversations, and there is a disagreement between human and gold-history evaluation in terms of model ranking. We further investigate how to improve automatic evaluations, and propose a question rewriting mechanism based on predicted history, which better correlates with human judgments. Finally, we discuss the impact of various modeling strategies and future directions towards better conversational question answering systems.
Neural Architecture Search (NAS) has attracted growing interest. To reduce the search cost, recent work has explored weight sharing across models and made major progress in One-Shot NAS. However, it has been observed that a model with higher one-shot model accuracy does not necessarily perform better when stand-alone trained. To address this issue, in this paper, we propose Progressive Automatic Design of search space, named PAD-NAS. Unlike previous approaches where the same operation search space is shared by all the layers in the supernet, we formulate a progressive search strategy based on operation pruning and build a layer-wise operation search space. In this way, PAD-NAS can automatically design the operations for each layer and achieve a trade-off between search space quality and model diversity. During the search, we also take the hardware platform constraints into consideration for efficient neural network model deployment. Extensive experiments on ImageNet show that our method can achieve state-of-the-art performance.
In real-world optimisation, it is common to face several sub-problems interacting and forming the main problem. There is an inter-dependency between the sub-problems, making it impossible to solve such a problem by focusing on only one component. The traveling thief problem~(TTP) belongs to this category and is formed by the integration of the traveling salesperson problem~(TSP) and the knapsack problem~(KP). In this paper, we investigate the inter-dependency of the TSP and the KP by means of quality diversity~(QD) approaches. QD algorithms provide a powerful tool not only to obtain high-quality solutions but also to illustrate the distribution of high-performing solutions in the behavioural space. We introduce a MAP-Elite based evolutionary algorithm using well-known TSP and KP search operators, taking the TSP and KP score as behavioural descriptor. Afterwards, we conduct comprehensive experimental studies that show the usefulness of using the QD approach applied to the TTP. First, we provide insights regarding high-quality TTP solutions in the TSP/KP behavioural space. Afterwards, we show that better solutions for the TTP can be obtained by using our QD approach and show that it can improve the best-known solution for a wide range of TTP instances used for benchmarking in the literature.
Online peer-to-peer support platforms enable conversations between millions of people who seek and provide mental health support. If successful, web-based mental health conversations could improve access to treatment and reduce the global disease burden. Psychologists have repeatedly demonstrated that empathy, the ability to understand and feel the emotions and experiences of others, is a key component leading to positive outcomes in supportive conversations. However, recent studies have shown that highly empathic conversations are rare in online mental health platforms. In this paper, we work towards improving empathy in online mental health support conversations. We introduce a new task of empathic rewriting which aims to transform low-empathy conversational posts to higher empathy. Learning such transformations is challenging and requires a deep understanding of empathy while maintaining conversation quality through text fluency and specificity to the conversational context. Here we propose PARTNER, a deep reinforcement learning agent that learns to make sentence-level edits to posts in order to increase the expressed level of empathy while maintaining conversation quality. Our RL agent leverages a policy network, based on a transformer language model adapted from GPT-2, which performs the dual task of generating candidate empathic sentences and adding those sentences at appropriate positions. During training, we reward transformations that increase empathy in posts while maintaining text fluency, context specificity and diversity. Through a combination of automatic and human evaluation, we demonstrate that PARTNER successfully generates more empathic, specific, and diverse responses and outperforms NLP methods from related tasks like style transfer and empathic dialogue generation. Our work has direct implications for facilitating empathic conversations on web-based platforms.
Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an attempt along this line by reformulating the training procedure from the trajectory optimization perspective. We first show that most widely-used algorithms for training DNNs can be linked to the Differential Dynamic Programming (DDP), a celebrated second-order trajectory optimization algorithm rooted in the Approximate Dynamic Programming. In this vein, we propose a new variant of DDP that can accept batch optimization for training feedforward networks, while integrating naturally with the recent progress in curvature approximation. The resulting algorithm features layer-wise feedback policies which improve convergence rate and reduce sensitivity to hyper-parameter over existing methods. We show that the algorithm is competitive against state-ofthe-art first and second order methods. Our work opens up new avenues for principled algorithmic design built upon the optimal control theory.
The present paper surveys neural approaches to conversational AI that have been developed in the last few years. We group conversational systems into three categories: (1) question answering agents, (2) task-oriented dialogue agents, and (3) chatbots. For each category, we present a review of state-of-the-art neural approaches, draw the connection between them and traditional approaches, and discuss the progress that has been made and challenges still being faced, using specific systems and models as case studies.
We consider the task of learning the parameters of a {\em single} component of a mixture model, for the case when we are given {\em side information} about that component, we call this the "search problem" in mixture models. We would like to solve this with computational and sample complexity lower than solving the overall original problem, where one learns parameters of all components. Our main contributions are the development of a simple but general model for the notion of side information, and a corresponding simple matrix-based algorithm for solving the search problem in this general setting. We then specialize this model and algorithm to four common scenarios: Gaussian mixture models, LDA topic models, subspace clustering, and mixed linear regression. For each one of these we show that if (and only if) the side information is informative, we obtain parameter estimates with greater accuracy, and also improved computation complexity than existing moment based mixture model algorithms (e.g. tensor methods). We also illustrate several natural ways one can obtain such side information, for specific problem instances. Our experiments on real data sets (NY Times, Yelp, BSDS500) further demonstrate the practicality of our algorithms showing significant improvement in runtime and accuracy.
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