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Anatomy of a Formal Proof
No full textInteractive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a formal axiomatic foundation. This article describes the experience of working with a proof assistant and considers the impact the technology will have on mathematics.12 page
Universal programmable waveguide arrays
No full textImplementing arbitrary unitary transformations is crucial for applications in quantum computing, signal processing, and machine learning. Unitaries govern quantum state evolution, enabling reversible transformations critical in quantum tasks like cryptography and simulation and playing key roles in classical domains such as dimensionality reduction and signal compression. Integrated optical waveguide arrays have emerged as a promising platform for these transformations, offering scalability for both quantum and classical systems. However, scalable and efficient methods for implementing arbitrary unitaries remain challenging. Here, we present a theoretical framework for realizing arbitrary unitary matrices through programmable waveguide arrays (PWAs). We provide a mathematical proof demonstrating that cascaded PWAs can implement any unitary matrix within practical constraints, along with a numerical optimization method for customized PWA designs. Our results establish PWAs as a universal and scalable architecture for quantum photonic computing, effectively bridging quantum and classical applications, and positioning PWAs as an enabling technology for advancements in quantum simulation, machine learning, secure communication, and signal processing
Observational Signatures of Dust Traffic Jams in Polar-Aligning Circumbinary Disks
No full textMisaligned circumbinary disks will produce dust traffic jams during alignment or anti-alignment to the binary orbital plane. We conduct a hydrodynamical simulation of an initially misaligned circumbinary disk undergoing polar alignment with multiple dust species. Due to differential precession between the gas and dust components, multiple dust traffic jams are produced within the disk during polar alignment. The radial locations of the dust traffic jams depend on the Stokes number of the grains, which depends on grain size. We compute the dust temperature structure using post-processing radiative transfer to produce continuum images at cm-wavelengths. Multiple distinct rings emerge in the continuum images, corresponding to the dust traffic jams. The angular resolution of upcoming observations from SKA and ngVLA will be sufficient to detect centimeter-sized grains in protoplanetary disks and resolve the widths of dust traffic jams. Therefore, dust traffic jams resulting from the differential precession of gas and dust in misaligned circumbinary disks will be a prime target for more extended wavelength observations.12 pages, 5 figures, accepted for publication in ApJ
The Many Inconsistencies of the Purity-Mixture Distinction in Standard Quantum Mechanics
Get PDFThe distinction between pure states and mixed states is a kernel ingredient of what is considered to be the standard formulation of quantum mechanics and plays today a kernel role in foundational debates about the meaning of quantum probability, the separability of quantum systems, the definition and measure of entanglement, etc. In this work we attempt to expose the many inconsistencies introduced by this distinction and the serious consequences this has for many ongoing research programs within quantum physics which apply these notions uncritically.21 pages, 10 figure
Large Language Models for Generative Information Extraction: A Survey
Get PDFInformation extraction (IE) aims to extract structural knowledge from plain natural language texts. Recently, generative Large Language Models (LLMs) have demonstrated remarkable capabilities in text understanding and generation. As a result, numerous works have been proposed to integrate LLMs for IE tasks based on a generative paradigm. To conduct a comprehensive systematic review and exploration of LLM efforts for IE tasks, in this study, we survey the most recent advancements in this field. We first present an extensive overview by categorizing these works in terms of various IE subtasks and techniques, and then we empirically analyze the most advanced methods and discover the emerging trend of IE tasks with LLMs. Based on a thorough review conducted, we identify several insights in technique and promising research directions that deserve further exploration in future studies. We maintain a public repository and consistently update related works and resources on GitHub (\href{https://github.com/quqxui/Awesome-LLM4IE-Papers}{LLM4IE repository})The article has been accepted by Frontiers of Computer Science (FCS), with the DOI: {10.1007/s11704-024-40555-y}. You can cite the FCS versio
Decision-Focused Learning with Directional Gradients
Get PDFWe propose a novel family of decision-aware surrogate losses, called Perturbation Gradient (PG) losses, for the predict-then-optimize framework. The key idea is to connect the expected downstream decision loss with the directional derivative of a particular plug-in objective, and then approximate this derivative using zeroth order gradient techniques. Unlike the original decision loss which is typically piecewise constant and discontinuous, our new PG losses is a Lipschitz continuous, difference of concave functions that can be optimized using off-the-shelf gradient-based methods. Most importantly, unlike existing surrogate losses, the approximation error of our PG losses vanishes as the number of samples grows. Hence, optimizing our surrogate loss yields a best-in-class policy asymptotically, even in misspecified settings. This is the first such result in misspecified settings, and we provide numerical evidence confirming our PG losses substantively outperform existing proposals when the underlying model is misspecified
Transition Constrained Bayesian Optimization via Markov Decision Processes
Get PDFBayesian optimization is a methodology to optimize black-box functions. Traditionally, it focuses on the setting where you can arbitrarily query the search space. However, many real-life problems do not offer this flexibility; in particular, the search space of the next query may depend on previous ones. Example challenges arise in the physical sciences in the form of local movement constraints, required monotonicity in certain variables, and transitions influencing the accuracy of measurements. Altogether, such transition constraints necessitate a form of planning. This work extends classical Bayesian optimization via the framework of Markov Decision Processes. We iteratively solve a tractable linearization of our utility function using reinforcement learning to obtain a policy that plans ahead for the entire horizon. This is a parallel to the optimization of an acquisition function in policy space. The resulting policy is potentially history-dependent and non-Markovian. We showcase applications in chemical reactor optimization, informative path planning, machine calibration, and other synthetic examples.10 pages main, 34 pages total, 17 figures, 2 tables. Accepted to NeurIPS 202
Epsilon-Greedy Thompson Sampling to Bayesian Optimization
Get PDFBayesian optimization (BO) has become a powerful tool for solving simulation-based engineering optimization problems thanks to its ability to integrate physical and mathematical understandings, consider uncertainty, and address the exploitation-exploration dilemma. Thompson sampling (TS) is a preferred solution for BO to handle the exploitation-exploration trade-off. While it prioritizes exploration by generating and minimizing random sample paths from probabilistic models -- a fundamental ingredient of BO -- TS weakly manages exploitation by gathering information about the true objective function after it obtains new observations. In this work, we improve the exploitation of TS by incorporating the -greedy policy, a well-established selection strategy in reinforcement learning. We first delineate two extremes of TS, namely the generic TS and the sample-average TS. The former promotes exploration, while the latter favors exploitation. We then adopt the -greedy policy to randomly switch between these two extremes. Small and large values of govern exploitation and exploration, respectively. By minimizing two benchmark functions and solving an inverse problem of a steel cantilever beam, we empirically show that -greedy TS equipped with an appropriate is more robust than its two extremes, matching or outperforming the better of the generic TS and the sample-average TS
ConDiSR: Contrastive Disentanglement and Style Regularization for Single Domain Generalization
Get PDFMedical data often exhibits distribution shifts, which cause test-time performance degradation for deep learning models trained using standard supervised learning pipelines. This challenge is addressed in the field of Domain Generalization (DG) with the sub-field of Single Domain Generalization (SDG) being specifically interesting due to the privacy- or logistics-related issues often associated with medical data. Existing disentanglement-based SDG methods heavily rely on structural information embedded in segmentation masks, however classification labels do not provide such dense information. This work introduces a novel SDG method aimed at medical image classification that leverages channel-wise contrastive disentanglement. It is further enhanced with reconstruction-based style regularization to ensure extraction of distinct style and structure feature representations. We evaluate our method on the complex task of multicenter histopathology image classification, comparing it against state-of-the-art (SOTA) SDG baselines. Results demonstrate that our method surpasses the SOTA by a margin of 1% in average accuracy while also showing more stable performance. This study highlights the importance and challenges of exploring SDG frameworks in the context of the classification task. The code is publicly available at https://github.com/BioMedIA-MBZUAI/ConDiSRA flaw was found in the results acquisitio
Aleph Filter: To Infinity in Constant Time
Get PDFFilter data structures are widely used in various areas of computer science to answer approximate set-membership queries. In many applications, the data grows dynamically, requiring their filters to expand along with the data. However, existing methods for expanding filters cannot maintain stable performance, memory footprint, and false positive rate (FPR) simultaneously. We address this problem with Aleph Filter, which makes the following contributions. (1) It supports all operations (insertions, queries, deletes, etc.) in constant time, no matter how much the data grows. (2) Given an estimate of how much the data will ultimately grow, Aleph Filter provides a memory vs. FPR trade-offs on par with static filters