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Object detection models, a prominent class of machine learning algorithms, aim to identify and precisely locate objects in images or videos. However, this task might yield uneven performances sometimes caused by the objects sizes and the quality of the images and labels used for training. In this paper, we highlight the importance of large objects in learning features that are critical for all sizes. Given these findings, we propose to introduce a weighting term into the training loss. This term is a function of the object area size. We show that giving more weight to large objects leads to improved detection scores across all object sizes and so an overall improvement in Object Detectors performances (+2 p.p. of mAP on small objects, +2 p.p. on medium and +4 p.p. on large on COCO val 2017 with InternImage-T). Additional experiments and ablation studies with different models and on a different dataset further confirm the robustness of our findings.

Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be highly desirable. In this paper, we initiate the study of program synthesis for quantum unitary programs that recursively define a family of unitary circuits for different input sizes, which are widely used in existing quantum programming languages. Specifically, we present QSynth, the first quantum program synthesis framework, including a new inductive quantum programming language, its specification, a sound logic for reasoning, and an encoding of the reasoning procedure into SMT instances. By leveraging existing SMT solvers, QSynth successfully synthesizes ten quantum unitary programs including quantum adder circuits, quantum eigenvalue inversion circuits and Quantum Fourier Transformation, which can be readily transpiled to executable programs on major quantum platforms, e.g., Q#, IBM Qiskit, and AWS Braket.

We present a simple functional programming language, called Dual PCF, that implements forward mode automatic differentiation using dual numbers in the framework of exact real number computation. The main new feature of this language is the ability to evaluate correctly up to the precision specified by the user -- in a simple and direct way -- the directional derivative of functionals as well as first order functions. In contrast to other comparable languages, Dual PCF also includes the recursive operator for defining functions and functionals. We provide a wide range of examples of Lipschitz functions and functionals that can be defined in Dual PCF. We use domain theory both to give a denotational semantics to the language and to prove the correctness of the new derivative operator using logical relations. To be able to differentiate functionals -- including on function spaces equipped with their compact-open topology that do not admit a norm -- we develop a domain-theoretic directional derivative that is Scott continuous and extends Clarke's subgradient of real-valued locally Lipschitz maps on Banach spaces to real-valued continuous maps on Hausdorff topological vector spaces. Finally, we show that we can express arbitrary computable linear functionals in Dual PCF.

Artificial intelligence and deep learning are currently reshaping numerical simulation frameworks by introducing new modeling capabilities. These frameworks are extensively investigated in the context of model correction and parameterization where they demonstrate great potential and often outperform traditional physical models. Most of these efforts in defining hybrid dynamical systems follow {offline} learning strategies in which the neural parameterization (called here sub-model) is trained to output an ideal correction. Yet, these hybrid models can face hard limitations when defining what should be a relevant sub-model response that would translate into a good forecasting performance. End-to-end learning schemes, also referred to as online learning, could address such a shortcoming by allowing the deep learning sub-models to train on historical data. However, defining end-to-end training schemes for the calibration of neural sub-models in hybrid systems requires working with an optimization problem that involves the solver of the physical equations. Online learning methodologies thus require the numerical model to be differentiable, which is not the case for most modeling systems. To overcome this difficulty and bypass the differentiability challenge of physical models, we present an efficient and practical online learning approach for hybrid systems. The method, called EGA for Euler Gradient Approximation, assumes an additive neural correction to the physical model, and an explicit Euler approximation of the gradients. We demonstrate that the EGA converges to the exact gradients in the limit of infinitely small time steps. Numerical experiments are performed on various case studies, including prototypical ocean-atmosphere dynamics. Results show significant improvements over offline learning, highlighting the potential of end-to-end online learning for hybrid modeling.

This article expands the framework of Bayesian inference and provides direct probabilistic methods for approaching inference tasks that are typically handled with information theory. We treat Bayesian probability updating as a random process and uncover intrinsic quantitative features of joint probability distributions called inferential moments. Inferential moments quantify shape information about how a prior distribution is expected to update in response to yet to be obtained information. Further, we quantify the unique probability distribution whose statistical moments are the inferential moments in question. We find a power series expansion of the mutual information in terms of inferential moments, which implies a connection between inferential theoretic logic and elements of information theory. Of particular interest is the inferential deviation, which is the expected variation of the probability of one variable in response to an inferential update of another. We explore two applications that analyze the inferential deviations of a Bayesian network to improve decision-making. We implement simple greedy algorithms for exploring sensor tasking using inferential deviations that generally outperform similar greedy mutual information algorithms in terms of root mean squared error between epistemic probability estimates and the ground truth probabilities they are estimating.

Graph-based interactive theorem provers offer a visual representation of proofs, explicitly representing the dependencies and inferences between each of the proof steps in a graph or hypergraph format. The number and complexity of these dependency links can determine how long it takes to verify the validity of the entire proof. Towards this end, we present a set of parallel algorithms for the formal verification of graph-based natural-deduction (ND) style proofs. We introduce a definition of layering that captures dependencies between the proof steps (nodes). Nodes in each layer can then be verified in parallel as long as prior layers have been verified. To evaluate the performance of our algorithms on proof graphs, we propose a framework for finding the performance bounds and patterns using directed acyclic network topologies (DANTs). This framework allows us to create concrete instances of DANTs for empirical evaluation of our algorithms. With this, we compare our set of parallel algorithms against a serial implementation with two experiments: one scaling both the problem size and the other scaling the number of threads. Our findings show that parallelization results in improved verification performance for certain DANT instances. We also show that our algorithms scale for certain DANT instances with respect to the number of threads.

Implementing precise detection of oil leaks in peak load equipment through image analysis can significantly enhance inspection quality and ensure the system's safety and reliability. However, challenges such as varying shapes of oil-stained regions, background noise, and fluctuating lighting conditions complicate the detection process. To address this, the integration of logical rule-based discrimination into image recognition has been proposed. This approach involves recognizing the spatial relationships among objects to semantically segment images of oil spills using a Mask RCNN network. The process begins with histogram equalization to enhance the original image, followed by the use of Mask RCNN to identify the preliminary positions and outlines of oil tanks, the ground, and areas of potential oil contamination. Subsequent to this identification, the spatial relationships between these objects are analyzed. Logical rules are then applied to ascertain whether the suspected areas are indeed oil spills. This method's effectiveness has been confirmed by testing on images captured from peak power equipment in the field. The results indicate that this approach can adeptly tackle the challenges in identifying oil-contaminated areas, showing a substantial improvement in accuracy compared to existing methods.

We propose a theoretical framework for formulating language model decoder algorithms with dynamic programming and information theory. With dynamic programming, we lift the design of decoder algorithms from the logit space to the action-state value function space, and show that the decoding algorithms are consequences of optimizing the action-state value functions. Each component in the action-state value function space has an information theoretical interpretation. With the lifting and interpretation, it becomes evident what the decoder algorithm is optimized for, and hence facilitating the arbitration of the tradeoffs in sensibleness, diversity, and attribution.

This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn useful representations, we systematically study the major components of our framework. We show that (1) composition of data augmentations plays a critical role in defining effective predictive tasks, (2) introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and (3) contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning. By combining these findings, we are able to considerably outperform previous methods for self-supervised and semi-supervised learning on ImageNet. A linear classifier trained on self-supervised representations learned by SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art, matching the performance of a supervised ResNet-50. When fine-tuned on only 1% of the labels, we achieve 85.8% top-5 accuracy, outperforming AlexNet with 100X fewer labels.

Neural machine translation (NMT) is a deep learning based approach for machine translation, which yields the state-of-the-art translation performance in scenarios where large-scale parallel corpora are available. Although the high-quality and domain-specific translation is crucial in the real world, domain-specific corpora are usually scarce or nonexistent, and thus vanilla NMT performs poorly in such scenarios. Domain adaptation that leverages both out-of-domain parallel corpora as well as monolingual corpora for in-domain translation, is very important for domain-specific translation. In this paper, we give a comprehensive survey of the state-of-the-art domain adaptation techniques for NMT.