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Computer programs containing calls to linear solvers are a known challenge for automatic differentiation. Previous publications advise against differentiating through the low-level solver implementation, and instead advocate for high-level approaches that express the derivative in terms of a modified linear system that can be solved with a separate solver call. Despite this ubiquitous advice, we are not aware of prior work comparing the accuracy of both approaches. With this article we thus empirically study a simple question: What happens if we ignore common wisdom, and differentiate through linear solvers?

Differentiable rendering methods promise the ability to optimize various parameters of 3d scenes to achieve a desired result. However, lighting design has so far received little attention in this field. In this paper, we introduce a method that enables continuous optimization of the arrangement of luminaires in a 3d scene via differentiable light tracing. Our experiments show two major issues when attempting to apply existing methods from differentiable path tracing to this problem: first, many rendering methods produce images, which restricts the ability of a designer to define lighting objectives to image space. Second, most previous methods are designed for scene geometry or material optimization and have not been extensively tested for the case of optimizing light sources. Currently available differentiable ray-tracing methods do not provide satisfactory performance, even on fairly basic test cases in our experience. In this paper, we propose a novel adjoint light tracing method that overcomes these challenges and enables gradient-based lighting design optimization in a view-independent (camera-free) way. Thus, we allow the user to paint illumination targets directly onto the 3d scene or use existing baked illumination data (e.g., light maps). Using modern ray-tracing hardware, we achieve interactive performance. We find light tracing advantageous over path tracing in this setting, as it naturally handles irregular geometry, resulting in less noise and improved optimization convergence. We compare our adjoint gradients to state-of-the-art image-based differentiable rendering methods. We also demonstrate that our gradient data works with various common optimization algorithms, providing good convergence behaviour. Qualitative comparisons with real-world scenes underline the practical applicability of our method.

We devise achievable encoding schemes for distributed source compression for computing inner products, symmetric matrix products, and more generally, square matrix products, which are a class of nonlinear transformations. To that end, our approach relies on devising nonlinear mappings of distributed sources, which are then followed by the structured linear encoding scheme, introduced by K\"orner and Marton. For different computation scenarios, we contrast our findings on the achievable sum rate with the state of the art to demonstrate the possible savings in compression rate. When the sources have special correlation structures, it is possible to achieve unbounded gains, as demonstrated by the analysis and numerical simulations.

Diabetic Retinopathy (DR), a prevalent complication in diabetes patients, can lead to vision impairment due to lesions formed on the retina. Detecting DR at an advanced stage often results in irreversible blindness. The traditional process of diagnosing DR through retina fundus images by ophthalmologists is not only time-intensive but also expensive. While classical transfer learning models have been widely adopted for computer-aided detection of DR, their high maintenance costs can hinder their detection efficiency. In contrast, Quantum Transfer Learning offers a more effective solution to this challenge. This approach is notably advantageous because it operates on heuristic principles, making it highly optimized for the task. Our proposed methodology leverages this hybrid quantum transfer learning technique to detect DR. To construct our model, we utilize the APTOS 2019 Blindness Detection dataset, available on Kaggle. We employ the ResNet-18, ResNet34, ResNet50, ResNet101, ResNet152 and Inception V3, pre-trained classical neural networks, for the initial feature extraction. For the classification stage, we use a Variational Quantum Classifier. Our hybrid quantum model has shown remarkable results, achieving an accuracy of 97% for ResNet-18. This demonstrates that quantum computing, when integrated with quantum machine learning, can perform tasks with a level of power and efficiency unattainable by classical computers alone. By harnessing these advanced technologies, we can significantly improve the detection and diagnosis of Diabetic Retinopathy, potentially saving many from the risk of blindness. Keywords: Diabetic Retinopathy, Quantum Transfer Learning, Deep Learning

Automated industries lead to high quality production, lower manufacturing cost and better utilization of human resources. Robotic manipulator arms have major role in the automation process. However, for complex manipulation tasks, hard coding efficient and safe trajectories is challenging and time consuming. Machine learning methods have the potential to learn such controllers based on expert demonstrations. Despite promising advances, better approaches must be developed to improve safety, reliability, and efficiency of ML methods in both training and deployment phases. This survey aims to review cutting edge technologies and recent trends on ML methods applied to real-world manipulation tasks. After reviewing the related background on ML, the rest of the paper is devoted to ML applications in different domains such as industry, healthcare, agriculture, space, military, and search and rescue. The paper is closed with important research directions for future works.

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.

Graph Neural Networks (GNNs) draw their strength from explicitly modeling the topological information of structured data. However, existing GNNs suffer from limited capability in capturing the hierarchical graph representation which plays an important role in graph classification. In this paper, we innovatively propose hierarchical graph capsule network (HGCN) that can jointly learn node embeddings and extract graph hierarchies. Specifically, disentangled graph capsules are established by identifying heterogeneous factors underlying each node, such that their instantiation parameters represent different properties of the same entity. To learn the hierarchical representation, HGCN characterizes the part-whole relationship between lower-level capsules (part) and higher-level capsules (whole) by explicitly considering the structure information among the parts. Experimental studies demonstrate the effectiveness of HGCN and the contribution of each component.

Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.

Medical image segmentation requires consensus ground truth segmentations to be derived from multiple expert annotations. A novel approach is proposed that obtains consensus segmentations from experts using graph cuts (GC) and semi supervised learning (SSL). Popular approaches use iterative Expectation Maximization (EM) to estimate the final annotation and quantify annotator's performance. Such techniques pose the risk of getting trapped in local minima. We propose a self consistency (SC) score to quantify annotator consistency using low level image features. SSL is used to predict missing annotations by considering global features and local image consistency. The SC score also serves as the penalty cost in a second order Markov random field (MRF) cost function optimized using graph cuts to derive the final consensus label. Graph cut obtains a global maximum without an iterative procedure. Experimental results on synthetic images, real data of Crohn's disease patients and retinal images show our final segmentation to be accurate and more consistent than competing methods.

Recent advance in fluorescence microscopy enables acquisition of 3D image volumes with better quality and deeper penetration into tissue. Segmentation is a required step to characterize and analyze biological structures in the images. 3D segmentation using deep learning has achieved promising results in microscopy images. One issue is that deep learning techniques require a large set of groundtruth data which is impractical to annotate manually for microscopy volumes. This paper describes a 3D nuclei segmentation method using 3D convolutional neural networks. A set of synthetic volumes and the corresponding groundtruth volumes are generated automatically using a generative adversarial network. Segmentation results demonstrate that our proposed method is capable of segmenting nuclei successfully in 3D for various data sets.