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In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimisation methods in machine learning, imaging and signal processing, etc. At each iteration SGD uses a single datum, or a small subset of data, resulting in highly scalable methods that are very attractive for large-scale inverse problems. Nonetheless, the theoretical analysis of SGD-based approaches for inverse problems has thus far been largely limited to Euclidean and Hilbert spaces. In this work we present a novel convergence analysis of SGD for linear inverse problems in general Banach spaces: we show the almost sure convergence of the iterates to the minimum norm solution and establish the regularising property for suitable a priori stopping criteria. Numerical results are also presented to illustrate features of the approach.

Metatheorems about type theories are often proven by interpreting the syntax into models constructed using categorical gluing. We propose to use only sconing (gluing along a global section functor) instead of general gluing. The sconing is performed internally to a presheaf category, and we recover the original glued model by externalization. Our method relies on constructions involving two notions of models: first-order models (with explicit contexts) and higher-order models (without explicit contexts). Sconing turns a displayed higher-order model into a displayed first-order model. Using these, we derive specialized induction principles for the syntax of type theory. The input of such an induction principle is a boilerplate-free description of its motives and methods, not mentioning contexts. The output is a section with computation rules specified in the same internal language. We illustrate our framework by proofs of canonicity, normalization and syntactic parametricity for type theory.

The complexity and dynamism of microservices pose significant challenges to system reliability, and thereby, automated troubleshooting is crucial. Effective root cause localization after anomaly detection is crucial for ensuring the reliability of microservice systems. However, two significant issues rest in existing approaches: (1) Microservices generate traces, system logs, and key performance indicators (KPIs), but existing approaches usually consider traces only, failing to understand the system fully as traces cannot depict all anomalies; (2) Troubleshooting microservices generally contains two main phases, i.e., anomaly detection and root cause localization. Existing studies regard these two phases as independent, ignoring their close correlation. Even worse, inaccurate detection results can deeply affect localization effectiveness. To overcome these limitations, we propose Eadro, the first end-to-end framework to integrate anomaly detection and root cause localization based on multi-source data for troubleshooting large-scale microservices. The key insights of Eadro are the anomaly manifestations on different data sources and the close connection between detection and localization. Thus, Eadro models intra-service behaviors and inter-service dependencies from traces, logs, and KPIs, all the while leveraging the shared knowledge of the two phases via multi-task learning. Experiments on two widely-used benchmark microservices demonstrate that Eadro outperforms state-of-the-art approaches by a large margin. The results also show the usefulness of integrating multi-source data. We also release our code and data to facilitate future research.

Quantum computers are believed to have the ability to process huge data sizes which can be seen in machine learning applications. In these applications, the data in general is classical. Therefore, to process them on a quantum computer, there is a need for efficient methods which can be used to map classical data on quantum states in a concise manner. On the other hand, to verify the results of quantum computers and study quantum algorithms, we need to be able to approximate quantum operations into forms that are easier to simulate on classical computers with some errors. Motivated by these needs, in this paper we study the approximation of matrices and vectors by using their tensor products obtained through successive Schmidt decompositions. We show that data with distributions such as uniform, Poisson, exponential, or similar to these distributions can be approximated by using only a few terms which can be easily mapped onto quantum circuits. The examples include random data with different distributions, the Gram matrices of iris flower, handwritten digits, 20newsgroup, and labeled faces in the wild. And similarly, some quantum operations such as quantum Fourier transform and variational quantum circuits with a small depth also may be approximated with a few terms that are easier to simulate on classical computers. Furthermore, we show how the method can be used to simplify quantum Hamiltonians: In particular, we show the application to randomly generated transverse field Ising model Hamiltonians. The reduced Hamiltonians can be mapped into quantum circuits easily and therefore can be simulated more efficiently.

Self-paced curriculum learning (SCL) has demonstrated its great potential in computer vision, natural language processing, etc. During training, it implements easy-to-hard sampling based on online estimation of data difficulty. Most SCL methods commonly adopt a loss-based strategy of estimating data difficulty and deweighting the `hard' samples in the early training stage. While achieving success in a variety of applications, SCL stills confront two challenges in a medical image analysis task, such as universal lesion detection, featuring insufficient and highly class-imbalanced data: (i) the loss-based difficulty measurer is inaccurate; ii) the hard samples are under-utilized from a deweighting mechanism. To overcome these challenges, in this paper we propose a novel mixed-order self-paced curriculum learning (Mo-SCL) method. We integrate both uncertainty and loss to better estimate difficulty online and mix both hard and easy samples in the same mini-batch to appropriately alleviate the problem of under-utilization of hard samples. We provide a theoretical investigation of our method in the context of stochastic gradient descent optimization and extensive experiments based on the DeepLesion benchmark dataset for universal lesion detection (ULD). When applied to two state-of-the-art ULD methods, the proposed mixed-order SCL method can provide a free boost to lesion detection accuracy without extra special network designs.

Motivated by a real-world application, we model and solve a complex staff scheduling problem. Tasks are to be assigned to workers for supervision. Multiple tasks can be covered in parallel by a single worker, with worker shifts being flexible within availabilities. Each worker has a different skill set, enabling them to cover different tasks. Tasks require assignment according to priority and skill requirements. The objective is to maximize the number of assigned tasks weighted by their priorities, while minimizing assignment penalties. We develop an adaptive large neighborhood search (ALNS) algorithm, relying on tailored destroy and repair operators. It is tested on benchmark instances derived from real-world data and compared to optimal results obtained by means of a commercial MIP-solver. Furthermore, we analyze the impact of considering three additional alternative objective functions. When applied to large-scale company data, the developed ALNS outperforms the previously applied solution approach.

We consider the problem of learning the dynamics of a linear system when one has access to data generated by an auxiliary system that shares similar (but not identical) dynamics, in addition to data from the true system. We use a weighted least squares approach, and provide a finite sample error bound of the learned model as a function of the number of samples and various system parameters from the two systems as well as the weight assigned to the auxiliary data. We show that the auxiliary data can help to reduce the intrinsic system identification error due to noise, at the price of adding a portion of error that is due to the differences between the two system models. We further provide a data-dependent bound that is computable when some prior knowledge about the systems is available. This bound can also be used to determine the weight that should be assigned to the auxiliary data during the model training stage.

Inferring chemical reaction networks (CRN) from concentration time series is a challenge encouragedby the growing availability of quantitative temporal data at the cellular level. This motivates thedesign of algorithms to infer the preponderant reactions between the molecular species observed ina given biochemical process, and build CRN structure and kinetics models. Existing ODE-basedinference methods such as SINDy resort to least square regression combined with sparsity-enforcingpenalization, such as Lasso. However, we observe that these methods fail to learn sparse modelswhen the input time series are only available in wild type conditions, i.e. without the possibility toplay with combinations of zeroes in the initial conditions. We present a CRN inference algorithmwhich enforces sparsity by inferring reactions in a sequential fashion within a search tree of boundeddepth, ranking the inferred reaction candidates according to the variance of their kinetics on theirsupporting transitions, and re-optimizing the kinetic parameters of the CRN candidates on the wholetrace in a final pass. We show that Reactmine succeeds both on simulation data by retrievinghidden CRNs where SINDy fails, and on two real datasets, one of fluorescence videomicroscopyof cell cycle and circadian clock markers, the other one of biomedical measurements of systemiccircadian biomarkers possibly acting on clock gene expression in peripheral organs, by inferringpreponderant regulations in agreement with previous model-based analyses. The code is available at//gitlab.inria.fr/julmarti/crninf/ together with introductory notebooks.

Accurate modeling of moving boundaries and interfaces is a difficulty present in many situations of computational mechanics. We use a new approach, X-Mesh, to simulate with the finite element method the interaction between two immiscible flows while keeping an accurate and sharp description of the interface without remeshing. The surface tension between the two fluids is added thanks to the ghost fluid method which when coupled with X-Mesh allows us to be exactly sharp in the pressure jump. This reduces the parasitic currents due to the surface tension down to the numerical precision.

Purpose of review: We review recent advances in algorithmic development and validation for modeling and control of soft robots leveraging the Koopman operator theory. Recent findings: We identify the following trends in recent research efforts in this area. (1) The design of lifting functions used in the data-driven approximation of the Koopman operator is critical for soft robots. (2) Robustness considerations are emphasized. Works are proposed to reduce the effect of uncertainty and noise during the process of modeling and control. (3) The Koopman operator has been embedded into different model-based control structures to drive the soft robots. Summary: Because of their compliance and nonlinearities, modeling and control of soft robots face key challenges. To resolve these challenges, Koopman operator-based approaches have been proposed, in an effort to express the nonlinear system in a linear manner. The Koopman operator enables global linearization to reduce nonlinearities and/or serves as model constraints in model-based control algorithms for soft robots. Various implementations in soft robotic systems are illustrated and summarized in the review.