arXiv subjects

Sebastian Ament

Publications and source records attributed to Sebastian Ament.

23 records · Page 2Linked to original sources

arXiv2020

Efficient Projection Algorithms onto the Weighted l1 Ball

Projected gradient descent has been proved efficient in many optimization and machine learning problems. The weighted $\ell_1$ ball has been shown effective in sparse system identification and features selection. In this paper we propose three new efficient algorithms for projecting any vector of finite length onto the weighted $\ell_1$ ball. The first two algorithms have a linear worst case complexity. The third one has a highly competitive performances in practice but the worst case has a quadratic complexity. These new algorithms are efficient tools for machine learning methods based on projected gradient descent such as compress sensing, feature selection. We illustrate this effectiveness by adapting an efficient compress sensing algorithm to weighted projections. We demonstrate the efficiency of our new algorithms on benchmarks using very large vectors. For instance, it requires only 8 ms, on an Intel I7 3rd generation, for projecting vectors of size $10^7$.

cs.LG↗

arXiv2020

Optical Identification of Materials Transformations in Oxide Thin Films

Recent advances in high-throughput experimentation for combinatorial studies have accelerated the discovery and analysis of materials across a wide range of compositions and synthesis conditions. However, many of the more powerful characterization methods are limited by speed, cost, availability, and/or resolution. To make efficient use of these methods, there is value in developing approaches for identifying critical compositions and conditions to be used as a-priori knowledge for follow-up characterization with high-precision techniques, such as micron-scale synchrotron based X-ray diffraction (XRD). Here we demonstrate the use of optical microscopy and reflectance spectroscopy to identify likely phase-change boundaries in thin film libraries. These methods are used to delineate possible metastable phase boundaries following lateral-gradient Laser Spike Annealing (lg-LSA) of oxide materials. The set of boundaries are then compared with definitive determinations of structural transformations obtained using high-resolution XRD. We demonstrate that the optical methods detect more than 95% of the structural transformations in a composition-gradient La-Mn-O library and a Ga$_2$O$_3$ sample, both subject to an extensive set of lg-LSA anneals. Our results provide quantitative support for the value of optically-detected transformations as a priori data to guide subsequent structural characterization, ultimately accelerating and enhancing the efficient implementation of $μ$m-resolution XRD experiments.

cond-mat.mtrl-sci↗

arXiv2019

Deep Reasoning Networks: Thinking Fast and Slow

We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with reasoning for solving complex tasks, typically in an unsupervised or weakly-supervised setting. DRNets exploit problem structure and prior knowledge by tightly combining logic and constraint reasoning with stochastic-gradient-based neural network optimization. We illustrate the power of DRNets on de-mixing overlapping hand-written Sudokus (Multi-MNIST-Sudoku) and on a substantially more complex task in scientific discovery that concerns inferring crystal structures of materials from X-ray diffraction data under thermodynamic rules (Crystal-Structure-Phase-Mapping). At a high level, DRNets encode a structured latent space of the input data, which is constrained to adhere to prior knowledge by a reasoning module. The structured latent encoding is used by a generative decoder to generate the targeted output. Finally, an overall objective combines responses from the generative decoder (thinking fast) and the reasoning module (thinking slow), which is optimized using constraint-aware stochastic gradient descent. We show how to encode different tasks as DRNets and demonstrate DRNets' effectiveness with detailed experiments: DRNets significantly outperform the state of the art and experts' capabilities on Crystal-Structure-Phase-Mapping, recovering more precise and physically meaningful crystal structures. On Multi-MNIST-Sudoku, DRNets perfectly recovered the mixed Sudokus' digits, with 100% digit accuracy, outperforming the supervised state-of-the-art MNIST de-mixing models. Finally, as a proof of concept, we also show how DRNets can solve standard combinatorial problems -- 9-by-9 Sudoku puzzles and Boolean satisfiability problems (SAT), outperforming other specialized deep learning models. DRNets are general and can be adapted and expanded to tackle other tasks.

cs.LG↗

arXiv2019

Exponentially-Modified Gaussian Mixture Model: Applications in Spectroscopy

We propose a novel exponentially-modified Gaussian (EMG) mixture residual model. The EMG mixture is well suited to model residuals that are contaminated by a distribution with positive support. This is in contrast to commonly used robust residual models, like the Huber loss or $\ell_1$, which assume a symmetric contaminating distribution and are otherwise asymptotically biased. We propose an expectation-maximization algorithm to optimize an arbitrary model with respect to the EMG mixture. We apply the approach to linear regression and probabilistic matrix factorization (PMF). We compare against other residual models, including quantile regression. Our numerical experiments demonstrate the strengths of the EMG mixture on both tasks. The PMF model arises from considering spectroscopic data. In particular, we demonstrate the effectiveness of PMF in conjunction with the EMG mixture model on synthetic data and two real-world applications: X-ray diffraction and Raman spectroscopy. We show how our approach is effective in inferring background signals and systematic errors in data arising from these experimental settings, dramatically outperforming existing approaches and revealing the data's physically meaningful components.

stat.ML↗

arXiv2017

Solving the stochastic Landau-Lifshitz-Gilbert-Slonczewski equation for monodomain nanomagnets : A survey and analysis of numerical techniques

The stochastic Landau-Lifshitz-Gilbert-Slonczewski (s-LLGS) equation is widely used to study the temporal evolution of the macrospin subject to spin torque and thermal noise. The numerical simulation of the s-LLGS equation requires an appropriate choice of stochastic calculus and numerical integration scheme. In this paper, we comprehensively evaluate the accuracy and complexity of various numerical techniques to solve the s-LLGS equation. We focus on implicit midpoint, Heun, and Euler-Heun methods that converge to the Stratonovich solution of the s-LLGS equation. By performing numerical tests for both strong (path-wise) and weak (statistical) convergence, we quantify the accuracy of various numerical schemes used to solve the s-LLGS equation. We demonstrate a new method intended to solve Stochastic Differential Equations (SDEs) with small noise (RK4-Heun), and test its capability to handle the s-LLGS equation. We also discuss the circuit implementation of nanomagnets for large-scale SPICE-based simulations. We evaluate the efficacy of SPICE in handling the stochastic dynamics of the multiplicative noise in the s-LLGS equation. Numerical schemes such as Euler and Gear, typically used by SPICE-based circuit simulators do not yield the expected outcome when solving the Stratonovich s-LLGS equation. While the trapezoidal method in SPICE does solve for the Stratonovich solution, its accuracy is limited by the minimum time step of integration in SPICE. We implement the s-LLGS equation in both its cartesian and spherical coordinates form in SPICE and compare the stability and accuracy of the two implementations. The results in this paper will serve as guidelines for researchers to understand the tradeoffs between accuracy and complexity of various numerical methods and the choice of appropriate calculus to solve the s-LLGS equation.

cs.CE↗