IA Scholar Query: On the monge property of matrices.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgWed, 03 Aug 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Feature Projection for Optimal Transport
https://scholar.archive.org/work/sqduch2fcrdondvxluvo47znfu
Optimal transport is now a standard tool for solving many problems in statistics and machine learning. The optimal "transport of probability measures" is also a recurring theme in stochastic control and distributed control, where in the latter application the probability measure corresponds to an empirical distribution associated with a large collection of distributed agents, subject to local and global control. The goal of this paper is to make precise these connections, which inspires new relaxations of optimal transport for application in new and traditional domains. The proposed relaxation replaces a target measure with a "moment class": a set of probability measures defined by generalized moment constraints. This is motivated by applications to control, outlier detection, and to address computational complexity. The main conclusions are (i) A characterization of the solution is obtained, similar to Kantorovich duality, in which one of the dual functions in the classical theory is replaced by a linear combination of the features defining the generalized moments. Hence the dimension of the optimization problem coincides with the number of constraints, even with an uncountable state space; (ii) By introducing regularization in the form of relative entropy, the solution can be interpreted as replacing a maximum with a softmax in the dual; (iii) In applications such as control for which it is not known a-priori if the moment class is non-empty, a relaxation is proposed whose solution admits a similar characterization; (iv) The gradient of the dual function can be expressed in terms of the expectation of the features under a tilted probability measure, which motivates Monte-Carlo techniques for computation.Thomas Le Corre, Ana Busic, Sean Meynwork_sqduch2fcrdondvxluvo47znfuWed, 03 Aug 2022 00:00:00 GMTVolatility modelling and calibration by optimal transport
https://scholar.archive.org/work/gktuprenkvc4xbrxophqnb4p64
This thesis studied volatility models for option pricing and their calibration methods using the optimal transport theory. The author first introduced theoretical results by casting a class of volatility model calibration problems as a type of convex optimisation problem. Based on the established results, the author proposed calibration methods with numerical methods to calibrate the local volatility model, stochastic volatility model and a joint model for SPX and VIX. The proposed methods efficiently and accurately capture the market dynamics.SHIYI WANGwork_gktuprenkvc4xbrxophqnb4p64Wed, 03 Aug 2022 00:00:00 GMTGeoECG: Data Augmentation via Wasserstein Geodesic Perturbation for Robust Electrocardiogram Prediction
https://scholar.archive.org/work/l6odtif5mjepfopf74grcmpqmu
There has been an increased interest in applying deep neural networks to automatically interpret and analyze the 12-lead electrocardiogram (ECG). The current paradigms with machine learning methods are often limited by the amount of labeled data. This phenomenon is particularly problematic for clinically-relevant data, where labeling at scale can be time-consuming and costly in terms of the specialized expertise and human effort required. Moreover, deep learning classifiers may be vulnerable to adversarial examples and perturbations, which could have catastrophic consequences, for example, when applied in the context of medical treatment, clinical trials, or insurance claims. In this paper, we propose a physiologically-inspired data augmentation method to improve performance and increase the robustness of heart disease detection based on ECG signals. We obtain augmented samples by perturbing the data distribution towards other classes along the geodesic in Wasserstein space. To better utilize domain-specific knowledge, we design a ground metric that recognizes the difference between ECG signals based on physiologically determined features. Learning from 12-lead ECG signals, our model is able to distinguish five categories of cardiac conditions. Our results demonstrate improvements in accuracy and robustness, reflecting the effectiveness of our data augmentation method.Jiacheng Zhu, Jielin Qiu, Zhuolin Yang, Douglas Weber, Michael A. Rosenberg, Emerson Liu, Bo Li, Ding Zhaowork_l6odtif5mjepfopf74grcmpqmuTue, 02 Aug 2022 00:00:00 GMTAn adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation
https://scholar.archive.org/work/ap6djrkskbdv7nvcezp3if4whe
In this work we are interested in stochastic particle methods for multi-objective optimization. The problem is formulated using parametrized, single-objective sub-problems which are solved simultaneously. To this end a consensus based multi-objective optimization method on the search space combined with an additional heuristic strategy to adapt parameters during the computations is proposed. The adaptive strategy aims to distribute the particles uniformly over the image space by using energy-based measures to quantify the diversity of the system. The resulting metaheuristic algorithm is mathematically analyzed using a mean-field approximation and convergence guarantees towards optimal points is rigorously proven. In addition, a gradient flow structure in the parameter space for the adaptive method is revealed and analyzed. Several numerical experiments shows the validity of the proposed stochastic particle dynamics and illustrate the theoretical findings.Giacomo Borghi, Michael Herty, Lorenzo Pareschiwork_ap6djrkskbdv7nvcezp3if4wheTue, 02 Aug 2022 00:00:00 GMTOptimal L^2 Extensions of Openness Type
https://scholar.archive.org/work/yk2nxi2apzf4bdg3laqiikgmzq
We study the following optimal L^2 extension problem of openness type: given a complex manifold M, a closed subvariety S⊂ M and a holomorphic vector bundle E→ M, for any L^2 holomorphic section f defined on some open neighborhood U of S, find an L^2 holomorphic section F on M such that F|_S = f|_S, and the L^2 norm of F on M is optimally controlled by the L^2 norm of f on U. Answering the above problem, we prove an optimal L^2 extension theorem of openness type on weakly pseudoconvex Kähler manifolds, which unifies and generalizes a couple of known results on such a problem. Moreover, we prove a product property for certain minimal L^2 extensions and give an alternative proof to a version of the above L^2 extension theorem. We also present some applications to the usual optimal L^2 extension theorem and the equality part of Suita's conjecture.Wang Xu, Xiangyu Zhouwork_yk2nxi2apzf4bdg3laqiikgmzqFri, 29 Jul 2022 00:00:00 GMTAn efficient semismooth Newton-AMG-based inexact primal-dual algorithm for generalized transport problems
https://scholar.archive.org/work/6lzddnfqfnbl3ddafiyyhms2ea
This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the time discretization of a proper dynamical system, and by using the tool of Lyapunov function, the global (super-)linear convergence rate is established for function residual and feasibility violation. The proposed algorithm contains an inner problem that possesses strong semismoothness property and motivates the use of the semismooth Newton iteration. By exploring the hidden structure of the problem itself, the linear system arising from the Newton iteration is transferred equivalently into a graph Laplacian system, for which a robust algebraic multigrid method is proposed and also analyzed via the famous Xu--Zikatanov identity. Finally, numerical experiments are provided to validate the efficiency of our method.Jun Hu, Hao Luo, Zihang Zhangwork_6lzddnfqfnbl3ddafiyyhms2eaThu, 28 Jul 2022 00:00:00 GMTDeconvoluting Charge Transfer Mechanisms in Conducting Redox Polymer-Based Photobioelectrocatalytic Systems
https://scholar.archive.org/work/gbaxs4nlt5eutnpse7rsk2yase
Poor electrochemical communication between biocatalysts and electrodes is a limitation to bioelectrocatalysis efficiency. An extensive library of polymers has been developed to alleviate this limitation. Conducting-redox polymers(CRPs) are a versatile tool with high structural/functional tunability. While charge transport in CRPs is well characterized, the understanding of charge transport mechanisms facilitated by CRPs within photobioelectrocatalytic systems remains limited. This study is a comprehensive analysis dissecting the complex kinetics of photobioelectrodes to provide a mechanistic overview of charge transfer during photobioelectrocatalysis. We quantitatively compare two biohybrids of metal-free CRP(polydihydroxyaniline) and photobiocatalyst(chloroplasts), formed utilizing two deposition strategies ('mixed' and 'layered'). The superior photobioelectrocatalytic performance of the 'layered' biohybrid compared to the 'mixed' is justified in terms of rate(Dapp), thermodynamic and kinetic barriers (H,Ea), frequency of molecular collisions(D0) during electron transport, and rate/resistance to heterogeneous electron transfer(k0,RCT). Our results indicate that the primary electron transfer mechanism across the biohybrids, constituting the CRP, is thermally activated intra- and inter-molecular electron hopping, as opposed to a polaron transfer model typical for branched CRP- or conducting polymer(CP)-containing biohybrids in literature. This work underscores the significance of subtle interplay between CRP structure and deposition strategy in tuning the interface, and the structural classification of CRPs in bioelectrocatalysis.Nipunika Samali Perera Weliwatte, Olja Simoska, Daniel Powell, Miharu Koh, Matteo Grattieri, Luisa Whittaker-Brooks, Carol Korzeniewski, Shelley D Minteerwork_gbaxs4nlt5eutnpse7rsk2yaseWed, 27 Jul 2022 00:00:00 GMTThermodynamic Unification of Optimal Transport: Thermodynamic Uncertainty Relation, Minimum Dissipation, and Thermodynamic Speed Limits
https://scholar.archive.org/work/6grr7c5wlbhclmwr44h5sivta4
Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transport theory concerns the means by which one can optimally transport a source distribution to a target distribution, deriving a useful metric between probability distributions, called the Wasserstein distance. Despite their seemingly unrelated nature, an intimate connection between these fields has been unveiled in the context of continuous-state Langevin dynamics, providing several important implications for nonequilibrium systems. In this study, we elucidate an analogous connection for discrete cases by developing a thermodynamic framework for discrete optimal transport. We first introduce a novel quantity called dynamical state mobility, which significantly improves the thermodynamic uncertainty relation and provides insights into the precision of currents in nonequilibrium Markov jump processes. We then derive variational formulas that connect the discrete Wasserstein distances to stochastic and quantum thermodynamics of discrete Markovian dynamics described by master equations. Specifically, we rigorously prove that the Wasserstein distance equals the minimum product of irreversible entropy production and dynamical state mobility over all admissible Markovian dynamics. These formulas not only unify the relationship between thermodynamics and the optimal transport theory for discrete and continuous cases but also generalize it to the quantum case. In addition, we demonstrate that the obtained variational formulas lead to remarkable applications in stochastic and quantum thermodynamics.Tan Van Vu, Keiji Saitowork_6grr7c5wlbhclmwr44h5sivta4Tue, 26 Jul 2022 00:00:00 GMTA characterisation of convex order using the 2-Wasserstein distance
https://scholar.archive.org/work/3kdm652djna73dir7cgwhytbte
We give a new characterisation of convex order using the 2-Wasserstein distance 𝒲_2: we show that two probability measures μ and ν on ℝ^d with finite second moments are in convex order (i.e. μ≼_cν) iff 𝒲_2(ν, ρ)^2-𝒲_2(μ,ρ)^2≤∫ |y|^2 ν(dy)- ∫ |x|^2 μ(dx) holds for all probability measures ρ on ℝ^d with bounded support. Our proof of this result relies on a quantitative bound for the infimum of ∫ f dν -∫ f dμ over all 1-Lipschitz functions f, which is obtained through optimal transport duality and Brenier's theorem. We use our new characterisation to derive new proofs of well-known one-dimensional characterisations of convex order as well as new computational methods for investigating convex order.Johannes Wiesel, Erica Zhangwork_3kdm652djna73dir7cgwhytbteTue, 26 Jul 2022 00:00:00 GMTGeometric Methods for Sampling, Optimisation, Inference and Adaptive Agents
https://scholar.archive.org/work/cipvt3b4qjacjexqwwdhptlmfm
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric structures to solve these problems efficiently. We show that a wide range of geometric theories emerge naturally in these fields, ranging from measure-preserving processes, information divergences, Poisson geometry, and geometric integration. Specifically, we explain how (i) leveraging the symplectic geometry of Hamiltonian systems enable us to construct (accelerated) sampling and optimisation methods, (ii) the theory of Hilbertian subspaces and Stein operators provides a general methodology to obtain robust estimators, (iii) preserving the information geometry of decision-making yields adaptive agents that perform active inference. Throughout, we emphasise the rich connections between these fields; e.g., inference draws on sampling and optimisation, and adaptive decision-making assesses decisions by inferring their counterfactual consequences. Our exposition provides a conceptual overview of underlying ideas, rather than a technical discussion, which can be found in the references herein.Alessandro Barp, Lancelot Da Costa, Guilherme França, Karl Friston, Mark Girolami, Michael I. Jordan, Grigorios A. Pavliotiswork_cipvt3b4qjacjexqwwdhptlmfmMon, 25 Jul 2022 00:00:00 GMTGoing beyond the Electric-Dipole Approximation in the Calculation of Absorption and (Magnetic) Circular Dichroism Spectra including Scalar Relativistic and Spin-Orbit Coupling Effects
https://scholar.archive.org/work/gqlzepxiwvanhnv7tobnax3v6a
In this work, a time-dependent density functional theory (TD-DFT) scheme for computing optical spectroscopic properties in the framework of linearly and circularly polarized light is presented. The scheme is based on a previously formulated theory for predicting optical absorption and magnetic circular dichroism (MCD) spectra. The scheme operates in the framework of the full semi-classical field-matter interaction operator, thus generating a powerful and general computational scheme capable of computing the absorption (ABS), circular dichroism (CD), and MCD spectra. In addition, our implementation includes the treatment of relativistic effects in the framework of quasidegenerate perturbation theory, which accounts for scalar relativistic effects (in the self-consistent field step) and spin-orbit coupling (in the TD-DFT step), as well as external magnetic field perturbations. Hence, this formalism is also able to probe spin-forbidden transitions. The random orientations of molecules are taken into account by a semi-numerical approach involving a Lebedev numerical quadrature alongside analytical integration. It is demonstrated the numerical quadrature requires as few as 14 points for satisfactory converged results thus leading to a highly efficient scheme, while the calculation of the exact transition moments creates no computational bottlenecks. It is demonstrated that at zero magnetic field, the CD spectrum is recovered while the sum of left and right circularly polarized light contributions provides the linear absorption spectrum. The virtues of this efficient and general protocol are demonstrated on a selected set of organic molecules where the various contributions to the spectral intensities have been analyzed in detail.Nicolas Oscar Foglia, Dimitrios Maganas, Frank Neesework_gqlzepxiwvanhnv7tobnax3v6aMon, 25 Jul 2022 00:00:00 GMTAnticanonically balanced metrics and the Hilbert-Mumford criterion for the δ_m-invariant of Fujita-Odaka
https://scholar.archive.org/work/xvyajvzzrbfy5mlrmveaxvqmea
We prove that the stability condition for Fano manifolds defined by Saito-Takahashi, given in terms of the sum of the Ding invariant and the Chow weight, is equivalent to the existence of anticanonically balanced metrics. Combined with the result by Rubinstein-Tian-Zhang, we obtain the following algebro-geometric corollary: the δ_m-invariant of Fujita-Odaka satisfies δ_m >1 if and only if the Fano manifold is stable in the sense of Saito-Takahashi, establishing a Hilbert-Mumford type criterion for δ_m >1. We also extend this result to the Kähler-Ricci g-solitons and the coupled Kähler-Einstein metrics, and as a by-product we obtain a formula for the asymptotic slope of the coupled Ding functional in terms of multiple test configurations.Yoshinori Hashimotowork_xvyajvzzrbfy5mlrmveaxvqmeaSat, 23 Jul 2022 00:00:00 GMTStrong c-concavity and stability in optimal transport
https://scholar.archive.org/work/qj2pnnzlsfho3g2odjwfij3bfy
The stability of solutions to optimal transport problems under variation of the measures is fundamental from a mathematical viewpoint: it is closely related to the convergence of numerical approaches to solve optimal transport problems and justifies many of the applications of optimal transport. In this article, we introduce the notion of strong c-concavity, and we show that it plays an important role for proving stability results in optimal transport for general cost functions c. We then introduce a differential criterion for proving that a function is strongly c-concave, under an hypothesis on the cost introduced originally by Ma-Trudinger-Wang for establishing regularity of optimal transport maps. Finally, we provide two examples where this stability result can be applied, for cost functions taking value +∞ on the sphere: the reflector problem and the Gaussian curvature measure prescription problem.Anatole Gallouëtwork_qj2pnnzlsfho3g2odjwfij3bfyFri, 22 Jul 2022 00:00:00 GMTOrnstein-Uhlenbeck Type Processes on Wasserstein Space
https://scholar.archive.org/work/lybbengjxrecrhbeq23twigtyu
The Wasserstein space 𝒫_2 consists of square integrable probability measures on ^d and is equipped with the intrinsic Riemannian structure. By using stochastic analysis on the tangent space, we construct the Ornstein-Uhlenbeck (O-U) process on 𝒫_2 whose generator is formulated as the intrinsic Laplacian with a drift. This process satisfies the log-Sobolev inequality and has L^2-compact Markov semigroup. Due to the important role played by O-U process in Malliavin calculus on the Wiener space, this measure-valued process should be a fundamental model to develop stochastic analysis on the Wasserstein space. Perturbations of the O-U process is also studied.Panpan Ren, Feng-Yu Wangwork_lybbengjxrecrhbeq23twigtyuFri, 22 Jul 2022 00:00:00 GMTEfficient degradation of organic dyes using peroxymonosulfate activated by magnetic graphene oxide
https://scholar.archive.org/work/x2ifs3wyobg73h77gciodrgpwa
Magnetic graphene oxide (MGO) was prepared and used as a catalyst to activate peroxymonosulfate (PMS) for degradation of Coomassie brilliant blue G250 (CBB). The effects of operation conditions including MGO dosage, PMS dosage and initial concentration of CBB were studied. CBB removal could reach 99.5% under optimum conditions, and high removals of 98.4-99.9% were also achieved for other organic dyes with varied structures, verifying the high efficiency and wide applicability of the MGO/PMS catalytic system. The effects of environmental factors including solution pH, inorganic ions and water matrices were also investigated. Reusability test showed that CBB removals maintained above 90% in five consecutive runs, indicating the acceptable recyclability of MGO. Based on quenching experiments, solvent exchange (H2O to D2O) and in situ open circuit potential (OCP) test, it was found that ˙OH, SO4˙- and high-valent iron species were responsible for the efficient degradation of CBB in the MGO/PMS system, while the contributions of O2˙-, 1O2 and the non-radical electron-transfer pathway were limited. Furthermore, the plausible degradation pathway of CBB was proposed based on density functional theory (DFT) calculations and liquid chromatography-mass spectrometry (LC-MS) results, and toxicity variation in the degradation process was evaluated by computerized structure-activity relationships (SARs) using green algae, daphnia, and fish as indicator species.Yawei Shi, Haonan Wang, Guobin Song, Yi Zhang, Liya Tong, Ya Sun, Guanghui Dingwork_x2ifs3wyobg73h77gciodrgpwaThu, 21 Jul 2022 00:00:00 GMTDistribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networks
https://scholar.archive.org/work/ep2vpp2lojczjhhaq67kb27gyi
Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies on the statistical properties of GANs. This paper provides approximation and statistical guarantees of GANs for the estimation of data distributions that have densities in a Hölder space. Our main result shows that, if the generator and discriminator network architectures are properly chosen, GANs are consistent estimators of data distributions under strong discrepancy metrics, such as the Wasserstein-1 distance. Furthermore, when the data distribution exhibits low-dimensional structures, we show that GANs are capable of capturing the unknown low-dimensional structures in data and enjoy a fast statistical convergence, which is free of curse of the ambient dimensionality. Our analysis for low-dimensional data builds upon a universal approximation theory of neural networks with Lipschitz continuity guarantees, which may be of independent interest.Minshuo Chen, Wenjing Liao, Hongyuan Zha, Tuo Zhaowork_ep2vpp2lojczjhhaq67kb27gyiThu, 21 Jul 2022 00:00:00 GMTCross Atlas Remapping via Optimal Transport (CAROT): Creating connectomes for any atlas when raw data is not available
https://scholar.archive.org/work/q3iu7gh4wzekrmycbmae7eee5e
Whether using large-scale projects---like the Human Connectome Project (HCP), the Adolescent Brain Cognitive Development (ABCD) study, Healthy Brain Network (HBN), and the UK Biobank---or pooling together several smaller studies, open-source, publicly available datasets allow for unpresented sample sizes and promote generalization efforts. Overall, releasing preprocessing data can enhance participant privacy, democratize science, and lead to unique scientific discoveries. But releasing preprocessed data also limits the choices available to the end-user. For connectomics, this is especially true as connectomes created from different atlases i.e., ways of dividing the brain into distinct regions) are not directly comparable. In addition, there exist several atlases with no gold standards, and more being developed yearly, making it unrealistic to have processed, open-source data available from all atlases. To address these limitations, we propose Cross Atlas Remapping via Optimal Transport (CAROT) to find a mapping between two atlases, allowing data processed from one atlas to be directly transformed into a connectome based on another atlas without needing raw data. To validate CAROT, we compare reconstructed connectomes against their original counterparts (i.e., connectomes generated directly from an atlas), demonstrate the utility of transformed connectomes in downstream analyses, and show how a connectome-based predictive model can be generalized to publicly available processed data that was processed with different atlases. Overall, CAROT can reconstruct connectomes from an extensive set of atlases---without ever needing the raw data---allowing already processed connectomes to be easily reused in a wide-range of analyses while eliminating wasted and duplicate processing efforts. We share this tool as both source code and as a stand-alone web application (http://carotproject.com/).Javid Dadashkarimi, Amin Karbasi, Dustin Scheinostwork_q3iu7gh4wzekrmycbmae7eee5eWed, 20 Jul 2022 00:00:00 GMTAn Extension of Heron's Formula to Tetrahedra, and the Projective Nature of Its Zeros
https://scholar.archive.org/work/wq4vgu5fmfdtrmsnbtmke6m3kq
A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in six simple rational functions of the areas of its four faces and three medial parallelograms, which will be referred to herein as interior faces. Geometrically, these rational functions are the areas of the triangles into which the exterior faces are divided by the points at which the tetrahedron's in-sphere touches those faces. This leads to a conjecture as to how the formula extends to n-dimensional simplices for all n > 3. Remarkably, for n = 3 the zeros of the polynomial constitute a five-dimensional semi-algebraic variety consisting almost entirely of collinear tetrahedra with vertices separated by infinite distances, but with generically well-defined distance ratios. These unconventional Euclidean configurations can be identified with a quotient of the Klein quadric by an action of a group of reflections isomorphic to ℤ_2^4, wherein four-point configurations in the affine plane constitute a distinguished three-dimensional subset. The paper closes by noting that the algebraic structure of the zeros in the affine plane naturally defines the associated 4-element, rank-3 chirotope, aka affine oriented matroid.Timothy F. Havelwork_wq4vgu5fmfdtrmsnbtmke6m3kqWed, 20 Jul 2022 00:00:00 GMTUnsupervised Ground Metric Learning using Wasserstein Singular Vectors
https://scholar.archive.org/work/pcfrnfbivrg2bnrh6wrumtw4oy
Defining meaningful distances between samples in a dataset is a fundamental problem in machine learning. Optimal Transport (OT) lifts a distance between features (the "ground metric") to a geometrically meaningful distance between samples. However, there is usually no straightforward choice of ground metric. Supervised ground metric learning approaches exist but require labeled data. In absence of labels, only ad-hoc ground metrics remain. Unsupervised ground metric learning is thus a fundamental problem to enable data-driven applications of OT. In this paper, we propose for the first time a canonical answer by simultaneously computing an OT distance between samples and between features of a dataset. These distance matrices emerge naturally as positive singular vectors of the function mapping ground metrics to OT distances. We provide criteria to ensure the existence and uniqueness of these singular vectors. We then introduce scalable computational methods to approximate them in high-dimensional settings, using stochastic approximation and entropic regularization. Finally, we showcase Wasserstein Singular Vectors on a single-cell RNA-sequencing dataset.Geert-Jan Huizing, Laura Cantini, Gabriel Peyréwork_pcfrnfbivrg2bnrh6wrumtw4oyTue, 19 Jul 2022 00:00:00 GMTTheseus: A Library for Differentiable Nonlinear Optimization
https://scholar.archive.org/work/k6ewgyyclfdttjj7w3knk6xbua
We present Theseus, an efficient application-agnostic open source library for differentiable nonlinear least squares (DNLS) optimization built on PyTorch, providing a common framework for end-to-end structured learning in robotics and vision. Existing DNLS implementations are application specific and do not always incorporate many ingredients important for efficiency. Theseus is application-agnostic, as we illustrate with several example applications that are built using the same underlying differentiable components, such as second-order optimizers, standard costs functions, and Lie groups. For efficiency, Theseus incorporates support for sparse solvers, automatic vectorization, batching, GPU acceleration, and gradient computation with implicit differentiation and direct loss minimization. We do extensive performance evaluation in a set of applications, demonstrating significant efficiency gains and better scalability when these features are incorporated. Project page: https://sites.google.com/view/theseus-aiLuis Pineda, Taosha Fan, Maurizio Monge, Shobha Venkataraman, Paloma Sodhi, Ricky Chen, Joseph Ortiz, Daniel DeTone, Austin Wang, Stuart Anderson, Jing Dong, Brandon Amos, Mustafa Mukadamwork_k6ewgyyclfdttjj7w3knk6xbuaTue, 19 Jul 2022 00:00:00 GMT