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Showing papers on "Equivariant map published in 2022"


Journal ArticleDOI
TL;DR: NequIP as mentioned in this paper is an E(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations, which achieves state-of-the-art accuracy on a challenging and diverse set of molecules and materials while exhibiting remarkable data efficiency.
Abstract: This work presents Neural Equivariant Interatomic Potentials (NequIP), an E(3)-equivariant neural network approach for learning interatomic potentials from ab-initio calculations for molecular dynamics simulations. While most contemporary symmetry-aware models use invariant convolutions and only act on scalars, NequIP employs E(3)-equivariant convolutions for interactions of geometric tensors, resulting in a more information-rich and faithful representation of atomic environments. The method achieves state-of-the-art accuracy on a challenging and diverse set of molecules and materials while exhibiting remarkable data efficiency. NequIP outperforms existing models with up to three orders of magnitude fewer training data, challenging the widely held belief that deep neural networks require massive training sets. The high data efficiency of the method allows for the construction of accurate potentials using high-order quantum chemical level of theory as reference and enables high-fidelity molecular dynamics simulations over long time scales.

133 citations


Proceedings ArticleDOI
18 Feb 2022-Robotics
TL;DR: This paper recognizes that the optimal grasp function is SE(2) -equivariant and can be modeled using an equivariant convolutional neural network, and is able to significantly improve the sample efficiency of grasp learning.

25 citations


Journal ArticleDOI
TL;DR: In this paper , the lattice gauge equivariant convolutional neural networks (L-CNNs) were proposed to learn and generalize gauge invariant quantities that traditional CNNs are incapable of finding.
Abstract: We propose lattice gauge equivariant convolutional neural networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers. Together with topological information, for example, from Polyakov loops, such a network can, in principle, approximate any gauge covariant function on the lattice. We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.

19 citations


Posted ContentDOI
16 Apr 2022-bioRxiv
TL;DR: A generative SE(3)-equivariant model is developed which significantly improves upon existing autoregressive methods and captures functional aspects of the underlying protein by accurately predicting the effects of point mutations through testing on Deep Mutational Scanning datasets.
Abstract: In this work, we establish a framework to tackle the inverse protein design problem; the task of predicting a protein’s primary sequence given its backbone conformation. To this end, we develop a generative SE(3)-equivariant model which significantly improves upon existing autoregressive methods. Conditioned on backbone structure, and trained with our novel partial masking scheme and side-chain conformation loss, we achieve state-of-the-art native sequence recovery on structurally independent CASP13, CASP14, CATH4.2, and TS50 test sets. On top of accurately recovering native sequences, we demonstrate that our model captures functional aspects of the underlying protein by accurately predicting the effects of point mutations through testing on Deep Mutational Scanning datasets. We further verify the efficacy of our approach by comparing with recently proposed inverse protein folding methods and by rigorous ablation studies.

18 citations


Proceedings ArticleDOI
18 Feb 2022
TL;DR: This paper proposes a novel version of Transporter Net that is equivariant to both pick and place orientation and achieves betterPick and place success rates than the baseline Transporter net model.
Abstract: Transporter Net is a recently proposed framework for pick and place that is able to learn good manipulation policies from a very few expert demonstrations. A key reason why Transporter Net is so sample efficient is that the model incorporates rotational equivariance into the pick module, i.e. the model immediately generalizes learned pick knowledge to objects presented in different orientations. This paper proposes a novel version of Transporter Net that is equivariant to both pick and place orientation. As a result, our model immediately generalizes place knowledge to different place orientations in addition to generalizing pick knowledge as before. Ultimately, our new model is more sample efficient and achieves better pick and place success rates than the baseline Transporter Net model.

18 citations


Journal ArticleDOI
Lubna Azmi1
TL;DR: LorentzNet as mentioned in this paper is a new symmetry-preserving deep learning model for jet tagging, which relies on an efficient Minkowski dot product attention for message passing.
Abstract: A bstract Deep learning methods have been increasingly adopted to study jets in particle physics. Since symmetry-preserving behavior has been shown to be an important factor for improving the performance of deep learning in many applications, Lorentz group equivariance — a fundamental spacetime symmetry for elementary particles — has recently been incorporated into a deep learning model for jet tagging. However, the design is computationally costly due to the analytic construction of high-order tensors. In this article, we introduce LorentzNet, a new symmetry-preserving deep learning model for jet tagging. The message passing of LorentzNet relies on an efficient Minkowski dot product attention. Experiments on two representative jet tagging benchmarks show that LorentzNet achieves the best tagging performance and improves significantly over existing state-of-the-art algorithms. The preservation of Lorentz symmetry also greatly improves the efficiency and generalization power of the model, allowing LorentzNet to reach highly competitive performance when trained on only a few thousand jets.

13 citations


Proceedings ArticleDOI
23 May 2022
TL;DR: Neural Descriptor Fields (NDFs) as mentioned in this paper encode both points and relative poses between an object and a target (such as a robot gripper or a rack used for hanging) via category-level descriptors.
Abstract: We present Neural Descriptor Fields (NDFs), an object representation that encodes both points and relative poses between an object and a target (such as a robot gripper or a rack used for hanging) via category-level descriptors. We employ this representation for object manipulation, where given a task demonstration, we want to repeat the same task on a new object instance from the same category. We propose to achieve this objective by searching (via optimization) for the pose whose descriptor matches that observed in the demonstration. NDFs are conveniently trained in a self-supervised fashion via a 3D auto-encoding task that does not rely on expert-labeled keypoints. Further, NDFs are SE(3)-equivariant, guaranteeing performance that generalizes across all possible 3D object translations and rotations. We demonstrate learning of manipulation tasks from few (∼5-10) demonstrations both in simulation and on a real robot. Our performance generalizes across both object instances and 6-DoF object poses, and significantly outperforms a recent baseline that relies on 2D descriptors. Project website: https://yilundu.github.io/ndf/

12 citations


Journal ArticleDOI
Kun-Li Lin1
TL;DR: In this paper , the authors introduced trigonometric and elliptic analogues of quiver Yangians, which they call toroidal quiver algebras and elliptic quiver algebra, respectively.
Abstract: The quiver Yangian, an infinite-dimensional algebra introduced recently in arXiv:2003.08909, is the algebra underlying BPS state counting problems for toric Calabi-Yau three-folds. We introduce trigonometric and elliptic analogues of quiver Yangians, which we call toroidal quiver algebras and elliptic quiver algebras, respectively. We construct the representations of the shifted toroidal and elliptic algebras in terms of the statistical model of crystal melting. We also derive the algebras and their representations from equivariant localization of three-dimensional $\mathcal{N}=2$ supersymmetric quiver gauge theories, and their dimensionally-reduced counterparts. The analysis of supersymmetric gauge theories suggests that there exist even richer classes of algebras associated with higher-genus Riemann surfaces and generalized cohomology theories.

11 citations


Journal ArticleDOI
20 May 2022
TL;DR: In this paper , special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type have been discussed, and the notions of charmenability and charfiniteness have been defined.
Abstract: We discuss special properties of the spaces of characters and positive definite functions, as well as their associated dynamics, for arithmetic groups of product type. Axiomatizing these properties, we define the notions of charmenability and charfiniteness and study their applications to the topological dynamics, ergodic theory and unitary representation theory of the given groups. To do that, we study singularity properties of equivariant normal ucp maps between certain von Neumann algebras. We apply our discussion also to groups acting on product of trees.

11 citations


Journal ArticleDOI
TL;DR: It is proved that the technique proposed works for any symmetric function, and benefits from the approximability of continuous symmetric functions by symmetric polynomials.
Abstract: Group Equivariant Operators (GEOs) are a fundamental tool in the research on neural networks, since they make available a new kind of geometric knowledge engineering for deep learning, which can exploit symmetries in artificial intelligence and reduce the number of parameters required in the learning process. In this paper we introduce a new method to build non-linear GEOs and non-linear Group Equivariant Non-Expansive Operators (GENEOs), based on the concepts of symmetric function and permutant. This method is particularly interesting because of the good theoretical properties of GENEOs and the ease of use of permutants to build equivariant operators, compared to the direct use of the equivariance groups we are interested in. In our paper, we prove that the technique we propose works for any symmetric function, and benefits from the approximability of continuous symmetric functions by symmetric polynomials. A possible use in Topological Data Analysis of the GENEOs obtained by this new method is illustrated.

10 citations


Journal ArticleDOI
TL;DR: In this paper , a scalable equivariant machine learning model based on local atomic environment descriptors is proposed to predict dielectric and magnetic tensorial properties of different ranks of a series of molecules.
Abstract: Embedding molecular symmetries into machine-learning models is key for efficient learning of chemico-physical scalar properties, but little evidence on how to extend the same strategy to tensorial quantities exists. Here we formulate a scalable equivariant machine-learning model based on local atomic environment descriptors. We apply it to a series of molecules and show that accurate predictions can be achieved for a comprehensive list of dielectric and magnetic tensorial properties of different ranks. These results show that equivariant models are a promising platform to extend the scope of machine learning in materials modelling.

Journal ArticleDOI
TL;DR: In this article , a generalized transformation equivariant representations (GTERs) is proposed to capture complex patterns of visual structures beyond linear equivariance under a transformation group, which can be extended to (semi-)supervised models by jointly maximizing the mutual information of the learned representation with both labels and transformations.
Abstract: Transformation equivariant representations (TERs) aim to capture the intrinsic visual structures that equivary to various transformations by expanding the notion of translation equivariance underlying the success of convolutional neural networks (CNNs). For this purpose, we present both deterministic AutoEncoding Transformations (AET) and probabilistic AutoEncoding Variational Transformations (AVT) models to learn visual representations from generic groups of transformations. While the AET is trained by directly decoding the transformations from the learned representations, the AVT is trained by maximizing the joint mutual information between the learned representation and transformations. This results in generalized TERs (GTERs) equivariant against transformations in a more general fashion by capturing complex patterns of visual structures beyond the conventional linear equivariance under a transformation group. The presented approach can be extended to (semi-)supervised models by jointly maximizing the mutual information of the learned representation with both labels and transformations. Experiments demonstrate the proposed models outperform the state-of-the-art models in both unsupervised and (semi-)supervised tasks. Moreover, we show that the unsupervised representation can even surpass the fully supervised representation pretrained on ImageNet when they are fine-tuned for the object detection task.

Journal ArticleDOI
TL;DR: In this article , a self-supervised learning strategy was proposed to enhance the performance of the original class activation maps (CAMs), which can be generated from image-level annotations, and the commonalities between image modalities can be employed as an efficient selfsupervisory signal.

Journal ArticleDOI
04 Jul 2022
TL;DR: In this paper , an analog of the quantum dynamical Weyl group acting in its equivariant K-theory was constructed for an arbitrary Nakajima quiver variety X, and the lattice part of this groupoid was identified with the operators of quantum difference equation for X.
Abstract: For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in $${{\,\mathrm{Pic}\,}}(X)\otimes {\mathbb {C}}$$ . We identify the lattice part of this groupoid with the operators of quantum difference equation for X. The cases of quivers of finite and affine type are illustrated by explicit examples.

Journal ArticleDOI
Rui Jiao, Jiaqi Han, Wenbing Huang, Yu Rong, Yang Liu 
TL;DR: This work proposes to adopt an equivariant energy-based model as the backbone for pretraining, which enjoys the merits of fulfilling the sym- metry of 3D space, and develops a node-level pretraining loss for force prediction, where the Riemann-Gaussian distribution is exploited to ensure the loss to be E(3)-invariant, enabling more robustness.
Abstract: Pretraining molecular representation models without labels is fundamental to various applications. Conventional methods mainly process 2D molecular graphs and focus solely on 2D tasks, making their pretrained models incapable of characterizing 3D geometry and thus defective for downstream 3D tasks. In this work, we tackle 3D molecular pretraining in a complete and novel sense. In particular, we first propose to adopt an equivariant energy-based model as the backbone for pretraining, which enjoys the merits of fulfilling the symmetry of 3D space. Then we develop a node-level pretraining loss for force prediction, where we further exploit the Riemann-Gaussian distribution to ensure the loss to be E(3)-invariant, enabling more robustness. Moreover, a graph-level noise scale prediction task is also leveraged to further promote the eventual performance. We evaluate our model pretrained from a large-scale 3D dataset GEOM-QM9 on two challenging 3D benchmarks: MD17 and QM9. Experimental results demonstrate the efficacy of our method against current state-of-the-art pretraining approaches, and verify the validity of our design for each proposed component. Code is available at https://github.com/jiaor17/3D-EMGP.

Journal ArticleDOI
TL;DR: In this article , the authors compare several notions of equivariant formality for complex K-theory with respect to a compact Lie group action, including surjectivity of the forgetful map and the weak Equivariant Formality of Harada-Landweber, and find all are equivalent under standard hypotheses.
Abstract: Abstract We compare several notions of equivariant formality for complex K-theory with respect to a compact Lie group action, including surjectivity of the forgetful map and the weak equivariant formality of Harada–Landweber, and find all are equivalent under standard hypotheses. As a consequence, we present an expression for the equivariant K-theory of the isotropy action of $H$ on a homogeneous space $G/H$ in all the classical cases. The proofs involve mainly homological algebra and arguments with the Atiyah–Hirzebruch–Leray–Serre spectral sequence, but a more general result depends on a map of spectral sequences from Hodgkin’s Künneth spectral sequence in equivariant K-theory to that in Borel cohomology that seems not to have been otherwise defined. The hypotheses for the main structure result are analogous to a previously announced characterization of cohomological equivariant formality, first proved here, expanding on the results of Shiga and Takahashi.

Journal ArticleDOI
Elif Başkaya1
TL;DR: In this paper , symmetry-preserving, physics-informed neural networks (S-PINNs) are proposed to enforce important physical laws including symmetries of solutions and conservation laws.

Proceedings ArticleDOI
28 Jan 2022
TL;DR: A novel, Möbius-equivariant spherical convolution operator, which is based on the following observation: to achieve equivariance, one only need to consider the lower-dimensional subgroup which transforms the positions of points as seen in the frames of their neighbors.
Abstract: Möbius transformations play an important role in both geometry and spherical image processing – they are the group of conformal automorphisms of 2D surfaces and the spherical equivalent of homographies. Here we present a novel, Möbius-equivariant spherical convolution operator which we call Möbius convolution; with it, we develop the foundations for Möbius-equivariant spherical CNNs. Our approach is based on the following observation: to achieve equivariance, we only need to consider the lower-dimensional subgroup which transforms the positions of points as seen in the frames of their neighbors. To efficiently compute Möbius convolutions at scale we derive an approximation of the action of the transformations on spherical filters, allowing us to compute our convolutions in the spectral domain with the fast Spherical Harmonic Transform. The resulting framework is flexible and descriptive, and we demonstrate its utility by achieving promising results in both shape classification and image segmentation tasks.

Journal ArticleDOI
TL;DR: The vertex functions of a 3D mirror pair, as solutions to the q-difference equations, satisfying particular asymptotic conditions, are related by the elliptic stable envelopes as discussed by the authors .

Journal ArticleDOI
TL;DR: PDE-G-CNN as discussed by the authors is a PDE-based framework that generalizes group equivariant convolutional neural networks (GCNNs) on homogeneous spaces, where geometrically meaningful PDE coefficients become the layer's trainable weights.
Abstract: We present a PDE-based framework that generalizes Group equivariant Convolutional Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE-solvers where geometrically meaningful PDE-coefficients become the layer's trainable weights. Formulating our PDEs on homogeneous spaces allows these networks to be designed with built-in symmetries such as rotation in addition to the standard translation equivariance of CNNs. Having all the desired symmetries included in the design obviates the need to include them by means of costly techniques such as data augmentation. We will discuss our PDE-based G-CNNs (PDE-G-CNNs) in a general homogeneous space setting while also going into the specifics of our primary case of interest: roto-translation equivariance. We solve the PDE of interest by a combination of linear group convolutions and non-linear morphological group convolutions with analytic kernel approximations that we underpin with formal theorems. Our kernel approximations allow for fast GPU-implementation of the PDE-solvers, we release our implementation with this article in the form of the LieTorch extension to PyTorch, available at https://gitlab.com/bsmetsjr/lietorch . Just like for linear convolution a morphological convolution is specified by a kernel that we train in our PDE-G-CNNs. In PDE-G-CNNs we do not use non-linearities such as max/min-pooling and ReLUs as they are already subsumed by morphological convolutions. We present a set of experiments to demonstrate the strength of the proposed PDE-G-CNNs in increasing the performance of deep learning based imaging applications with far fewer parameters than traditional CNNs.

Journal ArticleDOI
TL;DR: In this article , the authors define and study formal elementary spherical functions on a split real connected Lie group with finite center, which they call global and formal N-point spherical functions, and show that they produce eigenstates for spin versions of quantum hyperbolic Calogero-Moser systems.
Abstract: Let G be a split real connected Lie group with finite center. In the first part of the paper we define and study formal elementary spherical functions. They are formal power series analogues of elementary spherical functions on G in which the role of the quasi-simple admissible G-representations is replaced by Verma modules. For generic highest weight we express the formal elementary spherical functions in terms of Harish-Chandra series and integrate them to spherical functions on the regular part of G. We show that they produce eigenstates for spin versions of quantum hyperbolic Calogero–Moser systems. In the second part of the paper we define and study special subclasses of global and formal elementary spherical functions, which we call global and formal N-point spherical functions. Formal N-point spherical functions arise as limits of correlation functions for boundary Wess–Zumino–Witten conformal field theory on the cylinder when the position variables tend to infinity. We construct global N-point spherical functions in terms of compositions of equivariant differential intertwiners associated with principal series representations, and express them in terms of Eisenstein integrals. We show that the eigenstates of the quantum spin Calogero–Moser system associated to N-point spherical functions are also common eigenfunctions of a commuting family of first-order differential operators, which we call asymptotic boundary Knizhnik–Zamolodchikov–Bernard operators. These operators are explicitly given in terms of folded classical dynamical r-matrices and associated dynamical k-matrices.

Journal ArticleDOI
TL;DR: In this paper , the authors provide a convenient scheme and additional diagrammatics for working with Frobenius extensions responsible for key flavors of equivariant SL(2) link homology theories.
Abstract: The first two sections of the paper provide a convenient scheme and additional diagrammatics for working with Frobenius extensions responsible for key flavors of equivariant SL(2) link homology theories. The goal is to clarify some basic structures in the

Proceedings ArticleDOI
26 Jul 2022
TL;DR: A self-interpretable framework, Equivariant and Invariant Grounding for Interpretable VideoQA (EIGV), which is able to distinguish the causal scene from the environment information, and explicitly present the visual-linguistic alignment.
Abstract: Video Question Answering (VideoQA) is the task of answering the natural language questions about a video. Producing an answer requires understanding the interplay across visual scenes in video and linguistic semantics in question. However, most leading VideoQA models work as black boxes, which make the visual-linguistic alignment behind the answering process obscure. Such black-box nature calls for visual explainability that reveals "What part of the video should the model look at to answer the question?". Only a few works present the visual explanations in a post-hoc fashion, which emulates the target model's answering process via an additional method. Instead of post-hoc explainability, we focus on intrinsic interpretability to make the answering process transparent. At its core is grounding the question-critical cues as the causal scene to yield answers, while rolling out the question-irrelevant information as the environment scene. Taking a causal look at VideoQA, we devise a self-interpretable framework, Equivariant and Invariant Grounding for Interpretable VideoQA (EIGV). Specifically, the equivariant grounding encourages the answering to be sensitive to the semantic changes in the causal scene and question; in contrast, the invariant grounding enforces the answering to be insensitive to the changes in the environment scene. By imposing them on the answering process, EIGV is able to distinguish the causal scene from the environment information, and explicitly present the visual-linguistic alignment. Extensive experiments on three benchmark datasets justify the superiority of EIGV in terms of accuracy and visual interpretability over the leading baselines.

Journal ArticleDOI
TL;DR: In this article , an E(3)-equivariant deep learning framework is proposed to represent density functional theory (DFT) Hamiltonian as a function of material structure, which can naturally preserve the Euclidean symmetry even in the presence of spin-orbit coupling.
Abstract: Combination of deep learning and ab initio calculation has shown great promise in revolutionizing future scientific research, but how to design neural network models incorporating a priori knowledge and symmetry requirements is a key challenging subject. Here we propose an E(3)-equivariant deep-learning framework to represent density functional theory (DFT) Hamiltonian as a function of material structure, which can naturally preserve the Euclidean symmetry even in the presence of spin-orbit coupling. Our DeepH-E3 method enables very efficient electronic-structure calculation at ab initio accuracy by learning from DFT data of small-sized structures, making routine study of large-scale supercells ($> 10^4$ atoms) feasible. Remarkably, the method can reach sub-meV prediction accuracy at high training efficiency, showing state-of-the-art performance in our experiments. The work is not only of general significance to deep-learning method development, but also creates new opportunities for materials research, such as building Moir\'e-twisted material database.

Journal ArticleDOI
TL;DR: In this paper , the authors show that in the neighborhood of trivial solutions, variables can be chosen so that the form of the reduced vector field relies not only on the information of the linearized system at the critical point but also on the inherent symmetry.

Journal ArticleDOI
TL;DR: In this article , the authors apply extended Kalman filtering to the equivariant error state of a nonlinear control system and show that the error dynamics have a particularly nice form.
Abstract: Equivariance is a common and natural property of many nonlinear control systems, especially those associated with models of mechatronic and navigation systems. Such systems admit a symmetry, associated with the equivariance, that provides structure enabling the design of robust and high-performance observers. A key insight is to pose the observer state to lie in the symmetry group rather than on the system state space. This allows one to define a global intrinsic equivariant error but poses a challenge in defining internal dynamics for the observer. By choosing an equivariant lift of the system dynamics for the observer internal model, we show that the error dynamics have a particularly nice form. Applying the methodology of extended Kalman filtering to the equivariant error state yields a filter we term the equivariant filter. The geometry of the state-space manifold appears naturally as a curvature modification to the classical Riccati equation for extended Kalman filtering. The equivariant filter exploits the symmetry and respects the geometry of an equivariant system model, and thus yields high-performance, robust filters for a wide range of mechatronic and navigation systems.

Proceedings ArticleDOI
12 Oct 2022
TL;DR: This work aims at integrating self-supervised equivariant learning and attention-based multi-instance learning to improve rDR classification accuracy and conducts extensive validation experiments on the Eyepacs dataset, achieving an area under the receiver operating characteristic curve (AU ROC) of 0.958.
Abstract: Lesion appearance is a crucial clue for medical providers to distinguish referable diabetic retinopathy (rDR) from non-referable DR. Most existing large-scale DR datasets contain only image-level labels rather than pixel-based annotations. This motivates us to develop algorithms to classify rDR and segment lesions via image-level labels. This paper leverages self-supervised equivariant learning and attention-based multi-instance learning (MIL) to tackle this problem. MIL is an effective strategy to differentiate positive and negative instances, helping us discard background regions (negative instances) while localizing lesion regions (positive ones). However, MIL only provides coarse lesion localization and cannot distinguish lesions located across adjacent patches. Conversely, a self-supervised equivariant attention mechanism (SEAM) generates a segmentation-level class activation map (CAM) that can guide patch extraction of lesions more accurately. Our work aims at integrating both methods to improve rDR classification accuracy. We conduct extensive validation experiments on the Eyepacs dataset, achieving an area under the receiver operating characteristic curve (AU ROC) of 0.958, outperforming current state-of-the-art algorithms.

Journal ArticleDOI
TL;DR: In this paper, a special value formula for the Goss L-functions associated to abelian t-modules and Galois representations was proved. And an equivariant version of this formula was also obtained.

Journal ArticleDOI
TL;DR: In this article , the equivariant genera of strongly invertible and periodic knots were studied, and the authors found many new examples where the 4-genus is larger than 4-genera.
Abstract: We study the equivariant genera of strongly invertible and periodic knots. Our techniques include some new strongly invertible concordance group invariants, Donaldson's theorem, and the g-signature. We find many new examples where the equivariant 4-genus is larger than the 4-genus.

Journal ArticleDOI
TL;DR: This work characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theoryof M-ESTimation.
Abstract: We characterize the full classes of M-estimators for semiparametric models of general functionals by formally connecting the theory of consistent loss functions from forecast evaluation with the theory of M-estimation. This novel characterization result allows us to leverage existing results on loss functions known from the literature on forecast evaluation in estimation theory. We exemplify advantageous implications for the fields of robust, efficient, equivariant and Pareto-optimal M-estimation.