Explicit Correspondence Research Articles

Competing for Pixels: A Self-play Algorithm for Weakly-supervised Semantic Segmentation.

Weakly-supervised semantic segmentation (WSSS) methods, reliant on image-level labels indicating object presence, lack explicit correspondence between labels and regions of interest (ROIs), posing a significant challenge. Despite this, WSSS methods have attracted attention due to their much lower annotation costs compared to fully-supervised segmentation. Leveraging reinforcement learning (RL) self-play, we propose a novel WSSS method that gamifies image segmentation of a ROI. We formulate segmentation as a competition between two agents that compete to select ROI-containing patches until exhaustion of all such patches. The score at each time-step, used to compute the reward for agent training, represents likelihood of object presence within the selection, determined by an object presence detector pre-trained using only image-level binary classification labels of object presence. Additionally, we propose a game termination condition that can be called by either side upon exhaustion of all ROI-containing patches, followed by the selection of a final patch from each. Upon termination, the agent is incentivised if ROI-containing patches are exhausted or disincentivised if a ROI-containing patch is found by the competitor. This competitive setup ensures minimisation of over- or under-segmentation, a common problem with WSSS methods. Extensive experimentation across four datasets demonstrates significant performance improvements over recent state-of-the-art methods. Code: https://github.com/s-sd/spurl/tree/main/wss.

Swift-Mapping: Online Neural Implicit Dense Mapping in Urban Scenes

Online dense mapping of urban scenes is of paramount importance for scene understanding of autonomous navigation. Traditional online dense mapping methods fuse sensor measurements (vision, lidar, etc.) across time and space via explicit geometric correspondence. Recently, NeRF-based methods have proved the superiority of neural implicit representations by high-fidelity reconstruction of large-scale city scenes. However, it remains an open problem how to integrate powerful neural implicit representations into online dense mapping. Existing methods are restricted to constrained indoor environments and are too computationally expensive to meet online requirements. To this end, we propose Swift-Mapping, an online neural implicit dense mapping framework in urban scenes. We introduce a novel neural implicit octomap (NIO) structure that provides efficient neural representation for large and dynamic urban scenes while retaining online update capability. Based on that, we propose an online neural dense mapping framework that effectively manages and updates neural octree voxel features. Our approach achieves SOTA reconstruction accuracy while being more than 10x faster in reconstruction speed, demonstrating the superior performance of our method in both accuracy and efficiency.

Semi-modules and crystal bases via affine Deligne-Lusztig varieties

There are two combinatorial ways of parameterizing the Jb(F)-orbits of the irreducible components of affine Deligne-Lusztig varieties for GLn and superbasic b. One way is to use the extended semi-modules introduced by Viehmann. The other way is to use the crystal bases introduced by Kashiwara and Lusztig. In this paper, we give an explicit correspondence between them using the crystal structure.

Attribute-Aware Deep Hashing With Self-Consistency for Large-Scale Fine-Grained Image Retrieval.

Our work focuses on tackling large-scale fine-grained image retrieval as ranking the images depicting the concept of interests (i.e., the same sub-category labels) highest based on the fine-grained details in the query. It is desirable to alleviate the challenges of both fine-grained nature of small inter-class variations with large intra-class variations and explosive growth of fine-grained data for such a practical task. In this paper, we propose attribute-aware hashing networks with self-consistency for generating attribute-aware hash codes to not only make the retrieval process efficient, but also establish explicit correspondences between hash codes and visual attributes. Specifically, based on the captured visual representations by attention, we develop an encoder-decoder structure network of a reconstruction task to unsupervisedly distill high-level attribute-specific vectors from the appearance-specific visual representations without attribute annotations. Our models are also equipped with a feature decorrelation constraint upon these attribute vectors to strengthen their representative abilities. Then, driven by preserving original entities' similarity, the required hash codes can be generated from these attribute-specific vectors and thus become attribute-aware. Furthermore, to combat simplicity bias in deep hashing, we consider the model design from the perspective of the self-consistency principle and propose to further enhance models' self-consistency by equipping an additional image reconstruction path. Comprehensive quantitative experiments under diverse empirical settings on six fine-grained retrieval datasets and two generic retrieval datasets show the superiority of our models over competing methods. Moreover, qualitative results demonstrate that not only the obtained hash codes can strongly correspond to certain kinds of crucial properties of fine-grained objects, but also our self-consistency designs can effectively overcome simplicity bias in fine-grained hashing.

Lagrangian fillings in $A$-type and their Kálmán loop orbits

We compare two constructions of exact Lagrangian fillings of Legendrian positive braid closures, the Legendrian weaves of Casals–Zaslow, and the decomposable Lagrangian fillings of Ekholm–Honda–Kálmán, and show that they coincide for large families of Lagrangian fillings. As a corollary, we obtain an explicit correspondence between Hamiltonian isotopy classes of decomposable Lagrangian fillings of Legendrian (2,n) torus links described by Ekholm–Honda–Kálmán and the weave fillings constructed by Treumann and Zaslow. We apply this result to describe the orbital structure of the Kálmán loop and give a combinatorial criteria to determine the orbit size of a filling. We follow our geometric discussion with a Floer-theoretic proof of the orbital structure, where an identity studied by Euler in the context of continued fractions makes a surprise appearance. We conclude by giving a purely combinatorial description of the Kálmán loop action on the fillings discussed above in terms of edge flips of triangulations.

Compatibility of theta lifts and tempered condition

AbstractIn this note, assuming the nonvanishing result of explicit theta correspondence for the symplectic–orthogonal dual pair over quaternion algebra $\mathbb {H}$ , we show that, for metapletic–orthogonal dual pair over $\mathbb {R}$ and the symplectic–orthogonal dual pair over quaternion algebra $\mathbb {H}$ , the theta correspondence is compatible with tempered condition by directly estimating the matrix coefficients, without using the classification theorem.

Foliated-exotic duality in fractonic BF theories

There has been proposed two continuum descriptions of fracton systems: foliated quantum field theories (FQFTs) and exotic quantum field theories. Certain fracton systems are believed to admit descriptions by both, and hence a duality is expected between such a class of FQFTs and exotic QFTs. In this paper we study this duality in detail for concrete examples in 2+12+1 and 3+13+1 dimensions. In the examples, both sides of the continuum theories are of BFBF-type, and we find the explicit correspondences of gauge-invariant operators, gauge fields, parameters, and allowed singularities and discontinuities. This deepens the understanding of dualities in fractonic quantum field theories.

Multi-Modal Remote Sensing Image Segmentation with Intuition-Inspired Hypergraph Modeling.

Multi-modal remote sensing (RS) image segmentation aims to comprehensively utilize multiple RS modalities to assign pixel-level semantics to the studied scenes, which can provide a new perspective for global city understanding. Multi-modal segmentation inevitably encounters the challenge of modeling intra- and inter-modal relationships, i.e., object diversity and modal gaps. However, the previous methods are usually designed for a single RS modality, limited by the noisy collection environment and poor discrimination information. Neuropsychology and neuroanatomy confirm that the human brain performs the guiding perception and integrative cognition of multi-modal semantics through intuitive reasoning. Therefore, establishing a semantic understanding framework inspired by intuition to realize multi-modal RS segmentation becomes the main motivation of this work. Drived by the superiority of hypergraphs in modeling high-order relationships, we propose an intuition-inspired hypergraph network (I2HN) for multi-modal RS segmentation. Specifically, we present a hypergraph parser to imitate guiding perception to learn intra-modal object-wise relationships. It parses the input modality into irregular hypergraphs to mine semantic clues and generate robust mono-modal representations. In addition, we also design a hypergraph matcher to dynamically update the hypergraph structure from the explicit correspondence of visual concepts, similar to integrative cognition, to improve cross-modal compatibility when fusing multi-modal features. Extensive experiments on two multi-modal RS datasets show that the proposed I2HN outperforms the state-of-the-art models, achieving F1/mIoU accuracy 91.4%/82.9% on the ISPRS Vaihingen dataset, and 92.1%/84.2% on the MSAW dataset. The complete algorithm and benchmark results will be available online.

On deformation space analogies between Kleinian reflection groups and antiholomorphic rational maps

In a previous paper (Lodge et al. in Forum Math Sigma 10:e3, 2022), we constructed an explicit dynamical correspondence between certain Kleinian reflection groups and certain anti-holomorphic rational maps on the Riemann sphere. In this paper, we show that their deformation spaces share many striking similarities. We establish an analogue of Thurston’s compactness theorem for critically fixed anti-rational maps. We also characterize how deformation spaces interact with each other and study the monodromy representations of the union of all deformation spaces.

Generalized hydrodynamics of the KdV soliton gas

We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable systems. This is done by constructing the GHD description of the soliton gas for the Korteweg–de Vries equation. We further predict the exact form of the free energy density and flux, and of the static correlation matrices of conserved charges and currents, for the soliton gas. For this purpose, we identify the solitons’ statistics with that of classical particles, and confirm the resulting GHD static correlation matrices by numerical simulations of the soliton gas. Finally, we express conjectured dynamical correlation functions for the soliton gas by simply borrowing the GHD results. In principle, other conjectures are also immediately available, such as diffusion and large-deviation functions for fluctuations of soliton transport.

Deep-LIFT: Deep Label-Specific Feature Learning for Image Annotation.

Image annotation aims to jointly predict multiple tags for an image. Although significant progress has been achieved, existing approaches usually overlook aligning specific labels and their corresponding regions due to the weak supervised information (i.e., "bag of labels" for regions), thus failing to explicitly exploit the discrimination from different classes. In this article, we propose the deep label-specific feature (Deep-LIFT) learning model to build the explicit and exact correspondence between the label and the local visual region, which improves the effectiveness of feature learning and enhances the interpretability of the model itself. Deep-LIFT extracts features for each label by aligning each label and its region. Specifically, Deep-LIFTs are achieved through learning multiple correlation maps between image convolutional features and label embeddings. Moreover, we construct two variant graph convolutional networks (GCNs) to further capture the interdependency among labels. Empirical studies on benchmark datasets validate that the proposed model achieves superior performance on multilabel classification over other existing state-of-the-art methods.

A Credible and Robust Approach to Ego-Motion Estimation Using an Automotive Radar

Consistent motion estimation is fundamental for all mobile autonomous systems. While this sounds like an easy task, often, it is not the case because of changing environmental conditions affecting odometry obtained from vision, Lidar, or the wheels themselves. Unsusceptible to challenging lighting and weather conditions, radar sensors are an obvious alternative. Usually, automotive radars return a sparse point cloud, representing the surroundings. Utilizing this information to motion estimation is challenging due to unstable and phantom measurements, which result in a high rate of outliers. We introduce a credible and robust probabilistic approach to estimate the ego-motion based on these challenging radar measurements; intended to be used within a loosely-coupled sensor fusion framework. Compared to existing solutions, evaluated on the popular nuScenes dataset and others, we show that our proposed algorithm is more credible while not depending on explicit correspondence calculation.

P^3-Net: Part Mobility Parsing from Point Cloud Sequences via Learning Explicit Point Correspondence

Understanding an articulated 3D object with its movable parts is an essential skill for an intelligent agent. This paper presents a novel approach to parse 3D part mobility from point cloud sequences. The key innovation is learning explicit point correspondence from a raw unordered point cloud sequence. We propose a novel deep network called P^3-Net to parallelize trajectory feature extraction and point correspondence establishment, performing joint optimization between them. Specifically, we design a Match-LSTM module to reaggregate point features among different frames by a point correspondence matrix, a.k.a. the matching matrix. To obtain this matrix, an attention module is proposed to calculate the point correspondence. Moreover, we implement a Gumbel-Sinkhorn module to reduce the many-to-one relationship for better point correspondence. We conduct comprehensive evaluations on public benchmarks, including the motion dataset and the PartNet dataset. Results demonstrate that our approach outperforms SOTA methods on various 3D parsing tasks of part mobility, including motion flow prediction, motion part segmentation, and motion attribute (i.e. axis & range) estimation. Moreover, we integrate our approach into a robot perception module to validate its robustness.

Relating Stated Skein Algebras and Internal Skein Algebras

We give an explicit correspondence between stated skein algebras, which are defined via explicit relations on stated tangles in [Costantino F., L\^e T.T.Q., arXiv:1907.11400], and internal skein algebras, which are defined as internal endomorphism algebras in free cocompletions of skein categories in [Ben-Zvi D., Brochier A., Jordan D., J. Topol. 11 (2018), 874-917, arXiv:1501.04652] or in [Gunningham S., Jordan D., Safronov P., arXiv:1908.05233]. Stated skein algebras are defined on surfaces with multiple boundary edges and we generalise internal skein algebras in this context. Now, one needs to distinguish between left and right boundary edges, and we explain this phenomenon on stated skein algebras using a half-twist. We prove excision properties of multi-edges internal skein algebras using excision properties of skein categories, and agreeing with excision properties of stated skein algebras when $\mathcal{V} = \mathcal{U}_{q^2}(\mathfrak{sl}_2)\text{-}{\rm mod}^{\rm fin}$. Our proofs are mostly based on skein theory and we do not require the reader to be familiar with the formalism of higher categories.

The groupoid approach to equilibrium states on right LCM semigroup C∗$^*$‐algebras

Given a right LCM semigroup S $S$ and a homomorphism N : S → [ 1 , + ∞ ) $N\colon S\rightarrow [1,+\infty )$ , we use the groupoid approach to study the KMS β $_\beta$ -states on C ∗ ( S ) $C^*(S)$ with respect to the dynamics induced by N $N$ . We establish necessary and sufficient conditions for the existence and uniqueness of KMS β $_\beta$ -states. As an application, we show that the sufficient condition for the uniqueness obtained for so-called generalized scales is necessary as well. Our most complete results are obtained for inverse temperatures β $\beta$ at which the ζ $\zeta$ -function of N $N$ is finite. In this case, we get an explicit bijective correspondence between the KMS β $_\beta$ -states on C ∗ ( S ) $C^*(S)$ and the tracial states on C ∗ ( ker N ) $C^*(\operatorname{ker}N)$ .

Circle packings, kissing reflection groups and critically fixed anti-rational maps

Abstract In this article, we establish an explicit correspondence between kissing reflection groups and critically fixed anti-rational maps. The correspondence, which is expressed using simple planar graphs, has several dynamical consequences. As an application of this correspondence, we give complete answers to geometric mating problems for critically fixed anti-rational maps.

The colored Jones polynomials as vortex partition functions

We construct 3D mathcal{N} = 2 abelian gauge theories on mathbbm{S} 2 × mathbbm{S} 1 labeled by knot diagrams whose K-theoretic vortex partition functions, each of which is a building block of twisted indices, give the colored Jones polynomials of knots in mathbbm{S} 3. The colored Jones polynomials are obtained as the Wilson loop expectation values along knots in SU(2) Chern-Simons gauge theories on mathbbm{S} 3, and then our construction provides an explicit correspondence between 3D mathcal{N} = 2 abelian gauge theories and 3D SU(2) Chern-Simons gauge theories. We verify, in particular, the applicability of our constructions to a class of tangle diagrams of 2-bridge knots with certain specific twists.

Towards a Neural Graphics Pipeline for Controllable Image Generation

AbstractIn this paper, we leverage advances in neural networks towards forming a neural rendering for controllable image generation, and thereby bypassing the need for detailed modeling in conventional graphics pipeline. To this end, we present Neural Graphics Pipeline (NGP), a hybrid generative model that brings together neural and traditional image formation models. NGP decomposes the image into a set of interpretable appearance feature maps, uncovering direct control handles for controllable image generation. To form an image, NGP generates coarse 3D models that are fed into neural rendering modules to produce view‐specific interpretable 2D maps, which are then composited into the final output image using a traditional image formation model. Our approach offers control over image generation by providing direct handles controlling illumination and camera parameters, in addition to control over shape and appearance variations. The key challenge is to learn these controls through unsupervised training that links generated coarse 3D models with unpaired real images via neural and traditional (e.g., Blinn‐Phong) rendering functions, without establishing an explicit correspondence between them. We demonstrate the effectiveness of our approach on controllable image generation of single‐object scenes. We evaluate our hybrid modeling framework, compare with neural‐only generation methods (namely, DCGAN, LSGAN, WGAN‐GP, VON, and SRNs), report improvement in FID scores against real images, and demonstrate that NGP supports direct controls common in traditional forward rendering. Code is available at http://geometry.cs.ucl.ac.uk/projects/2021/ngp.

A correspondence between Ricci-flat Kerr and Kaluza-Klein AdS black hole

We establish an explicit correspondence of Einstein gravity on the squashed spheres that are the U(1) bundles over ℂℙm to the Kaluza-Klein AdS gravity on the tori. This allows us to map the Ricci-flat Kerr metrics in odd dimensions with all equal angular momenta to charged Kaluza-Klein AdS black holes that can be lifted to become singly rotating M-branes and D3-branes. Furthermore, we find maps between Ricci-flat gravitational instantons to the AdS domain walls. In particular the supersymmetric bolt instantons correspond to domain walls that can be interpreted as distributed M-branes and D3-branes, whilst the non-supersymmetric Taub-NUT solutions yield new domain walls that can be lifted to become solutions in M-theory or type IIB supergravity. The correspondence also inspires us to obtain a new superpotential in the Kaluza-Klein AdS gravity in four dimensions.

Mechanisms of stationary converted waves and their complexes in the multi-component AB system

Under investigation in this article is a multi-component AB system which models the self-induced transparency phenomenon. By using the modified Darboux transformation, we present the breather solutions of such system. We study the subtle mechanism that converts the breathing state into the solitary and periodic ones, through which we obtain various stationary nonlinear excitations such as the multi-peak solitons, (quasi) periodic waves, (quasi) anti-dark solitons, W-shaped solitons and M-shaped solitons which exhibit stationary feature. According to the analysis of the group velocity difference, we give the corresponding conversion rule and present the explicit correspondence of phase diagram of wave numbers for various converted waves, by which we show the gradient relation among these converted waves. Further, by separating the converted waves into the solitary wave as well as the periodic wave, we classify different kinds of nonlinear waves and indicate the difference of the superposition mechanism among them. We show that the breather and various converted waves are formed by different superposition modes between the solitary wave components with different localities and periodic wave components with different frequencies. By virtue of the second-order solutions, we consider all possible superposition situations of two nonlinear waves and present the corresponding nonlinear wave complexes. In particular, for the hybrid structure made of a breather and a nonlinear wave with variable velocity, we then discover that the nonlinear wave does not change its state under the conversion condition, leading to that an additional breathing structure or a dark structure is contained in the converted waves. Finally, we unveil the underlying relationship between the conversion and modulation instability.