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Di Yang

Publications and source records attributed to Di Yang.

At least 73 records · Page 4Linked to original sources
arXiv2024

On an infinite commuting ODE system associated to a simple Lie algebra

Inspired by a recent work of Dubrovin [7], for each simple Lie algebra $\mathfrak{g}$, we introduce an infinite family of pairwise commuting ODEs and define their $τ$-functions. We show that these $τ$-functions can be identified with the $τ$-functions for the Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type. Explicit examples for $\mathfrak{g}=A_1$ and $A_2$ are provided, which are connected to the KdV hierarchy and the Boussinesq hierarchy respectively.

nlin.SI↗
arXiv2024

HFNeRF: Learning Human Biomechanic Features with Neural Radiance Fields

In recent advancements in novel view synthesis, generalizable Neural Radiance Fields (NeRF) based methods applied to human subjects have shown remarkable results in generating novel views from few images. However, this generalization ability cannot capture the underlying structural features of the skeleton shared across all instances. Building upon this, we introduce HFNeRF: a novel generalizable human feature NeRF aimed at generating human biomechanic features using a pre-trained image encoder. While previous human NeRF methods have shown promising results in the generation of photorealistic virtual avatars, such methods lack underlying human structure or biomechanic features such as skeleton or joint information that are crucial for downstream applications including Augmented Reality (AR)/Virtual Reality (VR). HFNeRF leverages 2D pre-trained foundation models toward learning human features in 3D using neural rendering, and then volume rendering towards generating 2D feature maps. We evaluate HFNeRF in the skeleton estimation task by predicting heatmaps as features. The proposed method is fully differentiable, allowing to successfully learn color, geometry, and human skeleton in a simultaneous manner. This paper presents preliminary results of HFNeRF, illustrating its potential in generating realistic virtual avatars with biomechanic features using NeRF.

cs.CV↗
arXiv2024

GHNeRF: Learning Generalizable Human Features with Efficient Neural Radiance Fields

Recent advances in Neural Radiance Fields (NeRF) have demonstrated promising results in 3D scene representations, including 3D human representations. However, these representations often lack crucial information on the underlying human pose and structure, which is crucial for AR/VR applications and games. In this paper, we introduce a novel approach, termed GHNeRF, designed to address these limitations by learning 2D/3D joint locations of human subjects with NeRF representation. GHNeRF uses a pre-trained 2D encoder streamlined to extract essential human features from 2D images, which are then incorporated into the NeRF framework in order to encode human biomechanic features. This allows our network to simultaneously learn biomechanic features, such as joint locations, along with human geometry and texture. To assess the effectiveness of our method, we conduct a comprehensive comparison with state-of-the-art human NeRF techniques and joint estimation algorithms. Our results show that GHNeRF can achieve state-of-the-art results in near real-time.

cs.CV↗
arXiv2024

Galilean symmetry of the KdV hierarchy

By solving the infinitesimal Galilean symmetry for the KdV hierarchy, we obtain an explicit expression for the corresponding one-parameter Lie group, which we call the Galilean symmetry of the KdV hierarchy. As an application, we establish an explicit relationship between the non-abelian Born--Infeld partition function and the generalized Brézin--Gross--Witten partition function.

math-ph↗
arXiv2024

LAC: Latent Action Composition for Skeleton-based Action Segmentation

Skeleton-based action segmentation requires recognizing composable actions in untrimmed videos. Current approaches decouple this problem by first extracting local visual features from skeleton sequences and then processing them by a temporal model to classify frame-wise actions. However, their performances remain limited as the visual features cannot sufficiently express composable actions. In this context, we propose Latent Action Composition (LAC), a novel self-supervised framework aiming at learning from synthesized composable motions for skeleton-based action segmentation. LAC is composed of a novel generation module towards synthesizing new sequences. Specifically, we design a linear latent space in the generator to represent primitive motion. New composed motions can be synthesized by simply performing arithmetic operations on latent representations of multiple input skeleton sequences. LAC leverages such synthesized sequences, which have large diversity and complexity, for learning visual representations of skeletons in both sequence and frame spaces via contrastive learning. The resulting visual encoder has a high expressive power and can be effectively transferred onto action segmentation tasks by end-to-end fine-tuning without the need for additional temporal models. We conduct a study focusing on transfer-learning and we show that representations learned from pre-trained LAC outperform the state-of-the-art by a large margin on TSU, Charades, PKU-MMD datasets.

cs.CV↗
arXiv2023

Extract and Characterize Hairpin Vortices in Turbulent Flows

Hairpin vortices are one of the most important vortical structures in turbulent flows. Extracting and characterizing hairpin vortices provides useful insight into many behaviors in turbulent flows. However, hairpin vortices have complex configurations and might be entangled with other vortices, making their extraction difficult. In this work, we introduce a framework to extract and separate hairpin vortices in shear driven turbulent flows for their study. Our method first extracts general vortical regions with a region-growing strategy based on certain vortex criteria (e.g., $λ_2$) and then separates those vortices with the help of progressive extraction of ($λ_2$) iso-surfaces in a top-down fashion. This leads to a hierarchical tree representing the spatial proximity and merging relation of vortices. After separating individual vortices, their shape and orientation information is extracted. Candidate hairpin vortices are identified based on their shape and orientation information as well as their physical characteristics. An interactive visualization system is developed to aid the exploration, classification, and analysis of hairpin vortices based on their geometric and physical attributes. We also present additional use cases of the proposed system for the analysis and study of general vortices in other types of flows.

cs.HC↗
arXiv2023

Degree zero Gromov--Witten invariants for smooth curves

For a smooth projective curve, we derive a closed formula for the generating series of its Gromov--Witten invariants in genus $g$ and degree zero. It is known that the calculation of these invariants can be reduced to that of the $λ_g$ and $λ_{g-1}$ integrals on the moduli space of stable algebraic curves. The closed formula for the $λ_g$ integrals is given by the $λ_g$ conjecture, proved by Faber and Pandharipande. We compute in this paper the $λ_{g-1}$ integrals via solving the degree zero limit of the loop equation associated to the complex projective line.

math.AG↗
arXiv2023

The constrained KP hierarchy and the bigraded Toda hierarchy of $(M,1)$-type

In this paper, we extend the matrix-resolvent method to the study of the Dubrovin--Zhang type tau-functions for the constrained KP hierarchy and the bigraded Toda hierarchy of $(M,1)$-type. We show that the Dubrovin--Zhang type tau-function of an arbitrary solution to the bigraded Toda hierarchy of $(M,1)$-type is a Dubrovin--Zhang type tau-function for the constrained KP hierarchy, which generalizes the result in [10, 35] for the Toda lattice hierarchy and the NLS hierarchy corresponding to the $M=1$ case.

nlin.SI↗
arXiv2023

Simple Lie algebras, Drinfeld--Sokolov hierarchies, and multi-point correlation functions

For a simple Lie algebra $\mathfrak{g}$, we derive a simple algorithm for computing logarithmic derivatives of tau-functions of Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type in terms of $\mathfrak{g}$-valued resolvents. We show, for the topological solution to the lowest-weight-gauge Drinfeld--Sokolov hierarchy of $\mathfrak{g}$-type, the resolvents evaluated at zero satisfy the $\textit{topological ODE}$.

math-ph↗
arXiv2023

Architecture-agnostic Iterative Black-box Certified Defense against Adversarial Patches

The adversarial patch attack aims to fool image classifiers within a bounded, contiguous region of arbitrary changes, posing a real threat to computer vision systems (e.g., autonomous driving, content moderation, biometric authentication, medical imaging) in the physical world. To address this problem in a trustworthy way, proposals have been made for certified patch defenses that ensure the robustness of classification models and prevent future patch attacks from breaching the defense. State-of-the-art certified defenses can be compatible with any model architecture, as well as achieve high clean and certified accuracy. Although the methods are adaptive to arbitrary patch positions, they inevitably need to access the size of the adversarial patch, which is unreasonable and impractical in real-world attack scenarios. To improve the feasibility of the architecture-agnostic certified defense in a black-box setting (i.e., position and size of the patch are both unknown), we propose a novel two-stage Iterative Black-box Certified Defense method, termed IBCD.In the first stage, it estimates the patch size in a search-based manner by evaluating the size relationship between the patch and mask with pixel masking. In the second stage, the accuracy results are calculated by the existing white-box certified defense methods with the estimated patch size. The experiments conducted on two popular model architectures and two datasets verify the effectiveness and efficiency of IBCD.

cs.CV↗
arXiv2023

Self-Supervised Video Representation Learning via Latent Time Navigation

Self-supervised video representation learning aimed at maximizing similarity between different temporal segments of one video, in order to enforce feature persistence over time. This leads to loss of pertinent information related to temporal relationships, rendering actions such as `enter' and `leave' to be indistinguishable. To mitigate this limitation, we propose Latent Time Navigation (LTN), a time-parameterized contrastive learning strategy that is streamlined to capture fine-grained motions. Specifically, we maximize the representation similarity between different video segments from one video, while maintaining their representations time-aware along a subspace of the latent representation code including an orthogonal basis to represent temporal changes. Our extensive experimental analysis suggests that learning video representations by LTN consistently improves performance of action classification in fine-grained and human-oriented tasks (e.g., on Toyota Smarthome dataset). In addition, we demonstrate that our proposed model, when pre-trained on Kinetics-400, generalizes well onto the unseen real world video benchmark datasets UCF101 and HMDB51, achieving state-of-the-art performance in action recognition.

cs.CV↗
arXiv2023

On a new proof of the Okuyama--Sakai conjecture

In [41] Okuyama and Sakai gave a conjectural equality for the higher genus generalized Brézin--Gross--Witten (BGW) free energies. In a recent work [46] we established the Hodge-BGW correspondence on the relationship between certain special cubic Hodge integrals and the generalized BGW correlators, and a proof of the Okuyama--Sakai conjecture was also given ${\it ibid}$. In this paper, we give a new proof of the Okuyama--Sakai conjecture by a further application of the Dubrovin--Zhang theory for the KdV hierarchy.

math-ph↗
arXiv2023

Prompting Neural Machine Translation with Translation Memories

Improving machine translation (MT) systems with translation memories (TMs) is of great interest to practitioners in the MT community. However, previous approaches require either a significant update of the model architecture and/or additional training efforts to make the models well-behaved when TMs are taken as additional input. In this paper, we present a simple but effective method to introduce TMs into neural machine translation (NMT) systems. Specifically, we treat TMs as prompts to the NMT model at test time, but leave the training process unchanged. The result is a slight update of an existing NMT system, which can be implemented in a few hours by anyone who is familiar with NMT. Experimental results on several datasets demonstrate that our system significantly outperforms strong baselines.

cs.CL↗
arXiv2022

Affine Kac-Moody Algebras and Tau-Functions for the Drinfeld-Sokolov Hierarchies: the Matrix-Resolvent Method

For each affine Kac-Moody algebra $X_n^{(r)}$ of rank $\ell$, $r=1,2$, or $3$, and for every choice of a vertex $c_m$, $m=0,\dots,\ell$, of the corresponding Dynkin diagram, by using the matrix-resolvent method we define a gauge-invariant tau-structure for the associated Drinfeld-Sokolov hierarchy and give explicit formulas for generating series of logarithmic derivatives of the tau-function in terms of matrix resolvents, extending the results of [Mosc. Math. J. 21 (2021), 233-270, arXiv:1610.07534] with $r=1$ and $m=0$. For the case $r=1$ and $m=0$, we verify that the above-defined tau-structure agrees with the axioms of Hamiltonian tau-symmetry in the sense of [Adv. Math. 293 (2016), 382-435, arXiv:1409.4616] and [arXiv:math.DG/0108160].

math-ph↗
arXiv2022

On the large genus asymptotics of psi-class intersection numbers

Based on an explicit formula of the generating series for the $n$-point psi-class intersection numbers (cf. Bertola et. al. [4]), we give a novel proof of a conjecture of Delecroix et. al. [9] regarding the large genus uniform leading asymptotics of the psi-class intersection numbers. We also investigate polynomiality phenomenon in the large genera.

math.AG↗
arXiv2022

ViA: View-invariant Skeleton Action Representation Learning via Motion Retargeting

Current self-supervised approaches for skeleton action representation learning often focus on constrained scenarios, where videos and skeleton data are recorded in laboratory settings. When dealing with estimated skeleton data in real-world videos, such methods perform poorly due to the large variations across subjects and camera viewpoints. To address this issue, we introduce ViA, a novel View-Invariant Autoencoder for self-supervised skeleton action representation learning. ViA leverages motion retargeting between different human performers as a pretext task, in order to disentangle the latent action-specific `Motion' features on top of the visual representation of a 2D or 3D skeleton sequence. Such `Motion' features are invariant to skeleton geometry and camera view and allow ViA to facilitate both, cross-subject and cross-view action classification tasks. We conduct a study focusing on transfer-learning for skeleton-based action recognition with self-supervised pre-training on real-world data (e.g., Posetics). Our results showcase that skeleton representations learned from ViA are generic enough to improve upon state-of-the-art action classification accuracy, not only on 3D laboratory datasets such as NTU-RGB+D 60 and NTU-RGB+D 120, but also on real-world datasets where only 2D data are accurately estimated, e.g., Toyota Smarthome, UAV-Human and Penn Action.

cs.CV↗
arXiv2022

Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality

For each of the simple Lie algebras $\mathfrak{g}=A_l$, $D_l$ or $E_6$, we show that the all-genera one-point FJRW invariants of $\mathfrak{g}$-type, after multiplication by suitable products of Pochhammer symbols, are the coefficients of an algebraic generating function and hence are integral. Moreover, we find that the all-genera invariants themselves coincide with the coefficients of the unique calibration of the Frobenius manifold of $\mathfrak{g}$-type evaluated at a special point. For the $A_4$ (5-spin) case we also find two other normalizations of the sequence that are again integral and of at most exponential growth, and hence conjecturally are the Taylor coefficients of some period functions.

math.AG↗