Searcharxiv⌕ Search

arXiv subjects

Zhihao Duan

Publications and source records attributed to Zhihao Duan.

At least 37 records · Page 2Linked to original sources

Another Way to the Top: Exploit Contextual Clustering in Learned Image Coding

While convolution and self-attention are extensively used in learned image compression (LIC) for transform coding, this paper proposes an alternative called Contextual Clustering based LIC (CLIC) which primarily relies on clustering operations and local attention for correlation characterization and compact representation of an image. As seen, CLIC expands the receptive field into the entire image for intra-cluster feature aggregation. Afterward, features are reordered to their original spatial positions to pass through the local attention units for inter-cluster embedding. Additionally, we introduce the Guided Post-Quantization Filtering (GuidedPQF) into CLIC, effectively mitigating the propagation and accumulation of quantization errors at the initial decoding stage. Extensive experiments demonstrate the superior performance of CLIC over state-of-the-art works: when optimized using MSE, it outperforms VVC by about 10% BD-Rate in three widely-used benchmark datasets; when optimized using MS-SSIM, it saves more than 50% BD-Rate over VVC. Our CLIC offers a new way to generate compact representations for image compression, which also provides a novel direction along the line of LIC development.

eess.IV↗

Deep Hierarchical Video Compression

Recently, probabilistic predictive coding that directly models the conditional distribution of latent features across successive frames for temporal redundancy removal has yielded promising results. Existing methods using a single-scale Variational AutoEncoder (VAE) must devise complex networks for conditional probability estimation in latent space, neglecting multiscale characteristics of video frames. Instead, this work proposes hierarchical probabilistic predictive coding, for which hierarchal VAEs are carefully designed to characterize multiscale latent features as a family of flexible priors and posteriors to predict the probabilities of future frames. Under such a hierarchical structure, lightweight networks are sufficient for prediction. The proposed method outperforms representative learned video compression models on common testing videos and demonstrates computational friendliness with much less memory footprint and faster encoding/decoding. Extensive experiments on adaptation to temporal patterns also indicate the better generalization of our hierarchical predictive mechanism. Furthermore, our solution is the first to enable progressive decoding that is favored in networked video applications with packet loss.

eess.IV↗

Complexity Evaluation of Parallel Execution of the RAPiD Deep-Learning Algorithm on Intel CPU

Knowing how many and where are people in various indoor spaces is critical for reducing HVAC energy waste, space management, spatial analytics and in emergency scenarios. While a range of technologies have been proposed to detect and track people in large indoor spaces, ceiling-mounted fisheye cameras have recently emerged as strong contenders. Currently, RAPiD is the SOTA algorithm for people detection in images captured by fisheye cameras. However, in large spaces several overhead fisheye cameras are needed to assure high accuracy of counting and thus multiple instances of RAPiD must be executed simultaneously. This report evaluates inference time when multiple instances of RAPiD run in parallel on an Ubuntu NUC PC with Intel I7 8559U CPU. We consider three mechanisms of CPU-resource allocation to handle multiple instances of RAPiD: 1) managed by Ubuntu, 2) managed by user via operating-system calls to assign logical cores, and 3) managed by user via PyTorch-library calls to limit the number of threads used by PyTorch. Each scenario was evaluated on 300 images. The experimental results show, that when one or two instances of RAPiD are executed in parallel all three approaches result in similar inference times of 1.8sec and 3.2sec, respectively. However, when three or more instances of RAPiD run in parallel, limiting the number of threads used by PyTorch results in the shortest inference times. On average, RAPiD completes inference of 2 images simultaneously in about 3sec, 4 images in 6sec and 8 images in less than 14sec. This is important for real-time system design. In HVAC-application scenarios, with a typical reaction time of 10-15min, a latency of 14sec is negligible so a single 8559U CPU can support 8 camera streams thus reducing the system cost. However, in emergency scenarios, when time is of essence, a single CPU may be needed for each camera to reduce the latency to 1.8sec.

cs.DC↗

QARV: Quantization-Aware ResNet VAE for Lossy Image Compression

This paper addresses the problem of lossy image compression, a fundamental problem in image processing and information theory that is involved in many real-world applications. We start by reviewing the framework of variational autoencoders (VAEs), a powerful class of generative probabilistic models that has a deep connection to lossy compression. Based on VAEs, we develop a novel scheme for lossy image compression, which we name quantization-aware ResNet VAE (QARV). Our method incorporates a hierarchical VAE architecture integrated with test-time quantization and quantization-aware training, without which efficient entropy coding would not be possible. In addition, we design the neural network architecture of QARV specifically for fast decoding and propose an adaptive normalization operation for variable-rate compression. Extensive experiments are conducted, and results show that QARV achieves variable-rate compression, high-speed decoding, and a better rate-distortion performance than existing baseline methods. The code of our method is publicly accessible at https://github.com/duanzhiihao/lossy-vae

eess.IV↗

$\mathbb{Z}_N$ Duality and Parafermions Revisited

Given a two-dimensional bosonic theory with a non-anomalous $\mathbb{Z}_2$ symmetry, the orbifolding and fermionization can be understood holographically using three-dimensional BF theory with level $2$. From a Hamiltonian perspective, the information of dualities is encoded in a topological boundary state which is defined as an eigenstate of certain Wilson loop operators (anyons) in the bulk. We generalize this story to two-dimensional theories with non-anomalous $\mathbb{Z}_N$ symmetry, focusing on parafermionization. We find the generic operators defining different topological boundary states including orbifolding and parafermionization with $\mathbb{Z}_N$ or subgroups of $\mathbb{Z}_N$, and discuss their algebraic properties as well as the $\mathbb{Z}_N$ duality web.

hep-th↗

An Improved Upper Bound on the Rate-Distortion Function of Images

Recent work has shown that Variational Autoencoders (VAEs) can be used to upper-bound the information rate-distortion (R-D) function of images, i.e., the fundamental limit of lossy image compression. In this paper, we report an improved upper bound on the R-D function of images implemented by (1) introducing a new VAE model architecture, (2) applying variable-rate compression techniques, and (3) proposing a novel \ourfunction{} to stabilize training. We demonstrate that at least 30\% BD-rate reduction w.r.t. the intra prediction mode in VVC codec is achievable, suggesting that there is still great potential for improving lossy image compression. Code is made publicly available at https://github.com/duanzhiihao/lossy-vae.

eess.IV↗

On Classification of Fermionic Rational Conformal Field Theories

We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of spin structures should be invariant under a principal congruence subgroup of $\mathrm{PSL}(2,\mathbb{Z})$. The invariance strongly constrains the possible values of the central charge as well as the conformal weights in both Neveu-Schwarz and Ramond sectors, which improves the conventional holomorphic modular bootstrap method in a significant manner. This allows us to make much progress on the classification of fermionic rational conformal field theories with the number of independent characters less than five.

hep-th↗

Lossy Image Compression with Quantized Hierarchical VAEs

Recent research has shown a strong theoretical connection between variational autoencoders (VAEs) and the rate-distortion theory. Motivated by this, we consider the problem of lossy image compression from the perspective of generative modeling. Starting with ResNet VAEs, which are originally designed for data (image) distribution modeling, we redesign their latent variable model using a quantization-aware posterior and prior, enabling easy quantization and entropy coding at test time. Along with improved neural network architecture, we present a powerful and efficient model that outperforms previous methods on natural image lossy compression. Our model compresses images in a coarse-to-fine fashion and supports parallel encoding and decoding, leading to fast execution on GPUs. Code is available at https://github.com/duanzhiihao/lossy-vae.

eess.IV↗

Resurgence in complex Chern-Simons theory at generic levels

In this note we study the resurgent structure of $sl(2,\mathbb{C})$ Chern-Simons state integral models on knot complements $S^3\backslash\mathbf{4}_1,S^3\backslash\mathbf{5}_2$ with generic discrete level $k\geq 1$ and with small boundary holonomy deformation. The coefficients of the saddle point expansions are in the trace field of the knot extended by the holonomy parameter. Despite increasing complication of the asymptotic series as the level $k$ increases, the resurgent structure of the asymptotic series is universal: both the distribution of Borel plane singularities and the associated Stokes constants are independent of the level $k$.

hep-th↗

The descendants of the 3d-index

In the study of 3d-3d correspondence occurs a natural $q$-Weyl algebra associated to an ideal triangulation of a 3-manifold with torus boundary components, and a module of it. We study the action of this module on the (rotated) 3d-index of Dimofte-Gaiotto-Gukov and we conjecture some structural properties: bilinear factorization in terms of holomorphic blocks, pair of linear $q$-difference equations, the determination of the 3d-index in terms of a finite size matrix of rational functions and the asymptotic expansion of the $q$-series as $q$ tends to 1 to all orders. We illustrate our conjectures with computations for the case of the three simplest hyperbolic knots.

math.GT↗

Efficient Feature Compression for Edge-Cloud Systems

Optimizing computation in an edge-cloud system is an important yet challenging problem. In this paper, we consider a three-way trade-off between bit rate, classification accuracy, and encoding complexity in an edge-cloud image classification system. Our method includes a new training strategy and an efficient encoder architecture to improve the rate-accuracy performance. Our design can also be easily scaled according to different computation resources on the edge device, taking a step towards achieving a rate-accuracy-complexity (RAC) trade-off. Under various settings, our feature coding system consistently outperforms previous methods in terms of the RAC performance.

eess.IV↗

Opening the Black Box of Learned Image Coders

End-to-end learned lossy image coders (LICs), as opposed to hand-crafted image codecs, have shown increasing superiority in terms of the rate-distortion performance. However, they are mainly treated as black-box systems and their interpretability is not well studied. In this paper, we show that LICs learn a set of basis functions to transform input image for its compact representation in the latent space, as analogous to the orthogonal transforms used in image coding standards. Our analysis provides insights to help understand how learned image coders work and could benefit future design and development.

eess.IV↗

Hecke Relations, Cosets and the Classification of 2d RCFTs

We systemically study the Hecke relations and the $c=8k$ coset relations among 2d rational conformal field theories (RCFTs) with up to seven characters. We propose that the characters of any 2d RCFT -- unitary or non-unitary -- satisfying a holomorphic modular linear differential equation (MLDE) can be realized as either a Hecke image or the coset of a Hecke image with respect to a $c=8k$ theory. Benefited from the recent results on holomorphic modular bootstrap, we check this proposal for all admissible theories with up to five characters. We also find many new interesting Hecke relations. For example, the characters of WZW models $(E_{6})_2,(E_7)_2,(E_{7\frac12})_2$ can be realized as the Hecke images $\mathsf{T}_{13},\mathsf{T}_{19},\mathsf{T}_{19}$ of Virasoro minimal models $M_{\rm sub}(7,6),M(5,4),M_{\rm eff}(13,2)$ respectively. Besides, we find the characters associated to the second largest Fisher group $Fi_{23}$ and the Harada-Norton group $HN$ can be realized as the Hecke images $\mathsf{T}_{23},\mathsf{T}_{19}$ of the product theories $M_{\rm eff}(5,2)\otimes M_{\rm eff}(7,2)$ and $M_{\rm eff}(7,2)^{\otimes 2}$ respectively. Mathematically, our study provides a great many interesting examples of vector-valued modular functions up to rank seven.

hep-th↗

Can the energy bound $E \geq 0$ imply supersymmetry?

We utilize the integrality conjecture to show that the torus partition function of a fermionic rational conformal theory in the Ramond-Ramond sector becomes a constant when the bound $h^R \ge \frac{c}{24}$ is satisfied, where $h^R$ denote the conformal weights of Ramond states and $c$ is the central charge. The constant-valued Ramond-Ramond partition function strongly suggests the presence of supersymmetry unless a given theory has free fermions. The lower bound $h^R \ge \frac{c}{24}$ can then be identified with the unitarity bound of $\mathcal{N}=1$ supersymmetry. We thus propose that, for rational CFTs without free fermions, $(h^R-c/24) \geq 0$ can imply supersymmetry.

hep-th↗

Twisted 6d $(2,0)$ SCFTs on a Circle

We study twisted circle compactification of 6d $(2,0)$ SCFTs to 5d $\mathcal{N} = 2$ supersymmetric gauge theories with non-simply-laced gauge groups. We provide two complementary approaches towards the BPS partition functions, reflecting the 5d and 6d point of view respectively. The first is based on the blowup equations for the instanton partition function, from which in particular we determine explicitly the one-instanton contribution for all simple Lie groups. The second is based on the modular bootstrap program, and we propose a novel modular ansatz for the twisted elliptic genera that transform under the congruence subgroups $Γ_0(N)$ of $\text{SL}(2,\mathbb{Z})$. We conjecture a vanishing bound for the refined Gopakumar-Vafa invariants of the genus one fibered Calabi-Yau threefolds, upon which one can determine the twisted elliptic genera recursively. We use our results to obtain the 6d Cardy formulas and find universal behaviour for all simple Lie groups. In addition, the Cardy formulas remain invariant under the twist once the normalization of the compact circle is taken into account.

hep-th↗

Bootstrapping Fermionic Rational CFTs with Three Characters

Recently, the modular linear differential equation (MLDE) for level-two congruence subgroups $Γ_θ, Γ^{0}(2)$ and $Γ_0(2)$ of $\text{SL}_2(\mathbb{Z})$ was developed and used to classify the fermionic rational conformal field theories (RCFT). Two character solutions of the second-order fermionic MLDE without poles were found and their corresponding CFTs are identified. Here we extend this analysis to explore the landscape of three character fermionic RCFTs obtained from the third-order fermionic MLDE without poles. Especially, we focus on a class of the fermionic RCFTs whose Neveu-Schwarz sector vacuum character has no free-fermion currents and Ramond sector saturates the bound $h^{\text{R}} \ge \frac{c}{24}$, which is the unitarity bound for the supersymmetric case. Most of the solutions can be mapped to characters of the fermionized WZW models. We find the pairs of fermionic CFTs whose characters can be combined to produce $K(τ)$, the character of the $c=12$ fermionic CFT for $\text{Co}_0$ sporadic group.

hep-th↗

Fermionic Rational Conformal Field Theories and Modular Linear Differential Equations

We define Modular Linear Differential Equations (MLDE) for the level-two congruence subgroups $Γ_\vartheta$, $Γ^0(2)$ and $Γ_0(2)$ of $\text{SL}_2(\mathbb Z)$. Each subgroup corresponds to one of the spin structures on the torus. The pole structures of the fermionic MLDEs are investigated by exploiting the valence formula for the level-two congruence subgroups. We focus on the first and second order holomorphic MLDEs without poles and use them to find a large class of `Fermionic Rational Conformal Field Theories', which have non-negative integer coefficients in the $q$-series expansion of their characters. We study the detailed properties of these fermionic RCFTs, some of which are supersymmetric. This work also provides a starting point for the classification of the fermionic Modular Tensor Category.

hep-th↗

Weyl invariant Jacobi forms along Higgsing trees

Using topological string techniques, we compute BPS counting functions of 5d gauge theories which descend from 6d superconformal field theories upon circle compactification. Such theories are naturally organized in terms of nodes of Higgsing trees. We demonstrate that the specialization of the partition function as we move from the crown to the root of a tree is determined by homomorphisms between rings of Weyl invariant Jacobi forms. Our computations are made feasible by the fact that symmetry enhancements of the gauge theory which are manifest on the massless spectrum are inherited by the entire tower of BPS particles. In some cases, these symmetry enhancements have a nice relation to the 1-form symmetry of the associated gauge theory.

hep-th↗