arXiv subjects

Zhihao Duan

Publications and source records attributed to Zhihao Duan.

At least 19 recordsLinked to original sources

arXiv2026

Superstrip Algebras and Nonperturbative Spectra in Fermionic Theories

This is an extended version of arXiv:2511.22129. We develop a general construction of the superstrip algebra $\mathbf{sStr}_{\mathscr C}(\mathcal M)$, the fermionic counterpart of the strip algebra, for a gapped $(1+1)$-dimensional system with a fermionic superfusion category $\mathscr C$ and the vacuum structure described by the supermodule category $\mathcal M$. As illustrations, we work out the superstrip algebra for two simple examples: the fermionic variant of the Fibonacci fusion category and the q-type $\mathbb{Z}_2$ symmetry. We then apply the framework to the gapped IR phases of the $\mathcal N=2$ and $\mathcal N=1$ superconformal minimal models deformed by their least relevant operator and compute the Witten indices. We explain how the particle and soliton spectra, together with their fermion parity, are organized into representations of the corresponding superstrip algebras. A mixed 't Hooft anomaly between the spontaneously broken symmetry and the unbroken fermion parity $(-1)^F$ further forces each $\mathcal N =2$ soliton to carry a fractional fermion number. Finally, we set up the boundary SymTFT for fermionic systems and reproduce the results in several examples studied in this paper.

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arXiv2026

On the Schubert calculus of the quantum K-theory for partial flag manifolds: a 3d A-model perspective

We further investigate the 3d gauged linear sigma model (GLSM)/~quantum K-theory correspondence for partial flag manifolds $X \equiv {\rm Fl}(\boldsymbol{k};n)$. This is a 3d uplift of the 2d GLSM/quantum cohomology correspondence with the 3d theory compactified on $\mathbb{R}^2\times S^1_β$. Recently, a set of half-BPS line operators, called Schubert line defects, were constructed that correspond to the Schubert classes in the K-theory ring of $X$. Utilizing algebro-geometric algorithms, we compute $2$-point and $3$-point correlation functions of these line operators in the 3d A-model regime of the theory. These are interpreted as genus-$0$ K-theoretic Gromov--Witten invariants, and they produce the K-theoretic Littlewood--Richardson coefficients of the quantum K-theory ring of $X$. We show how this works explicitly in examples, going beyond the existing results in the literature. Taking the small $β$ limit, we apply these techniques to the resulting 2d GLSM. We explicitly compute the quantum cohomology ring relations of $X$ for some cases and match with existing results in the literature in examples.

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arXiv2025

Fermionic Non-invertible Symmetry Behind Supersymmetric ADE Solitons

The non-perturbative constraints imposed by intrinsic fermionic non-invertible symmetries in 1+1 dimensional gapped systems remain largely unexplored. In this letter, we propose the superstrip algebra as a unified framework to catalog the categorical symmetry data in a massive fermionic model. The algebra and its representations explicitly encode the vacuum structure, soliton degeneracies, and their quantum numbers. As a demonstration, we apply this framework to the $\mathcal N=2$ minimal models with their least relevant deformation. We show that this specific deformation alone preserves a non-invertible superfusion category, a fermionic variant of $\text{SU}(2)_k$ known to underlie the $ADE$ classification of critical theories. Its superstrip algebra then accounts for the origin of the resulting $ADE$-type soliton spectrum and their fractional fermion number. Although our primary examples are supersymmetric and integrable, our framework itself relies on neither property, providing a new powerful tool for studying a broad class of strongly-coupled fermionic systems.

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arXiv2025

Flexible Mixed Precision Quantization for Learned Image Compression

Despite its improvements in coding performance compared to traditional codecs, Learned Image Compression (LIC) suffers from large computational costs for storage and deployment. Model quantization offers an effective solution to reduce the computational complexity of LIC models. However, most existing works perform fixed-precision quantization which suffers from sub-optimal utilization of resources due to the varying sensitivity to quantization of different layers of a neural network. In this paper, we propose a Flexible Mixed Precision Quantization (FMPQ) method that assigns different bit-widths to different layers of the quantized network using the fractional change in rate-distortion loss as the bit-assignment criterion. We also introduce an adaptive search algorithm which reduces the time-complexity of searching for the desired distribution of quantization bit-widths given a fixed model size. Evaluation of our method shows improved BD-Rate performance under similar model size constraints compared to other works on quantization of LIC models. We have made the source code available at gitlab.com/viper-purdue/fmpq.

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arXiv2025

CL-LoRA: Continual Low-Rank Adaptation for Rehearsal-Free Class-Incremental Learning

Class-Incremental Learning (CIL) aims to learn new classes sequentially while retaining the knowledge of previously learned classes. Recently, pre-trained models (PTMs) combined with parameter-efficient fine-tuning (PEFT) have shown remarkable performance in rehearsal-free CIL without requiring exemplars from previous tasks. However, existing adapter-based methods, which incorporate lightweight learnable modules into PTMs for CIL, create new adapters for each new task, leading to both parameter redundancy and failure to leverage shared knowledge across tasks. In this work, we propose ContinuaL Low-Rank Adaptation (CL-LoRA), which introduces a novel dual-adapter architecture combining \textbf{task-shared adapters} to learn cross-task knowledge and \textbf{task-specific adapters} to capture unique features of each new task. Specifically, the shared adapters utilize random orthogonal matrices and leverage knowledge distillation with gradient reassignment to preserve essential shared knowledge. In addition, we introduce learnable block-wise weights for task-specific adapters, which mitigate inter-task interference while maintaining the model's plasticity. We demonstrate CL-LoRA consistently achieves promising performance under multiple benchmarks with reduced training and inference computation, establishing a more efficient and scalable paradigm for continual learning with pre-trained models.

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arXiv2025

Low-Rank Adaptation of Pre-trained Vision Backbones for Energy-Efficient Image Coding for Machine

Image Coding for Machines (ICM) focuses on optimizing image compression for AI-driven analysis rather than human perception. Existing ICM frameworks often rely on separate codecs for specific tasks, leading to significant storage requirements, training overhead, and computational complexity. To address these challenges, we propose an energy-efficient framework that leverages pre-trained vision backbones to extract robust and versatile latent representations suitable for multiple tasks. We introduce a task-specific low-rank adaptation mechanism, which refines the pre-trained features to be both compressible and tailored to downstream applications. This design minimizes trainable parameters and reduces energy costs for multi-task scenarios. By jointly optimizing task performance and entropy minimization, our method enables efficient adaptation to diverse tasks and datasets without full fine-tuning, achieving high coding efficiency. Extensive experiments demonstrate that our framework significantly outperforms traditional codecs and pre-processors, offering an energy-efficient and effective solution for ICM applications. The code and the supplementary materials will be available at: https://gitlab.com/viper-purdue/efficient-compression.

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arXiv2025

Accelerating Learned Image Compression Through Modeling Neural Training Dynamics

As learned image compression (LIC) methods become increasingly computationally demanding, enhancing their training efficiency is crucial. This paper takes a step forward in accelerating the training of LIC methods by modeling the neural training dynamics. We first propose a Sensitivity-aware True and Dummy Embedding Training mechanism (STDET) that clusters LIC model parameters into few separate modes where parameters are expressed as affine transformations of reference parameters within the same mode. By further utilizing the stable intra-mode correlations throughout training and parameter sensitivities, we gradually embed non-reference parameters, reducing the number of trainable parameters. Additionally, we incorporate a Sampling-then-Moving Average (SMA) technique, interpolating sampled weights from stochastic gradient descent (SGD) training to obtain the moving average weights, ensuring smooth temporal behavior and minimizing training state variances. Overall, our method significantly reduces training space dimensions and the number of trainable parameters without sacrificing model performance, thus accelerating model convergence. We also provide a theoretical analysis on the Noisy quadratic model, showing that the proposed method achieves a lower training variance than standard SGD. Our approach offers valuable insights for further developing efficient training methods for LICs.

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arXiv2025

Balanced Rate-Distortion Optimization in Learned Image Compression

Learned image compression (LIC) using deep learning architectures has seen significant advancements, yet standard rate-distortion (R-D) optimization often encounters imbalanced updates due to diverse gradients of the rate and distortion objectives. This imbalance can lead to suboptimal optimization, where one objective dominates, thereby reducing overall compression efficiency. To address this challenge, we reformulate R-D optimization as a multi-objective optimization (MOO) problem and introduce two balanced R-D optimization strategies that adaptively adjust gradient updates to achieve more equitable improvements in both rate and distortion. The first proposed strategy utilizes a coarse-to-fine gradient descent approach along standard R-D optimization trajectories, making it particularly suitable for training LIC models from scratch. The second proposed strategy analytically addresses the reformulated optimization as a quadratic programming problem with an equality constraint, which is ideal for fine-tuning existing models. Experimental results demonstrate that both proposed methods enhance the R-D performance of LIC models, achieving around a 2\% BD-Rate reduction with acceptable additional training cost, leading to a more balanced and efficient optimization process. Code will be available at https://gitlab.com/viper-purdue/Balanced-RD.

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arXiv2025

Web of 4D Dualities, Supersymmetric Partition functions and SymTFT

We study $\mathbb{Z}_N$ one-form center symmetries in four-dimensional gauge theories using the symmetry topological field theory (SymTFT). In this context, the associated TFT in the five-dimensional bulk is the BF model. We revisit its canonical quantization and construct topological boundary states on several important classes of four manifolds that are spin, non-spin and torsional. We highlight a web of four-dimensional dualities, which can be naturally interpreted within the SymTFT framework. We also point out an intriguing class of four-dimensional gauge theories that exhibit mixed 't Hooft anomaly between one-form symmetries. In the second part of this work, we extend the SymTFT to account for various quantities protected by supersymmetry (SUSY) in SUSY gauge theories. We proposed that their behaviour under various symmetry operations are entirely captured by the topological boundary of the SymTFT, resulting in strong constraints. Concrete examples are considered, including the Witten index, the lens space index and the Donaldson-Witten and Vafa-Witten partition functions.

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arXiv2024

3d $\mathcal{N}=4$ Mirror Symmetry, TQFTs, and 't Hooft Anomaly Matching

Any local unitary 3d $\mathcal{N}=4$ superconformal field theory (SCFT) has a corresponding "universal" relevant deformation that takes it to a gapped phase. This deformation preserves all continuous internal symmetries, $\mathcal{S}$, and therefore also preserves any 't Hooft anomalies supported purely in $\mathcal{S}$. We describe the resulting phase diagram in the case of SCFTs that arise as the endpoints of renormalization group flows from 3d $\mathcal{N}=4$ Abelian gauge theories with any number of $U(1)$ gauge group factors and arbitrary integer charges for the matter fields. We argue that the universal deformations take these QFTs to Abelian fractional quantum Hall states in the infrared (IR), and we explain how to match 't Hooft anomalies between the non-topological ultraviolet theories and the IR topological quantum field theories (TQFTs). Along the way, we give a proof that 3d $\mathcal{N}=4$ mirror symmetry of our Abelian gauge theories descends to a duality of these TQFTs. Finally, using our anomaly matching discussion, we describe how to connect, via the renormalization group, abstract local unitary 3d $\mathcal{N}=4$ SCFTs with certain 't Hooft anomalies for their internal symmetries to IR phases (partially) described by Abelian spin Chern-Simons theories.

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arXiv2024

High-Efficiency Neural Video Compression via Hierarchical Predictive Learning

The enhanced Deep Hierarchical Video Compression-DHVC 2.0-has been introduced. This single-model neural video codec operates across a broad range of bitrates, delivering not only superior compression performance to representative methods but also impressive complexity efficiency, enabling real-time processing with a significantly smaller memory footprint on standard GPUs. These remarkable advancements stem from the use of hierarchical predictive coding. Each video frame is uniformly transformed into multiscale representations through hierarchical variational autoencoders. For a specific scale's feature representation of a frame, its corresponding latent residual variables are generated by referencing lower-scale spatial features from the same frame and then conditionally entropy-encoded using a probabilistic model whose parameters are predicted using same-scale temporal reference from previous frames and lower-scale spatial reference of the current frame. This feature-space processing operates from the lowest to the highest scale of each frame, completely eliminating the need for the complexity-intensive motion estimation and compensation techniques that have been standard in video codecs for decades. The hierarchical approach facilitates parallel processing, accelerating both encoding and decoding, and supports transmission-friendly progressive decoding, making it particularly advantageous for networked video applications in the presence of packet loss. Source codes will be made available.

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arXiv2024

Electromagnetic Duality for Line Defect Correlators in $\mathcal{N}=4$ Super Yang-Mills Theory

We study particular integrated correlation functions of two superconformal primary operators of the stress tensor multiplet in the presence of a half-BPS line defect labelled by electromagnetic charges $(p,q)$ in $\mathcal{N}=4$ supersymmetric Yang-Mills theory (SYM) with gauge group $SU(N)$. An important consequence of ${\rm SL}(2,\mathbb{Z})$ electromagnetic duality in $\mathcal{N}=4$ SYM is that correlators of line defect operators with different charges $(p,q)$ must be related in a non-trivial manner when the complex coupling $τ=θ/(2π)+4πi /g_{_{\rm YM}}^2$ is transformed appropriately. In this work we introduce a novel class of real-analytic functions whose automorphic properties with respect to ${\rm SL}(2,\mathbb{Z})$ match the expected transformations of line defect operators in $\mathcal{N}=4$ SYM under electromagnetic duality. At large $N$ and fixed $τ$, the correlation functions we consider are related to scattering amplitudes of two gravitons from extended $(p,q)$-strings in the holographic dual type IIB superstring theory. We show that the large-$N$ expansion coefficients of the integrated two-point line defect correlators are given by finite linear combinations with rational coefficients of elements belonging to this class of automorphic functions. On the other hand, for any fixed value of $N$ we conjecture that the line defect integrated correlators can be expressed as formal infinite series over such automorphic functions. The resummation of this series produces a simple lattice sum representation for the integrated line defect correlator that manifests its automorphic properties. We explicitly demonstrate this construction for the cases with gauge group $SU(2)$ and $SU(3)$. Our results give direct access to non-perturbative integrated correlators in the presence of an 't Hooft-line defect, observables otherwise very difficult to compute by other means.

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arXiv2024

On Efficient Neural Network Architectures for Image Compression

Recent advances in learning-based image compression typically come at the cost of high complexity. Designing computationally efficient architectures remains an open challenge. In this paper, we empirically investigate the impact of different network designs in terms of rate-distortion performance and computational complexity. Our experiments involve testing various transforms, including convolutional neural networks and transformers, as well as various context models, including hierarchical, channel-wise, and space-channel context models. Based on the results, we present a series of efficient models, the final model of which has comparable performance to recent best-performing methods but with significantly lower complexity. Extensive experiments provide insights into the design of architectures for learned image compression and potential direction for future research. The code is available at \url{https://gitlab.com/viper-purdue/efficient-compression}.

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arXiv2024

Learning to Classify New Foods Incrementally Via Compressed Exemplars

Food image classification systems play a crucial role in health monitoring and diet tracking through image-based dietary assessment techniques. However, existing food recognition systems rely on static datasets characterized by a pre-defined fixed number of food classes. This contrasts drastically with the reality of food consumption, which features constantly changing data. Therefore, food image classification systems should adapt to and manage data that continuously evolves. This is where continual learning plays an important role. A challenge in continual learning is catastrophic forgetting, where ML models tend to discard old knowledge upon learning new information. While memory-replay algorithms have shown promise in mitigating this problem by storing old data as exemplars, they are hampered by the limited capacity of memory buffers, leading to an imbalance between new and previously learned data. To address this, our work explores the use of neural image compression to extend buffer size and enhance data diversity. We introduced the concept of continuously learning a neural compression model to adaptively improve the quality of compressed data and optimize the bitrates per pixel (bpp) to store more exemplars. Our extensive experiments, including evaluations on food-specific datasets including Food-101 and VFN-74, as well as the general dataset ImageNet-100, demonstrate improvements in classification accuracy. This progress is pivotal in advancing more realistic food recognition systems that are capable of adapting to continually evolving data. Moreover, the principles and methodologies we've developed hold promise for broader applications, extending their benefits to other domains of continual machine learning systems.

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arXiv2024

Flexible Variable-Rate Image Feature Compression for Edge-Cloud Systems

Feature compression is a promising direction for coding for machines. Existing methods have made substantial progress, but they require designing and training separate neural network models to meet different specifications of compression rate, performance accuracy and computational complexity. In this paper, a flexible variable-rate feature compression method is presented that can operate on a range of rates by introducing a rate control parameter as an input to the neural network model. By compressing different intermediate features of a pre-trained vision task model, the proposed method can scale the encoding complexity without changing the overall size of the model. The proposed method is more flexible than existing baselines, at the same time outperforming them in terms of the three-way trade-off between feature compression rate, vision task accuracy, and encoding complexity. We have made the source code available at https://github.com/adnan-hossain/var_feat_comp.git.

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arXiv2024

Theoretical Bound-Guided Hierarchical VAE for Neural Image Codecs

Recent studies reveal a significant theoretical link between variational autoencoders (VAEs) and rate-distortion theory, notably in utilizing VAEs to estimate the theoretical upper bound of the information rate-distortion function of images. Such estimated theoretical bounds substantially exceed the performance of existing neural image codecs (NICs). To narrow this gap, we propose a theoretical bound-guided hierarchical VAE (BG-VAE) for NIC. The proposed BG-VAE leverages the theoretical bound to guide the NIC model towards enhanced performance. We implement the BG-VAE using Hierarchical VAEs and demonstrate its effectiveness through extensive experiments. Along with advanced neural network blocks, we provide a versatile, variable-rate NIC that outperforms existing methods when considering both rate-distortion performance and computational complexity. The code is available at BG-VAE.

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arXiv2024

Probing Image Compression For Class-Incremental Learning

Image compression emerges as a pivotal tool in the efficient handling and transmission of digital images. Its ability to substantially reduce file size not only facilitates enhanced data storage capacity but also potentially brings advantages to the development of continual machine learning (ML) systems, which learn new knowledge incrementally from sequential data. Continual ML systems often rely on storing representative samples, also known as exemplars, within a limited memory constraint to maintain the performance on previously learned data. These methods are known as memory replay-based algorithms and have proven effective at mitigating the detrimental effects of catastrophic forgetting. Nonetheless, the limited memory buffer size often falls short of adequately representing the entire data distribution. In this paper, we explore the use of image compression as a strategy to enhance the buffer's capacity, thereby increasing exemplar diversity. However, directly using compressed exemplars introduces domain shift during continual ML, marked by a discrepancy between compressed training data and uncompressed testing data. Additionally, it is essential to determine the appropriate compression algorithm and select the most effective rate for continual ML systems to balance the trade-off between exemplar quality and quantity. To this end, we introduce a new framework to incorporate image compression for continual ML including a pre-processing data compression step and an efficient compression rate/algorithm selection method. We conduct extensive experiments on CIFAR-100 and ImageNet datasets and show that our method significantly improves image classification accuracy in continual ML settings.

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arXiv2024

Towards Backward-Compatible Continual Learning of Image Compression

This paper explores the possibility of extending the capability of pre-trained neural image compressors (e.g., adapting to new data or target bitrates) without breaking backward compatibility, the ability to decode bitstreams encoded by the original model. We refer to this problem as continual learning of image compression. Our initial findings show that baseline solutions, such as end-to-end fine-tuning, do not preserve the desired backward compatibility. To tackle this, we propose a knowledge replay training strategy that effectively addresses this issue. We also design a new model architecture that enables more effective continual learning than existing baselines. Experiments are conducted for two scenarios: data-incremental learning and rate-incremental learning. The main conclusion of this paper is that neural image compressors can be fine-tuned to achieve better performance (compared to their pre-trained version) on new data and rates without compromising backward compatibility. Our code is available at https://gitlab.com/viper-purdue/continual-compression

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