arXiv subjects

Haoran Zhu

Publications and source records attributed to Haoran Zhu.

At least 37 records · Page 2Linked to original sources

arXiv2026

UHR-DETR: Efficient End-to-End Small Object Detection for Ultra-High-Resolution Remote Sensing Imagery

Ultra-High-Resolution (UHR) imagery has become essential for modern remote sensing, offering unprecedented spatial coverage. However, detecting small objects in such vast scenes presents a critical dilemma: retaining the original resolution for small objects causes prohibitive memory bottlenecks. Conversely, conventional compromises like image downsampling or patch cropping either erase small objects or destroy context. To break this dilemma, we propose UHR-DETR, an efficient end-to-end transformer-based detector designed for UHR imagery. First, we introduce a Coverage-Maximizing Sparse Encoder that dynamically allocates finite computational resources to informative high-resolution regions, ensuring maximum object coverage with minimal spatial redundancy. Second, we design a Global-Local Decoupled Decoder. By integrating macroscopic scene awareness with microscopic object details, this module resolves semantic ambiguities and prevents scene fragmentation. Extensive experiments on the UHR imagery datasets (e.g., STAR and SODA-A) demonstrate the superiority of UHR-DETR under strict hardware constraints (e.g., a single 24GB RTX 3090). It achieves a 2.8\% mAP improvement while delivering a 10$\times$ inference speedup compared to standard sliding-window baselines on the STAR dataset. Our codes and models will be available at https://github.com/Li-JingFang/UHR-DETR.

cs.CV↗

arXiv2026

Spectral gap of biased adjacent-transposition chains

We establish a sharp lower bound on the spectral gap of the biased adjacent-transposition Markov chain on the symmetric group. As a consequence, we resolve a longstanding conjecture of Fill, proving that among all regular probability vectors, the minimum spectral gap of the transition matrix is attained by the uniform probability vector. We also characterise the regular probability vectors attaining the minimum spectral gap and determine the exact multiplicity of the corresponding second-largest eigenvalue. Our proof relies on a novel algebraic decomposition of the transition matrix into elementary orthogonal projections.

math.PR↗

arXiv2026

Generalized Small Object Detection:A Point-Prompted Paradigm and Benchmark

Small object detection (SOD) remains challenging due to extremely limited pixels and ambiguous object boundaries. These characteristics lead to challenging annotation, limited availability of large-scale high-quality datasets, and inherently weak semantic representations for small objects. In this work, we first address the data limitation by introducing TinySet-9M, the first large-scale, multi-domain dataset for small object detection. Beyond filling the gap in large-scale datasets, we establish a benchmark to evaluate the effectiveness of existing label-efficient detection methods for small objects. Our evaluation reveals that weak visual cues further exacerbate the performance degradation of label-efficient methods in small object detection, highlighting a critical challenge in label-efficient SOD. Secondly, to tackle the limitation of insufficient semantic representation, we move beyond training-time feature enhancement and propose a new paradigm termed Point-Prompt Small Object Detection (P2SOD). This paradigm introduces sparse point prompts at inference time as an efficient information bridge for category-level localization, enabling semantic augmentation. Building upon the P2SOD paradigm and the large-scale TinySet-9M dataset, we further develop DEAL (DEtect Any smalL object), a scalable and transferable point-prompted detection framework that learns robust, prompt-conditioned representations from large-scale data. With only a single click at inference time, DEAL achieves a 31.4% relative improvement over fully supervised baselines under strict localization metrics (e.g., AP75) on TinySet-9M, while generalizing effectively to unseen categories and unseen datasets. Our project is available at https://zhuhaoraneis.github.io/TinySet-9M/.

cs.CV↗

arXiv2026

A symmetry formula for correlation functions in the superintegrable chiral Potts spin chain

We prove an exact finite-volume symmetry formula for two-point functions in the periodic $N$-state superintegrable chiral Potts spin chain. We show that, for every chain length $L$ and every simultaneous eigenvector of the Hamiltonian and the one-site translation operator, the correlations satisfy $\langle Z_0^r Z_R^{\dagger r}\rangle^*=\langle Z_0^r Z_{L-R}^{\dagger r}\rangle$ for $1\leqslant r\leqslant N-1$. Hence, whenever $L$ is even, the midpoint correlation $\langle Z_0^r Z_{L/2}^{\dagger r}\rangle$ is real. Then we generalise the three-state chain case to arbitrary $N$ and to every translation eigensector. This resolves a conjecture of Fabricius and McCoy.

math-ph↗

arXiv2026

Infinitesimal deformations of $\mathfrak{sl}_2$ with a twisted Jacobi identity

We show that whenever \[ [\,\cdot,\cdot]_t = [\,\cdot,\cdot]_0 + t[\,\cdot,\cdot]_1,\qquad α_t = \mathrm{id} + tα_1 \] define an infinitesimal Hom--Lie deformation of $\mathfrak{sl}_2(\mathbb K)$ over $\mathbb K[t]/(t^2)$ and $(\mathfrak{sl}_2(\mathbb K),[\,\cdot,\cdot]_0,α_1)$ is a Hom--Lie algebra, then the deformed bracket $[\,\cdot,\cdot]_t$ satisfies the ordinary Jacobi identity over $\mathbb K[t]$. This solves a conjecture of Makhlouf and Silvestrov from 2010.

math.RA↗

arXiv2026

A note on some spectral properties of generalised pancake graphs

We prove that the spectral gap of generalised pancake graphs is strictly less than 2 and strictly less than 1 for burnt pancake graphs. In addition, we establish lower bounds on the multiplicities of certain integer eigenvalues of generalised pancake graphs. Together, these results settle two recent conjectures of Blanco and Buehrle.

math.CO↗

arXiv2026

Aldous property for full-flag Johnson graphs

We show that the full-flag Johnson graph has spectral gap equal to that of its Schreier quotient arising from the point-stabiliser equitable partition. Our results confirm two conjectures posed by Huang, Huang, and Cioabă, which imply an Aldous-type spectral-gap phenomenon for full-flag Johnson graphs.

math.CO↗

arXiv2026

Vertex operators, infinite wedge representations, and correlation functions of the t-Schur measure

We study the $t$-Schur measure on partitions, defined by $ \mathbb{P}(λ)=Z^{-1}S_λ(x;t)s_λ(y) $, where $S_λ(x;t)$ denotes the $t$-Schur symmetric functions and $s_λ(y)$ the ordinary Schur functions, and $Z$ is the normalising constant. Using vertex operator calculus, we realise $S_λ(x;t)$ in the charged free-fermion Fock space, yielding a $t$-deformation of the classical boson-fermion correspondence. These realisations give vertex-algebraic proofs of the $t$-Cauchy identities and $t$-Gessel identity. Building on this framework, we compute the correlation functions of the $t$-Schur measure and show that the associated point process is determinantal, with an explicit correlation kernel. The Poissonised $t$-Plancherel measure appears as a specialisation of our construction, so its correlation functions follow as a corollary. As an application, we derive the limiting distribution for the length of the longest ascent pair in a random permutation. Our results interpolate the Schur case at $t=0$, connect to the Schur-$Q$ theory at $t=-1$, and provide a probabilistic interpretation of a natural $t$-refinement of increasing subsequences via a generalised RSK correspondence.

math-ph↗

arXiv2026

Self-Supervised JEPA-based World Models for LiDAR Occupancy Completion and Forecasting

Autonomous driving, as an agent operating in the physical world, requires the fundamental capability to build \textit{world models} that capture how the environment evolves spatiotemporally in order to support long-term planning. At the same time, scalability demands learning such models in a self-supervised manner; \textit{joint-embedding predictive architecture (JEPA)} enables learning world models via leveraging large volumes of unlabeled data without relying on expensive human annotations. In this paper, we propose \textbf{AD-LiST-JEPA}, a self-supervised world model for autonomous driving that predicts future spatiotemporal evolution from LiDAR data using a JEPA framework. We evaluate the quality of the learned representations through a downstream LiDAR-based occupancy completion and forecasting (OCF) task, which jointly assesses perception and prediction. Proof of concept experiments show better OCF performance with pretrained encoder after JEPA-based world model learning.

cs.CV↗

arXiv2026

RefProtoFL: Communication-Efficient Federated Learning via External-Referenced Prototype Alignment

Federated learning (FL) enables collaborative model training without sharing raw data in edge environments, but is constrained by limited communication bandwidth and heterogeneous client data distributions. Prototype-based FL mitigates this issue by exchanging class-wise feature prototypes instead of full model parameters; however, existing methods still suffer from suboptimal generalization under severe communication constraints. In this paper, we propose RefProtoFL, a communication-efficient FL framework that integrates External-Referenced Prototype Alignment (ERPA) for representation consistency with Adaptive Probabilistic Update Dropping (APUD) for communication efficiency. Specifically, we decompose the model into a private backbone and a lightweight shared adapter, and restrict federated communication to the adapter parameters only. To further reduce uplink cost, APUD performs magnitude-aware Top-K sparsification, transmitting only the most significant adapter updates for server-side aggregation. To address representation inconsistency across heterogeneous clients, ERPA leverages a small server-held public dataset to construct external reference prototypes that serve as shared semantic anchors. For classes covered by public data, clients directly align local representations to public-induced prototypes, whereas for uncovered classes, alignment relies on server-aggregated global reference prototypes via weighted averaging. Extensive experiments on standard benchmarks demonstrate that RefProtoFL attains higher classification accuracy than state-of-the-art prototype-based FL baselines.

cs.LG↗

arXiv2025

BiHom-Lie brackets and the Toda equation

We introduce a BiHom-type skew-symmetric bracket on $\mathfrak{gl}(V)$ built from two commuting inner automorphisms $α=Ad_ψ$ and $β=Ad_ϕ$ with $ψ,ϕ\in \mathfrak{gl}(V)$ and integers $i,j$. We prove that $(\mathfrak{gl}(V),[\cdot,\cdot]^{(i,j)}_{(ψ,ϕ)},α,β)$ is a BiHom--Lie algebra, and we study the Lax equation obtained by replacing the commutator in the finite nonperiodic Toda lattice by this bracket. For the symmetric choice $ϕ=ψ$ with $(i,j)=(0,0)$, the deformed flow is equivariant under conjugation and becomes gauge-equivalent, via $\widetilde L=ψ^{-1}Lψ$, to a Toda-type Lax equation with a conjugated triangular projection. In particular, scalar deformations amount to a constant rescaling of time. On embedded $2\times2$ blocks, we derive explicit trigonometric and hyperbolic formulas that make symmetry constraints (e.g. tracelessness) transparent. In the asymmetric hyperbolic case, we exhibit a trace obstruction showing that the right-hand side is generically not a commutator, which amounts to symmetry breaking of the isospectral property. We further extend the construction to the weakly coupled Toda lattice with an indefinite metric and provide explicit $2\times2$ solutions via an inverse-scattering calculation, clarifying and correcting certain formulas in the literature. The classical Toda dynamics are recovered at special parameter values.

nlin.SI↗

arXiv2025

The Complexity of Recognizing Facets for the Knapsack Polytope

The complexity class DP is the class of all languages that are the intersection of a language in NP and a language in coNP. It was conjectured that recognizing a facet for the knapsack polytope is DP-complete. We provide a positive answer to this conjecture. Moreover, despite the \DP-hardness of the recognition problem, we give a polynomial time algorithm for deciding if an inequality with a fixed number of distinct coefficients defines a facet of a knapsack polytope.

math.OC↗

arXiv2025

Self-Supervised Representation Learning with Joint Embedding Predictive Architecture for Automotive LiDAR Object Detection

Recently, self-supervised representation learning relying on vast amounts of unlabeled data has been explored as a pre-training method for autonomous driving. However, directly applying popular contrastive or generative methods to this problem is insufficient and may even lead to negative transfer. In this paper, we present AD-L-JEPA, a novel self-supervised pre-training framework with a joint embedding predictive architecture (JEPA) for automotive LiDAR object detection. Unlike existing methods, AD-L-JEPA is neither generative nor contrastive. Instead of explicitly generating masked regions, our method predicts Bird's-Eye-View embeddings to capture the diverse nature of driving scenes. Furthermore, our approach eliminates the need to manually form contrastive pairs by employing explicit variance regularization to avoid representation collapse. Experimental results demonstrate consistent improvements on the LiDAR 3D object detection downstream task across the KITTI3D, Waymo, and ONCE datasets, while reducing GPU hours by 1.9x-2.7x and GPU memory by 2.8x-4x compared with the state-of-the-art method Occupancy-MAE. Notably, on the largest ONCE dataset, pre-training on 100K frames yields a 1.61 mAP gain, better than all other methods pre-trained on either 100K or 500K frames, and pre-training on 500K frames yields a 2.98 mAP gain, better than all other methods pre-trained on either 500K or 1M frames. AD-L-JEPA constitutes the first JEPA-based pre-training method for autonomous driving. It offers better quality, faster, and more GPU-memory-efficient self-supervised representation learning. The source code of AD-L-JEPA is ready to be released.

cs.RO↗

arXiv2025

Sweedler duality for Hom-(co)algebras and Hom-(co)modules

We establish a dual version of infinite-dimensional Hom-algebras and Hom-modules by using the Sweedler duality construction. Additionally, linear morphisms between infinite-dimensional Hom-algebras (resp. Hom-modules) and Hom-coalgebras (resp. Hom-comodules) are derived under this construction. As an application, we present a Hom-type binary linearly recursive sequence and show that the Sweedler duality construction can be utilized to determine the minimal polynomials of finite-codimensional ideals.

math.RA↗

arXiv2025

Machine Unlearning for Robust DNNs: Attribution-Guided Partitioning and Neuron Pruning in Noisy Environments

Deep neural networks (DNNs) have achieved remarkable success across diverse domains, but their performance can be severely degraded by noisy or corrupted training data. Conventional noise mitigation methods often rely on explicit assumptions about noise distributions or require extensive retraining, which can be impractical for large-scale models. Inspired by the principles of machine unlearning, we propose a novel framework that integrates attribution-guided data partitioning, discriminative neuron pruning, and targeted fine-tuning to mitigate the impact of noisy samples. Our approach employs gradient-based attribution to probabilistically distinguish high-quality examples from potentially corrupted ones without imposing restrictive assumptions on the noise. It then applies regression-based sensitivity analysis to identify and prune neurons that are most vulnerable to noise. Finally, the resulting network is fine-tuned on the high-quality data subset to efficiently recover and enhance its generalization performance. This integrated unlearning-inspired framework provides several advantages over conventional noise-robust learning approaches. Notably, it combines data-level unlearning with model-level adaptation, thereby avoiding the need for full model retraining or explicit noise modeling. We evaluate our method on representative tasks (e.g., CIFAR-10 image classification and speech recognition) under various noise levels and observe substantial gains in both accuracy and efficiency. For example, our framework achieves approximately a 10% absolute accuracy improvement over standard retraining on CIFAR-10 with injected label noise, while reducing retraining time by up to 47% in some settings. These results demonstrate the effectiveness and scalability of the proposed approach for achieving robust generalization in noisy environments.

cs.LG↗

arXiv2025

Kronecker coefficients and Harrison centres of the representation ring of the symmetric group

We present a computational approach to studying the structure of the representation ring of the symmetric group in dimension six. The Kronecker coefficients and all power formulae of irreducible representations of $S_6$ are computed using the character theory of finite groups. In addition, considering direct sum decomposition of tensor products of different irreducible representations of $S_6$, we characterise generators of the representation ring $\mathcal{R}(S_6)$, show that its unit group $U(\mathcal{R}(S_6))$ is a Klein four-group, and related results on the structure of primitive idempotents. Furthermore, we introduce the Harrison centre theory to study the representation ring and show that the Harrison centre of the cubic form induced by the generating relations of $\mathcal{R}(S_6)$ is isomorphic to itself. Finally, we conclude with some open problems for future consideration.

math.RT↗

arXiv2024

Oriented Tiny Object Detection: A Dataset, Benchmark, and Dynamic Unbiased Learning

Detecting oriented tiny objects, which are limited in appearance information yet prevalent in real-world applications, remains an intricate and under-explored problem. To address this, we systemically introduce a new dataset, benchmark, and a dynamic coarse-to-fine learning scheme in this study. Our proposed dataset, AI-TOD-R, features the smallest object sizes among all oriented object detection datasets. Based on AI-TOD-R, we present a benchmark spanning a broad range of detection paradigms, including both fully-supervised and label-efficient approaches. Through investigation, we identify a learning bias presents across various learning pipelines: confident objects become increasingly confident, while vulnerable oriented tiny objects are further marginalized, hindering their detection performance. To mitigate this issue, we propose a Dynamic Coarse-to-Fine Learning (DCFL) scheme to achieve unbiased learning. DCFL dynamically updates prior positions to better align with the limited areas of oriented tiny objects, and it assigns samples in a way that balances both quantity and quality across different object shapes, thus mitigating biases in prior settings and sample selection. Extensive experiments across eight challenging object detection datasets demonstrate that DCFL achieves state-of-the-art accuracy, high efficiency, and remarkable versatility. The dataset, benchmark, and code are available at https://chasel-tsui.github.io/AI-TOD-R/.

cs.CV↗

arXiv2024

Tiny Object Detection with Single Point Supervision

Tiny objects, with their limited spatial resolution, often resemble point-like distributions. As a result, bounding box prediction using point-level supervision emerges as a natural and cost-effective alternative to traditional box-level supervision. However, the small scale and lack of distinctive features of tiny objects make point annotations prone to noise, posing significant hurdles for model robustness. To tackle these challenges, we propose Point Teacher--the first end-to-end point-supervised method for robust tiny object detection in aerial images. To handle label noise from scale ambiguity and location shifts in point annotations, Point Teacher employs the teacher-student architecture and decouples the learning into a two-phase denoising process. In this framework, the teacher network progressively denoises the pseudo boxes derived from noisy point annotations, guiding the student network's learning. Specifically, in the first phase, random masking of image regions facilitates regression learning, enabling the teacher to transform noisy point annotations into coarse pseudo boxes. In the second phase, these coarse pseudo boxes are refined using dynamic multiple instance learning, which adaptively selects the most reliable instance from dynamically constructed proposal bags around the coarse pseudo boxes. Extensive experiments on three tiny object datasets (i.e., AI-TOD-v2, SODA-A, and TinyPerson) validate the proposed method's effectiveness and robustness against point location shifts. Notably, relying solely on point supervision, our Point Teacher already shows comparable performance with box-supervised learning methods. Codes and models will be made publicly available.

cs.CV↗