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Jie Gao

Publications and source records attributed to Jie Gao.

At least 37 records · Page 2Linked to original sources
arXiv2026

Behavior Foundations for Quadruped Robots: ABot-C0 Technical Report

The motion controller is one of the most fundamental modules in embodied intelligence systems. Driven by large-scale human motion-capture data and the motion-tracking paradigm, humanoid control has achieved remarkable progress in recent years. However, migrating this recipe to the quadrupedal setting is far less straightforward: animal motion data is scarcer and harder to capture at scale than human data, and cross-embodiment retargeting remains fragile. We present ABot-C0, a generalist motion-control system for quadruped robots that establishes three complementary behavior foundations: a scalable multi-source motion-data pipeline, robust policy learning across motion tracking, locomotion, and scene interaction, and a unified deployment stack for reliable real-world operation. Fundamentally, we construct a data pyramid through conditional video-generation synthesis, annotated motion capture, teleoperation, and human design, producing 16,074 physically feasible motion clips as the data foundation for diverse motion-learning demands. With large-scale motion data, a Flow-Matching generalist policy demonstrates, for the first time, a scaling law for quadruped motion tracking: performance improves consistently as training scales up, with zero-shot capability to track unseen motions. We then go a step further toward robust all-terrain locomotion by adopting a three-stage privileged-to-perceptive framework with temporal LiDAR memory and terrain-predictive supervision. Collectively, these components form a motion generalist that coordinates multi-policy execution, smooth behavior transitions, energy-efficient control, and safety mechanisms for real-world deployment. Extensive experiments on urban-terrain autonomous navigation and companion-style multimodal interaction demonstrate that quadruped robots can move beyond functional demos toward product-level behavioral intelligence.

cs.RO↗
arXiv2026

HiFA4: Training-Free 4-bit FlashAttention on Ascend HIF4 NPUs for LLM Inference

We present HiFA4, a post-training operator-level design that executes both QK^T and PV in FlashAttention as 4-bit HIF4 Cube GEMMs for LLM inference on Ascend NPUs, while maintaining the online softmax state in FP16. To our knowledge, HiFA4 is the first Ascend-HIF4-targeted design of this kind evaluated on standard NLP benchmarks. HiFA4 combines two mechanisms. Smooth-QK applies a calibration-static per-channel equivalent rescaling to Q and K after RoPE, transferring quantization difficulty from K to Q without per-tile online reduction at inference. P-Reordering accumulates the softmax normalizer from the same quantized attention weights P_hat used in the PV GEMM, rather than from a higher-precision reconstruction. We show that this inconsistent formulation introduces a coherent output-scaling error, and validate the effect on a Qwen3-8B Layer-0 MMLU trace, where all 3.6M measured attention tiles exhibit net probability-mass loss with median epsilon_bar = -0.064. P-Reordering also allows the normalizer to be fused into the PV Cube GEMM. Across five LLMs, HiFA4 reduces quantization-induced decision drift. On Qwen3-8B, it recovers 37.5% of the accuracy gap introduced by direct HIF4 quantization, narrows the sample-weighted accuracy loss from 1.12 pp to 0.70 pp, reduces BF16-inconsistent MMLU predictions from 16.3% to 8.2%, and cuts MMLU accuracy regressions by 57% (1071 to 465). On Gemma2-9B, mild smoothing keeps HiFA4 within 0.7 pp of BF16 while reducing MMLU regressions by 27%. On LLaMA3.1-8B, Mistral-7B, and Phi-4B, where Smooth-QK is disabled, P-Reordering with the adopted Q-Mean auxiliary still reduces full-set MMLU regressions by 41-52%. A preliminary instruction-scheduling analysis projects a 35.4% critical-path latency reduction relative to BF16 by fusing the softmax normalizer into the PV Cube GEMM; on-hardware validation is left to future work.

cs.LG↗
arXiv2026

One Reflection Is Not Enough: Self-Correcting Autonomous Research via Multi-Hypothesis Failure Attribution

Autonomous research agents can now draft hypotheses, write code, run experiments, and produce papers, but they remain brittle when experiments fail. Under the prevailing paradigm, failure recovery is usually delegated to a single free-form reflection: a rich trajectory of metrics, logs, and design choices is compressed into one verbal critique, which often leads either to localized trial-and-error or to hard pivots that discard useful context. We propose SAGE, a Self-correcting, Autonomous, Grounded Experimenter, to tackle this failure-recovery bottleneck. Its core mechanism, Multi-Hypothesis Failure Attribution (MHFA), treats recovery as a structured causal diagnosis. By analyzing dynamic trajectory features, MHFA systematically generates multiple evidence-grounded explanations for a failure, independently evaluates their severity, and deterministically routes the verified root cause to the correct intervention level (hypothesis, experimental design, or implementation). To guarantee scientific honesty, SAGE further employs a grounded reporting mechanism that explicitly constrains drafted results to actual measured values, redacting hallucinated numbers. On a 12-topic, 5-domain benchmark, SAGE increases metrics-bearing outputs from 42% to 92% over a reflection baseline, improves artifact quality from 5.00 to 6.75/10, and blindly outscores AI-Scientist-v2 (52.0 vs. 48.2), with gains concentrated in code development and execution. While fully autonomous scientific writing and generating conference-ready papers remain notoriously difficult open problems for the entire field, SAGE successfully produces significantly more reliable and higher-quality scientific artifacts. Ultimately, by coupling structured recovery with explicit grounding constraints, SAGE significantly outperforms monolithic reflection paradigms, establishing a highly trustworthy foundation for future autonomous research.

cs.AI↗
arXiv2026

NIM4-ASR: Towards Efficient, Robust, and Customizable Real-Time LLM-Based ASR

Integrating large language models (LLMs) into automatic speech recognition (ASR) has become a mainstream paradigm in recent years. Although existing LLM-based ASR models demonstrate impressive performance on public benchmarks, their training remains predominantly data-driven, leaving key practical challenges insufficiently addressed -- particularly limited downward scalability in resource-constrained deployments and hallucinations under acoustically challenging conditions. To address these issues, we present NIM4-ASR, a production-oriented LLM-based ASR framework optimized for both efficiency and robustness. Grounded in a principled delineation of functional roles between the encoder and the LLM, we redesign the multi-stage training paradigm to align each module with its intended capability boundary. Specifically, we reformulate the pre-training architecture and objective to mitigate the modality gap and improve parameter efficiency; introduce an iterative asynchronous SFT stage to preserve acoustic fidelity and constrain representation drift; and design an ASR-specialized reinforcement learning stage to further enhance recognition quality and robustness. We additionally incorporate a suite of production-oriented optimizations, including robustness under noisy and silent conditions, real-time streaming inference, and hotword customization via retrieval-augmented generation (RAG). Experiments show that NIM4-ASR achieves state-of-the-art performance on multiple public benchmarks with merely 2.3B parameters, while substantially outperforming larger-scale competitors on internal benchmarks -- particularly in entity-intensive real-world scenarios. NIM4-ASR further supports million-scale hotword customization via RAG with sub-millisecond retrieval latency, enabling efficient adaptation to emerging entities and personalized user requirements.

eess.AS↗
arXiv2026

Multi-Modal Hyper-Graph Fusion for Low-Light Crowd Counting

Crowd counting is a fundamental task in computer vision. However, crowd counting in low-light environments remains largely underexplored, despite its practical importance in the real world. Existing methods mainly focus on well-lit scenes or rely on single-modality Red-Green-Blue (RGB) representations, which often become unreliable under extreme darkness and complex non-uniform illumination. To handle this problem, we construct three new low-light crowd counting benchmarks, which consist of two synthetic datasets, SHA\_Dark and SHB\_Dark, and a real-world benchmark LC-Crowd (Low-light Crowd Dataset). Inspired by Retinex-based physical modeling, we introduce depth and Canny edge cues as complementary geometric and structural priors to enhance the intrinsic reflectance representation under low-light conditions. We propose a Multi-Modal Hyper-Graph Fusion module, which formulates RGB appearance, depth geometry, and edge structure cues as nodes in a unified hyper-graph and explicitly captures their high-order complementary relationships via dynamic hyperedge construction and message passing. Furthermore, to adaptively allocate computation in dense prediction, we propose a Deformable Rectangular Sparse Attention (DRSA) module, which concentrates computation on informative regions through anchor-aware estimation and adaptive rectangular window modeling. Based on these designs, we develop a unified Low-Light Counting Network (LCNet) for robust low-light crowd counting. Extensive experiments on three benchmarks demonstrate that the proposed method achieves the best overall performance against existing state-of-the-art (SOTA) methods. The code is in the supplementary material. The datasets will be made public upon acceptance.

cs.CV↗
arXiv2026

RT-Counter: Real-Time Text-Guided Open-Vocabulary Object Counting

Text-guided open-vocabulary object counting (TOOC) aims to count objects belonging to the categories specified by natural language descriptions. Although vision-language pre-trained models have been successful applied to TOOC tasks, they still struggle with fine-grained spatial understanding and real-time inference requirements in counting scenarios. To address these limitations, this paper proposes a real-time TOOC framework, called the Real-Time Counter (RT-Counter), that achieves not only good counting accuracy but also high computational efficiency. RT-Counter designs a novel Visual Prototype Textualization (VPT) module that can project learned visual features into a text feature space and then generate features containing the abstract information that is hard to capture with visual prototypes and the detailed prototype information that is difficult to describe in text, enhancing the object-level visual-language model's counting capabilities. Additionally, RT-Counter incorporates our Weaving Transformer (Weaformer) layers, maintaining high descriptive power at a fraction of the computational cost. The Weaformer layer adopts a novel hybrid attention mechanism that can efficiently weave together local and global visual features. Extensive experiments on three public datasets show that RT-Counter successfully breaks the accuracy-speed trade-off in TOOC. While achieving a competitive MAE of 13.30 on FSC147, RT-Counter operates at 112.48 FPS, making it 7.4x faster and over 4$\times$ more parameter-efficient than the existing leading methods in TOOC. Our work aims at balancing high accuracy and real-time performance in TOOC. Code is available at: https://github.com/Jason-Mar1/RT-Counter.

cs.CV↗
arXiv2026

MambaCount: Efficient Text-guided Open-vocabulary Object Counting with Spatial Sparse State Space Duality Block

Text-guided Open-vocabulary Object Counting (TOOC) aims to estimate the number of objects described by text prompts, which is particularly challenging in dense scenes with large scale variations. Existing TOOC approaches predominantly rely on Transformers, whose quadratic complexity with respect to image resolution limits their scalability. Mamba offers a promising alternative due to its linear complexity. However, previous Mamba-based methods have two main limitations. On the one hand, the inherent causal formulation of Mamba constrains the bidirectional spatial dependency modeling required by non-causal vision tasks. On the other hand, existing Mamba-based vision models often overlook the unconstrained high entropy in the spatial token responses, which can weaken local details and high-frequency cues. To address these limitations, we propose MambaCount, an efficient framework built on the Spatial Sparse State Space Duality (S^4D) block. Specifically, we analyze and reconstruct the decay dynamics of hidden states in Mamba to alleviate the dependency constraints introduced by causal modeling. Moreover, we introduce a Spatial Token Selection (STS) sub-block to reduce the unconstrained high entropy in spatial token responses within Mamba. In addition, we design Multi-Granularity Prototypes (MGP) to identify object-like regions at different semantic levels, improving cross-modal alignment and interpretability. Extensive experiments on FSC-147 demonstrate that MambaCount achieves state-of-the-art performance among methods without secondary querying, obtaining a test MAE of 12.23, while retaining linear complexity.

cs.CV↗
arXiv2026

Ling and Ring 2.6 Technical Report: Efficient and Instant Agentic Intelligence at Trillion-Parameter Scale

Efficient and scalable agentic intelligence requires models that can deliver both low-latency responses and strong reasoning capabilities while remaining practical to train, serve, and deploy. In this report, we present Ling-2.6 and Ring-2.6, a family of models designed to address this challenge at scale. Ling-2.6 is optimized for instant response generation and high capability per output token, whereas Ring-2.6 is tailored for deeper reasoning and more advanced agentic workflows. Instead of training from scratch, we upgrade the Ling-2.0 base model through architectural migration pre-training and large-scale post-training. This upgrade is guided by a unified co-design of model architecture, optimization objectives, serving systems, and agent training environments, enabling improvements in both model capability and deployment efficiency. At the architectural level, we introduce a hybrid linear attention design that integrates Lightning Attention with MLA, improving the efficiency of long-context training and decoding. To further enhance token efficiency, we optimize capability per output token through Evolutionary Chain-of-Thought, Linguistic Unit Policy Optimization, bidirectional preference alignment, and shortest-correct-response distillation. For agentic capabilities, we propose KPop, a reinforcement learning framework designed to support stable training of Ring-2.6-1T on large-scale environment-grounded data. KPop improves training efficiency through asynchronous scheduling across coding, search, tool use, and workflow execution, enabling scalable learning from complex agent-environment interactions. Together, Ling-2.6 and Ring-2.6 provide a practical pathway toward efficient, scalable, and open agentic systems. We open-source all checkpoints in the 2.6 family to support further research and development in practical agentic intelligence.

cs.CL↗
arXiv2026

SkyShield: Occupancy as a Safety Interface for Low-Altitude UAV Autonomy

For low-altitude Unmanned Aerial Vehicle (UAV) autonomy, 3D spatial understanding is not merely a perception objective, but the safety interface between human instructions and physical flight. In human-scale urban airspace below 20 meters, thin geometry, occlusions, vegetation, and urban clutter define whether an aerial agent can safely enter the space ahead. However, existing UAV datasets mainly provide 2D annotations or 3D boxes, while driving-oriented occupancy benchmarks assume stable ground-level sensor rigs. Both miss the defining regime of low-altitude flight: a front-facing monocular camera observing occupied and free space from a moving aerial body with frame-wise changing 6-DoF pose and camera extrinsics. To bridge this gap, we introduce SkyShield, to the best of our knowledge the first front-view monocular semantic occupancy benchmark for urban UAV flight below 20 meters. Built on CARLA, SkyShield contains 36K front-view UAV samples across diverse urban scenes and weather conditions, pairing each image with frame-wise 6-DoF UAV pose, frame-wise dynamic camera geometry, UAV states, and front-frustum semantic occupancy labels. We further propose KAR-mIoU, a UAV-centric and dynamics-aware metric that re-weights voxel-level evaluation by kinematic reachability and time-to-collision, revealing safety-critical risks hidden by conventional mIoU. To tackle this challenging new setting, we provide SkyOcc, a geometry-first monocular baseline that integrates frame-wise UAV attitude into projection, fuses temporal occupancy features, and applies safety-prior optimization to preserve sparse collision-critical structures. Together, SkyShield, KAR-mIoU, and SkyOcc establish occupancy as a safety interface for low-altitude aerial autonomy. Code and dataset will be released publicly.

cs.CV↗
arXiv2026

Status report towards implementation of a Compton polarimeter at BEPCII

Precision beam polarization measurements based on Compton polarimeters are essential for the physics program of future high-energy colliders. In order to prepare for these and to extend the scope of physics measurements of the BESIII experiment at the BEPCII, a diagnostic of electron beam transverse polarization at BEPCII is of interest. The design and status report of the commissioning, until July 2025, of this device is reported in this paper. We report unambiguous observation of Compton interaction, discuss current limitations of the experimental setup and draw prospects for improvements and actual measurement of electron beam polarization in the near future.

physics.acc-ph↗
arXiv2026

Mixture of Complementary Agents for Robust LLM Ensemble

Multi-AI collaboration, such as ensembling or debating large language models (LLMs), is a promising paradigm for aggregating information and boosting performance. A foundational step in these pipelines is to feed the responses of several proposer LLMs into a summarizer LLM, which synthesizes a better answer. However, choosing which proposers to include is non-trivial. Existing approaches primarily focus either on accuracy (picking the strongest models) or diversity (ensuring variety), and often overlook the interactions among proposers and with the summarizer. We reframe proposer selection as a combinatorial selection problem akin to feature selection, where the value of an LLM lies in its complementarity with others. However, directly applying standard feature-selection algorithms is impractical in the LLM setting due to prohibitive time complexity. Motivated by this limitation, we explore an extensive range of computationally feasible, greedy-style selection algorithms that assess complementarity using a small labeled set. Our experiments validate complementarity as a guiding principle for proposer selection and identify methods that achieve the best performance-cost trade-offs in practice.

cs.LG↗
arXiv2026

Can Vision Language Models Be Adaptive in Mathematics Education? A Learner Model-based Rubric Study

Adaptive learning refers to educational technologies that track learners' learning progress and adapt the instructional process based on individual learners' learning performance. It is increasingly recognized as critical for developing an effective learning support tool. Vision language models (VLMs) have seen adoption in mathematics education, and students have been using them as learning aids for personalized instruction. However, it is unknown whether VLMs have the ability to adapt to different learner profiles when providing mathematical instructions. Current VLMs lack a systematic evaluation framework for this adaptivity to different learner profiles in mathematics tutoring tasks. To address this gap, we draw on the learner model from the adaptive learning framework (Shute and Towle, 2018) and propose a learner model-based rubric. Our rubric formalizes adaptivity assessment into three aspects: cognitive aspects, motivational aspects, and complexity. We also evaluate two additional dimensions of VLM responses: correctness (of answers and solutions) and quality (of the response itself). Our experimental results show measurable differences in adaptivity across models and also reveal that current VLMs struggle to consistently produce learner model-based instructional responses, especially when receiving limited learner information.

cs.CL↗
arXiv2026

Context, Reasoning, and Hierarchy: A Cost-Performance Study of Compound LLM Agent Design in an Adversarial POMDP

Deploying compound LLM agents in adversarial, partially observable sequential environments requires navigating several design dimensions: (1) what the agent sees, (2) how it reasons, and (3) how tasks are decomposed across components. Yet practitioners lack guidance on which design choices improve performance versus merely increase inference costs. We present a controlled study of compound LLM agent design in CybORG CAGE-2, a cyber defense environment modeled as a Partially Observable Markov Decision Process (POMDP). Reward is non-positive, so all configurations operate in a failure-mitigation mode. Our evaluation spans five model families, six models, and twelve configurations (3,475 episodes) with token-level cost accounting. We vary context representation (raw observations vs. a deterministic state-tracking layer with compressed history), deliberation (self-questioning, self-critique, and self-improvement tools, with optional chain-of-thought prompting), and hierarchical decomposition (monolithic ReAct vs. delegation to specialized sub-agents). We find that: (1) Programmatic state abstraction delivers the largest returns per token spent (RPTS), improving mean return by up to 76% over raw observations. (2) Distributing deliberation tools across a hierarchy degrades performance relative to hierarchy alone for all five model families, reaching up to 3.4$\times$ worse mean return while using 1.8-2.7$\times$ more tokens. We call this destructive pattern a deliberation cascade. (3) Hierarchical decomposition without deliberation achieves the best absolute performance for most models, and context engineering is generally more cost-effective than deliberation. These findings suggest a design principle for structured adversarial POMDPs: invest in programmatic infrastructure and clean task decomposition rather than deeper per-agent reasoning, as these strategies can interfere when combined.

cs.AI↗
arXiv2026

FORGE: Self-Evolving Agent Memory With No Weight Updates via Population Broadcast

Can LLM agents improve decision-making through self-generated memory without gradient updates? We propose FORGE (Failure-Optimized Reflective Graduation and Evolution), a staged, population-based protocol that evolves prompt-injected natural-language memory for hierarchical ReAct agents. FORGE wraps a Reflexion-style inner loop, where a dedicated reflection agent (using the same underlying LLM, no distillation from a stronger model) converts failed trajectories into reusable knowledge artifacts: textual heuristics (Rules), few-shot demonstrations (Examples), or both (Mixed), with an outer loop that propagates the best-performing instance's memory to the population between stages and freezes converged instances via a graduation criterion. We evaluate on CybORG CAGE-2, a stochastic network-defense POMDP at a 30-step horizon against the B-line attacker, where all four tested LLM families (Gemini-2.5-Flash-Lite, Grok-4-Fast, Llama-4-Maverick, Qwen3-235B) exhibit strongly negative, heavy-tailed zero-shot rewards. Compared against both a zero-shot baseline and a Reflexion baseline (isolated single-stream learning), FORGE improves average evaluation return by 1.7-7.7$\times$ over zero-shot and by 29-72% over Reflexion in all 12 model-representation conditions, reducing major-failure rates (below $-100$) to as low as $\sim$1%. We find that (1) population broadcast is critical mechanism, with a no-graduation ablation confirming that broadcast carries the performance gains while graduation primarily saves compute; (2) Examples achieves the strongest returns for three of four models, Rules offers the best cost-reliability profile with $\sim$40% fewer tokens; and (3) weaker baseline models benefit disproportionately, suggesting FORGE may mitigate capability gaps rather than amplify strong models. All evidence is confined to CAGE-2 B-line; cross-family findings are directional evidence.

cs.AI↗
arXiv2026

How to Interpret Agent Behavior

Autonomous agents such as Claude Code and Codex now operate for hours or even days. Understanding their runtime behavior has become critical for downstream tasks such as diagnosing inefficiencies, fixing bugs, and ensuring better oversight. A primary way to gain this understanding is analyzing the reasoning trajectories and execution traces these agents generate. Yet such data remains in unstructured natural-language form, making it difficult for humans to interpret at scale. We introduce ACT*ONOMY (a combination of Action and Taxonomy), a taxonomy for describing and analyzing agent behavior at runtime. ACT*ONOMY has two components: (1) the taxonomy itself, developed through Grounded Theory and structured as a three-level hierarchy of 10 actions, 46 subactions, and 120 leaf categories; and (2) an open repository that hosts the living taxonomy, provides an automated analysis pipeline that applies it to agent trajectories analysis, and defines an extension protocol for customization and growth. Our experiments show that ACTONOMY can compare behavioral profiles across agents and characterize a single agent's behavior across diverse trajectories, surfacing patterns indicative of failure modes. By providing a shared vocabulary, ACT*ONOMY helps researchers, agent designers, and end users interpret agent behavior more consistently, enabling better oversight and control.

cs.AI↗
arXiv2026

Charting the Diameter Computation Landscape on Intersection Graphs in the Plane

Computing the diameter of the intersection graphs of objects is a basic problem in computational geometry. Previous works showed that the complexity of computing the diameter mainly depends on the object types: for unit disks and squares in 2D, the problem is solvable in truly subquadratic time, while for other objects, including unit segments and equilateral triangles in 2D or unit balls and axis-parallel unit cubes in 3D, there is no truly subquadratic time algorithm under the Orthogonal Vector (OV) hypothesis. We undertake a comprehensive study of computing the diameter of geometric intersection graphs for various types of objects. We discover many new irregularities, showing that the landscape is extremely nuanced: the source of hardness is a combination of the object type, the true diameter value, and how the objects intersect with each other. Our highlighted results for the 2D case include: 1. The diameter of non-degenerate, axis-aligned line segments can be computed in truly subquadratic time. Previous hardness result for line segments applies only to degenerate instances. On the other hand, for the degenerate case, we show that a truly subquadratic time algorithm exists when the true diameter is constant. 2. An almost-linear-time algorithm for unit-square graphs of constant diameter. Previous algorithms rely on succinct representation assuming bounded VC-dimension; for such a strategy $Ω(n^{7/4})$ time is an inherent barrier. 3. An $\tilde{O}(n^{4/3})$-time algorithm to decide if the diameter of a unit-disk graph is at most 2. This improves upon the recent algorithm with running time $\tilde{O}(n^{2-1/9})$. 4. Deciding if the diameter of intersection graphs of fat triangles or line segments is at most 2 is truly subquadratic-hard under fine-grained complexity assumptions. Previous lower bounds only hold when deciding if diameter is at most 3.

cs.CG↗
arXiv2026

Enhancing Cross-Problem Vehicle Routing via Federated Learning

Vehicle routing problems (VRPs) constitute a core optimization challenge in modern logistics and supply chain management. The recent neural combinatorial optimization (NCO) has demonstrated superior efficiency over some traditional algorithms. While serving as a primary NCO approach for solving general VRPs, current cross-problem learning paradigms are still subject to performance degradation and generalizability decay, when transferring from simple VRP variants to those involving different and complex constraints. To strengthen the paradigms, this paper offers an innovative "Multi-problem Pre-train, then Single-problem Fine-tune" framework with Federated Learning (MPSF-FL). This framework exploits the common knowledge of a federated global model to foster efficient cross-problem knowledge sharing and transfer among local models for single-problem fine-tuning. In this way, local models effectively retain common VRP knowledge from up-to-date global model, while being efficiently adapted to downstream VRPs with heterogeneous complex constraints. Experimental results demonstrate that our framework not only enhances the performance in diverse VRPs, but also improves the generalizability in unseen problems.

cs.AI↗
arXiv2026

Packing Compact Subgraphs with Applications to Districting

Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and that satisfy additional composition requirements, such as a minimum population/weight threshold or balanced weight types (e.g., political affiliations). We aim to maximize coverage by disjoint districts that meet these requirements. In this work, we present new results that substantially improve the previously known bounds on balanced star districts for planar and minor-free graphs (Dharangutte et al. 2025). In particular, we improve the approximation factor from $O(\log n)$ to $O(1)$ for packing balanced star districts using the exact same algorithm, but with a refined analysis. We also extend the results beyond planar graphs to minor-free graphs and an even broader family of graphs of bounded expansion. Additionally, we obtain an $O(1)$ approximation for packing radius-$k$ districts (with a constant $k$) in planar and apex-minor-free graphs. In order to get a $(1+\varepsilon)$ approximation on the max coverage, we show that this can be achieved if we allow a slight relaxation of the balancedness parameters (by a factor that can be made arbitrarily close to $1$), for bounded radius-$k$ districts on planar and apex-minor-free graphs. We show that all of these results can also be obtained if we enforce a minimum weight threshold for each district as the composition requirement, rather than balancedness. We present various results on hardness and hardness of approximation for this variant, by graph and district types.

cs.DS↗