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Brendan Juba, Kuldeep S. Meel

Given a Boolean relational specification between inputs and outputs, the problem of functional synthesis is to construct a function that maps each assignment of the input to an assignment of the output such that each tuple of input and output assignments meets the specification. The past decade has witnessed significant improvement in the scalability of functional synthesis tools, allowing them to handle problems with tens of thousands of variables. A common ingredient in these approaches is their reliance on SAT solvers, thereby exploiting the breakthrough advances in SAT solving over the past three decades. While the recent techniques have been shown to perform well in practice, there is little theoretical understanding of the limitations and power of these approaches. The primary contribution of this work is to initiate a systematic theoretical investigation into the power of functional synthesis approaches that rely on NP oracles. We first show that even when small Skolem functions exist, naive bit-by-bit learning approaches fail due to the relational nature of specifications. We establish fundamental limitations of interpolation-based approaches proving that even when small Skolem functions exist, resolution-based interpolation must produce exponential-size circuits. We prove that access to an NP oracle is inherently necessary for efficient synthesis. Our main technical result shows that it is possible to use NP oracles to synthesize small Skolem functions in time polynomial in the size of the specification and the size of the smallest sufficient set of witnesses, establishing positive results for a broad class of relational specifications.

Hannes Ihalainen, Dieter Vandesande, André Schidler, Jeremias Berg, Bart Bogaerts, Matti Järvisalo

The implicit hitting set (IHS) approach offers a general framework for solving computationally hard combinatorial optimization problems declaratively. IHS iterates between a decision oracle used for extracting sources of inconsistency and an optimizer for computing so-called hitting sets (HSs) over the accumulated sources of inconsistency. While the decision oracle is language-specific, the optimizers is usually instantiated through integer programming. We explore alternative algorithmic techniques for hitting set optimization based on different ways of employing pseudo-Boolean (PB) reasoning as well as stochastic local search. We extensively evaluate the practical feasibility of the alternatives in particular in the context of pseudo-Boolean (0-1 IP) optimization as one of the most recent instantiations of IHS. Highlighting a trade-off between efficiency and reliability, while a commercial IP solver turns out to remain the most effective way to instantiate HS computations, it can cause correctness issues due to numerical instability; in fact, we show that exact HS computations instantiated via PB reasoning can be made competitive with a numerically exact IP solver. Furthermore, the use of PB reasoning as a basis for HS computations allows for obtaining certificates for the correctness of IHS computations, generally applicable to any IHS instantiation in which reasoning in the declarative language at hand can be captured in the PB-based proof format we employ.

Li Zheng, Liangbin Xie, Jiantao Zhou, He YiMin

Stable Diffusion (SD) often produces degraded outputs when the training dataset contains adversarial noise. Adversarial purification offers a promising solution by removing adversarial noise from contaminated data. However, existing purification methods are primarily designed for classification tasks and fail to address SD-specific adversarial strategies, such as attacks targeting the VAE encoder, UNet denoiser, or both. To address the gap in SD security, we propose Universal Diffusion Adversarial Purification (UDAP), a novel framework tailored for defending adversarial attacks targeting SD models. UDAP leverages the distinct reconstruction behaviors of clean and adversarial images during Denoising Diffusion Implicit Models (DDIM) inversion to optimize the purification process. By minimizing the DDIM metric loss, UDAP can effectively remove adversarial noise. Additionally, we introduce a dynamic epoch adjustment strategy that adapts optimization iterations based on reconstruction errors, significantly improving efficiency without sacrificing purification quality. Experiments demonstrate UDAP’s robustness against diverse adversarial methods, including PID (VAE-targeted), Anti-DreamBooth (UNet-targeted), MIST (hybrid), and robustness-enhanced variants like Anti-Diffusion (Anti-DF) and MetaCloak. UDAP also generalizes well across SD versions and text prompts, showcasing its practical applicability in real-world scenarios.

Wei Yao, Yunlian Sun, Hongwen Zhang, Yebin Liu, Jinhui Tang

Generating high-fidelity full-body human interactions with dynamic objects and static scenes remains a critical challenge in computer graphics and animation. Existing methods for human-object interaction often neglect scene context, leading to implausible penetrations, while human-scene interaction approaches struggle to coordinate fine-grained manipulations with long-range navigation. To address these limitations, we propose HOSIG, a novel framework for synthesizing full-body interactions through hierarchical scene perception. Our method decouples the task into three key components: 1) a scene-aware grasp pose generator that ensures collision-free whole-body postures with precise hand-object contact by integrating local geometry constraints, 2) a heuristic navigation algorithm that autonomously plans obstacle-avoiding paths in complex indoor environments via compressed 2D floor maps and dual-component spatial reasoning, and 3) a scene-guided motion diffusion model that generates trajectory-controlled, full-body motions with finger-level accuracy by incorporating spatial anchors and dual-space gradient-based guidance. Extensive experiments on the TRUMANS dataset demonstrate superior performance over state-of-the-art methods. Notably, our framework supports unlimited motion length through autoregressive generation and requires minimal manual intervention. This work bridges the critical gap between scene-aware navigation and dexterous object manipulation, advancing the frontier of embodied interaction synthesis.

Xinjie Xu, Shuyu Cheng, Dongwei Xu, Qi Xuan, Chen Ma

In hard-label black-box adversarial attacks, where only the top-1 predicted label is accessible, the prohibitive query complexity poses a major obstacle to practical deployment. In this paper, we focus on optimizing a representative class of attacks that search for the optimal ray direction yielding the minimum ℓ₂-norm perturbation required to move a benign image into the adversarial region. Inspired by Nesterov's Accelerated Gradient (NAG), we propose a momentum-based algorithm, ARS-OPT, which proactively estimates the gradient with respect to a future ray direction inferred from accumulated momentum. We provide a theoretical analysis of its convergence behavior, showing that ARS-OPT enables more accurate directional updates and achieves faster, more stable optimization. To further accelerate convergence, we incorporate surrogate-model priors into ARS-OPT's gradient estimation, resulting in PARS-OPT with enhanced performance. The superiority of our approach is supported by theoretical guarantees under standard assumptions. Extensive experiments on ImageNet and CIFAR-10 demonstrate that our method surpasses 13 state-of-the-art approaches in query efficiency.

Zeyu Xiao, Mingyang Sun, Yimin Cong, Lintao Wang, Dongliang Kou, Zhenyi Wu, Dingkang Yang, Peng Zhai, Zeyu Wang, Lihua Zhang

Joint rendering and deformation of mesh and 3D Gaussian Splatting (3DGS) have significant value as both representations offer complementary advantages for graphics applications. However, due to differences in representation and rendering pipelines, existing studies render meshes and 3DGS separately, making it difficult to accurately handle occlusions and transparency. Moreover, the deformed 3DGS still suffers from visual artifacts due to the sensitivity to the topology quality of the proxy mesh. These issues pose serious obstacles to the joint use of 3DGS and meshes, making it difficult to adapt 3DGS to conventional mesh-oriented graphics pipelines. We propose UniMGS, the first unified framework for rasterizing mesh and 3DGS in a single-pass anti-aliased manner, with a novel binding strategy for 3DGS deformation based on proxy mesh. Our key insight is to blend the colors of both triangle and Gaussian fragments by anti-aliased α-blending in a single pass, achieving visually coherent results with precise handling of occlusion and transparency. To improve the visual appearance of the deformed 3DGS, our Gaussian-centric binding strategy employs a proxy mesh and spatially associates Gaussians with the mesh faces, significantly reducing rendering artifacts. With these two components, UniMGS enables the visualization and manipulation of 3D objects represented by mesh or 3DGS within a unified framework, opening up new possibilities in embodied AI, virtual reality, and gaming. We will release our source code to facilitate future research.

Xuexin Wu, Zhenhui Ding, Huisi Wu, Jing Qin

Recent advances in deep learning have led to significant improvements in nuclei segmentation from histological images, particularly when labels of all classes are available simultaneously during training. However, in clinical practice, real-world scenarios require a model to perform well in an incremental learning setting, where we anticipate the model to achieve satisfactory performance on previously unseen data while effectively mitigating catastrophic forgetting of old classes. Most previous methods alleviate forgetting by distilling old class knowledge through prototypes; however, they fail to adequately capture fine-grained details to address the challenge of high class similarity, which is particularly severe in histological images. To overcome these limitations, we propose a novel incremental learning method for nuclei segmentation (we call it CiNuSeg), which is composed of two key innovative modules. First, we propose a new Anchor-driven Consistency Learning (ACL) module to construct multi-level class anchors within each sample to effectively capture fine structural and textural details of nuclei, thereby significantly mitigating forgetting. Second, we develop a Dual Region Regularization (DRR) module to suppress new class representations within old class regions while enhancing new class representations within new class regions, strengthening the model's ability to discriminate between different nuclei types and improving inter-class separability. We further introduce an Adaptive Temperature Tuning (ATT) strategy to dynamically balance model stability and plasticity. Extensive experiments conducted on benchmarking MoNuSAC and CoNSeP pathological datasets demonstrate the effectiveness of our method, consistently achieving better performance than SOTAs in different settings. Codes will be available upon publication.

Zeqing Wang, Bowen Zheng, Xingyi Yang, Zhenxiong Tan, Yuecong Xu, Xinchao Wang

Diffusion Transformer (DiT)-based video diffusion models generate high-quality videos at scale but incur prohibitive processing latency and memory costs for long videos. To address this, we propose a novel distributed inference strategy, termed DualParal. The core idea is that, instead of generating an entire video on a single GPU, we parallelize computation by partitioning both video frames and model layers across multiple GPUs. However, a naive parallel implementation is not feasible. Because all frames need to share the same noise level, they can't be processed independently. Instead, every step must wait for all others to finish, which cancels out the speed benefits of parallel processing. We overcome this obstacle with a block-wise denoising scheme. Namely, we segment the video into sequential blocks, each with a different noise level. As a result, we process them in a pipeline across the GPUs. Each GPU, holding a subset of the model layers, processes a specific block of frames and passes the results to the next GPU, enabling asynchronous computation and communication. To further optimize performance, we incorporate two key enhancements. Firstly, each GPU uses a feature cache technique to reduce the overhead of smooth transitions by reusing only features involved in cross-frame computation from the prior block, minimizing inter-GPU communication and redundant computation. Secondly, we employ a coordinated noise initialization strategy, ensuring globally consistent temporal dynamics by sharing initial noise patterns across GPUs. Together, these enable fast, artifact-free, and infinitely long video generation. Applied to the latest diffusion transformer video generator, our method efficiently produces 1,025-frame videos with up to 6.54x lower latency and 1.48x lower memory cost on 8xRTX 4090 GPUs.

Xiaoyang Wang, Hongping Gan

Deep Unrolling Networks (DUNs) integrate classical optimization recovery problems in Compressed Sensing (CS) with sophisticated deep learning network architectures, leading to substantial breakthroughs. However, prevailing DUNs generally face challenges concerning solidified gradient descent step size strategies, inadequate feature extraction within the iterative stage and limited information interaction between iterative stages. To overcome these obstacles, we propose SCU-Net, a channel-focused unrolling network inspired by the renowned spectral projected gradient optimization algorithm. In particular, we tailore two pivotal components, Barzilai-Borwein-gradient Descent Optimizer (BBDO) and Channel-guided Cross-attention Reconstruction Module (CCRM), to collaboratively undertake the reconstruction task. BBDO leverages a gradient calculation strategy based on BB step size to enhance data fidelity optimization, while CCRM addresses the intricate mapping issue associated with sparse induction, encompassing customized functionalities from Adaptive Channel Interaction Layer (ACIL) and Spatially Augmented Channel-aware Unit (SACU). Among them, ACIL amalgamates convolution operations and channel attention mechanisms to achieve meticulous information screening alongside efficient feature enhancement. SACU introduces dual reinforcement variables to bolster information exchange across different iterative stages, coupled with the optimization of cross-attention to facilitate the modeling of long-distance dependencies. Extensive experiments in both image CS and magnetic resonance imaging exhibit that our SCU-Net manifests superior performance, surpassing state-of-the-art methods.

Dayong Liang, Xiao-Yong Wei, Changmeng Zheng

Hallucination continues to pose a major obstacle in the reasoning capabilities of large language models (LLMs). Although the Multi-Agent Debate (MAD) paradigm offers a promising solution by promoting consensus among multiple agents to enhance reliability, it relies on the unrealistic assumption that all debaters are rational and reflective, which is a condition that may not hold when agents themselves are prone to hallucinations. To address this gap, we introduce the Multi-agent Undercover Gaming (MUG) protocol, inspired by social deduction games like ''Who is Undercover?''. MUG reframes MAD as a process of detecting ''undercover'' agents (those suffering from hallucinations) by employing multimodal counterfactual tests. Specifically, we modify reference images to introduce counterfactual evidence and observe whether agents can accurately identify these changes, providing ground-truth for identifying hallucinating agents and enabling robust, crowd-powered multimodal reasoning. MUG advances MAD protocols along three key dimensions: (1) enabling factual verification beyond statistical consensus through counterfactual testing; (2) introducing cross-evidence reasoning via dynamically modified evidence sources instead of relying on static inputs; and (3) fostering active reasoning, where agents engage in probing discussions rather than passively answering questions. Collectively, these innovations offer a more reliable and effective framework for multimodal reasoning in LLMs.

Zhangyu Lai, Yilin Lu, Xinyang Li, Jianghang Lin, Yansong Qu, Ming Li, Liujuan Cao

Visual anomaly detection is limited by the lack of sufficient anomaly data. While existing anomaly synthesis methods have made remarkable progress, achieving both realism and diversity in synthesis remains a major obstacle. To address this, we propose AnomalyPainter, a novel framework that breaks the diversity-realism trade-off dilemma through synergizing Vision Language Large Model (VLLM), Latent Diffusion Model (LDM), and our newly introduced texture library Tex-9K. Tex-9K is a professional texture library containing 75 categories and 8792 texture assets crafted for diverse anomaly synthesis. Leveraging VLLM's general knowledge, reasonable anomaly text descriptions are generated for each industrial object and matched with relevant diverse textures from Tex-9K. These textures then guide the LDM via ControlNet to paint on normal images. Furthermore, we introduce Texture-Aware Latent Init to stabilize the natural-image-trained ControlNet for industrial images. Extensive experiments show that AnomalyPainter outperforms existing methods in realism, diversity, and generalization, achieving superior downstream performance.

Yuanmin Huang, Wenxuan Li, Mi Zhang, Xiaohan Zhang, Xiaoyu You, Min Yang

Deep neural networks have recently achieved notable progress in 3D point cloud recognition, yet their vulnerability to adversarial perturbations poses critical security challenges in practical deployments. Conventional defense mechanisms struggle to address the evolving landscape of multifaceted attack patterns. Through systematic analysis of existing defenses, we identify that their unsatisfactory performance primarily originates from an entangled feature space, where adversarial attacks can be performed easily. To this end, we present 3D-ANC, a novel approach that capitalizes on the Neural Collapse (NC) mechanism to orchestrate discriminative feature learning. In particular, NC depicts where last-layer features and classifier weights jointly evolve into a simplex equiangular tight frame (ETF) arrangement, establishing maximally separable class prototypes. However, leveraging this advantage in 3D recognition confronts two substantial challenges: (1) prevalent class imbalance in point cloud datasets, and (2) complex geometric similarities between object categories. To tackle these obstacles, our solution combines an ETF-aligned classification module with an adaptive training framework consisting of representation-balanced learning (RBL) and dynamic feature direction loss (FDL). 3D-ANC seamlessly empowers existing models to develop disentangled feature spaces despite the complexity in 3D data distribution. Comprehensive evaluations state that 3D-ANC significantly improves the robustness of models with various structures on two datasets. For instance, DGCNN's classification accuracy is elevated from 27.2% to 80.9% on ModelNet40 -- a 53.7% absolute gain that surpasses leading baselines by 34.0%.

Chunyong Hu, Qi Luo, Jianyun Xu, Song Wang, Qiang Li, Sheng Yang

In the realm of autonomous driving, accurately detecting surrounding obstacles is crucial for effective decision-making. Traditional methods primarily rely on 3D bounding boxes to represent these obstacles, which often fail to capture the complexity of irregularly shaped, real-world objects. To overcome these limitations, we present GUIDE, a novel framework that utilizes 3D Gaussians for instance detection and occupancy prediction. Unlike conventional occupancy prediction methods, GUIDE also offers robust tracking capabilities. Our framework employs a sparse representation strategy, using Gaussian-to-Voxel Splatting to provide fine-grained, instance-level occupancy data without the computational demands associated with dense voxel grids. Experimental validation on the nuScenes dataset demonstrates GUIDE's performance, with an instance occupancy mAP of 21.61, marking a 50% improvement over existing methods, alongside competitive tracking capabilities. GUIDE establishes a new benchmark in autonomous perception systems, effectively combining precision with computational efficiency to better address the complexities of real-world driving environments.

Liang Hou, Cong Liu, Mingwu Zheng, Xin Tao, Pengfei Wan, Di Zhang, Kun Gai

Resolution generalization in image generation tasks enables the production of higher-resolution images with lower training resolution overhead. However, a key obstacle for diffusion transformers in addressing this problem is the mismatch between positional encodings seen at inference and those used during training. Existing strategies such as positional encodings interpolation, extrapolation, or hybrids, do not fully resolve this mismatch. In this paper, we propose a novel two-dimensional randomized positional encodings, namely RPE-2D, that prioritizes the order of image patches rather than their absolute distances, enabling seamless high- and low-resolution generation without training on multiple resolutions. Concretely, RPE-2D independently samples positions along the horizontal and vertical axes over an expanded range during training, ensuring that the encodings used at inference lie within the training distribution and thereby improving resolution generalization. We further introduce a simple random resize-and-crop augmentation to strengthen order modeling and add micro-conditioning to indicate the applied cropping pattern. On the ImageNet dataset, RPE-2D achieves state-of-the-art resolution generalization performance, outperforming competitive methods when trained at 256^2 and evaluated at 384^2 and 512^2, and when trained at 512^2 and evaluated at 768^2 and 1024^2. RPE-2D also exhibits outstanding capabilities in low-resolution image generation, multi-stage training acceleration, and multi-resolution inheritance.

Yuzhe Duan, Xuanxuan Ren, Guizhe Dong, Xu Yang, Yanhua Yang

The Segment Anything Model 2 (SAM2) has established a new benchmark for high-precision image and video segmentation, offering significant potential for a wide range of computer vision tasks. Despite its impressive performance, the model's substantial computational and memory requirements present a significant obstacle to its practical deployment on resource-constrained devices. In this paper, we introduce a novel framework for optimizing SAM2 through two synergistic, importance-driven strategies: quantization and memory management. Specifically, an Importance-driven Mixed-Precision Quantization scheme, which analyzes the sensitivity of each layer using a Weight-Activation Importance Score, is employed to enable a targeted bit-width assignment, preserving model accuracy by keeping critical layers at higher precision. Then, the Selective Importance-driven Synthesis (SIS) mechanism is proposed to address the inefficient accumulation of redundant data in the memory bank. SIS intelligently compresses the memory by identifying the most contextually similar historical frames and synthesizing them into a single, representative feature, thereby preserving informational diversity while enhancing temporal context understanding. Extensive experiments on the COCO and SA-V benchmarks validate our approach, showing that our optimized model consistently outperforms state-of-the-art quantization methods. Our work provides a principled framework for the co-design of quantization and dynamic memory management, offering a practical path toward deploying powerful video segmentation models in real-world applications.

Shuang Chen, Tom Krajnik, Farshad Arvin, Amir Atapour-Abarghouei

Biologically plausible and energy-efficient frameworks such as Spiking Neural Networks (SNNs) have not been sufficiently explored in low-level vision tasks. Taking image deraining as an example, this study addresses the representation of the inherent high-pass characteristics of spiking neurons, specifically in image deraining and innovatively proposes the Visual LIF (VLIF) neuron, overcoming the obstacle of lacking spatial contextual understanding present in traditional spiking neurons. To tackle the limitation of frequency-domain saturation inherent in conventional spiking neurons, we leverage the proposed VLIF to introduce the Spiking Decomposition and Enhancement Module and the lightweight Spiking Multi-scale Unit for hierarchical multi-scale representation learning. Extensive experiments across five benchmark deraining datasets demonstrate that our approach significantly outperforms state-of-the-art SNN-based deraining methods, achieving this superior performance with only 13% of their energy consumption. These findings establish a solid foundation for deploying SNNs in high-performance, energy-efficient low-level vision tasks.

Qiang Bai, Bojian Wu, Xi Yang, Zhizhong Han

Neural signed distance functions (SDFs) have been a vital representation to represent 3D shapes or scenes with neural networks. An SDF is an implicit function that can query signed distances at specific coordinates for recovering a 3D surface. Although implicit functions work well on a single shape or scene, they pose obstacles when analyzing multiple SDFs with high-fidelity geometry details, due to the limited information encoded in the latent space for SDFs and the loss of geometry details. To overcome these obstacles, we introduce a method to represent multiple SDFs in a common space, aiming to recover more high-fidelity geometry details with more compact latent representations. Our key idea is to take full advantage of the benefits of generalization-based and overfitting-based learning strategies, which manage to preserve high-fidelity geometry details with compact latent codes. Based on this framework, we also introduce a novel sampling strategy to sample training queries. The sampling can improve the training efficiency and eliminate artifacts caused by the influence of other SDFs. We report numerical and visual evaluations on widely used benchmarks to validate our designs and show advantages over the latest methods in terms of the representative ability and compactness.

Baiqiang Wu, Yang Li

Multimodal emotion recognition plays a crucial role in enhancing the intelligence of human-computer interaction and emotional understanding. However, conventional approaches face challenges such as scarcity of annotated data, significant modality heterogeneity, and temporal misalignment. To address these issues, we propose DHCM-CACL, a novel self-supervised emotion recognition framework integrating EEG and facial expressions. During the pre-training phase, we propose a Dynamic Hierarchical Cross-modal Mamba module (DHCM), which models long-term dependencies through dynamic state matrices, incorporates forgetting gates for noise suppression, and constructs a hierarchical cross-modal interaction structure, effectively achieving cross-modal temporal alignment and mitigating modality heterogeneity. Subsequently, we propose a Confidence-Adaptive Contrastive Learning module (CACL) that dynamically adjusts sample weights using gated confidence signals derived from DHCM to compute loss, prioritizing reliable samples while suppressing noisy instances through adaptive weighting, thereby enhancing representation reliability and generalization in data-scarce scenarios. During the fine-tuning phase, we integrate a cross-modal attention gating mechanism to reinforce temporal associations and adopt an evidence-aware joint optimization objective, providing probabilistic credibility outputs for emotion prediction. Experimental results on the DEAP and MAHNOB-HCI datasets demonstrate that our approach achieves state-of-the-art performance in emotion classification under both subject-dependent and subject-independent settings.

Aakash Kumar Agarwal, Moyuru Yamada

This paper tackles the fundamental failure of Large Language Models (LLMs) to solve new tasks when prompted with a sufficient, yet overly complex, set of multi-modal episodes. This failure stems from the model's inability to distill underlying patterns from the noisy experiences. We propose Hypothesis-Driven Reasoning (HDR), a framework that enhances LLM reasoning by building an explicit semantic memory—a set of hypotheses induced from the multi-modal episodes. HDR employs a two-stage pipeline. It first extracts potential factors from the episodes and then iteratively refines hypotheses by generate-verify loop with the factors. We first empirically demonstrates this failure and the potential of sematic memory, showing that oracle hypotheses can boost accuracy from 35.3% to 92.0% on a novel task we designed. We then evaluate our HDR, achieving near-oracle performance and significantly outperforming baselines, especially on smaller models. This paper validates a shift from unstructured in-context recall to explicit knowledge abstraction for robust reasoning.

Shuxin Zhuang, Linjian Meng, Shuxin Li, Minming Li, Youzhi Zhang

Urban Network Security Games (UNSGs), which model the strategic allocation of limited security resources on city road networks, are critical for urban safety. However, finding a Nash Equilibrium (NE) in large-scale UNSGs is challenging due to their massive and combinatorial action spaces. One common approach to addressing these games is the Policy-Space Response Oracle (PSRO) framework, which requires computing best responses (BR) at each iteration. However, precisely computing exact BRs is impractical in large-scale games, and employing reinforcement learning to approximate BRs inevitably introduces errors that limit the overall effectiveness of the PSRO methods. Recent advancements in leveraging non-convex stochastic optimization to approximate an NE offer a promising alternative to the burdensome BR computation. However, utilizing existing stochastic optimization techniques with an unbiased loss function for UNSGs remains challenging because the action spaces are too vast to be effectively represented by neural networks. To address these issues, we introduce Tree-based Stochastic Optimization (TSO), a framework that bridges the gap between the stochastic optimization paradigm for NE-finding and the demands of UNSGs. Specifically, we employ the tree-based action representation that maps the whole action space onto a tree structure, addressing the challenge faced by neural networks in representing actions when the action space cannot be enumerated. We then incorporate this representation into the loss function and theoretically demonstrate its equivalence to the unbiased loss function. To further enhance the quality of the converged solution, we introduce a sample-and-prune mechanism that reduces the risk of being trapped in suboptimal local optima. Extensive experimental results indicate the superiority of TSO over other baseline algorithms in addressing the UNSGs.