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Applications · Chemistry and Drug Discovery

Yiming Yang, Zhiyuan Zhou, Yueming Yin, Hoi-Yeung Li, Adams Kong

Accurate prediction of protein-ligand bioactivity is a cornerstone of modern drug discovery, yet current deep learning methods often struggle with out-of-domain (OOD) generalization. The existing methods rely on access to source data, making them impractical in scenarios where data cannot be accessed due to confidentiality, privacy concerns or intellectual property restrictions. In this paper, we provide the first exploration of a more realistic setting for bioactivity prediction, where models are expected to adapt to out-of-domain distributions without access to source data. Motivated by the critical role of binding-relevant interactions in determining ligand-protein bioactivity, we introduce an uncertainty-weighted consistency strategy, in which original samples with high confidence guide their augmented counterparts by minimizing feature distance. This encourages the model to focus on informative interaction regions while suppressing reliance on spurious or non-causal substructures. To further enhance representation discriminability and prevent feature collapse, we integrate a contrastive optimization objective that pulls together augmented views of the same complex and pushes away views from different complexes. Together, these two components enable the learning of invariant, bioactivity-aware representations, allowing robust adaptation under distribution shifts. Extensive experiments across DTIGN, SIU 0.6, and DrugOOD demonstrate that our framework consistently outperforms state-of-the-art baselines under scaffold, protein, and assay based OOD settings. Especially on the eight subsets of DTIGN, it improves Pearson’s $R$ by 8.2\% and Kendall’s Tau $\tau$ by 5.8\% on average over the best baseline, underscoring its effectiveness as a source data-absent solution for OOD bioactivity prediction.

Deep Learning · Theory

Jianzhe Wei, Siyu Chen, Jianliang He, Zhuoran Yang

Transformers have demonstrated remarkable in-context learning abilities, adapting to new tasks from just a few examples without parameter updates. However, theoretical understanding of this phenomenon typically assumes fixed dependency structures, while real-world sequences exhibit flexible, context-dependent relationships. We address this gap by investigating whether transformers can learn causal structures -- the underlying dependencies between sequence elements -- directly from in-context examples. We propose a novel framework using Markov chains with randomly sampled causal dependencies, where transformers must infer which tokens depend on which predecessors to make accurate predictions. Our key contributions are threefold: (1) We prove that a two-layer transformer with relative positional embeddings can implement Bayesian Model Averaging (BMA), the optimal statistical algorithm for causal structure inference; (2) Through extensive experiments and parameter-level analysis, we demonstrate that transformers trained on this task approximate BMA, with attention patterns directly reflecting the inferred causal structures; (3) We provide information-theoretic guarantees showing how transformers recover causal dependencies and extend our analysis to continuous dynamical systems, revealing fundamental differences in representational requirements. Our findings bridge the gap between empirical observations of in-context learning and theoretical understanding, showing that transformers can perform sophisticated statistical inference over structural uncertainty.

Optimization · Learning for Optimization

Zhuoyan Li, Aditya Bansal, Jinzhao Li, Shishuang He, Zhuoran Lu, Mutian Zhang, Qin Liu, Yiwei Yang, Swati Jain, Ming Yin 等

Large language models (LLMs) are increasingly used to automate feature engineering in tabular learning. Given task-specific information, LLMs can propose diverse feature transformation operations to enhance downstream model performance. However, current approaches typically assign the LLM as a black-box optimizer, responsible for both proposing and selecting operations based solely on its internal heuristics, which often lack calibrated estimations of operation utility and consequently lead to repeated exploration of low-yield operations without a principled strategy for prioritizing promising directions. In this paper, we propose a human–LLM collaborative feature engineering framework for tabular learning. We begin by decoupling the transformation operation proposal and selection processes, where LLMs are used solely to generate operation candidates, while the selection is guided by explicitly modeling the utility and uncertainty of each proposed operation. Since accurate utility estimation can be difficult especially in the early rounds of feature engineering, we design a mechanism within the framework that selectively elicits and incorporates human expert preference feedback—comparing which operations are more promising—into the selection process to help identify more effective operations. Our evaluations on both the synthetic study and the real user study demonstrate that the proposed framework improves feature engineering performance across a variety of tabular datasets and reduces users’ cognitive load during the feature engineering process.

Social Aspects · Trustworthy Machine Learning

Matthieu Bou, Nyal Patel, Arjun Jagota, Satyapriya Krishna, Sonali Parbhoo

The objectives that Large Language Models (LLMs) implicitly optimize remain dangerously opaque, making trustworthy alignment and auditing a grand challenge. While Inverse Reinforcement Learning (IRL) can infer reward functions from behaviour, existing approaches either produce a single, overconfident reward estimate or fail to address the fundamental ambiguity of the task (non-identifiability). This paper introduces a principled auditing framework that re-frames reward inference from a simple estimation task to a comprehensive process for verification. Our framework leverages Bayesian IRL to not only recover a distribution over objectives but to enable three critical audit capabilities: (i) Quantifying and systematically reducing non-identifiability by demonstrating posterior contraction over sequential rounds of evidence; (ii) Providing actionable, uncertainty-aware diagnostics that expose spurious shortcuts and identify out-of-distribution prompts where the inferred objective cannot be trusted; and (iii) Validating policy-level utility by showing that the refined, low-uncertainty reward can be used directly in RLHF to achieve training dynamics and toxicity reductions comparable to the ground-truth alignment process. Empirically, our framework successfully audits a detoxified LLM and generalizes beyond detoxification to a helpfulness preference setting, yielding a well-calibrated and interpretable objective that strengthens alignment guarantees. Overall, this work provides a practical toolkit for auditors, safety teams, and regulators to verify what LLMs are truly trying to achieve, moving us toward more trustworthy and accountable AI.

General Machine Learning · Probabilistic Methods

Brendan Ross, Noël Vouitsis, Atiyeh Ashari Ghomi, Rasa Hosseinzadeh, Ji Xin, Zhaoyan Liu, Yi Sui, Shiyi Hou, Kin Kwan Leung, Gabriel Loaiza-Ganem 等

Although large language models (LLMs) are becoming increasingly capable of solving challenging real-world tasks, accurately quantifying their uncertainty remains a critical open problem—one that limits their applicability in high-stakes domains. This challenge is further compounded by the closed-source, black-box nature of many state-of-the-art LLMs. Moreover, LLM-based systems can be highly sensitive to the prompts that bind them together, which often require significant manual tuning (i.e., prompt engineering). In this work, we address these challenges by viewing LLM-based systems through a Bayesian lens. We interpret prompts as textual parameters in a statistical model, allowing us to use a small training dataset to perform Bayesian inference over these prompts. This novel perspective enables principled uncertainty quantification over both the model’s textual parameters and its downstream predictions, while also incorporating prior beliefs about these parameters expressed in free-form text. To perform Bayesian inference— a difficult problem even for well-studied data modalities—we introduce Metropolis-Hastings through LLM Proposals (MHLP), a novel Markov chain Monte Carlo (MCMC) algorithm that combines prompt optimization techniques with standard MCMC methods. MHLP is a turnkey modification to existing LLM pipelines, including those that rely exclusively on closed-source models. Empirically, we demonstrate that our method yields improvements in both predictive accuracy and uncertainty quantification (UQ) on a range of LLM benchmarks and UQ tasks. More broadly, our work demonstrates a viable path for incorporating methods from the rich Bayesian literature into the era of LLMs, paving the way for more reliable and calibrated LLM-based systems.

Reinforcement Learning · Deep RL

Shenao Zhang, Yaqing Wang, Yinxiao Liu, Tianqi Liu, Peter Grabowski, Eugene Ie, Zhaoran Wang, Yunxuan Li

Large Language Models (LLMs) trained via Reinforcement Learning (RL) have exhibited strong reasoning capabilities and emergent reflective behaviors, such as rethinking and error correction, as a form of in-context exploration. However, the Markovian policy obtained from conventional RL training does not give rise to reflective exploration behaviors since the policy depends on the history only through the state and therefore has no incentive to enrich identical states with additional context. Instead, RL exploration is only useful during training to learn the optimal policy in a trial-and-error manner. Therefore, it remains unclear whether reflective reasoning will emerge during RL, or why it is beneficial. To remedy this, we recast reflective exploration within a Bayesian RL framework, which optimizes the expected return under a posterior distribution over Markov decision processes induced by the training data. This Bayesian formulation admits uncertainty-adaptive policies that, through belief updates, naturally incentivize information-gathering actions and induce self-reflection behaviors. Our resulting algorithm, BARL, instructs the LLM to stitch and switch strategies based on the observed outcomes, offering principled guidance on when and how the model should reflectively explore. Empirical results on both synthetic and mathematical reasoning tasks demonstrate that BARL outperforms conventional RL approaches, achieving superior test-time performance and token efficiency. Our code is available at https://github.com/shenao-zhang/BARL.

Reinforcement Learning · Online

Kaustubh Mani, Yann Pequignot, Vincent Mai, Liam Paull

Safe exploration is a prerequisite for deploying reinforcement learning (RL) agents in safety-critical domains. In this paper, we approach safe exploration through the lens of epistemic uncertainty, where the actor’s sensitivity to parameter perturbations serves as a practical proxy for regions of high uncertainty. We propose Sharpness-Aware Policy Optimization (SHAPO), a sharpness-aware policy update rule that evaluates gradients at perturbed parameters, making policy updates pessimistic with respect to the actor’s epistemic uncertainty. Analytically we show that this adjustment implicitly reweighs policy gradients, amplifying the influence of rare unsafe actions while tempering contributions from already safe ones, thereby biasing learning toward conservative behavior in under-explored regions. Across several continuous-control tasks, our method consistently improves both safety and task performance over existing baselines, significantly expanding their Pareto frontiers.

Xiaolei Lu, Shamim Nemati

Accurate prediction of the need for invasive mechanical ventilation (IMV) in intensive care units (ICUs) patients is crucial for timely interventions and resource allocation. However, variability in patient populations, clinical practices, and electronic health record (EHR) systems across institutions introduces domain shifts that degrade the generalization performance of predictive models during deployment. Test-Time Training (TTT) has emerged as a promising approach to mitigate such shifts by adapting models dynamically during inference without requiring labeled target-domain data. In this work, we introduce Adaptive Test-Time Training (AdaTTT), an enhanced TTT framework tailored for EHR-based IMV prediction in ICU settings. We begin by deriving information-theoretic bounds on the test-time prediction error and demonstrate that it is constrained by the uncertainty between the main and auxiliary tasks. To enhance their alignment, we introduce a self-supervised learning framework with pretext tasks: reconstruction and masked feature modeling optimized through a dynamic masking strategy that emphasizes features critical to the main task. Additionally, to improve robustness against domain shifts, we incorporate prototype learning and employ Partial Optimal Transport (POT) for flexible, partial feature alignment while maintaining clinically meaningful patient representations. Experiments across multi-center ICU cohorts demonstrate competitive classification performance on different test-time adaptation benchmarks.

Optimization · Optimization and Learning under Uncertainty

Koji Ichikawa, Kei Takemura, Tatsuya Matsuoka

This paper addresses online inventory optimization (OIO), an extension of online convex optimization. OIO is a sequential decision-making process in inventory management cycles consisting of order arrival, stock consumption, and new order placement. One key challenge in OIO is managing demand fluctuations. However, most existing algorithms still cannot sufficiently handle this because they focus on a static regret guarantee, comparing their performance to a fixed order-up-to level strategy. In non-stationary environments, such static comparator is unsuitable due to demand fluctuations. In this paper, we propose an algorithm with near-optimal dynamic regret guarantee for OIO. Our algorithm also offers an improvement of $\sqrt{L_{\max}}$ for the static regret upper bound in existing studies. Here, $L_{\max}$ refers to the maximum sell-out period. Our algorithm employs a simple two-stage projection strategy, through which we prove that the OIO is connected to the smoothed online convex optimization.

Deep Learning · Everything Else

Ruicheng Ao, Zeping Min, Tingyu Zhu, Wotao Yin, Xinshang Wang

We introduce ResiliBench, a benchmark that evaluates LLM workflow execution under simulated realistic conditions of instruction quality variability and tool execution uncertainty. Unlike existing benchmarks that encounter these challenges incidentally, our work makes uncertainty the primary focus of systematic study. The benchmark incorporates three key aspects: (1) modeling of probabilistic tool behaviors through parameterized error models that simulate real-world API failure patterns, (2) provision of MDP-derived workflows that maximize expected success rates, and (3) systematic evaluation of model robustness through controlled perturbations of workflow instruction quality. Our construction pipeline generates 5,040 tasks from a tool library of 30 APIs. The evaluation conducted across widely used large language models under conditions of probabilistic tool failures and varying instruction quality reveals notable performance differences. Specifically, MDP-optimal workflow prompts achieve an average success rate of 62.1\%, Chain-of-Thought prompts yield an average success rate of 50.8\%, and flawed workflow prompts result in an average success rate of 54.3\%. Our benchmark is available at https://github.com/Archer222arc/ResiliBench.

Reinforcement Learning · Deep RL

Thomas Rupf, Marco Bagatella, Marin Vlastelica, Andreas Krause

Behavior Foundation Models (BFMs) are capable of retrieving high-performing policy for any reward function specified directly at test-time, commonly referred to as zero-shot reinforcement learning (RL). While this is a very efficient process in terms of compute, it can be less so in terms of data: as a standard assumption, BFMs require computing rewards over a non-negligible inference dataset, assuming either access to a functional form of rewards, or significant labeling efforts. To alleviate these limitations, we tackle the problem of task inference purely through interaction with the environment at test-time. We propose OpTI-BFM, an optimistic decision criterion that directly models uncertainty over reward functions and guides BFMs in data collection for task inference. Formally, we provide a regret bound for well- trained BFMs through a direct connection to upper-confidence algorithms for linear bandits. Empirically, we evaluate OpTI-BFM on established zero-shot benchmarks, and observe that it enables successor-features-based BFMs to identify and optimize an unseen reward function in a handful of episodes with minimal compute overhead.

Applications · Physics

Utkarsh Utkarsh, Danielle Maddix, Ruijun Ma, Michael W Mahoney, Bernie Wang

We present ProbHardE2E, a probabilistic forecasting framework that incorporates hard operational/physical constraints and provides uncertainty quantification. Our methodology uses a novel differentiable probabilistic projection layer (DPPL) that can be combined with a wide range of neural network architectures. DPPL allows the model to learn the system in an end-to-end manner, compared to other approaches where constraints are satisfied either through a post-processing step or at inference. ProbHardE2E optimizes a strictly proper scoring rule, without making any distributional assumptions on the target, which enables it to obtain robust distributional estimates (in contrast to existing approaches that generally optimize likelihood-based objectives, which can be biased by their distributional assumptions and model choices); and it can incorporate a range of non-linear constraints (increasing the power of modeling and flexibility). We apply ProbHardE2E in learning partial differential equations with uncertainty estimates and to probabilistic time-series forecasting, showcasing it as a broadly applicable general framework that connects these seemingly disparate domains. Our code is available at https://github.com/amazon-science/probharde2e.

Optimization · Optimization and Learning under Uncertainty

Zhiyun Jiang, Tianming Zhao, Chunqiu xia, Albert Zomaya

Learning-augmented scheduling uses ML predictions to improve decision-making under uncertainty. Many algorithms in this class have been proposed with better theoretical guarantees than the classic methods. Translating these theoretical results into practice, however, requires an understanding of real workloads. Such an understanding is hard to develop because existing production traces either lack the ground-truth processing times or are not publicly available, while synthetic benchmarks fail to represent real-world complexity. We fill this gap by introducing *Alibaba Trace for Learning-Augmented Scheduling (ATLAS)*, a research-ready dataset derived from Alibaba's Platform of Artificial Intelligence (PAI) cluster trace—a production system that processes hundreds of thousands of ML jobs per day. The ATLAS dataset has been cleaned and features engineered to represent the inputs and constraints of non-clairvoyant scheduling, including user tags, resource requests (CPU/GPU/memory), and job structures with ground-truth processing times. We develop a prediction benchmark reporting prediction error metrics, along with feature importance analysis, and introduce a novel multiple-stage ML model. We also provide a scheduling benchmark for minimizing the total completion time, max-stretch, and makespan. ATLAS is a reproducible foundation for researchers to study learning-augmented scheduling on real workloads, available at https://github.com/zhiyunjiang0810/non-clairvoyant-with-predictions.

Applications · Neuroscience, Cognitive Science

Balázs Meszéna, Keith Murray, Julien Corbo, Batuhan Erkat, Márton Hajnal, Pierre-Olivier Polack, Gergo Orban

The brain interprets visual information through learned regularities, a computation formalized as performing probabilistic inference under a prior. The visual cortex establishes priors for this inference, some of which are delivered through widely established top-down connections that inform low-level cortices about statistics represented at higher levels in the cortical hierarchy. While evidence supports that adaptation leads to priors reflecting the structure of natural images, it remains unclear if similar priors can be flexibly acquired when learning a specific task. To investigate this, we built a generative model of V1 that we optimized for performing a simple discrimination task and analyzed it along with large scale recordings from mice performing an analogous task. In line with recent successful approaches, we assumed that neuronal activity in V1 can be identified with latent posteriors in the generative model, providing an opportunity to investigate the contributions of task-related priors to neuronal responses. To obtain a flexible test bed for this analysis, we extended the VAE formalism so that a task can be flexibly and data-efficiently acquired by reusing previously learned representations. Task-specific priors learned by this Task-Amortized VAE were used to investigate biases in mice and model when presenting stimuli that violated the trained task statistics. Mismatch between learned task statistics and incoming sensory evidence showed signatures of uncertainty in stimulus category in the posterior of TAVAE, reflecting properties of bimodal response profile in V1 recordings. The task-optimized generative model could account for various characteristics of V1 population activity, including within-day updates to the population responses. Our results confirm that flexible task-specific contextual priors can be learned on-demand by the visual system and can be deployed as early as the entry level of the visual cortex.

Computer Vision · Image and Video Generation

Han Song, Yucheng Zhou, Jianbing Shen, Yu Cheng

Combining Chain-of-Thought (CoT) with Reinforcement Learning (RL) improves text-to-image (T2I) generation, yet the underlying interaction between CoT's exploration and RL's optimization remains unclear. We present a systematic entropy-based analysis that yields three key insights: (1) CoT expands the generative exploration space, while RL contracts it toward high-reward regions; (2) final reward is strongly negatively correlated with both the mean and variance of image-token entropy, highlighting the need to reduce uncertainty and instability; and (3) the entropy of the textual CoT directly governs downstream image quality, with lower-entropy CoTs leading to better generations. Motivated by these findings, we propose Entropy-Guided Group Relative Policy Optimization (EG-GRPO), a fine-tuning strategy that reallocates optimization budget by uncertainty: low-entropy tokens are excluded from reward-driven updates to preserve stability, while high-entropy tokens receive an entropy bonus that encourages structured exploration without collapse. Experiments on standard T2I benchmarks demonstrate that EG-GRPO achieves state-of-the-art performance.

Applications · Robotics

Suhyeok Jang, Dongyoung Kim, Changyeon Kim, Youngsuk Kim, Jinwoo Shin

Vision-Language-Action models (VLAs) have demonstrated remarkable performance in robot control. However, they remain fundamentally limited in tasks that require high precision due to their single-inference paradigm. While test-time scaling approaches using external verifiers have shown promise, they require additional training and fail to generalize to unseen conditions. We propose Masking Distribution Guided Selection (MG-Select), a novel test-time scaling framework for VLAs that leverages the model's internal properties without requiring additional training or external modules. Our approach utilizes KL divergence from a reference action token distribution as a confidence metric for selecting optimal action from multiple candidates. We introduce a reference distribution generated by the same VLA but with randomly masked states and language conditions as inputs, providing action uncertainty while remaining aligned with the target task distribution. Additionally, we propose a joint training strategy that enables the model to learn both conditional and unconditional distributions by applying dropout to state and language conditions, thereby further improving the quality of the reference distribution. Our experiments demonstrate that MG-Select provides a reliable reference for action selection through task-relevant condition masking and consistently improves base models across diverse simulation and real-world benchmarks.

Bin Rao, Haicheng Liao, Yanchen Guan, Chengyue Wang, Bonan Wang, Jiaxun Zhang, Zhenning Li

Accurately predicting the future trajectories of traffic agents is essential in autonomous driving. However, due to the inherent imbalance in trajectory distributions, tail data in natural datasets often represents more complex and hazardous scenarios. Existing studies typically rely solely on a base model's prediction error, without considering the diversity and uncertainty of long-tail trajectory patterns. We propose an adaptive momentum and decoupled contrastive learning framework (AMD), which integrates unsupervised and supervised contrastive learning strategies. By leveraging an improved momentum contrast learning (MoCo-DT) and decoupled contrastive learning (DCL) module, our framework enhances the model's ability to recognize rare and complex trajectories. Additionally, we design four types of trajectory random augmentation methods and introduce an online iterative clustering strategy, allowing the model to dynamically update pseudo-labels and better adapt to the distributional shifts in long-tail data. We propose three different criteria to define long-tail trajectories and conduct extensive comparative experiments on the nuScenes and ETH/UCY datasets. The results show that AMD not only achieves optimal performance in long-tail trajectory prediction but also demonstrates outstanding overall prediction accuracy.

Zixuan Hu, Dongxiao Li, Xinzhu Ma, Shixiang Tang, Xiaotong Li, Wenhan Yang, Ling-Yu Duan

Accurate monocular 3D object detection (M3OD) is pivotal for safety-critical applications like autonomous driving, yet its reliability deteriorates significantly under real-world domain shifts caused by environmental or sensor variations. To address these shifts, Test-Time Adaptation (TTA) methods have emerged, enabling models to adapt to target distributions during inference. While prior TTA approaches recognize the positive correlation between low uncertainty and high generalization ability, they fail to address the dual uncertainty inherent to M3OD: semantic uncertainty (ambiguous class predictions) and geometric uncertainty (unstable spatial localization). To bridge this gap, we propose Dual Uncertainty Optimization (DUO), the first TTA framework designed to jointly minimize both uncertainties for robust M3OD. Through a convex optimization lens, we introduce an innovative convex structure of the focal loss and further derive a novel conjugate loss, enabling label-agnostic uncertainty weighting and balanced learning for high-uncertainty objects. In parallel, we design a semantic-aware normal field constraint that preserves geometric coherence in regions with clear semantic cues, reducing uncertainty from the unstable 3D representation. This dual-branch mechanism forms a complementary loop: enhanced spatial perception improves semantic classification, and robust semantic predictions further refine spatial understanding. Extensive experiments demonstrate the superiority of DUO over existing methods across various datasets and domain shift types. The source code is available at https://github.com/hzcar/DUO.

Tuo Feng, Wenguan Wang, Yi Yang

In autonomous driving, accurately predicting occupancy and motion is crucial for safe navigation within dynamic environments. However, existing methods often suffer from difficulties in handling complex scenes and uncertainty arising from sensor data. To address these issues, we propose a new Gaussian-based World Model (GWM), seamlessly integrating raw multi-modal sensor inputs. In 1st stage, Gaussian representation learner utilizes self-supervised pretraining to learn robust Gaussian representation. Gaussian representation integrates semantic and geometric information and establishes a robust probabilistic understanding of the environment. In 2nd stage, GWM seamlessly integrates learning, simulation, and planning into a unified framework, empowering the uncertainty-aware simulator & planner to jointly forecast future scene evolutions and vehicle trajectories. Simulator generates future scene predictions by modeling both static and dynamic elements, while planner calculates optimal paths to minimize collision risks, thus enhancing navigation safety. Overall, GWM employs a sensor-to-planning world model that directly processes raw sensor data, setting it apart from previous methods. Experiments show that GWM outperforms state-of-the-art approaches by 1.46% in semantic comprehension and 0.07m in motion prediction. Moreover, we provide an in-depth analysis of Gaussian representations under complex scenarios.

Qi Zhang, Chi Huang, Qian Zhang, Nan Li, Wei Feng

The latest advancements in scene relighting have been predominantly driven by inverse rendering with 3D Gaussian Splatting (3DGS). However, existing methods remain overly reliant on densely sampled images under static illumination conditions, which is prohibitively expensive and even impractical in real-world scenarios. In this paper, we propose a novel learning from Sparse views under Unconstrained illuminations Relightable 3D Gaussian Splatting (dubbed SU-RGS), to address this challenge by jointly optimizing 3DGS representations, surface materials, and environment illuminations (i.e., unknown and various lighting conditions in training) using only sparse input views. Firstly, SU-RGS presents a varying appearance rendering strategy, enabling each 3D Gaussian can perform inconsistent color under various lightings. Next, SU-RGS establishes the multi-view semantic consistency by constructing hierarchical semantics pseudo-labels across inter-views, to compensate for extra supervisions and facilitate sparse inverse rendering for confronting unconstrained illuminations. Additionally, we introduce an adaptive transient object perception component that integrates the scene geometry and semantics in a fine-grained manner, to quantify and eliminate the uncertainty of the foreground. Extensive experiments on both synthetic and real-world challenging datasets demonstrate the effectiveness of SU-RGS, achieving the state-of-the-art performance for scene inverse rendering by learning 3DGS from only sparse views under unconstrained illuminations.