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Probabilistic Methods · Everything Else

Themistoklis Haris, Fabian Spaeh, Spyridon Konstantinos Dragazis, Charalampos Tsourakakis

Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network centrality analysis, ranking and recommendation systems, and epidemiology. In this work, we develop local algorithms for estimating hitting times between a pair of vertices $u,v$ without accessing the full graph, overcoming scalability issues of prior global methods. Our first algorithm uses the key insight that hitting time computations can be truncated at the meeting time of two independent random walks from $u$ and $v$. This leads to an efficient estimator analyzed via the Kronecker product graph and Markov Chain Chernoff bounds. We also present an algorithm extending the work of Peng et al. [2021] that introduces a novel adaptation of the spectral cutoff technique to account for the asymmetry of hitting times. This adaptation captures the directionality of the underlying random walk and requires non-trivial modifications to ensure accuracy and efficiency. In addition to the algorithmic upper bounds, we also provide tight asymptotic lower bounds. Finally, we reveal a connection between hitting time estimation and distribution testing, and we validate our algorithms using experiments on both real and synthetic data.

General Machine Learning · Representation Learning

Ziwen Wang, Jiajun Fan, Thao Nguyen, Heng Ji, Ge Liu

Contrastive learning has proven to be highly efficient and adaptable in shaping representation spaces across diverse modalities by pulling similar samples together and pushing dissimilar ones apart. However, two key limitations persist: (1) Without explicit regulation of the embedding distribution, semantically related instances can inadvertently be pushed apart unless complementary signals guide pair selection, and (2) excessive reliance on large in-batch negatives and tailored augmentations hinders generalization. To address these limitations, we propose Variational Supervised Contrastive Learning (VarCon), which reformulates supervised contrastive learning as variational inference over latent class variables and maximizes a posterior-weighted evidence lower bound (ELBO) that replaces exhaustive pair-wise comparisons for efficient class-aware matching and grants fine-grained control over intra-class dispersion in the embedding space. Trained exclusively on image data, our experiments on CIFAR-10, CIFAR-100, ImageNet-100, and ImageNet-1K show that VarCon (1) achieves state-of-the-art performance for contrastive learning frameworks, reaching 79.36% Top-1 accuracy on ImageNet-1K and 78.29% on CIFAR-100 with a ResNet-50 encoder while converging in just 200 epochs; (2) yields substantially clearer decision boundaries and semantic organization in the embedding space, as evidenced by KNN classification, hierarchical clustering results, and transfer-learning assessments; and (3) demonstrates superior performance in few-shot learning than supervised baseline and superior robustness across various augmentation strategies.

Applications · Robotics

Yanping Fu, Xinyuan Liu, Tianyu Li, Yike Ma, Yucheng Zhang, Feng Dai

Topology reasoning, which unifies perception and structured reasoning, plays a vital role in understanding intersections for autonomous driving. However, its performance heavily relies on the accuracy of lane detection, particularly at connected lane endpoints. Existing methods often suffer from lane endpoints deviation, leading to incorrect topology construction. To address this issue, we propose TopoPoint, a novel framework that explicitly detects lane endpoints and jointly reasons over endpoints and lanes for robust topology reasoning. During training, we independently initialize point and lane query, and proposed Point-Lane Merge Self-Attention to enhance global context sharing through incorporating geometric distances between points and lanes as an attention mask . We further design Point-Lane Graph Convolutional Network to enable mutual feature aggregation between point and lane query. During inference, we introduce Point-Lane Geometry Matching algorithm that computes distances between detected points and lanes to refine lane endpoints, effectively mitigating endpoint deviation. Extensive experiments on the OpenLane-V2 benchmark demonstrate that TopoPoint achieves state-of-the-art performance in topology reasoning (48.8 on OLS). Additionally, we propose DET$_p$ to evaluate endpoint detection, under which our method significantly outperforms existing approaches (52.6 v.s. 45.2 on DET$_p$). The code is released at https://github.com/Franpin/TopoPoint.

Applications · Chemistry and Drug Discovery

Yihan Zhu, Gang Liu, Eric Inae, Tengfei Luo, Meng Jiang

Polymers are large macromolecules composed of repeating structural units known as monomers and are widely applied in fields such as energy storage, construction, medicine, and aerospace. However, existing graph neural network methods, though effective for small molecules, only model the single unit of polymers and fail to produce consistent vector representations for the true polymer structure with varying numbers of units. To address this challenge, we introduce Graph Repetition Invariance (GRIN), a novel method to learn polymer representations that are invariant to the number of repeating units in their graph representations. GRIN integrates a graph-based maximum spanning tree alignment with repeat-unit augmentation to ensure structural consistency. We provide theoretical guarantees for repetition‐invariance from both model and data perspectives, demonstrating that three repeating units are the minimal augmentation required for optimal invariant representation learning. GRIN outperforms state-of-the-art baselines on both homopolymer and copolymer benchmarks, learning stable, repetition-invariant representations that generalize effectively to polymer chains of unseen sizes.

Applications · Everything Else

Yang Zhao, Pu Wang, Hao Frank Yang

Designing optimal prompts and reasoning processes for large language models (LLMs) on domain-specific tasks is both necessary and challenging in real-world applications. Determining how to integrate domain knowledge, enhance reasoning efficiency, and even provide domain experts with refined knowledge integration hints are particularly crucial yet unresolved tasks. In this research, we propose Evolutionary Graph Optimization for Prompting (EGO-Prompt), an automated framework to designing better prompts, efficient reasoning processes and providing enhanced causal-informed process. EGO-Prompt begins with a general prompt and fault-tolerant initial Semantic Causal Graph (SCG) descriptions, constructed by human experts, which is then automatically refined and optimized to guide LLM reasoning. Recognizing that expert-defined SCGs may be partial or imperfect and that their optimal integration varies across LLMs, EGO-Prompt integrates a novel causal-guided textual gradient process in two steps: first, generating nearly deterministic reasoning guidance from the SCG for each instance, and second, adapting the LLM to effectively utilize the guidance alongside the original input. The iterative optimization algorithm further refines both the SCG and the reasoning mechanism using textual gradients with ground-truth. We tested the framework on real-world public health, transportation and human behavior tasks. EGO-Prompt achieves 7.32\%–12.61\% higher F1 than cutting-edge methods, and allows small models to reach the performence of larger models at under 20\% of the original cost. It also outputs a refined, domain-specific SCG that improves interpretability.

Computer Vision · Vision Models & Multimodal

Tianhe Wu, Jian Zou, Jie Liang, Lei Zhang, Kede Ma

DeepSeek-R1 has demonstrated remarkable effectiveness in incentivizing reasoning and generalization capabilities of large language models (LLMs) through reinforcement learning. Nevertheless, the potential of reasoning-induced computation has not been thoroughly explored in the context of image quality assessment (IQA), a task depending critically on visual reasoning. In this paper, we introduce VisualQuality-R1, a reasoning-induced no-reference IQA (NR-IQA) model, and we train it with reinforcement learning to rank, a learning algorithm tailored to the intrinsically relative nature of visual quality. Specifically, for a pair of images, we employ group relative policy optimization to generate multiple quality scores for each image. These estimates are used to compute comparative probabilities of one image having higher quality than the other under the Thurstone model. Rewards for each quality estimate are defined using continuous fidelity measures rather than discretized binary labels. Extensive experiments show that the proposed VisualQuality-R1 consistently outperforms discriminative deep learning-based NR-IQA models as well as a recent reasoning-induced quality regression method. Moreover, VisualQuality-R1 is capable of generating contextually rich, human-aligned quality descriptions, and supports multi-dataset training without requiring perceptual scale realignment. These features make VisualQuality-R1 especially well-suited for reliably measuring progress in a wide range of image processing tasks like super-resolution and image generation.

Deep Learning · Graph Neural Networks

Kai Wang, Siqiang Luo, Caihua Shan, Yifei Shen

Inspired by the success of large language models, there is a trend toward developing graph foundation models to conduct diverse downstream tasks in various domains. However, current models often require extra fine-tuning to apply their learned structural and semantic representations to new graphs, which limits their versatility. Recent breakthroughs in zero-shot inductive reasoning on knowledge graphs (KGs), offer us a new perspective on extending KG reasoning to general graph applications. In this paper, we introduce SCR, a unified graph reasoning framework designed to train on knowledge graphs and effectively generalize across a wide range of graph tasks and domains. We begin by designing the task-specific KG structures to establish a unified topology for different task formats. Then we propose semantic-conditioned message passing, a novel mechanism addressing the inherent semantic isolation in traditional KG reasoning, by jointly modeling structural and semantic invariance patterns in graph representations. Evaluated on 38 diverse datasets spanning node-, link-, and graph-level tasks, SCR achieves substantial performance gains over existing foundation models and supervised baselines, demonstrating its remarkable efficacy and adaptability.

General Machine Learning · Causality

Dominik Meier, Sujai Hiremath, PROMIT GHOSAL, Kyra Gan

Distinguishing cause and effect from bivariate observational data is a foundational problem in many disciplines, but challenging without additional assumptions. Additive noise models (ANMs) are widely used to enable sample-efficient bivariate causal discovery. However, conventional ANM-based methods fail when unobserved mediators corrupt the causal relationship between variables. This paper makes three key contributions: first, we rigorously characterize why standard ANM approaches break down in the presence of unmeasured mediators. Second, we demonstrate that prior solutions for hidden mediation are brittle in finite sample settings, limiting their practical utility. To address these gaps, we propose Bivariate Denoising Diffusion (BiDD) for causal discovery, a method designed to handle latent noise introduced by unmeasured mediators. Unlike prior methods that infer directionality through mean squared error loss comparisons, our approach introduces a novel independence test statistic: during the noising and denoising processes for each variable, we condition on the other variable as input and evaluate the independence of the predicted noise relative to this input. We prove asymptotic consistency of BiDD under the ANM, and conjecture that it performs well under hidden mediation. Experiments on synthetic and real-world data demonstrate consistent performance, outperforming existing methods in mediator-corrupted settings while maintaining strong performance in mediator-free settings.

Applications

Zhenyu Pan, Yucheng Lu, Han Liu

We present MetaFind, a scene-aware multi-modal retrieval framework designed to enhance scene generation in the metaverse by retrieving 3D assets from large-scale repositories. MetaFind addresses two core challenges: (i) inconsistent asset retrieval that overlooks spatial, semantic, and stylistic constraints, and (ii) the absence of a standardized retrieval paradigm specifically tailored for 3D asset retrieval, as existing approaches predominantly rely on general-purpose 3D shape representation models. Our key innovation is a retrieval mechanism that enhances both spatial reasoning and style consistency by jointly modeling object-level features (including appearance) and scene-level layout structures. Methodologically, MetaFind introduces a plug-and-play layout encoder that captures both spatial relationships and object appearance features, ensuring retrieved 3D assets are contextually and stylistically coherent with the existing scene. The framework supports iterative scene construction by continuously adapting retrieval results to current scene updates. Empirical evaluations demonstrate the improved spatial and stylistic consistency of MetaFind in various retrieval tasks compared to baseline methods.

Computer Vision · 3D Rendering & Reconstruction

Aly El Hakie, Yiren Lu, Yu Yin, Michael Jenkins, Yehe Liu

Opaque objects reconstructed by 3D Gaussian Splatting (3DGS) often exhibit a falsely transparent surface, leading to inconsistent background and internal patterns under camera motion in interactive viewing. This issue stems from the ill-posed optimization in 3DGS. During training, background and foreground Gaussians are blended via $\alpha$-compositing and optimized solely against the input RGB images using a photometric loss. As this process lacks an explicit constraint on surface opacity, the optimization may incorrectly assign transparency to opaque regions, resulting in view-inconsistent and falsely transparent output. This issue is difficult to detect in standard evaluation settings (i.e., rendering static images), but becomes particularly evident in object-centric reconstructions under interactive viewing. Although other causes of view-inconsistency, such as popping artifacts, have been explored previously, false transparency has not been explicitly identified. To the best of our knowledge, we are the first to quantify, characterize, and develop solutions for this "false transparency" artifact, an under-reported artifact in 3DGS. Our strategy, Noise Guided Splatting (NGS), encourages surface Gaussians to adopt higher opacity by injecting opaque noise Gaussians in the object volume during training, requiring only minimal modifications to the existing splatting process. To quantitatively evaluate false transparency in static renderings, we propose a novel transmittance-based metric that measures the severity of this artifact. In addition, we introduce a customized, high-quality object-centric scan dataset exhibiting pronounced transparency issues, and we augment popular existing datasets (e.g., DTU) with complementary infill noise specifically designed to assess the robustness of 3D reconstruction methods to false transparency. Experiments across multiple datasets show that NGS substantially reduces false transparency while maintaining competitive performance on standard rendering metrics (e.g., PSNR), demonstrating its overall effectiveness.

Applications · Everything Else

Yibo Zhao, Yang Zhao, Hongru Du, Hao Frank Yang

Decision-making models for individuals, particularly in high-stakes scenarios like vaccine uptake, often diverge from population optimal predictions. This gap arises from the uniqueness of the individual decision-making process, shaped by numerical attributes (e.g., cost, time) and linguistic influences (e.g., personal preferences and constraints). Developing upon Utility Theory and leveraging the textual-reasoning capabilities of Large Language Models (LLMs), this paper proposes an Adaptive Textual-symbolic Human-centric Reasoning framework (ATHENA) to address the optimal information integration. ATHENA uniquely integrates two stages: First, it discovers robust, group-level symbolic utility functions via LLM-augmented symbolic discovery; Second, it implements individual-level semantic adaptation, creating personalized semantic templates guided by the optimal utility to model personalized choices. Validated on real-world travel mode and vaccine choice tasks, ATHENA consistently outperforms utility-based, machine learning, and other LLM-based models, lifting F1 score by at least 6.5\% over the strongest cutting-edge models. Further, ablation studies confirm that both stages of ATHENA are critical and complementary, as removing either clearly degrades overall predictive performance. By organically integrating symbolic utility modeling and semantic adaptation, ATHENA provides a new scheme for modeling human-centric decisions. The project page can be found at https://yibozh.github.io/Athena.

Computer Vision · Classification and Understanding

Yanghao Wang, Long Chen

Although today's pretrained discriminative vision-language models (e.g., CLIP) have demonstrated strong perception abilities, such as zero-shot image classification, they also suffer from the bag-of-words problem and spurious bias. To mitigate these problems, some pioneering studies leverage powerful generative models (e.g., pretrained diffusion models) to realize generalizable image classification, dubbed Diffusion Classifier (DC). Specifically, by randomly sampling a Gaussian noise, DC utilizes the differences of denoising effects with different category conditions to classify categories. Unfortunately, an inherent and notorious weakness of existing DCs is noise instability: different random sampled noises lead to significant performance changes. To achieve stable classification performance, existing DCs always ensemble the results of hundreds of sampled noises, which significantly reduces the classification speed. To this end, we firstly explore the role of noise in DC, and conclude that: there are some ``good noises'' that can relieve the instability. Meanwhile, we argue that these good noises should meet two principles: 1) Frequency Matching: noise should destroy the specific frequency signals; 2) Spatial Matching: noise should destroy the specific spatial areas. Regarding both principles, we propose a novel Noise Optimization method to learn matching (i.e., good) noise for DCs: NoOp. For frequency matching, NoOp first optimizes a dataset-specific noise: Given a dataset and a timestep $t$, optimize one randomly initialized parameterized noise. For Spatial Matching, NoOp trains a Meta-Network that adopts an image as input and outputs image-specific noise offset. The sum of optimized noise and noise offset will be used in DC to replace random noise. Extensive ablations on various datasets demonstrated the effectiveness of NoOp. It is worth noting that our noise optimization is orthogonal to existing optimization methods (e.g., prompt tuning), our NoOP can even benefit from these methods to further boost performance.

Yi-Kai Zhang, Shiyin Lu, Qingguo Chen, Weihua Luo, De-Chuan Zhan, Han-Jia Ye

Recently, test-time scaling of Large Language Models (LLMs) has emerged as a practical alternative to parameter and data scaling. Reasoning tasks often require large-scale, RLVR-based LLMs, while more economical LLMs can handle simpler tasks. Routing an LLM tailored to *suitability* (*i.e.*, capability and cost) ensures usability and efficiency. We introduce LLMRec, which routes the most suitable LLM to the user query without pre-inference on the candidate LLM zoo. It pioneeringly reframes the LLM routing problem as a comprehensive recommendation system (RecSys) task. Our core insight is that an LLM's suitability for a query is a complex, latent signal equal to user-item preference. LLMRec systematically engineers features for candidate LLMs (intrinsic attributes and capability distributions), queries (general semantics and meta-dimensional info), and context (inference type, cost budgets). It also incorporates behavioral features to learn high-order interactions. LLMRec is designed to generalize to out-of-domain datasets and adapt to new LLMs as the model zoo evolves. We define the metric with the Pareto frontier under user-specified cost budgets. Across six datasets, LLMRec achieves an average cost reduction of over 38% while maintaining accuracy and consistently outperforming baselines in converging toward the Pareto frontier.

Applications · Physics

Ziyu Xiang, Kenna Ashen, Xiaofeng Qian, Xiaoning Qian

Symbolic regression (SR) seeks interpretable analytical expressions that uncover the governing relationships within data, providing mechanistic insight beyond 'black-box' models. However, existing SR methods often suffer from two key limitations: (1) *redundant representations* that fail to capture mathematical equivalences and higher-order operand relations, breaking permutation invariance and hindering efficient learning; and (2) *sparse rewards* caused by incomplete incorporation of constraints that can only be evaluated on full expressions, such as constant fitting or physical-law verification. To address these challenges, we propose a unified framework, **Graph-based Symbolic Regression (GSR)**, which compresses the search space through a permutation-invariant representation, Expression Graphs (EGs), that intrinsically encode expression equivalences via a term-rewriting system (TRS) and a directed acyclic graph (DAG) structure; and mitigates reward sparsity via employing hybrid neural-guided Monte-Carlo tree search (hnMCTS) on EGs, where the constraint-informed neural guidance enables direct incorporation of expression-level constraint priors, and an adaptive $\epsilon$-UCB policy balances exploration and exploitation. Theoretical analyses establish the uniqueness of our proposed EG representation and the convergence of the hnMCTS algorithm. Experiments on synthetic and real-world scientific datasets demonstrate the efficiency and accuracy of GSR in discovering underlying expressions and adhering to physical laws, offering practical solutions for scientific discovery.

Junyoung Park, Dalton Jones, Matthew Morse, Raghavv Goel, Mingu Lee, Christopher Lott

We demonstrate that geometrically distinctive keys during LLM inference tend to have high attention scores. Based on the phenomenon we propose KeyDiff, a training-free KV cache eviction method based solely on key similarity. Unlike other KV cache eviction methods, KeyDiff can process arbitrarily long prompts within strict resource constraints and efficiently generate responses. We provide a theoretical basis for KeyDiff by relating key diversity with attention scores. These results imply KeyDiff can efficiently identify the most important tokens to retain. Notably KeyDiff does not rely on attention scores, allowing the use of optimized attention mechanisms like FlashAttention. Under a strict memory allowance, we demonstrate the effectiveness of KeyDiff for the Llama and Qwen model families by observing a performance gap of less than 0.04\% with 8K cache budget (~23\% KV cache reduction) from the non-evicting baseline on LongBench for Llama 3.1-8B and Llama 3.2-3B. We also observe near baseline performance for Deepseek-R1-Distill-Llama-8B on the Math500 reasoning benchmark and decrease end-to-end inference latency by up to 30\% compared to the other token-eviction methods.

Optimization · Optimization and Learning under Uncertainty

Christopher Yeh, Nicolas Christianson, Adam Wierman, Yisong Yue

While deep learning models often achieve high predictive accuracy, their predictions typically do not come with any provable guarantees on risk or reliability, which are critical for deployment in high-stakes applications. The framework of conformal risk control (CRC) provides a distribution-free, finite-sample method for controlling the expected value of any bounded monotone loss function and can be conveniently applied post-hoc to any pre-trained deep learning model. However, many real-world applications are sensitive to tail risks, as opposed to just expected loss. In this work, we develop a method for controlling the general class of Optimized Certainty-Equivalent (OCE) risks, a broad class of risk measures which includes as special cases the expected loss (generalizing the original CRC method) and common tail risks like the conditional value-at-risk (CVaR). Furthermore, standard post-hoc CRC can degrade average-case performance due to its lack of feedback to the model. To address this, we introduce "conformal risk training," an end-to-end approach that differentiates through conformal OCE risk control _during model training or fine-tuning_. Our method achieves provable risk guarantees while demonstrating significantly improved average-case performance over post-hoc approaches on applications to controlling classifiers' false negative rate and controlling financial risk in battery storage operation.

Theory · Learning Theory

Weikuo Wang, Yue Liao, Huan Luo

A major problem of kernel-based methods (e.g., least squares support vector machines, LS-SVMs) for solving linear/nonlinear ordinary differential equations (ODEs) is the prohibitive $O(an^3)$ ($a=1$ for linear ODEs and 27 for nonlinear ODEs) part of their computational complexity with increasing temporal discretization points $n$. We propose a novel Nyström-accelerated LS-SVMs framework that breaks this bottleneck by reformulating ODEs as primal-space constraints. Specifically, we derive for the first time an explicit Nyström-based mapping and its derivatives from one-dimensional temporal discretization points to a higher $m$-dimensional feature space ($1< m\le n$), enabling the learning process to solve linear/nonlinear equation systems with $m$-dependent complexity. Numerical experiments on sixteen benchmark ODEs demonstrate: 1) $10-6000$ times faster computation than classical LS-SVMs and physics-informed neural networks (PINNs), 2) comparable accuracy to LS-SVMs ($<0.13\%$ relative MAE, RMSE, and $\left \| y-\hat{y} \right \| _{\infty } $difference) while maximum surpassing PINNs by 72\% in RMSE, and 3) scalability to $n=10^4$ time steps with $m=50$ features. This work establishes a new paradigm for efficient kernel-based ODEs learning without significantly sacrificing the accuracy of the solution.

Probabilistic Methods · Everything Else

Emile van Krieken, Pasquale Minervini, Edoardo Maria Ponti, Antonio Vergari

Neurosymbolic (NeSy) predictors combine neural perception with symbolic reasoning to solve tasks like visual reasoning. However, standard NeSy predictors assume conditional independence between the symbols they extract, thus limiting their ability to model interactions and uncertainty --- often leading to overconfident predictions and poor out-of-distribution generalisation. To overcome the limitations of the independence assumption, we introduce _neurosymbolic diffusion models_ (NeSyDMs), a new class of NeSy predictors that use discrete diffusion to model dependencies between symbols. Our approach reuses the independence assumption from NeSy predictors at each step of the diffusion process, enabling scalable learning while capturing symbol dependencies and uncertainty quantification. Across both synthetic and real-world benchmarks — including high-dimensional visual path planning and rule-based autonomous driving — NeSyDMs achieve state-of-the-art accuracy among NeSy predictors and demonstrate strong calibration.

Probabilistic Methods · Bayesian Models and Methods

Russell Tsuchida, Jiawei Liu, Cheng Soon Ong, Dino Sejdinovic

Squared families of probability distributions have been studied and applied in numerous machine learning contexts. Typically, they appear as likelihoods, where their advantageous computational, geometric and statistical properties are exploited for fast estimation algorithms, representational properties and statistical guarantees. Here, we investigate the use of squared families as prior beliefs in Bayesian inference. We find that they can form helpful conjugate families, often allowing for closed-form and tractable Bayesian inference and marginal likelihoods. We apply such conjugate families to Bayesian regression in feature space using end-to-end learnable neural network features. Such a setting allows for a rich multi-modal alternative to Gaussian processes with neural network features, often called deep kernel learning. We demonstrate our method on few shot learning, outperforming existing neural methods based on Gaussian processes and normalising flows.

Computer Vision · 3D Rendering & Reconstruction

Hyeongmin Lee, Kyungjune Baek

Dynamic 4D Gaussian Splatting (4DGS) effectively extends the high-speed rendering capabilities of 3D Gaussian Splatting (3DGS) to represent volumetric videos. However, the large number of Gaussians, substantial temporal redundancies, and especially the absence of an entropy-aware compression framework result in large storage requirements. Consequently, this poses significant challenges for practical deployment, efficient edge-device processing, and data transmission. In this paper, we introduce a novel end-to-end RD-optimized compression framework tailored for 4DGS, aiming to enable flexible, high-fidelity rendering across varied computational platforms. Leveraging Fully Explicit Dynamic Gaussian Splatting (Ex4DGS), one of the state-of-the-art 4DGS methods, as our baseline, we start from the existing 3DGS compression methods for compatibility while effectively addressing additional challenges introduced by the temporal axis. In particular, instead of storing motion trajectories independently per point, we employ a wavelet transform to reflect the real-world smoothness prior, significantly enhancing storage efficiency. This approach yields significantly improved compression ratios and provides a user-controlled balance between compression efficiency and rendering quality. Extensive experiments demonstrate the effectiveness of our method, achieving up to 91$\times$ compression compared to the original Ex4DGS model while maintaining high visual fidelity. These results highlight the applicability of our framework for real-time dynamic scene rendering in diverse scenarios, from resource-constrained edge devices to high-performance environments. The source code is available at https://github.com/HyeongminLEE/RD4DGS.