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Duy-Tho Le, Trung Pham, Jianfei Cai, Hamid Rezatofighi

Optimizing the similarity between parametric shapes is crucial for numerous computer vision tasks, where Intersection over Union (IoU) stands as the canonical measure. However, existing optimization methods exhibit significant shortcomings: regression-based losses like L1/L2 lack correlation with IoU, IoU-based losses are unstable and limited to simple shapes, and task-specific methods are computationally intensive and not generalizable across domains. As a result, the current landscape of parametric shape objective functions has become scattered, with each domain proposing distinct IoU approximations. To address this, we unify the parametric shape optimization objective functions by introducing Marginalized Generalized IoU (MGIoU), a novel loss function that overcomes these challenges by projecting structured convex shapes onto their unique shape Normals to compute one-dimensional normalized GIoU. MGIoU offers a simple, efficient, fully differentiable approximation strongly correlated with IoU. We extend MGIoU to MGIoU+ that supports optimizing unstructured convex shapes. Together, MGIoU and MGIoU+ unify parametric shape optimization across diverse applications. Experiments on standard benchmarks demonstrate that MGIoU and MGIoU+ demonstrate higher performance while reducing loss computation latency up to 10-40x. Also, MGIoU and MGIoU+ satisfy metric properties and scale-invariance, ensuring robustness as an objective function. We further propose MGIoU- for minimizing overlaps in tasks like collision-free trajectory prediction.

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.

Ziwei Zhang, Zhao Li, Zhuojun Jiang, Jiangyi Yin, Xuebin Wang, Jiangchao Chen, Qingyun Liu

Stringent regulations like General Data Protection Regulation (GDPR) mandate that an application's code-level data handling must align with its natural-language privacy policy, creating a critical auditing challenge. However, existing methods, predominantly reliant on static analysis, suffer from a critical limitation: in their pursuit of soundness via over-approximation, they exhibit "semantic blindness"—detecting what data flows exist but not why. This leads to an overwhelming volume of false positives, rendering automated auditing impractical. To bridge this gap, we introduce PriAgent, a novel framework that approaches compliance auditing as a multi-stage, AI-driven reasoning task. Instead of a monolithic model, PriAgent deploys a team of specialized agents that execute a divide-and-conquer strategy. They systematically prune the analysis space by abstracting data flows, pinpoint semantic loci critical for inspection, and perform on-demand summarization of large code blocks to ensure scalability. PriAgent leverages Retrieval-Augmented Generation (RAG) with a curated knowledge base of Android APIs, equipping agents to discern potentially non-compliant behavior from benign functionality. By correlating code-level evidence with the app's stated privacy policy, PriAgent delivers a holistic and explainable verdict for each potential violation. Our evaluations demonstrate that PriAgent significantly reduces false positives, enabling a more scalable and precise compliance audit.

Jiahao Wang, Shuangjia Zheng

The ability to engineer optimized protein variants has transformative potential for biotechnology and medicine. Prior sequence-based optimization methods struggle with the high-dimensional complexities due to the epistasis effect and the disregard for structural constraints. To address this, we propose HADES, a Bayesian optimization method utilizing Hamiltonian dynamics to efficiently sample from a structure-aware approximated posterior. Leveraging momentum and uncertainty in the simulated physical movements, HADES enables rapid transition of proposals toward promising areas. A position discretization procedure is introduced to propose discrete protein sequences from such continuous state system. The posterior surrogate is powered by a two-stage encoder-decoder framework to determine the structure and function relationships between mutant neighbors, consequently learning a smoothed landscape to sample from. Extensive experiments demonstrate that our method outperforms state-of-the-art baselines in in-silico evaluations across most metrics. Remarkably, our approach offers a unique advantage by leveraging the mutual constraints between protein structure and sequence, facilitating the design of protein sequences with similar structures and optimized properties.

Yuancheng Sun, Yuxuan Ren, Zhaoming Chen, Xu Han, Kang Liu, Qiwei Ye

Accurate exploration of protein conformational ensembles is essential for uncovering function but remains hard because molecular-dynamics (MD) simulations suffer from high computational costs and energy-barrier trapping. This paper presents Energy Preference Optimization (EPO), an online refinement algorithm that turns a pretrained protein ensemble generator into an energy-aware sampler without extra MD trajectories. Specifically, EPO leverages stochastic differential equation sampling to explore the conformational landscape and incorporates a novel energy-ranking mechanism based on list-wise preference optimization. Crucially, EPO introduces a practical upper bound to efficiently approximate the intractable probability of long sampling trajectories in continuous-time generative models, making it easily adaptable to existing pretrained generators. On Tetrapeptides, ATLAS, and Fast-Folding benchmarks, EPO successfully generates diverse and physically realistic ensembles, establishing a new state-of-the-art in nine evaluation metrics. These results demonstrate that energy-only preference signals can efficiently steer generative models toward thermodynamically consistent conformational ensembles, providing an alternative to long MD simulations and widening the applicability of learned potentials in structural biology and drug discovery.

Andrzej Mizera, Jakub Zarzycki

Cellular reprogramming, the artificial transformation of one cell type into another, has been attracting increasing research attention due to its therapeutic potential for complex diseases. However, identifying effective reprogramming strategies through classical wet-lab experiments is hindered by long time commitments and high costs. Although computational methods have been proposed to address this challenge, exact state-of-the-art techniques suffer from limited scalability owing to the notorious state space explosion problem. To overcome this limitation, we explore deep reinforcement learning (DRL) for controlling holistic Boolean network models of complex biological systems, such as gene regulatory and signalling pathway networks. We formulate a novel control problem for Boolean network models operating under the asynchronous update mode, specifically tailored to the context of cellular reprogramming. To solve it, we devise GATTACA - a DRL-based computational framework explicitly designed for scalability, capable of handling large and complex network models where exact methods fail. To facilitate scalability of our framework, we consider our previously introduced concept of a pseudo-attractor and improve the procedure for effective identification of pseudo-attractor states. We incorporate graph neural networks with graph convolution operations into the artificial neural network approximator of the DRL agent's action-value function. The new architecture allows us to leverage the available knowledge on the structure of a biological system and to indirectly, yet effectively, encode the system's dynamics into a latent representation. Experiments on several large-scale, real-world biological networks from the literature demonstrate the scalability and effectiveness of our approach.

Ziwei Li, Shuzi Niu, Tao Yuan, Huiyuan Li, Wenjia Wu

Fill-ins are new nonzero elements in the summation of the upper and lower triangular factors generated during LU factorization. For large sparse matrices, they will increase the memory usage and computational time, and be reduced through proper row or column arrangement, namely matrix reordering. Finding a row or column permutation with the minimal fill-ins is NP-hard, and surrogate objectives are designed to derive fill-in reduction permutations or learn a reordering function. However, there is no theoretical guarantee between the golden criterion and these surrogate objectives. Here we propose to learn a reordering network by minimizing l1 norm of triangular factors of the reordered matrix to approximate the exact number of fill-ins. The reordering network utilizes a graph encoder to predict row or column node scores. For inference, it is easy and fast to derive the permutation from sorting algorithms for matrices. For gradient based optimization, there is a large gap between the predicted node scores and resultant triangular factors in the optimization objective. To bridge the gap, we first design two reparameterization techniques to obtain the permutation matrix from node scores. The matrix is reordered by multiplying the permutation matrix. Then we introduce the factorization process into the objective function to arrive at target triangular factors. The overall objective function is optimized with the alternating direction method of multipliers and proximal gradient descent. Experimental results on benchmark sparse matrix collection SuiteSparse show the fill-in and LU factorization time reduction of our proposed method is 0.2% and 17.8% compared with state-of-the-art baselines.

Noam Koren, Ralf J. J. Mackenbach, Ruud J. G. Van Sloun, Kira Radinsky, Daniel Freedman

Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equations (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong assumptions about the structure of the kernel integral operator, assumptions which may limit expressivity. We present SVD-NO, a neural operator that explicitly parameterizes the kernel by its singular-value decomposition (SVD) and then carries out the integral directly in the low-rank basis. Two lightweight networks learn the left and right singular functions, a diagonal parameter matrix learns the singular values, and a Gram-matrix regularizer enforces orthonormality. As SVD-NO approximates the full kernel, it obtains a high degree of expressivity. Furthermore, due to its low-rank structure the computational complexity of applying the operator remains reasonable, leading to a practical system. In extensive evaluations on five diverse benchmark equations, SVD-NO achieves a new state of the art. In particular, SVD-NO provides greater performance gains on PDEs whose solutions are highly spatially variable.

Heasung Kim, Taekyun Lee, Hyeji Kim, Gustavo De Veciana

Weighted sampling--sampling from a probability density function (PDF) proportional to the product of a base PDF and a weight function--is a fundamental technique with wide-ranging applications in variance reduction, biased sampling, data augmentation, and more. Leveraging the increasing availability of pretrained score-based generative models (SGMs), we propose a training-free weighted sampling framework that approximates the backward diffusion process of the target distribution by augmenting the pretrained base score function with an auxiliary guidance term, in a principled and computationally efficient manner. Our approach builds on two key components: a lightweight approximation of the guidance that avoids costly higher-order derivatives of both the score and weight functions, and an uncertainty-aware scheduler that dynamically adjusts the guidance strength based on a temporal analysis of approximation error. Together, these components enable accurate and stable sampling without relying on particle-based resampling or Hessian evaluations commonly required by existing methods. We validate the effectiveness of our method from synthetic to large-scale settings such as Stable Diffusion XL, where our framework achieves 1.2xto 4.7xspeedups while consistently matching or outperforming state-of-the-art baselines in task performance. These results position our method as a scalable and inference-efficient solution for task-adaptive, time-sensitive sampling in generative applications.

Qing Zhou, Bingxuan Zhao, Tao Yang, Hongyuan Zhang, Junyu Gao, Qi Wang

Dynamic data pruning accelerates deep learning by selectively omitting less informative samples during training. While per-sample loss is a common importance metric, obtaining it can be challenging or infeasible for complex models or loss functions, often requiring significant implementation effort. This work proposes the Batch Loss Score (BLS), a computationally efficient alternative using an Exponential Moving Average (EMA) of readily available batch losses to assign scores to individual samples. We frame the batch loss, from the perspective of a single sample, as a noisy measurement of its scaled individual loss, with noise originating from stochastic batch composition. It is formally shown that the EMA mechanism functions as a first-order low-pass filter, attenuating high-frequency batch composition noise. This yields a score approximating the smoothed and persistent contribution of the individual sample to the loss, providing a theoretical grounding for BLS as a proxy for sample importance. BLS demonstrates remarkable code integration simplicity (three-line injection) and readily adapts existing per-sample loss-based methods (one-line proxy). Its effectiveness is demonstrated by enhancing two such methods to losslessly prune 20%-50% of samples across 14 datasets, 11 tasks and 18 models, highlighting its utility and broad applicability, especially for complex scenarios where per-sample loss is difficult to access. Code is available at https://github.com/mrazhou/BLS.

Yiyang Lu, Qiao Sun, Xianbang Wang, Zhicheng Jiang, Hanhong Zhao, Kaiming He

Normalizing Flows (NFs) have been established as a principled framework for generative modeling. Standard NFs consist of a forward process and a reverse process: the forward process maps data to noise, while the reverse process generates samples by inverting it. Typical NF forward transformations are constrained by explicit invertibility, ensuring that the reverse process can serve as their exact analytic inverse. Recent developments in TARFlow and its variants have revitalized NF methods by combining Transformers and autoregressive flows, but have also exposed causal decoding as a major bottleneck. In this work, we introduce Bidirectional Normalizing Flow (BiFlow), a framework that removes the need for an exact analytic inverse. BiFlow learns a reverse model that approximates the underlying noise-to-data inverse mapping, enabling more flexible loss functions and architectures. Experiments on ImageNet demonstrate that BiFlow, compared to its causal decoding counterpart, improves generation quality while accelerating sampling by up to two orders of magnitude. BiFlow yields state-of-the-art results among NF-based methods and competitive performance among single-evaluation ("1-NFE") methods. Following recent encouraging progress on NFs, we hope our work will draw further attention to this classical paradigm.

Huajie Tan, Sixiang Chen, Yijie Xu, Zixiao Wang, Cheng Chi, Yuheng Ji, Yaoxu Lyu, Zhongxia Zhao, Xiansheng Chen, Peterson Co 等

The primary obstacle for applying reinforcement learning (RL) to real-world robotics is the design of effective reward functions. While recently learning-based Process Reward Models (PRMs) are a promising direction, they are often hindered by two fundamental limitations: their reward models lack step-aware understanding and rely on single-view perception, leading to unreliable assessments of fine-grained manipulation progress; and their reward shaping procedures are theoretically unsound, often inducing a semantic trap that misguides policy optimization. To address these, we introduce Dopamine-Reward, a novel reward modeling method for learning a general-purpose, step-aware process reward model from multi-view inputs. At its core is our General Reward Model (GRM), trained on a vast 3,400+ hour dataset, which leverages Step-wise Reward Discretization for structural understanding and Multi-Perspective Reward Fusion to overcome perceptual limitations. Building upon Dopamine-Reward, we propose Dopamine-RL, a robust policy learning framework that employs a theoretically-sound Policy-Invariant Reward Shaping method, which enables the agent to leverage dense rewards for efficient self-improvement without altering the optimal policy, thereby fundamentally avoiding the semantic trap. Extensive experiments across diverse simulated and real-world tasks validate our approach. GRM achieves state-of-the-art accuracy in reward assessment, and Dopamine-RL built on GRM significantly improves policy learning efficiency. For instance, after GRM is adapted to a new task in a one-shot manner from a single expert trajectory, the resulting reward model enables Dopamine-RL to improve the policy from near-zero to 95% success with only 150 online rollouts (approximately 1 hour of real robot interaction), while retaining strong generalization across tasks.

Xinyu Zhou, Jiawei Zhang, Stephen J. Wright

Diffusion models achieve remarkable generation quality, yet face a fundamental challenge known as memorization, where generated samples can replicate training samples exactly. We develop a theoretical framework to explain this phenomenon by showing that the empirical score function (the score function corresponding to the empirical distribution) is a weighted sum of the score functions of Gaussian distributions, in which the weights are sharp softmax functions. This structure causes individual training samples to dominate the score function, resulting in sampling collapse. In practice, approximating the empirical score function with a neural network can partially alleviate this issue and improve generalization. Our theoretical framework explains why: In training, the neural network learns a smoother approximation of the weighted sum, allowing the sampling process to be influenced by local manifolds rather than single points. Leveraging this insight, we propose two novel methods to further enhance generalization: (1) Noise Unconditioning enables each training sample to adaptively determine its score function weight to increase the effect of more training samples, thereby preventing single-point dominance and mitigating collapse. (2) Temperature Smoothing introduces an explicit parameter to control the smoothness. By increasing the temperature in the softmax weights, we naturally reduce the dominance of any single training sample and mitigate memorization. Experiments across multiple datasets validate our theoretical analysis and demonstrate the effectiveness of the proposed methods in improving generalization while maintaining high generation quality.

Qiang He, Yaozong Yang, Kaibin Wang, Ziteng Wei, Feifei Chen, Caslon Chua, Yun Yang

Visual models are deployed on many Internet-of-Things (IoT) devices to power a variety of visual applications at the network edge. These models often need to be fine-tuned on-device continually to adapt to changing operating environments timely. However, the computing and energy overheads incurred are often overwhelming for resource-constrained IoT devices. Existing methods score sample importance based on the entire model via multi-epoch training, incurring overhead that may even exceed the training overhead reduction. To reduce these fine-tuning overheads, this paper presents LoPrune, a novel data pruning method that identifies and removes samples with negligible contributions to model adaptation. The key idea is to evaluate sample importance via a Trainable Subspace Alignment (TSA) Score to align the importance estimation with accurate update directions of the learnable adapter, i.e., Low-Rank Adaptation (LoRA). Specifically, LoPrune projects the influence function onto the LoRA subspace, enforcing consistency between the importance score and the model's updatable directions while substantially reducing the problem's dimensionality. It then leverages Kronecker-Factored Approximate Curvature to approximate the change of learnable adapter induced by a sample as its TSA score, retaining higher-scoring samples. Experiments with four representative visual models fine-tuned on three datasets demonstrate that compared with the best state-of-the-art data pruning baselines, LoPrune can reduce fine-tuning overhead by up to 72.9%, achieving a 3.69 xtraining speedup while improving fine-tuning accuracy by 3.50%.

Merve Gulle, Junno Yun, Yasar Utku Alcalar, Mehmet Akcakaya

Diffusion models have found extensive use in solving inverse problems, by sampling from an approximate posterior distribution of data given the measurements. Recently, consistency models (CMs) have been proposed to directly predict the final output from any point on the diffusion ODE trajectory, enabling high-quality sampling in just a few neural function evaluations (NFEs). CMs have also been utilized for inverse problems, but existing CM-based solvers either require additional task-specific training or utilize data fidelity operations with slow convergence, limiting their applicability to large-scale problems and making them difficult to extend to nonlinear settings. In this work, we reinterpret CMs as proximal operators of a prior, enabling their integration into plug-and-play (PnP) frameworks. Specifically, we propose PnP-CM, an ADMM-based PnP solver that provides a unified framework for solving a wide range of inverse problems, and incorporates noise perturbations and momentum-based updates to improve performance in the low-NFE regime. We evaluate our approach on a diverse set of linear and nonlinear inverse problems. We also train and apply CMs to MRI data for the first time. Our results show that PnP-CM achieves high-quality reconstructions in as few as 4 NFEs, and produces meaningful results in 2 steps, highlighting its effectiveness in real-world inverse problems while outperforming existing CM-based approaches.

Jakob Paul Zimmermann, Georg Loho

It has been demonstrated in various contexts that monotonicity leads to better explainability in neural networks. However, not every function can be well approximated by a monotone neural network.We demonstrate that monotonicity can still be used in two ways to boost explainability. First, we use an adaptation of the decomposition of a trained ReLU network into two monotone and convex parts, thereby overcoming numerical obstacles from an inherent blowup of the weights in this procedure. Our proposed saliency methods -- SplitCAM and SplitLRP --improve onstate of the art results on both VGG16 and Resnet18 networks on ImageNet-S across all Quantus saliency metric categories.Second, we exhibit that training a model as the difference between two monotone neural networks results in a system with strong self-explainability properties.

ZeBin Ji, Yang Hu, Xiuli Bi, Bo Liu, Bin Xiao

It is essential for understanding neural network decisions to interpret the functionality (also known as concepts) of neurons. Existing approaches describe neuron concepts by generating natural language descriptions, thereby advancing the understanding of the neural network's decision-making mechanism. However, these approaches assume that each neuron has well-defined functions and provides discriminative features for neural network decision-making. In fact, some neurons may be redundant or may offer misleading concepts. Thus, the descriptions for such neurons may cause misinterpretations of the factors driving the neural network's decisions. To address the issue, we introduce a verification of neuron functions, which checks whether the generated concept highly activates the corresponding neuron. Furthermore, we propose a Select-Hypothesize-Verify framework for interpreting neuron functionality. This framework consists of: 1) selecting activation samples that best capture a neuron's well-defined functional behavior through activation-distribution analysis; 2) forming hypotheses about concepts for the selected neurons; and 3) verifying whether the generated concepts accurately reflect the functionality of the neuron. Extensive experiments show that our method produces more accurate neuron concepts. Our generated concepts activate the corresponding neurons with a probability approximately 1.5 times that of the current state-of-the-art method.

Youqi Pan, Wugen Zhou, Hongbin Zha

Although 3D Gaussian Splatting (3DGS) has achieved impressive performance in real-time rendering, its unordered Gaussians make level-of-detail (LoD) construction and model compression highly challenging, limiting its applicability in customized scenarios.In this work, we propose a learning-based Gaussian hierarchy representation that ranks Gaussians by their contribution to the scene, enabling flexible LoD representations across arbitrary Gaussian counts.We first introduce a unified, continuous formulation and metric for Gaussian hierarchy. Then, we introduce a hierarchy-based modulated rendering method built upon a Differentiable Decreasing Step Function, which enables efficient hierarchy learning while maintaining approximately equivalent rendering. Moreover, we develop a PDF-Guided Active-Region Sampling strategy that encourages the learned hierarchy to become widely distributed within its value range.Our method requires no additional training stages and produces Gaussian hierarchies within training time comparable to classical 3DGS. Experiments on multiple datasets show that our approach achieves performance comparable to or surpassing state-of-the-art methods in both LoD rendering and model pruning.

Roy Velich, Arkadi Piven, David Bensaïd, Daniel Cremers, Thomas Dagès, Ron Kimmel

We introduce a novel framework that directly learns a spectral basis for shape and manifold analysis from unstructured data, eliminating the need for traditional operator selection, discretization, and eigensolvers. Grounded in optimal-approximation theory, we train a network to decompose an implicit approximation operator by minimizing the reconstruction error in the learned basis over a chosen distribution of probe functions. For suitable distributions, they can be seen as an approximation of the Laplacian operator and its eigendecomposition, which are fundamental in geometry processing. Furthermore, our method recovers in a unified manner not only the spectral basis, but also the implicit metric's sampling density and the eigenvalues of the underlying operator. Notably, our unsupervised method makes no assumption on the data manifold, such as meshing or manifold dimensionality, allowing it to scale to arbitrary datasets of any dimension. On point clouds lying on surfaces in 3D and high-dimensional image manifolds, our approach yields meaningful spectral bases, that can resemble those of the Laplacian, without explicit construction of an operator. By replacing the traditional operator selection, construction, and eigendecomposition with a learning-based approach, our framework offers a principled, data-driven alternative to conventional pipelines. This opens new possibilities in geometry processing for unstructured data, particularly in high-dimensional spaces.

Shaoxuan He, Benlei Cui, Bukun Huang, Zhizeng Ye, Yunyun Sun, Longtao Huang, Hui Xue, Yang Yang, Haiwen Hong, Jingqun Tang 等

Despite achieving state-of-the-art generation quality, diffusion models are hindered by the substantial computational burden of their iterative sampling process. While feature caching techniques achieve effective acceleration at higher step counts (e.g., 50 steps), they exhibit critical limitations in the practical low-step regime of 20-30 steps. As the interval between steps increases, polynomial-based extrapolators like TaylorSeer suffer from error accumulation and trajectory drift. Meanwhile, conventional caching strategies often overlook the distinct dynamical properties of different denoising phases. To address these challenges, we propose Trajectory-Consistent Pade(TC-Pade) approximation, a feature prediction framework grounded in Pade approximation. By modeling feature evolution through rational functions, our approach captures asymptotic and transitional behaviors more accurately than Taylor-based methods. To enable stable and trajectory-consistent sampling under reduced step counts, TC-Pade incorporates (1) adaptive coefficient modulation that leverages historical cached residuals to detect subtle trajectory transitions, and (2) step-aware prediction strategies tailored to the distinct dynamics of early, mid, and late sampling stages. Extensive experiments on DiT-XL/2, FLUX.1-dev, and Wan2.1 across both image and video generation demonstrate the effectiveness of TC-Pade. For instance, TC-Pade achieves 2.88xacceleration on FLUX.1-dev and 1.72xon Wan2.1 while maintaining high quality across FID, CLIP, Aesthetic, and VBench-2.0 metrics, substantially outperforming existing feature caching methods.