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General Machine Learning · Representation Learning

Félix Lefebvre, Gael Varoquaux

Many machine learning tasks can benefit from external knowledge. Large knowledge graphs store such knowledge, and embedding methods can be used to distill it into ready-to-use vector representations for downstream applications. For this purpose, current models have however two limitations: they are primarily optimized for link prediction, via local contrastive learning, and their application to the largest graphs requires significant engineering effort due to GPU memory limits. To address these, we introduce SEPAL: a Scalable Embedding Propagation ALgorithm for large knowledge graphs designed to produce high-quality embeddings for downstream tasks at scale. The key idea of SEPAL is to ensure global embedding consistency by optimizing embeddings only on a small core of entities, and then propagating them to the rest of the graph with message passing. We evaluate SEPAL on 7 large-scale knowledge graphs and 46 downstream machine learning tasks. Our results show that SEPAL significantly outperforms previous methods on downstream tasks. In addition, SEPAL scales up its base embedding model, enabling fitting huge knowledge graphs on commodity hardware. Our code is available at: .

Reinforcement Learning · Multi-agent

Riccardo Zamboni, Mirco Mutti, Marcello Restelli

In reinforcement learning, we typically refer to *unsupervised* pre-training when we aim to pre-train a policy without a priori access to the task specification, i.e., rewards, to be later employed for efficient learning of downstream tasks. In single-agent settings, the problem has been extensively studied and mostly understood. A popular approach casts the unsupervised objective as maximizing the *entropy* of the state distribution induced by the agent's policy, from which principles and methods follow. In contrast, little is known about state entropy maximization in multi-agent settings, which are ubiquitous in the real world. What are the pros and cons of alternative problem formulations in this setting? How hard is the problem in theory, how can we solve it in practice? In this paper, we address these questions by first characterizing those alternative formulations and highlighting how the problem, even when tractable in theory, is non-trivial in practice. Then, we present a scalable, decentralized, trust-region policy search algorithm to address the problem in practical settings. Finally, we provide numerical validations to both corroborate the theoretical findings and pave the way for unsupervised multi-agent reinforcement learning via state entropy maximization in challenging domains, showing that optimizing for a specific objective, namely *mixture entropy*, provides an excellent trade-off between tractability and performances.

Probabilistic Methods

Wentao Wu, Shiyuan He, Jianhua Guo

Bayesian networks (BNs), represented by directed acyclic graphs (DAGs), provide a principled framework for modeling complex dependencies among random variables. As data dimensionality increases into the tens of thousands, fitting and marginalizing a full BN becomes computationally prohibitive—particularly when inference is only needed for a small subset of variables. Estimation-collapsibility addresses this challenge by ensuring that directly fitting a submodel, obtained by ignoring non-essential variables, still yields exact inference on target variables. However, current DAG-based criterion for checking estimation-collapsibility is computationally intensive, involving exhaustive vertex searches and iterative removals. Additionally, practical applications typically identify the underlying DAG only up to its Markov equivalence class, represented by a completed partially directed acyclic graph (CPDAG). To bridge this gap, we introduce sequential $c$-simplicial sets—a novel graphical characterization of estimation-collapsibility applicable directly to CPDAGs. We further propose DSCS, a computationally efficient algorithm for verifying estimation-collapsibility within CPDAG framework that scales effectively to high-dimensional BNs. Extensive numerical experiments demonstrate the practicality, scalability, and efficiency of our proposed approach.

Optimization

Elfarouk Harb, Yousef Yassin, Chandra Chekuri

We consider the following question: given a submodular or supermodular set function $f:2^V \to \mathbb{R}$, how should one minimize or maximize its average value $f(S)/|S|$ over non-empty subsets $S\subseteq V$? This problem generalizes several well-known objectives including Densest Subgraph (DSG), Densest Supermodular Set (DSS), and Submodular Function Minimization (SFM). Motivated by recent applications [39, 31], we formalize two new broad problems: the Unrestricted Sparsest Submodular Set (USSS) and Unrestricted Densest Supermodular Set (UDSS) which allow negative and non-monotone functions. Using classical results we observe that DSS, SFM, USSS, UDSS, and MNP are all equivalent under strongly polynomial-time reductions. This equivalence enables algorithmic cross-over: methods designed for one problem can be repurposed to solve others efficiently. In particular we use the perspective of the minimum norm point in the base polyhedron of a sub/supermodular function which, via Fujishige's results, yields the dense decomposition as a byproduct. Via this perspective we show that a recent converging heuristic for DSS, \textsc{SuperGreedy++} [15, 29], and Wolfe’s minimum norm point algorithm are both universal solvers for all of these problems. On the theoretical front, we explain the observation made in recent work [39, 31] that \textsc{SuperGreedy++} appears to work well even in settings beyond DSS. Surprisingly, we also show that this simple algorithm can be used for Submodular Function Minimization, including for example that it can act as an effective minimum $st$ cut algorithm. On the empirical front, we explore the utility of several different algorithms including Fujishige-Wolfe min-norm point algorithm for recent problems. We conduct over 400 experiments across seven problem types and large-scale synthetic and real-world datasets (up to $\approx 100$ million edges). Our results reveal that methods historically considered inefficient, such as convex-programming methods, flow-based solvers, and Fujishige-Wolfe’s algorithm, outperform state-of-the-art task-specific baselines by orders of magnitude on concrete problems like HNSN [39]. These findings challenge prevailing assumptions and demonstrate that with the right framing, general optimization algorithms can be both scalable and state-of-the-art for supermodular and submodular ratio problems.

Computer Vision · Classification and Understanding

Zhiqi Pang, Lingling Zhao, Junjie Wang, Chunyu Wang

Visible-infrared person re-identification (VI-ReID) aims to match visible and infrared images of the same individual. Supervised VI-ReID (SVI-ReID) methods have achieved promising performance under the guidance of manually annotated identity labels. However, the substantial annotation cost severely limits their scalability in real-world applications. As a result, unsupervised VI-ReID (UVI-ReID) methods have attracted increasing attention. These methods typically rely on pseudo-labels generated by clustering and matching algorithms to replace manual annotations. Nevertheless, the quality of pseudo-labels is often difficult to guarantee, and low-quality pseudo-labels can significantly hinder model performance improvements. To address these challenges, we explore the use of attribute arrays extracted by a large vision-language model (LVLM) to enhance VI-ReID, and propose a novel LVLM-driven attribute-aware modeling (LVLM-AAM) approach. Specifically, we first design an attribute-aware reliable labeling strategy, which refines intra-modality clustering results based on image-level attributes and improves inter-modality matching by grouping clusters according to cluster-level attributes. Next, we develop an explicit-implicit attribute fusion module, which integrates explicit and implicit attributes to obtain more fine-grained identity-related text features. Finally, we introduce an attribute-aware contrastive learning module, which jointly leverages static and dynamic text features to promote modality-invariant feature learning. Extensive experiments conducted on VI-ReID datasets validate the effectiveness of the proposed LVLM-AAM and its individual components. LVLM-AAM not only significantly outperforms existing unsupervised methods but also surpasses several supervised methods.

Deep Learning · Algorithms

Haotian Sun, Yitong Li, Yuchen Zhuang, Niao He, Hanjun Dai, Bo Dai

Contrastive Language-Image Pretraining (CLIP) has demonstrated strong zero-shot performance across diverse downstream text-image tasks. Existing CLIP methods typically optimize a contrastive objective using negative samples drawn from each minibatch. To achieve robust representation learning, these methods require extremely large batch sizes and escalate computational demands to hundreds or even thousands of GPUs. Prior approaches to mitigate this issue often compromise downstream performance, prolong training duration, or face scalability challenges with very large datasets. To overcome these limitations, we propose AmorLIP, an efficient CLIP pretraining framework that amortizes expensive computations involved in contrastive learning through lightweight neural networks, which substantially improves training efficiency and performance. Leveraging insights from a spectral factorization of energy-based models, we introduce novel amortization objectives along with practical techniques to improve training stability. Extensive experiments across 38 downstream tasks demonstrate the superior zero-shot classification and retrieval capabilities of AmorLIP, consistently outperforming standard CLIP baselines with substantial relative improvements of up to 12.24%.

Social Aspects · Accountability, Transparency and Interpretability

Sheng-Yu Wang, Aaron Hertzmann, Alexei Efros, Richard Zhang, Jun-Yan Zhu

Data attribution for text-to-image models aims to identify the training images that most significantly influenced a generated output. Existing attribution methods involve considerable computational resources for each query, making them impractical for real-world applications. We propose a novel approach for scalable and efficient data attribution. Our key idea is to distill a slow, unlearning-based attribution method to a feature embedding space for efficient retrieval of highly influential training images. During deployment, combined with efficient indexing and search methods, our method successfully finds highly influential images without running expensive attribution algorithms. We show extensive results on both medium-scale models trained on MSCOCO and large-scale Stable Diffusion models trained on LAION, demonstrating that our method can achieve better or competitive performance in a few seconds, faster than existing methods by 2,500x - 400,000x. Our work represents a meaningful step towards the large-scale application of data attribution methods on real-world models such as Stable Diffusion.

Social Aspects · Accountability, Transparency and Interpretability

Landon Butler, Abhineet Agarwal, Justin Kang, Yigit Efe Erginbas, Bin Yu, Kannan Ramchandran

Large Language Models (LLMs) have achieved remarkable performance by capturing complex interactions between input features. To identify these interactions, most existing approaches require enumerating all possible combinations of features up to a given order, causing them to scale poorly with the number of inputs $n$. Recently, Kang et al. (2025) proposed SPEX, an information-theoretic approach that uses interaction sparsity to scale to $n \approx 10^3$ features. SPEX greatly improves upon prior methods but requires tens of thousands of model inferences, which can be prohibitive for large models. In this paper, we observe that LLM feature interactions are often *hierarchical*—higher-order interactions are accompanied by their lower-order subsets—which enables more efficient discovery. To exploit this hierarchy, we propose ProxySPEX, an interaction attribution algorithm that first fits gradient boosted trees to masked LLM outputs and then extracts the important interactions. Experiments across four challenging high-dimensional datasets show that ProxySPEX more faithfully reconstructs LLM outputs by 20\% over marginal attribution approaches while using *$10\times$ fewer inferences* than SPEX. By accounting for interactions, ProxySPEX efficiently identifies the most influential features, providing a scalable approximation of their Shapley values. Further, we apply ProxySPEX to two interpretability tasks. *Data attribution*, where we identify interactions among CIFAR-10 training samples that influence test predictions, and *mechanistic interpretability*, where we uncover interactions between attention heads, both within and across layers, on a question-answering task. The ProxySPEX algorithm is available at .

Deep Learning · Generative Models and Autoencoders

Yingqing Guo, Yukang Yang, Hui Yuan, Mengdi Wang

Training-free guidance enables controlled generation in diffusion and flow models, but most methods rely on gradients and assume differentiable objectives. This work focuses on training-free guidance addressing challenges from non-differentiable objectives and discrete data distributions. We propose TreeG: Tree Search-Based Path Steering Guidance, applicable to both continuous and discrete settings in diffusion and flow models. TreeG offers a unified framework for training-free guidance by proposing, evaluating, and selecting candidates at each step, enhanced with tree search over active paths and parallel exploration. We comprehensively investigate the design space of TreeG over the candidate proposal module and the evaluation function, instantiating TreeG into three novel algorithms. Our experiments show that TreeG consistently outperforms top guidance baselines in symbolic music generation, small molecule design, and enhancer DNA design with improvements of 29.01%, 26.38%, and 18.43%. Additionally, we identify an inference-time scaling law showing TreeG's scalability in inference-time computation.

Social Aspects · Accountability, Transparency and Interpretability

Darin Tsui, Aryan Musharaf, Yigit Efe Erginbas, Justin Kang, Amirali Aghazadeh

The growing adoption of machine learning models for biological sequences has intensified the need for interpretable predictions, with Shapley values emerging as a theoretically grounded standard for model explanation. While effective for local explanations of individual input sequences, scaling Shapley-based interpretability to extract global biological insights requires evaluating thousands of sequences—incurring exponential computational cost per query. We introduce SHAP zero, a novel algorithm that amortizes the cost of Shapley value computation across large-scale biological datasets. After a one-time model sketching step, SHAP zero enables near-zero marginal cost for future queries by uncovering an underexplored connection between Shapley values, high-order feature interactions, and the sparse Fourier transform of the model. Applied to models of guide RNA efficacy, DNA repair outcomes, and protein fitness, SHAP zero explains predictions orders of magnitude faster than existing methods, recovering rich combinatorial interactions previously inaccessible at scale. This work opens the door to principled, efficient, and scalable interpretability for black-box sequence models in biology.

Deep Learning · Generative Models and Autoencoders

Zhange Zhang, Zhicheng Geng, Yuqing Ma, Tianbo Wang, Kai Lv, Xianglong Liu

Large Language Models (LLMs) have demonstrated broad applications but suffer from issues like hallucinations, erroneous outputs and outdated knowledge. Model editing emerges as an effective solution to refine knowledge in LLMs, yet existing methods typically depend on structured knowledge representations. However, real-world knowledge is primarily embedded within complex, unstructured text. Existing structured knowledge editing approaches face significant challenges when handling the entangled and intricate knowledge present in unstructured text, resulting in issues such as representation ambiguity and editing conflicts. To address these challenges, we propose a Conflict-Aware Knowledge Editing in the Wild (CAKE) framework, the first framework explicitly designed for editing knowledge extracted from wild unstructured text. CAKE comprises two core components: a Semantic-augmented Graph Representation module and a Conflict-aware Knowledge Editing strategy. The Semantic-augmented Graph Representation module enhances knowledge encoding through structural disambiguation, relational enrichment, and semantic diversification. Meanwhile, the Conflict-aware Knowledge Editing strategy utilizes a graph-theoretic coloring algorithm to disentangle conflicted edits by allocating them to orthogonal parameter subspaces, thereby effectively mitigating editing conflicts. Experimental results on the AKEW benchmark demonstrate that CAKE significantly outperforms existing methods, achieving a 15.43\% improvement in accuracy on llama3 editing tasks. Our framework successfully bridges the gap between unstructured textual knowledge and reliable model editing, enabling more robust and scalable updates for practical LLM applications.

Optimization · Stochastic & Convex Optimization

Junyu Huang, Qilong Feng, Zhen Zhang, Beirong Cui, Jianxin Wang

Local search is a powerful clustering technique that provides high-quality solutions with theoretical guarantees. With distance-based sampling strategies, local search methods can achieve constant approximations for clustering with linear running time in data size. Despite their effectiveness, existing algorithms still face scalability issues as they require scanning the entire dataset for iterative center swaps. This typically leads to an O(ndk) running time, where n is the data size, d is the dimension, k is the number of clusters. To further improve the efficiency of local search algorithms, we propose new methods based on adaptive sampling and bandit strategies. Specifically, adaptive sampling can well approximate the distance-based sampling distribution without maintaining pairwise distances between data points and the centers, enabling fast and accurate sampling in sublinear time after an $\tilde{O}(nd)$ time preprocessing step. The bandit strategy models the best swap pair selection as a bandit problem, where a grouping strategy is proposed for fast identification of the optimal swap pair. With these techniques, our proposed algorithm can achieve constant approximation in expected running time $\tilde{O}(nd + k^4)$ under mild assumptions on optimal clusters and swap pair distributions. Our approach also extends naturally to the k-median objective, achieving constant approximation in expected running time $\tilde{O}(nd + \sqrt{n}k^3)$ without distributional assumptions. Empirical results demonstrate that our algorithm achieves up to 1000× speedup over existing local search methods on datasets with 100 million points, while delivering comparable clustering quality. Compared to coreset-based approaches, it also provides up to 80× speedup and consistently yields better clustering results.

Reinforcement Learning · Multi-agent

Nathan Corecco, Batuhan Yardim, Vinzenz Thoma, Zebang Shen, Niao He

Designing incentives for a multi-agent system to induce a desirable Nash equilibrium is both a crucial and challenging problem appearing in many decision-making domains, especially for a large number of agents $N$. Under the exchangeability assumption, we formalize this incentive design (ID) problem as a parameterized mean-field game (PMFG), aiming to reduce complexity via an infinite-population limit. We first show that when dynamics and rewards are Lipschitz, the finite-$N$ ID objective is approximated by the PMFG at rate $\mathcal{O}(\frac{1}{\sqrt{N}})$. Moreover, beyond the Lipschitz-continuous setting, we prove the same $\mathcal{O}(\frac{1}{\sqrt{N}})$ decay for the important special case of sequential auctions, despite discontinuities in dynamics, through a tailored auction-specific analysis. Built on our novel approximation results, we further introduce our Adjoint Mean-Field Incentive Design (AMID) algorithm, which uses explicit differentiation of iterated equilibrium operators to compute gradients efficiently. By uniting approximation bounds with optimization guarantees, AMID delivers a powerful, scalable algorithmic tool for many-agent (large $N$) ID. Across diverse auction settings, the proposed AMID method substantially increases revenue over first-price formats and outperforms existing benchmark methods.

General Machine Learning · Everything Else

Louis Allain, Sébastien Da Veiga, Brian Staber

Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of adaptivity, although several works introduced practically efficient alternate procedures. In this work, we build upon recent ideas that rely on recasting the CP problem as a statistical learning problem, directly targeting coverage and adaptivity. This statistical learning problem is based on reproducible kernel Hilbert spaces (RKHS) and kernel sum-of-squares (SoS) methods. First, we extend previous results with a general representer theorem and exhibit the dual formulation of the learning problem. Crucially, such dual formulation can be solved efficiently by accelerated gradient methods with several hundreds or thousands of samples, unlike previous strategies based on off-the-shelf semidefinite programming algorithms. Second, we introduce a new hyperparameter tuning strategy tailored specifically to target adaptivity through bounds on test-conditional coverage. This strategy, based on the Hilbert-Schmidt Independence Criterion (HSIC), is introduced here to tune kernel lengthscales in our framework, but has broader applicability since it could be used in any CP algorithm where the score function is learned. Finally, extensive experiments are conducted to show how our method compares to related work. All figures can be reproduced with the accompanying code at https://www.gitlab.com/drti/ksos-bands.

Dionysis Arvanitakis, Vaidehi Srinivas, Aravindan Vijayaraghavan

Tensor decomposition is a canonical non-convex optimization problem that is computationally challenging, and yet important due to applications in factor analysis and parameter estimation of latent variable models. In practice, scalable iterative methods, particularly Alternating Least Squares (ALS), remain the workhorse for tensor decomposition despite the lack of global convergence guarantees. A popular approach to tackle challenging non-convex optimization problems is overparameterization--- on input an $n \times n \times n$ tensor of rank $r$, the algorithm can output a decomposition of potentially rank $k$ (potentially larger than $r$). On the theoretical side, overparameterization for iterative methods is challenging to reason about and requires new techniques. The work of Wang et al., (NeurIPS 2020) makes progress by showing that a variant of gradient descent globally converges when overparameterized to $k=O(r^{7.5} \log n)$. Our main result shows that overparameterization provably enables global convergence of ALS: on input a third order $n \times n \times n$ tensor with a decomposition of rank $r \ll n$, ALS overparameterized with rank $k=O(r^2)$ achieves global convergence with high probability under random initialization. Moreover our analysis also gives guarantees for the more general low-rank approximation problem. The analysis introduces new techniques for understanding iterative methods in the overparameterized regime based on new matrix anticoncentration arguments.

Deep Learning · Algorithms

Chu Xu, Xinke Jiang, Rihong Qiu, Jiaran Gao, Junfeng Zhao

Measuring parameter importance is crucial for understanding and optimizing large language models (LLMs). Existing work predominantly focuses on pruning or probing at neuron/feature levels without fully considering the cooperative behaviors of model parameters. In this paper, we introduce a novel approach--Model Shapley to quantify parameter importance based on the Shapley value, a principled method from cooperative game theory that captures both individual and synergistic contributions among parameters, via only one gradient backpropagation. We derive a scalable second-order approximation to compute Shapley values at the parameter level, leveraging blockwise Fisher information for tractability in large-scale settings. Our method enables fine-grained differentiation of parameter importance, facilitating targeted knowledge injection and model compression. Through mini-batch Monte Carlo updates and efficient approximation of the Hessian structure, we achieve robust Shapley-based attribution with only modest computational overhead. Experimental results indicate that this cooperative game perspective enhances interpretability, guides more effective parameter-specific fine-tuning and model compressing, and paves the way for continuous model improvement in various downstream tasks.

Deep Learning · Generative Models and Autoencoders

Samuel Howard, Peter Potaptchik, George Deligiannidis

Recent advances in flow-based generative modelling have provided scalable methods for computing the Schrödinger Bridge (SB) between distributions, a dynamic form of entropy-regularised Optimal Transport (OT) for the quadratic cost. The successful Iterative Markovian Fitting (IMF) procedure solves the SB problem via sequential bridge-matching steps, presenting an elegant and practical approach with many favourable properties over the more traditional Iterative Proportional Fitting (IPF) procedure. Beyond the standard setting, optimal transport can be generalised to the multi-marginal case in which the objective is to minimise a cost defined over several marginal distributions. Of particular importance are costs defined over a tree structure, from which Wasserstein barycentres can be recovered as a special case. In this work, we extend the IMF procedure to solve for the tree-structured SB problem. Our resulting algorithm inherits the many advantages of IMF over IPF approaches in the tree-based setting. In the case of Wasserstein barycentres, our approach can be viewed as extending the widely used fixed-point approach to use flow-based entropic OT solvers, while requiring only simple bridge-matching steps at each iteration.

General Machine Learning · Everything Else

Yicong Jiang, Zheng Tracy Ke

Vertex hunting (VH) is the task of estimating a simplex from noisy data points and has many applications in areas such as network and text analysis. We introduce a new variant, semi-supervised vertex hunting (SSVH), in which partial information is available in the form of barycentric coordinates for some data points, known only up to an unknown transformation. To address this problem, we develop a method that leverages properties of orthogonal projection matrices, drawing on novel insights from linear algebra. We establish theoretical error bounds for our method and demonstrate that it achieves a faster convergence rate than existing unsupervised VH algorithms. Finally, we apply SSVH to two practical settings---semi-supervised network mixed membership estimation and semi-supervised topic modeling---resulting in efficient and scalable algorithms.

Data-centric AI · Data-centric AI methods and tools

Jiongli Zhu, Parjanya Prashant, Alex Cloninger, Babak Salimi

Data valuation techniques quantify each training example's contribution to model performance, providing a principled basis for data cleaning, acquisition, and selection. Existing valuation methods remain inadequate: \emph{model-based} techniques depend on a single fitted model and inherit its biases, while \emph{algorithm-based} approaches like Data Shapley scale poorly due to their need to train multiple models. Recent work has proposed model-agnostic alternatives based on Wasserstein distance between the training set and a clean reference set, but exact computation is expensive and approximations often misrank examples. We introduce KAIROS, a model-agnostic framework that values examples by their contribution to the Maximum Mean Discrepancy (MMD) between the training set and a clean reference distribution. Unlike Wasserstein methods, MMD admits a closed-form solution that requires no approximations and is scalable to large datasets. Additionally, KAIROS enables efficient online valuation: adding a new batch of $m$ examples requires only $O(mN)$ computation to update all scores, compared to $O(N^2)$ in prior work where $N$ is the training set size. Empirical evaluations on noise, mislabeling, and poisoning benchmarks show that KAIROS consistently outperforms state-of-the-art baselines in both accuracy and runtime. On ImageNet, KAIROS achieves up to 15 $\times$ speedup over the fastest baseline while maintaining superior data valuation quality. Our results demonstrate that model-agnostic methods can match or exceed model-based approaches in performance while scaling to large datasets.

Deep Learning · Algorithms

Weilin Wan, Weizhong Zhang, Cheng Jin

Data selection improves computational efficiency by choosing informative subsets of training samples. However, existing methods ignore the compute budget, treating data selection and importance evaluation independently of compute budget constraints. Yet empirical studies show no algorithm can consistently outperform others (or even random selection) across varying budgets. We therefore argue that compute budget must be integral to data-selection strategies, since different budgets impose distinct requirements on data quantity, quality, and distribution for effective training. To this end, we propose a novel Computational budget-Aware Data Selection (CADS) method and naturally formulate it into a bilevel optimization framework, where the inner loop trains the model within the constraints of the computational budget on some selected subset of training data, while the outer loop optimizes data selection based on model evaluation. Our technical contributions lie in addressing two main challenges in solving this bilevel optimization problem: the expensive Hessian matrix estimation for outer-loop gradients and the computational burden of achieving inner-loop optimality during iterations. To solve the first issue, we propose a probabilistic reparameterization strategy and compute the gradient using a Hessian-free policy gradient estimator. To address the second challenge, we transform the inner optimization problem into a penalty term in the outer objective, further discovering that we only need to estimate the minimum of a one-dimensional loss to calculate the gradient, significantly improving efficiency. To accommodate different data selection granularities, we present two complementary CADS variants: an example-level version (CADS-E) offering fine-grained control and a source-level version (CADS-S) aggregating samples into source groups for scalable, efficient selection without sacrificing effectiveness. Extensive experiments show that our method achieves performance gains of up to 14.42\% over baselines in vision and language benchmarks. Additionally, CADS achieves a 3-20× speedup compared to conventional bilevel implementations, with acceleration correlating positively with compute budget size.