The paper investigates how AI‑generated data, treated as anomalies linked to main data points, influences batch decompositions and undersampling in random datasets. Using redundancy graphs and iterative methods, it derives bounds for the minimum size of a strongly dissimilar decomposition and shows a phase transition: when anomalies are few, the minimum size depends on main data, but beyond a threshold it is dominated by anomalies. Additionally, the authors present a size criticality result for strong similarity in randomly undersampled datasets, illustrated with categorical data examples where the overall space far exceeds the dataset size.
arXiv:2606. 18209v1 Announce Type: new Abstract: Dataset distillation (DD) has emerged as a prominent approach in data centric machine learning, aiming to synthesize compact training sets for efficient training by compressing the information in large datasets into a small number of synthetic samples.
The paper introduces a unified framework for dataset condensation (DC) that generalizes existing methods by using discrepancy measures to quantify the distance between probability distributions. It extends the traditional goal of DC—creating a small synthetic dataset that preserves generalization—to include additional objectives such as robustness and privacy. The framework positions DC as a formal approximation problem, broadening its applicability across different machine learning regimes.
arXiv:2609.06394v1 Announce Type: cross Abstract: Massive datasets in modern machine learning have made data reduction a central challenge, particularly for clustering tasks where memory and computat...
arXiv:2606. 11235v1 Announce Type: new Abstract: A key step in knowledge discovery is the evaluation of data mining results.
The paper introduces Backward Kernel Herding, an algorithm that iteratively removes data points to create representative subsets for kernel learning, achieving performance comparable to state‑of‑the‑art methods while speeding up subsampling when the reduced size is less than half the original dataset. It also proposes Flexible Kernel Thinning, an extension that allows construction of subsets of any size, not just successive halvings, and demonstrates that this method often yields the best predictive performance. Experiments on Gaussian Processes and Kernel Support Vector Machines show that Backward Kernel Herding excels in training‑time efficiency, while Flexible Kernel Thinning offers superior predictive accuracy and competitive memory usage, emphasizing the need to choose a reduction strategy based on the desired trade‑off between performance, cost, and memory.
arXiv:2606. 01155v1 Announce Type: cross Abstract: Scaling laws for dense LLMs under infinite data are well explored, but how sparsity interacts with limited data is not.
arXiv:2606. 28573v1 Announce Type: new Abstract: Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions.
The paper compares two popular data‑integration techniques—Stack‑SVD, which concatenates datasets before performing singular value decomposition, and SVD‑Stack, which first decomposes each dataset separately and then aggregates the leading singular vectors. By deriving exact asymptotic performance expressions and phase transitions in a proportional regime, the authors show that neither method uniformly dominates the other when unweighted, but optimally weighted Stack‑SVD outperforms optimally weighted SVD‑Stack when the low‑rank signal is fully shared. They also demonstrate that SVD‑Stack can excel with partially shared components and provide practical algorithms for estimating optimal weights, supported by simulations and genomic experiments.
arXiv:2505. 23869v4 Announce Type: replace-cross Abstract: A proposition that connects randomness and compression is put forward via Gibbs entropy over set of measurement vectors associated with a compression process.
arXiv:2502. 06434v2 Announce Type: replace-cross Abstract: Dataset pruning (DP) and dataset distillation (DD) fundamentally differ in their outputs: DP selects original image subsets, while DD generates synthetic images.
arXiv:2603. 15263v2 Announce Type: replace-cross Abstract: Self-supervised learning (SSL) has revolutionized representation learning, with Joint-Embedding Architectures (JEAs) emerging as an effective approach for capturing semantic features.
arXiv:2606. 18833v1 Announce Type: new Abstract: This paper introduces a semi-supervised clustering framework grounded in the statistical duality between grouping principles and anomaly detection.