Subspace
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Related Articles from SNS
Subspace-Decomposed JEPAs: Disentangling Progression and Content in Latent World Models
arXiv:2605.31111v1 Announce Type: new Abstract: Joint-Embedding Predictive Architectures (JEPAs) learn compact latent world models by predicting future embeddings, but no single coordinate of the latent is designated to encode task progression. We carve the JEPA latent into two orthogonal subspaces with disjoint roles: a low-dimensional progression subspace shaped by a cosine-margin triplet loss, and a high-dimensional content subspace regularised by the existing SIGReg objective of LeWM. We...
Sequential Subspace Mode Adaptation for the Reduced-Order Homogenization of Dissipative Microstructures using E3C Hyper-Reduction
arXiv:2606.02089v1 Announce Type: new Abstract: Three-dimensional inelastic computational homogenization of complex engineering components requires a multitude of nonlinear microstructural simulations, making it computationally expensive. This work investigates a projection-based model order reduction (pMOR) method with 'Sequential Subspace Mode Adaptation', which can be easily integrated into existing codes using linear subspaces. Starting with a 'conventional' linear subspace strain...
Koopman Subspace Pruning in Reproducing Kernel Hilbert Spaces via Principal Vectors
arXiv:2604.01459v2 Announce Type: replace Abstract: Data-driven approximations of the infinite-dimensional Koopman operator rely on finite-dimensional projections, where the predictive accuracy of the resulting models hinges heavily on the invariance of the chosen subspace. Subspace pruning systematically discards geometrically misaligned directions to enhance this invariance proximity, which formally corresponds to the largest principal angle between the subspace and its image under the...
A Unified Algebraic Framework for Subspace Pruning in Koopman Operator Approximation via Principal Vectors
arXiv:2603.29001v2 Announce Type: replace Abstract: Finite-dimensional approximations of the Koopman operator rely critically on identifying nearly invariant subspaces. This invariance proximity can be rigorously quantified via the principal angles between a candidate subspace and its image under the operator. To systematically minimize this error, we propose an algebraic framework for subspace pruning utilizing principal vectors.
Native Hierarchical and Compositional Representations with Subspace Embeddings
arXiv:2508.16687v2 Announce Type: replace Abstract: Traditional embeddings represent datapoints as vectors, which makes similarity easy to compute but limits how well they capture hierarchies and compositionality. We propose a fundamentally different approach: representing concepts as linear subspaces. By spanning multiple dimensions, subspaces can model broader concepts with higher-dimensional regions and nest more specific concepts within them.
MIC: Maximizing Informational Capacity in Adaptive Representations via Isotropic Subspace Alignment
arXiv:2605.29987v2 Announce Type: replace Abstract: Although multi-scales representation learning enables elastic-dimension embeddings, nested subspaces often suffer from dimensional redundancy and spectral collapse. To address this, we introduce MIC, a framework that optimizes the geometric landscape of multi-granular embeddings through isotropic subspace alignment.
Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations
arXiv:2605.13135v2 Announce Type: replace Abstract: The accuracy of Koopman operator approximations over finite-dimensional spaces relies critically on their invariance properties. These can be rigorously quantified via the principal angles between a candidate subspace and its image under the Koopman operator. This paper proposes a unified algebraic framework for subspace pruning designed to systematically refine the invariance error.
The Sharp Phase Transition of Tyler's M-Estimator for Robust Subspace Recovery
arXiv:2606.06782v1 Announce Type: new Abstract: Robust Subspace Recovery (RSR) aims to identify an underlying d-dimensional subspace from a dataset heavily corrupted by outliers. Complexity-theoretic results establish a threshold for the problem's computational hardness based on the dimension-scaled signal-to-noise ratio (DS-SNR): the problem is SSE-hard when the DS-SNR is strictly less than 1, and solvable via practical algorithms when it is greater than 1 under general position...
Parameter-Efficient Subspace Decoupling ViT for Mitigating Multi-Task Negative Transfer in Histological Scoring
arXiv:2605.29852v2 Announce Type: replace Abstract: Histological scoring is essential for diagnosing Non-Alcoholic Fatty Liver Disease (NAFLD), yet its automation remains challenging due to the high annotation cost and negative transfer among the strongly correlated NAFLD Activity Score (NAS) indicators in multi-task learning. To address this issue, we propose a subspace-decoupled multi-task Vision Transformer (ViT) that integrates lightweight task-specific Adapters with orthogonality-based...
Sequential Subspace Noise Injection Prevents Accuracy Collapse in Certified Unlearning
Announce Type: replace Abstract: Certified unlearning based on differential privacy offers strong guarantees but remains largely impractical: the noisy fine-tuning approaches proposed so far achieve these guarantees but severely reduce model accuracy. We propose sequential noise scheduling, which distributes the noise budget across orthogonal subspaces of the parameter space, rather than injecting it all at once. This simple modification mitigates the destructive effect of noise while...