Subspace Kernel Learning on Tensor Sequences
arXiv:2603.19546v1 Announce Type: new Abstract: Learning from structured multi-way data, represented as higher-order tensors, requires capturing complex interactions across tensor modes while remaining computationally efficient. We introduce Uncertainty-driven Kernel Tensor Learning (UKTL), a novel kernel framework for $M$-mode tensors that compares mode-wise subspaces derived from tensor unfoldings, enabling expressive and robust similarity measure. To handle large-scale tensor data, we propose a scalable Nystr\"{o}m kernel linearization with dynamically learned pivot tensors obtained via soft $k$-means clustering. A key innovation of UKTL is its uncertainty-aware subspace weighting, which adaptively down-weights unreliable mode components based on estimated confidence, improving robustness and interpretability in comparisons between input and pivot tensors. Our framework is fully end-to-end trainable and naturally incorporates both multi-way and multi-mode interactions through struc
arXiv:2603.19546v1 Announce Type: new Abstract: Learning from structured multi-way data, represented as higher-order tensors, requires capturing complex interactions across tensor modes while remaining computationally efficient. We introduce Uncertainty-driven Kernel Tensor Learning (UKTL), a novel kernel framework for $M$-mode tensors that compares mode-wise subspaces derived from tensor unfoldings, enabling expressive and robust similarity measure. To handle large-scale tensor data, we propose a scalable Nystr\"{o}m kernel linearization with dynamically learned pivot tensors obtained via soft $k$-means clustering. A key innovation of UKTL is its uncertainty-aware subspace weighting, which adaptively down-weights unreliable mode components based on estimated confidence, improving robustness and interpretability in comparisons between input and pivot tensors. Our framework is fully end-to-end trainable and naturally incorporates both multi-way and multi-mode interactions through structured kernel compositions. Extensive evaluations on action recognition benchmarks (NTU-60, NTU-120, Kinetics-Skeleton) show that UKTL achieves state-of-the-art performance, superior generalization, and meaningful mode-wise insights. This work establishes a principled, scalable, and interpretable kernel learning paradigm for structured multi-way and multi-modal tensor sequences.
Executive Summary
The article introduces a novel kernel framework, Uncertainty-driven Kernel Tensor Learning (UKTL), for learning from structured multi-way data. UKTL compares mode-wise subspaces derived from tensor unfoldings, enabling expressive and robust similarity measures. The framework is scalable, fully end-to-end trainable, and incorporates multi-way and multi-mode interactions. Evaluations on action recognition benchmarks demonstrate state-of-the-art performance, superior generalization, and meaningful mode-wise insights. UKTL's uncertainty-aware subspace weighting and pivot tensors obtained through soft k-means clustering are key innovations. This work establishes a principled, scalable, and interpretable kernel learning paradigm for structured multi-way and multi-modal tensor sequences.
Key Points
- ▸ UKTL introduces a novel kernel framework for learning from structured multi-way data.
- ▸ The framework compares mode-wise subspaces derived from tensor unfoldings for expressive and robust similarity measures.
- ▸ UKTL is scalable, fully end-to-end trainable, and incorporates multi-way and multi-mode interactions.
Merits
Strength in Expressiveness
UKTL's ability to compare mode-wise subspaces derived from tensor unfoldings enables expressive and robust similarity measures, making it a significant advancement in the field.
Scalability
UKTL's use of Nystr"{o}m kernel linearization with dynamically learned pivot tensors makes it scalable for large-scale tensor data.
Interpretability
UKTL's uncertainty-aware subspace weighting and pivot tensors obtained through soft k-means clustering provide meaningful mode-wise insights and improve interpretability.
Demerits
Complexity
UKTL's framework may be computationally complex, especially for large-scale tensor data, which could limit its practical applicability.
Overfitting
The use of soft k-means clustering to obtain pivot tensors may lead to overfitting, especially if the number of clusters is not carefully chosen.
Expert Commentary
The article introduces a novel and innovative framework for learning from structured multi-way data. UKTL's use of mode-wise subspaces and uncertainty-aware subspace weighting is a significant advancement in the field of tensor learning. However, the framework's complexity and potential for overfitting are concerns that need to be addressed. Overall, UKTL is a promising approach that has the potential to impact various applications and industries.
Recommendations
- ✓ Further research is needed to address the complexity and potential for overfitting in UKTL.
- ✓ The use of UKTL in real-world applications should be explored to demonstrate its practical efficacy.
Sources
Original: arXiv - cs.LG