Efficient approximations for Tucker-core regularization

Determine whether TensorSketch-based Tucker approximation and randomized tensor sparsification can reduce the training cost of HRIL’s Tucker-core synergy regularizer while preserving its representation-learning and synergy-capture benefits.

Background

HRIL constructs a projected cross-moment tensor whose size grows exponentially with the number of modalities, creating substantial computational and storage overhead during training. The paper reports that HRIL increases per-step runtime substantially relative to CoMM, although the regularizer is not used during inference.

The paper identifies TensorSketch-based Tucker approximation and randomized tensor sparsification as possible ways to reduce this cost. Their effects on the optimization process and final performance are not evaluated, leaving the efficiency–accuracy trade-off unresolved.

References

Potential ways to reduce this cost include TensorSketch-based Tucker approximation, which uses compressed representations in Tucker computations, and randomized tensor sparsification, which samples and reweights tensor entries before decomposition. Applying these approximations to our Tucker-core regularizer and evaluating their effects on training remain future work.

— HRIL: Learning Multimodal Synergy via Higher-Order Tensor Modeling  (2610.12393 - Dai et al., 8 Oct 2026) in Appendix, Section 'Computational Complexity and Runtime Analysis'