When Gradient Optimization Is Not Enough: $\dagger$ Dispersive and Anchoring Geometric Regularizer for Multimodal Learning

Multimodal learning aims to integrate complementary information from heterogeneous modalities, yet strong optimization alone does not guaranty well-structured representations. Even under carefully balanced training schemes, multimodal models often exhibit geometric pathologies, including intra-modal representation collapse and sample-level cross-modal inconsistency, which degrade both unimodal robustness and multimodal fusion. We identify representation geometry as a missing control axis in multimodal learning and propose \regName, a lightweight geometry-aware regularization framework. \regName enforces two complementary constraints on intermediate embeddings: an intra-modal dispersive regularization that promotes representation diversity, and an inter-modal anchoring regularization that bounds sample-level cross-modal drift without rigid alignment. The proposed regularizer is plug-and-play, requires no architectural modifications, and is compatible with various training paradigms. Extensive experiments across multiple multimodal benchmarks demonstrate consistent improvements in both multimodal and unimodal performance, showing that explicitly regulating representation geometry effectively mitigates modality trade-offs.

KOALA++: Efficient Kalman-Based Optimization of Neural Networks with Gradient-Covariance Products

We propose KOALA++, a scalable Kalman-based optimization algorithm that explicitly models structured gradient uncertainty in neural network training. Unlike second-order methods, which rely on expensive second order gradient calculation, our method directly estimates the parameter covariance matrix by recursively updating compact gradient covariance products. This design improves upon the original KOALA framework that assumed diagonal covariance by implicitly capturing richer uncertainty structure without storing the full covariance matrix and avoiding large matrix inversions. Across diverse tasks, including image classification and language modeling, KOALA++ achieves accuracy on par or better than state-of-the-art first- and second-order optimizers while maintaining the efficiency of first-order methods.