Deep MSFOP: Multiple Spectral filter Operators Preservation in Deep Functional Maps for Unsupervised Shape Matching

We propose a novel constraint called Multiple Spectral filter Operators Preservation (MSFOR) to compute functional maps and based on it, develop an efficient deep functional map architecture called Deep MSFOP for shape matching. The core idea is that, instead of using the general descriptor preservation constraint, we require our maps to preserve multiple spectral filter operators. This allows us to incorporate more informative geometrical information, contained in different frequency bands of functions, into the functional map computing. This can be confirmed by that some previous techniques like wavelet preservation and LBO commutativity are actually our special cases. Moreover, we also develop a very efficient way to compute the maps with MSFOP constraint, which can be conveniently embedded into the deep learning, especially having learnable filter operators. Utilizing the above results, we finally design our Deep MSFOP pipeline, equipped with a suitable unsupervised loss jointly penalizing the functional map and the underlying pointwise map. Our deep functional map has notable advantages, including that the functional map is more geometrically informative and guaranteed to be proper, and the computing is numerically stable. Extensive experimental results on different datasets demonstrate that our approach outperforms the existing state-of-the-art methods, especially in challenging settings like non-isometric and inconsistent topology datasets.

Pareto Invariant Representation Learning for Multimedia Recommendation

Multimedia recommendation involves personalized ranking tasks, where multimedia content is usually represented using a generic encoder. However, these generic representations introduce spurious correlations that fail to reveal users' true preferences. Existing works attempt to alleviate this problem by learning invariant representations, but overlook the balance between independent and identically distributed (IID) and out-of-distribution (OOD) generalization. In this paper, we propose a framework called Pareto Invariant Representation Learning (PaInvRL) to mitigate the impact of spurious correlations from an IID-OOD multi-objective optimization perspective, by learning invariant representations (intrinsic factors that attract user attention) and variant representations (other factors) simultaneously. Specifically, PaInvRL includes three iteratively executed modules: (i) heterogeneous identification module, which identifies the heterogeneous environments to reflect distributional shifts for user-item interactions; (ii) invariant mask generation module, which learns invariant masks based on the Pareto-optimal solutions that minimize the adaptive weighted Invariant Risk Minimization (IRM) and Empirical Risk (ERM) losses; (iii) convert module, which generates both variant representations and item-invariant representations for training a multi-modal recommendation model that mitigates spurious correlations and balances the generalization performance within and cross the environmental distributions. We compare the proposed PaInvRL with state-of-the-art recommendation models on three public multimedia recommendation datasets (Movielens, Tiktok, and Kwai), and the experimental results validate the effectiveness of PaInvRL for both within- and cross-environmental learning.