Multi-view representation learning aims to capture comprehensive information from multiple views of a shared context. Recent works intuitively apply contrastive learning to different views in a pairwise manner, which is still scalable: view-specific noise is not filtered in learning view-shared representations; the fake negative pairs, where the negative terms are actually within the same class as the positive, and the real negative pairs are coequally treated; evenly measuring the similarities between terms might interfere with optimization. Importantly, few works study the theoretical framework of generalized self-supervised multi-view learning, especially for more than two views. To this end, we rethink the existing multi-view learning paradigm from the perspective of information theory and then propose a novel information theoretical framework for generalized multi-view learning. Guided by it, we build a multi-view coding method with a three-tier progressive architecture, namely Information theory-guided hierarchical Progressive Multi-view Coding (IPMC). In the distribution-tier, IPMC aligns the distribution between views to reduce view-specific noise. In the set-tier, IPMC constructs self-adjusted contrasting pools, which are adaptively modified by a view filter. Lastly, in the instance-tier, we adopt a designed unified loss to learn representations and reduce the gradient interference. Theoretically and empirically, we demonstrate the superiority of IPMC over state-of-the-art methods.

Multi-view representation learning captures comprehensive information from multiple views of a shared context. Recent works intuitively apply contrastive learning (CL) to learn representations, regarded as a pairwise manner, which is still scalable: view-specific noise is not filtered in learning view-shared representations; the fake negative pairs, where the negative terms are actually within the same class as the positive, and the real negative pairs are coequally treated; and evenly measuring the similarities between terms might interfere with optimization. Importantly, few works research the theoretical framework of generalized self-supervised multi-view learning, especially for more than two views. To this end, we rethink the existing multi-view learning paradigm from the information theoretical perspective and then propose a novel information theoretical framework for generalized multi-view learning. Guided by it, we build a multi-view coding method with a three-tier progressive architecture, namely Information theory-guided heuristic Progressive Multi-view Coding (IPMC). In the distribution-tier, IPMC aligns the distribution between views to reduce view-specific noise. In the set-tier, IPMC builds self-adjusted pools for contrasting, which utilizes a view filter to adaptively modify the pools. Lastly, in the instance-tier, we adopt a designed unified loss to learn discriminative representations and reduce the gradient interference. Theoretically and empirically, we demonstrate the superiority of IPMC over state-of-the-art methods.

In this paper, we introduce a novel algorithm to solve projected model counting (PMC). PMC asks to count solutions of a Boolean formula with respect to a given set of projected variables, where multiple solutions that are identical when restricted to the projected variables count as only one solution. Our algorithm exploits small treewidth of the primal graph of the input instance. It runs in time $O({2^{2^{k+4}} n^2})$ where k is the treewidth and n is the input size of the instance. In other words, we obtain that the problem PMC is fixed-parameter tractable when parameterized by treewidth. Further, we take the exponential time hypothesis (ETH) into consideration and establish lower bounds of bounded treewidth algorithms for PMC, yielding asymptotically tight runtime bounds of our algorithm.