If hhas the form (1), we have h = g f . Hence, we obtain h h = g2 f (1 f). Since 0 f <1 and f >0, we have h h <0. Now, from the other direction, suppose we know h h <0. To prove that hmust have the form (1), we first show that h(0)h() >0 ( 0), (2) namely, h() always keeps the same sign with h(0).

Many applications involve multi-type event data. Understanding the complex influences of the events on each other is critical to discover useful knowledge and to predict future events and their types. Existing methods either ignore or partially account for these influences. Recent works use recurrent neural networks to model the event rate. While being highly expressive, they couple all the temporal dependencies in a black-box and can hardly extract meaningful knowledge. More important, most methods assume an exponential time decay of the influence strength, which is over-simplified and can miss many important strength varying patterns.

Available: https://openreview.net/forum?id=m5Qsh0kBQG [4] Q. Lu, J. Ren, and Z. Wang, "Using genetic programming with prior formula knowledge to solve symbolic regression problem," Computational intelligence and neuroscience, vol. For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? A.1 Model Overview with Pseudo Codes In this subsection, we provide a high-level summary of our framework for better understanding. We present the summary in the form of pseudo codes, shown in Algorithm 1. Algorithm 1 The Overview of the Proposed Framework.

Learning the underlying equation from data is a fundamental problem in many disciplines. Recent advances rely on Neural Networks (NNs) but do not provide theoretical guarantees in obtaining the exact equations owing to the non-convexity of NNs. In this paper, we propose Convex Neural Symbolic Learning (CONSOLE) to seek convexity under mild conditions. The main idea is to decompose the recovering process into two steps and convexify each step.

We remind important related works to understand how our AdvInfoNCE stands and its role in rich literature. Our work is related to the literature on contrastive learning-based collaborative filtering (CL-based CF) methods, and theoretical understanding of contrastive loss in collaborative filtering. A.1 Contrastive Learning-based Collaborative Filtering The latest CL-based CF methods can roughly fall into two research lines. The second category, referred to as "loss-based" approaches, mainly focuses on the modification of contrastive loss. In loss-based CF models, interacted items serve as positive instances. The prevailing augmentation-based paradigm in CL-based CF methods is to employ user-item bipartite graph augmentations to generate contrasting views. These contrasting views are then treated as positive instances in the application of contrastive loss, such as InfoNCE loss, to further enhance collaborative filtering signals.