  Existing Collaborative Filtering (CF) methods are mostly designed based on
the idea of matching, i.e., by learning user and item embeddings from data
using shallow or deep models, they try to capture the associative relevance
patterns in data, so that a user embedding can be matched with relevant item
embeddings using designed or learned similarity functions. However, as a
cognition rather than a perception intelligent task, recommendation requires
not only the ability of pattern recognition and matching from data, but also
the ability of cognitive reasoning in data. In this paper, we propose to
advance Collaborative Filtering (CF) to Collaborative Reasoning (CR), which
means that each user knows part of the reasoning space, and they collaborate
for reasoning in the space to estimate preferences for each other. Technically,
we propose a Neural Collaborative Reasoning (NCR) framework to bridge learning
and reasoning. Specifically, we integrate the power of representation learning
and logical reasoning, where representations capture similarity patterns in
data from perceptual perspectives, and logic facilitates cognitive reasoning
for informed decision making. An important challenge, however, is to bridge
differentiable neural networks and symbolic reasoning in a shared architecture
for optimization and inference. To solve the problem, we propose a modularized
reasoning architecture, which learns logical operations such as AND ($\wedge$),
OR ($\vee$) and NOT ($\neg$) as neural modules for implication reasoning
($\rightarrow$). In this way, logical expressions can be equivalently organized
as neural networks, so that logical reasoning and prediction can be conducted
in a continuous space. Experiments on real-world datasets verified the
advantages of our framework compared with both shallow, deep and reasoning
models.
