We propose Information Lattice Learning (ILL) as a general framework to learn rules of a signal (e.g., an image or a probability distribution). In our definition, a rule is a coarsened signal used to help us gain one interpretable insight about the original signal. To make full sense of what might govern the signal’s intrinsic structure, we seek multiple disentangled rules arranged in a hierarchy, called a lattice. Compared to representation/rule-learning models optimized for a specific task (e.g., classification), ILL focuses on explainability: it is designed to mimic human experiential learning and discover rules akin to those humans can distill and comprehend. This paper details the math and algorithms of ILL, and illustrates how it addresses the fundamental question “what makes X an X” by creating rule-based explanations designed to help humans understand. Our focus is on explaining X rather than (re)generating it. We present applications in knowledge discovery, using ILL to distill music theory from scores and chemical laws from molecules and further revealing connections between them. We show ILL’s efficacy and interpretability on benchmarks and assessments, as well as a demonstration of ILL-enhanced classifiers achieving human-level digit recognition using only one or a few MNIST training examples (1–10 per class).

Humans' abstraction ability plays a key role in concept learning and knowledge discovery. This theory paper presents the mathematical formulation for computationally emulating human-like abstractions---computational abstraction---and abstraction processes developed hierarchically from innate priors like symmetries. We study the nature of abstraction via a group-theoretic approach, formalizing and practically computing abstractions as symmetry-driven hierarchical clustering. Compared to data-driven clustering like k-means or agglomerative clustering (a chain), our abstraction model is data-free, feature-free, similarity-free, and globally hierarchical (a lattice). This paper also serves as a theoretical generalization of several existing works. These include generalizing Shannon's information lattice, specialized algorithms for certain symmetry-induced clusterings, as well as formalizing knowledge discovery applications such as learning music theory from scores and chemistry laws from molecules. We consider computational abstraction as a first step towards a principled and cognitive way of achieving human-level concept learning and knowledge discovery.

Concrete is the most widely used engineered material in the world with more than 10 billion tons produced annually. Unfortunately, with that scale comes a significant burden in terms of energy, water, and release of greenhouse gases and other pollutants; indeed 8% of worldwide carbon emissions are attributed to the production of cement, a key ingredient in concrete. As such, there is interest in creating concrete formulas that minimize this environmental burden, while satisfying engineering performance requirements including compressive strength. Specifically for computing, concrete is a major ingredient in the construction of data centers.

Abstraction and realization are bilateral processes that are key in deriving intelligence and creativity. In many domains, the two processes are approached through \emph{rules}: high-level principles that reveal invariances within similar yet diverse examples. Under a probabilistic setting for discrete input spaces, we focus on the rule realization problem which generates input sample distributions that follow the given rules. More ambitiously, we go beyond a mechanical realization that takes whatever is given, but instead ask for proactively selecting reasonable rules to realize. This goal is demanding in practice, since the initial rule set may not always be consistent and thus intelligent compromises are needed. We formulate both rule realization and selection as two strongly connected components within a single and symmetric bi-convex problem, and derive an efficient algorithm that works at large scale. Taking music compositional rules as the main example throughout the paper, we demonstrate our model's efficiency in not only music realization (composition) but also music interpretation and understanding (analysis).

Ranking users in social networks is a well-studied problem, typically solved by algorithms that leverage network structure to identify influential users and recommend people to follow. In the last decade, however, curation --- users sharing and promoting content in a network --- has become a central social activity, as platforms like Facebook, Twitter, Pinterest, and GitHub drive growth and engagement by connecting users through content and content to users. While existing algorithms reward users that are highly active with higher rankings, they fail to account for users' curatorial taste. This paper introduces CuRank, an algorithm for ranking users and content in social networks by explicitly modeling three characteristics of a good curator: discerning taste, high activity, and timeliness. We evaluate CuRank on datasets from two popular social networks --- GitHub and Vine --- and demonstrate its efficacy at ranking content and identifying good curators.