Igor Mineyev

Haizi Yu, Igor Mineyev, Lav R. Varshney et al.

Humans can generalize from only a few examples and from little pretraining on similar tasks. Yet, machine learning (ML) typically requires large data to learn or pre-learn to transfer. Motivated by nativism and artificial general intelligence, we directly model human-innate priors in abstract visual tasks such as character and doodle recognition. This yields a white-box model that learns general-appearance similarity by mimicking how humans naturally ``distort'' an object at first sight. Using just nearest-neighbor classification on this cognitively-inspired similarity space, we achieve human-level recognition with only $1$--$10$ examples per class and no pretraining. This differs from few-shot learning that uses massive pretraining. In the tiny-data regime of MNIST, EMNIST, Omniglot, and QuickDraw benchmarks, we outperform both modern neural networks and classical ML. For unsupervised learning, by learning the non-Euclidean, general-appearance similarity space in a $k$-means style, we achieve multifarious visual realizations of abstract concepts by generating human-intuitive archetypes as cluster centroids.

Haizi Yu, Igor Mineyev, Lav R. Varshney

Abstraction plays a key role in concept learning and knowledge discovery; this paper is concerned with computational abstraction. In particular, we study the nature of abstraction through a group-theoretic approach, formalizing it as symmetry-driven---as opposed to data-driven---hierarchical clustering. Thus, the resulting clustering framework is data-free, feature-free, similarity-free, and globally hierarchical---the four key features that distinguish it from common data clustering models such as $k$-means. Beyond a theoretical foundation for abstraction, we also present a top-down and a bottom-up approach to establish an algorithmic foundation for practical abstraction-generating methods. Lastly, via both a theoretical explanation and a real-world application, we illustrate that further coupling of our abstraction framework with statistics realizes Shannon's information lattice and even further, brings learning into the picture. This not only presents one use case of our proposed computational abstraction, but also gives a first step towards a principled and cognitive way of automatic concept learning and knowledge discovery.