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We present a dataset and experiments on applying recurrent neural networks (RNNs) for guiding clause selection in the connection tableau proof calculus. The RNN encodes a sequence of literals from the current branch of the partial proof…
We introduce the notion of a definable category--a category equivalent to a full subcategory of a locally finitely presentable category that is closed under products, directed colimits and pure subobjects. Definable subcategories are…
Over the years, reasoning over knowledge graphs (KGs), which aims to infer new conclusions from known facts, has mostly focused on static KGs. The unceasing growth of knowledge in real life raises the necessity to enable the inductive…
GNN-based approaches for learning general policies across planning domains are limited by the expressive power of $C_2$, namely; first-order logic with two variables and counting. This limitation can be overcame by transitioning to…
In this series we introduce and investigate the concept of connectoids, which captures the connectivity structure of various discrete objects like undirected graphs, directed graphs, bidirected graphs, hypergraphs or finitary matroids. In…
Theory revision integrates inductive learning and background knowledge by combining training examples with a coarse domain theory to produce a more accurate theory. There are two challenges that theory revision and other theory-guided…
This paper presents abstract art created by neural networks and broadly recognizable across various computer vision systems. The existence of abstract forms that trigger specific labels independent of neural architecture or training set…
In a large, possibly infinite population, each subject is colored red with probability $p$, independently of the others. Then, a finite sub-population is selected, possibly as a function of the coloring. The imbalance in the sub-population…
The complicated syntax structure of natural language is hard to be explicitly modeled by sequence-based models. Graph is a natural structure to describe the complicated relation between tokens. The recent advance in Graph Neural Networks…
Vectors are universal mathematical objects that can represent text, images, speech, or a mix of these data modalities. That happens regardless of whether data is represented by hand-crafted features or learnt embeddings. Collect a large…
We prove a deletion-contraction formula for motivic Feynman rules given by the classes of the affine graph hypersurface complement in the Grothendieck ring of varieties. We derive explicit recursions and generating series for these motivic…
Suppose $G$ is a real reductive group. The determination of the irreducible unitary representations of $G$ is one of the major unsolved problem in representation theory. There is evidence to suggest that every irreducible unitary…
We provide a new characterization of enriched accessible categories by introducing the two new notions of virtual reflectivity and virtual orthogonality as a generalization of the usual reflectivity and orthogonality conditions for locally…
Applying convolutional neural networks to large images is computationally expensive because the amount of computation scales linearly with the number of image pixels. We present a novel recurrent neural network model that is capable of…
Reinforcement learning with verifiable rewards (RLVR) has been a main driver of recent breakthroughs in large reasoning models. Yet it remains a mystery how rewards based solely on final outcomes can help overcome the long-horizon barrier…
Recurrent connections in the visual cortex are thought to aid object recognition when part of the stimulus is occluded. Here we investigate if and how recurrent connections in artificial neural networks similarly aid object recognition. We…
Modern generative models demonstrate impressive capabilities, likely stemming from an ability to identify and manipulate abstract concepts underlying their training data. However, fundamental questions remain: what determines the concepts a…
Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data such as 2D and 3D images, video, and other data where…
A celebrated unit distance conjecture due to Erd\H os says that that the unit distances cannot arise more than $C_{\epsilon}n^{1+\epsilon}$ times (for any $\epsilon>0$) among $n$ points in the Euclidean plane (see e.g. \cite{SST84} and the…
Graph convolutions have gained popularity due to their ability to efficiently operate on data with an irregular geometric structure. However, graph convolutions cause over-smoothing, which refers to representations becoming more similar…