Neural Discovery of Permutation Subgroups

We consider the problem of discovering subgroup $H$ of permutation group $S_{n}$. Unlike the traditional $H$-invariant networks wherein $H$ is assumed to be known, we present a method to discover the underlying subgroup, given that it satisfies certain conditions. Our results show that one could discover any subgroup of type $S_{k} (k \leq n)$ by learning an $S_{n}$-invariant function and a linear transformation. We also prove similar results for cyclic and dihedral subgroups. Finally, we provide a general theorem that can be extended to discover other subgroups of $S_{n}$. We also demonstrate the applicability of our results through numerical experiments on image-digit sum and symmetric polynomial regression tasks.

A Unified Framework for Discovering Discrete Symmetries

We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral and cyclic subgroups. At the core of the framework is a novel architecture composed of linear and tensor-valued functions that expresses functions invariant to these subgroups in a principled manner. The structure of the architecture enables us to leverage multi-armed bandit algorithms and gradient descent to efficiently optimize over the linear and the tensor-valued functions, respectively, and to infer the symmetry that is ultimately learnt. We also discuss the necessity of the tensor-valued functions in the architecture. Experiments on image-digit sum and polynomial regression tasks demonstrate the effectiveness of our approach.

GPT-Neo for commonsense reasoning-a theoretical and practical lens

Recent work has demonstrated substantial gains in pre-training large-scale unidirectional language models such as the GPT-2, GPT-3, and GPT-neo, followed by fine-tuning on a downstream task. In this paper, we evaluate the performance of the GPT-neo 1.3 billion model for commonsense reasoning tasks. We assess the model performance on six commonsense reasoning benchmark tasks and report the accuracy scores for these tasks. When fine-tuned using the right set of hyperparameters, we obtain competitive scores on three of these tasks but struggle when the dataset size is significantly smaller. The low model performance on a few of these tasks suggests the inherent difficulty in these datasets and since it fails to establish coherent patterns given their limited training samples. We also investigate and substantiate our results using visualization and conduct numerous inference tests to understand the model performance better. Finally, we conduct thorough robustness tests using various methods to gauge the model performance under numerous settings. These findings suggest a promising path for exploring smaller language models than the GPT-3 175 billion model to perform tasks requiring natural language understanding.