Structured World Representations in Maze-Solving Transformers

Transformer models underpin many recent advances in practical machine learning applications, yet understanding their internal behavior continues to elude researchers. Given the size and complexity of these models, forming a comprehensive picture of their inner workings remains a significant challenge. To this end, we set out to understand small transformer models in a more tractable setting: that of solving mazes. In this work, we focus on the abstractions formed by these models and find evidence for the consistent emergence of structured internal representations of maze topology and valid paths. We demonstrate this by showing that the residual stream of only a single token can be linearly decoded to faithfully reconstruct the entire maze. We also find that the learned embeddings of individual tokens have spatial structure. Furthermore, we take steps towards deciphering the circuity of path-following by identifying attention heads (dubbed $\textit{adjacency heads}$), which are implicated in finding valid subsequent tokens.

A Configurable Library for Generating and Manipulating Maze Datasets

Understanding how machine learning models respond to distributional shifts is a key research challenge. Mazes serve as an excellent testbed due to varied generation algorithms offering a nuanced platform to simulate both subtle and pronounced distributional shifts. To enable systematic investigations of model behavior on out-of-distribution data, we present $\texttt{maze-dataset}$, a comprehensive library for generating, processing, and visualizing datasets consisting of maze-solving tasks. With this library, researchers can easily create datasets, having extensive control over the generation algorithm used, the parameters fed to the algorithm of choice, and the filters that generated mazes must satisfy. Furthermore, it supports multiple output formats, including rasterized and text-based, catering to convolutional neural networks and autoregressive transformer models. These formats, along with tools for visualizing and converting between them, ensure versatility and adaptability in research applications.

Sparse Relational Reasoning with Object-Centric Representations

We investigate the composability of soft-rules learned by relational neural architectures when operating over object-centric (slot-based) representations, under a variety of sparsity-inducing constraints. We find that increasing sparsity, especially on features, improves the performance of some models and leads to simpler relations. Additionally, we observe that object-centric representations can be detrimental when not all objects are fully captured; a failure mode to which CNNs are less prone. These findings demonstrate the trade-offs between interpretability and performance, even for models designed to tackle relational tasks.