Language Models, Graph Searching, and Supervision Adulteration: When More Supervision is Less and How to Make More More

This work concerns the path-star task, a minimal example of searching over a graph. The graph, $G$, is star-shaped with $D$ arms radiating from a start node, $s$. A language model (LM) is given $G$, $s$, and a target node $t$, which ends one of the arms and is tasked with generating the arm containing $t$. The minimal nature of this task means only a single choice needs to be made: which of the $D$ arms contains $t$? Decoder-only LMs fail to solve this elementary task above $1/D$ chance due to a learned shortcut that absorbs training supervision. We show how this pathology is caused by excess supervision and we present a series of solutions demonstrating that the task is solvable via decoder-only LMs. We find that the task's minimal nature causes its difficulty, as it prevents task decomposition. Our solutions provide insight into the pathology and its implications for LMs trained via next-token prediction.

The Mystery of the Pathological Path-star Task for Language Models

The recently introduced path-star task is a minimal task designed to exemplify limitations to the abilities of language models (Bachmann and Nagarajan, 2024). It involves a path-star graph where multiple arms radiate from a single starting node and each node is unique. Given the start node and a specified target node that ends an arm, the task is to generate the arm containing that target node. This is straightforward for a human but surprisingly difficult for language models, which did not outperform the random baseline. The authors hypothesized this is due to a deficiency in teacher-forcing and the next-token prediction paradigm. We demonstrate the task is learnable using teacher-forcing in alternative settings and that the issue is partially due to representation. We introduce a regularization method using structured samples of the same graph but with differing target nodes, improving results across a variety of model types. We provide RASP proofs showing the task is theoretically solvable. Finally, we find settings where an encoder-only model can consistently solve the task.

Language Modelling via Learning to Rank

We consider language modelling (LM) as a multi-label structured prediction task by re-framing training from solely predicting a single ground-truth word to ranking a set of words which could continue a given context. To avoid annotating top-$k$ ranks, we generate them using pre-trained LMs: GPT-2, BERT, and Born-Again models. This leads to a rank-based form of knowledge distillation (KD). We also develop a method using $N$-grams to create a non-probabilistic teacher which generates the ranks without the need of a pre-trained LM. We confirm the hypotheses that we can treat LMing as a ranking task and that we can do so without the use of a pre-trained LM. We show that rank-based KD generally improves perplexity (PPL), often with statistical significance, when compared to Kullback-Leibler-based KD. Surprisingly, given the simplicity of the method, $N$-grams act as competitive teachers and achieve similar performance as using either BERT or a Born-Again model teachers. GPT-2 always acts as the best teacher, though, and using it and a Transformer-XL student on Wiki-02, rank-based KD reduces a cross-entropy baseline from 65.27 to 55.94 and against a KL-based KD of 56.70.