Transformers Struggle to Learn to Search

Search is an ability foundational in many important tasks, and recent studies have shown that large language models (LLMs) struggle to perform search robustly. It is unknown whether this inability is due to a lack of data, insufficient model parameters, or fundamental limitations of the transformer architecture. In this work, we use the foundational graph connectivity problem as a testbed to generate effectively limitless high-coverage data to train small transformers and test whether they can learn to perform search. We find that, when given the right training distribution, the transformer is able to learn to search. We analyze the algorithm that the transformer has learned through a novel mechanistic interpretability technique that enables us to extract the computation graph from the trained model. We find that for each vertex in the input graph, transformers compute the set of vertices reachable from that vertex. Each layer then progressively expands these sets, allowing the model to search over a number of vertices exponential in the number of layers. However, we find that as the input graph size increases, the transformer has greater difficulty in learning the task. This difficulty is not resolved even as the number of parameters is increased, suggesting that increasing model scale will not lead to robust search abilities. We also find that performing search in-context (i.e., chain-of-thought) does not resolve this inability to learn to search on larger graphs.

MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs

Large language models (LLMs) can solve arithmetic word problems with high accuracy, but little is known about how well they generalize to problems that are more complex than the ones on which they have been trained. Empirical investigations of such questions are impeded by two major flaws of current evaluations: (i) much of the evaluation data is contaminated, in the sense that it has already been seen during training, and (ii) benchmark datasets do not capture how problem proofs may be arbitrarily complex in various ways. As a step towards addressing these issues, we present a framework for evaluating LLMs on problems that have arbitrarily complex arithmetic proofs, called MathGAP. MathGAP generates problems that follow fixed proof specifications -- along with chain-of-thought reasoning annotations -- enabling systematic studies on generalization with respect to arithmetic proof complexity. We apply MathGAP to analyze how in-context learning interacts with generalization to problems that have more complex proofs. We find that among the models tested, most show a significant decrease in performance as proofs get deeper and wider. This effect is more pronounced in complex, nonlinear proof structures, which are challenging even for GPT-4o. Surprisingly, providing in-context examples from the same distribution as the test set is not always beneficial for performance. In particular, zero-shot prompting as well as demonstrating a diverse range of examples that are less complex than the test data sometimes yield similar or higher accuracies.

A Practical Review of Mechanistic Interpretability for Transformer-Based Language Models

Mechanistic interpretability (MI) is an emerging sub-field of interpretability that seeks to understand a neural network model by reverse-engineering its internal computations. Recently, MI has garnered significant attention for interpreting transformer-based language models (LMs), resulting in many novel insights yet introducing new challenges. However, there has not been work that comprehensively reviews these insights and challenges, particularly as a guide for newcomers to this field. To fill this gap, we present a comprehensive survey outlining fundamental objects of study in MI, techniques that have been used for its investigation, approaches for evaluating MI results, and significant findings and applications stemming from the use of MI to understand LMs. In particular, we present a roadmap for beginners to navigate the field and leverage MI for their benefit. Finally, we also identify current gaps in the field and discuss potential future directions.

LLMs Are Prone to Fallacies in Causal Inference

Recent work shows that causal facts can be effectively extracted from LLMs through prompting, facilitating the creation of causal graphs for causal inference tasks. However, it is unclear if this success is limited to explicitly-mentioned causal facts in the pretraining data which the model can memorize. Thus, this work investigates: Can LLMs infer causal relations from other relational data in text? To disentangle the role of memorized causal facts vs inferred causal relations, we finetune LLMs on synthetic data containing temporal, spatial and counterfactual relations, and measure whether the LLM can then infer causal relations. We find that: (a) LLMs are susceptible to inferring causal relations from the order of two entity mentions in text (e.g. X mentioned before Y implies X causes Y); (b) if the order is randomized, LLMs still suffer from the post hoc fallacy, i.e. X occurs before Y (temporal relation) implies X causes Y. We also find that while LLMs can correctly deduce the absence of causal relations from temporal and spatial relations, they have difficulty inferring causal relations from counterfactuals, questioning their understanding of causality.

Foundational Challenges in Assuring Alignment and Safety of Large Language Models

This work identifies 18 foundational challenges in assuring the alignment and safety of large language models (LLMs). These challenges are organized into three different categories: scientific understanding of LLMs, development and deployment methods, and sociotechnical challenges. Based on the identified challenges, we pose $200+$ concrete research questions.

Do Language Models Exhibit the Same Cognitive Biases in Problem Solving as Human Learners?

There is increasing interest in employing large language models (LLMs) as cognitive models. For such purposes, it is central to understand which cognitive properties are well-modeled by LLMs, and which are not. In this work, we study the biases of LLMs in relation to those known in children when solving arithmetic word problems. Surveying the learning science literature, we posit that the problem-solving process can be split into three distinct steps: text comprehension, solution planning and solution execution. We construct tests for each one in order to understand which parts of this process can be faithfully modeled by current state-of-the-art LLMs. We generate a novel set of word problems for each of these tests, using a neuro-symbolic method that enables fine-grained control over the problem features. We find evidence that LLMs, with and without instruction-tuning, exhibit human-like biases in both the text-comprehension and the solution-planning steps of the solving process, but not during the final step which relies on the problem's arithmetic expressions (solution execution).

Noisy Exemplars Make Large Language Models More Robust: A Domain-Agnostic Behavioral Analysis

Recent advances in prompt engineering enable large language models (LLMs) to solve multi-hop logical reasoning problems with impressive accuracy. However, there is little existing work investigating the robustness of LLMs with few-shot prompting techniques. Therefore, we introduce a systematic approach to test the robustness of LLMs in multi-hop reasoning tasks via domain-agnostic perturbations. We include perturbations at multiple levels of abstractions (e.g. lexical perturbations such as typos, and semantic perturbations such as the inclusion of intermediate reasoning steps in the questions) to conduct behavioral analysis on the LLMs. Throughout our experiments, we find that models are more sensitive to certain perturbations such as replacing words with their synonyms. We also demonstrate that increasing the proportion of perturbed exemplars in the prompts improves the robustness of few-shot prompting methods.

Personas as a Way to Model Truthfulness in Language Models

Large Language Models are trained on vast amounts of text from the internet, which contains both factual and misleading information about the world. Can language models discern truth from falsehood in this contradicting data? Expanding on the view that LLMs can model different agents producing the corpora, we hypothesize that they can cluster truthful text by modeling a truthful persona: a group of agents that are likely to produce truthful text and share similar features. For example, trustworthy sources like Wikipedia and Science usually use formal writing styles and make consistent claims. By modeling this persona, LLMs can generalize truthfulness beyond the specific contexts in which each agent generated the training text. For example, the model can infer that the agent "Wikipedia" will behave truthfully on topics that were only generated by "Science" because they share a persona. We first show evidence for the persona hypothesis via two observations: (1) we can probe whether a model's answer will be truthful before it is generated; (2) finetuning a model on a set of facts improves its truthfulness on unseen topics. Next, using arithmetics as a synthetic environment, we show that language models can separate true and false statements, and generalize truthfulness across agents; but only if agents in the training data share a truthful generative process that enables the creation of a truthful persona. Overall, our findings suggest that models can exploit hierarchical structures in the data to learn abstract concepts like truthfulness.

Retrieval-Augmented Chain-of-Thought in Semi-structured Domains

Applying existing question answering (QA) systems to specialized domains like law and finance presents challenges that necessitate domain expertise. Although large language models (LLMs) have shown impressive language comprehension and in-context learning capabilities, their inability to handle very long inputs/contexts is well known. Tasks specific to these domains need significant background knowledge, leading to contexts that can often exceed the maximum length that existing LLMs can process. This study explores leveraging the semi-structured nature of legal and financial data to efficiently retrieve relevant context, enabling the use of LLMs for domain-specialized QA. The resulting system outperforms contemporary models and also provides useful explanations for the answers, encouraging the integration of LLMs into legal and financial NLP systems for future research.

World Models for Math Story Problems

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.