Mathematical reasoning is an increasingly important indicator of large language model (LLM) capabilities, yet we lack understanding of how LLMs process even simple mathematical tasks. To address this, we reverse engineer how three mid-sized LLMs compute addition. We first discover that numbers are represented in these LLMs as a generalized helix, which is strongly causally implicated for the tasks of addition and subtraction, and is also causally relevant for integer division, multiplication, and modular arithmetic. We then propose that LLMs compute addition by manipulating this generalized helix using the "Clock" algorithm: to solve $a+b$, the helices for $a$ and $b$ are manipulated to produce the $a+b$ answer helix which is then read out to model logits. We model influential MLP outputs, attention head outputs, and even individual neuron preactivations with these helices and verify our understanding with causal interventions. By demonstrating that LLMs represent numbers on a helix and manipulate this helix to perform addition, we present the first representation-level explanation of an LLM's mathematical capability.

What mechanisms underlie linguistic generalization in large language models (LLMs)? This question has attracted considerable attention, with most studies analyzing the extent to which the language skills of LLMs resemble rules. As of yet, it is not known whether linguistic generalization in LLMs could equally well be explained as the result of analogical processes, which can be formalized as similarity operations on stored exemplars. A key shortcoming of prior research is its focus on linguistic phenomena with a high degree of regularity, for which rule-based and analogical approaches make the same predictions. Here, we instead examine derivational morphology, specifically English adjective nominalization, which displays notable variability. We introduce a new method for investigating linguistic generalization in LLMs: focusing on GPT-J, we fit cognitive models that instantiate rule-based and analogical learning to the LLM training data and compare their predictions on a set of nonce adjectives with those of the LLM, allowing us to draw direct conclusions regarding underlying mechanisms. As expected, rule-based and analogical models explain the predictions of GPT-J equally well for adjectives with regular nominalization patterns. However, for adjectives with variable nominalization patterns, the analogical model provides a much better match. Furthermore, GPT-J's behavior is sensitive to the individual word frequencies, even for regular forms, a behavior that is consistent with an analogical account of regular forms but not a rule-based one. These findings refute the hypothesis that GPT-J's linguistic generalization on adjective nominalization involves rules, suggesting similarity operations on stored exemplars as the underlying mechanism. Overall, our study suggests that analogical processes play a bigger role in the linguistic generalization of LLMs than previously thought.

Prompt engineering, as an efficient and effective way to leverage Large Language Models (LLM), has drawn a lot of attention from the research community. The existing research primarily emphasizes the importance of adapting prompts to specific tasks, rather than specific LLMs. However, a good prompt is not solely defined by its wording, but also binds to the nature of the LLM in question. In this work, we first quantitatively demonstrate that different prompts should be adapted to different LLMs to enhance their capabilities across various downstream tasks in NLP. Then we novelly propose a model-adaptive prompt optimizer (MAPO) method that optimizes the original prompts for each specific LLM in downstream tasks. Extensive experiments indicate that the proposed method can effectively refine prompts for an LLM, leading to significant improvements over various downstream tasks.

Knowledge editing methods (KEs) can update language models' obsolete or inaccurate knowledge learned from pre-training. However, KEs can be used for malicious applications, e.g., inserting misinformation and toxic content. Knowing whether a generated output is based on edited knowledge or first-hand knowledge from pre-training can increase users' trust in generative models and provide more transparency. Driven by this, we propose a novel task: detecting edited knowledge in language models. Given an edited model and a fact retrieved by a prompt from an edited model, the objective is to classify the knowledge as either unedited (based on the pre-training), or edited (based on subsequent editing). We instantiate the task with four KEs, two LLMs, and two datasets. Additionally, we propose using the hidden state representations and the probability distributions as features for the detection. Our results reveal that, using these features as inputs to a simple AdaBoost classifiers establishes a strong baseline. This classifier requires only a limited amount of data and maintains its performance even in cross-domain settings. Last, we find it more challenging to distinguish edited knowledge from unedited but related knowledge, highlighting the need for further research. Our work lays the groundwork for addressing malicious model editing, which is a critical challenge associated with the strong generative capabilities of LLMs.

As large language models (LLMs) are widely deployed, targeted editing of their knowledge has become a critical challenge. Recently, advancements in model editing techniques, such as Rank-One Model Editing (ROME), have paved the way for updating LLMs with new knowledge. However, the efficacy of these methods varies across different types of knowledge. This study investigates the capability of knowledge editing methods to incorporate new knowledge with varying degrees of "perplexingness", a term we use to describe the initial difficulty LLMs have in understanding new concepts. We begin by quantifying the "perplexingness" of target knowledge using pre-edit conditional probabilities, and assess the efficacy of edits through post-edit conditional probabilities. Utilizing the widely-used CounterFact dataset, we find significant negative correlations between the "perplexingness" of the new knowledge and the edit efficacy across all 12 scenarios. To dive deeper into this phenomenon, we introduce a novel dataset, HierarchyData, consisting of 99 hyponym-hypernym pairs across diverse categories. Our analysis reveal that more abstract concepts (hypernyms) tend to be more perplexing than their specific counterparts (hyponyms). Further exploration into the influence of knowledge hierarchy on editing outcomes indicates that knowledge positioned at higher hierarchical levels is more challenging to modify in some scenarios. Our research highlights a previously overlooked aspect of LLM editing: the variable efficacy of editing methods in handling perplexing knowledge. By revealing how hierarchical relationships can influence editing outcomes, our findings offer new insights into the challenges of updating LLMs and pave the way for more nuanced approaches to model editing in the future.

Despite significant progress in model editing methods, their application in real-world scenarios remains challenging as they often cause large language models (LLMs) to collapse. Among them, ROME is particularly concerning, as it could disrupt LLMs with only a single edit. In this paper, we study the root causes of such collapse. Through extensive analysis, we identify two primary factors that contribute to the collapse: i) inconsistent handling of prefixed and unprefixed keys in the parameter update equation may result in very small denominators, causing excessively large parameter updates; ii) the subject of collapse cases is usually the first token, whose unprefixed key distribution significantly differs from the prefixed key distribution in autoregressive transformers, causing the aforementioned issue to materialize. To validate our analysis, we propose a simple yet effective approach: uniformly using prefixed keys during editing phase and adding prefixes during the testing phase. The experimental results show that the proposed solution can prevent model collapse while maintaining the effectiveness of the edits.

Knowledge editing aims to rectify inaccuracies in large language models (LLMs) without costly retraining for outdated or erroneous knowledge. However, current knowledge editing methods primarily focus on single editing, failing to meet the requirements for lifelong editing. This study reveals a performance degradation encountered by knowledge editing in lifelong editing, characterized by toxicity buildup and toxicity flash, with the primary cause identified as pattern unmatch. We introduce a knowledge editing approach named Wise-Layer Knowledge Editor (WilKE), which selects editing layer based on the pattern matching degree of editing knowledge across different layers in language models. Experimental results demonstrate that, in lifelong editing, WilKE exhibits an average improvement of 46.2% and 67.8% on editing GPT2-XL and GPT-J relative to state-of-the-art knowledge editing methods.

Although model editing has shown promise in revising knowledge in Large Language Models (LLMs), its impact on the inherent capabilities of LLMs is often overlooked. In this work, we reveal a critical phenomenon: even a single edit can trigger model collapse, manifesting as significant performance degradation in various benchmark tasks. However, benchmarking LLMs after each edit, while necessary to prevent such collapses, is impractically time-consuming and resource-intensive. To mitigate this, we propose using perplexity as a surrogate metric, validated by extensive experiments demonstrating changes in an edited model's perplexity are strongly correlated with its downstream task performances. We further conduct an in-depth study on sequential editing, a practical setting for real-world scenarios, across various editing methods and LLMs, focusing on hard cases from our previous single edit studies. The results indicate that nearly all examined editing methods result in model collapse after only few edits. To facilitate further research, we have utilized GPT-3.5 to develop a new dataset, HardEdit, based on those hard cases. This dataset aims to establish the foundation for pioneering research in reliable model editing and the mechanisms underlying editing-induced model collapse. We hope this work can draw the community's attention to the potential risks inherent in model editing practices.

In this paper, we investigate the output token probability information in the output embedding of language models. We provide an approximate common log-linear encoding of output token probabilities within the output embedding vectors and demonstrate that it is accurate and sparse when the output space is large and output logits are concentrated. Based on such findings, we edit the encoding in output embedding to modify the output probability distribution accurately. Moreover, the sparsity we find in output probability encoding suggests that a large number of dimensions in the output embedding do not contribute to causal language modeling. Therefore, we attempt to delete the output-unrelated dimensions and find more than 30% of the dimensions can be deleted without significant movement in output distribution and degeneration on sequence generation. Additionally, in training dynamics, we use such encoding as a probe and find that the output embeddings capture token frequency information in early steps, even before an obvious convergence starts.

Recent work using Rank-One Model Editing (ROME), a popular model editing method, has shown that there are certain facts that the algorithm is unable to edit without breaking the model. Such edits have previously been called disabling edits. These disabling edits cause immediate model collapse and limits the use of ROME for sequential editing. In this paper, we show that disabling edits are an artifact of irregularities in the implementation of ROME. With this paper, we provide a more stable implementation ROME, which we call r-ROME and show that model collapse is no longer observed when making large scale sequential edits with r-ROME, while further improving generalization and locality of model editing compared to the original implementation of ROME. We also provide a detailed mathematical explanation of the reason behind disabling edits.