Pre-trained large language models (LLMs) exhibit impressive mathematical reasoning capabilities, yet how they compute basic arithmetic, such as addition, remains unclear. This paper shows that pre-trained LLMs add numbers using Fourier features -- dimensions in the hidden state that represent numbers via a set of features sparse in the frequency domain. Within the model, MLP and attention layers use Fourier features in complementary ways: MLP layers primarily approximate the magnitude of the answer using low-frequency features, while attention layers primarily perform modular addition (e.g., computing whether the answer is even or odd) using high-frequency features. Pre-training is crucial for this mechanism: models trained from scratch to add numbers only exploit low-frequency features, leading to lower accuracy. Introducing pre-trained token embeddings to a randomly initialized model rescues its performance. Overall, our analysis demonstrates that appropriate pre-trained representations (e.g., Fourier features) can unlock the ability of Transformers to learn precise mechanisms for algorithmic tasks.

Classical planning approaches guarantee finding a set of actions that can achieve a given goal state when possible, but require an expert to specify logical action semantics that govern the dynamics of the environment. Researchers have shown that Large Language Models (LLMs) can be used to directly infer planning steps based on commonsense knowledge and minimal domain information alone, but such plans often fail on execution. We bring together the strengths of classical planning and LLM commonsense inference to perform domain induction, learning and validating action pre- and post-conditions based on closed-loop interactions with the environment itself. We propose PSALM, which leverages LLM inference to heuristically complete partial plans emitted by a classical planner given partial domain knowledge, as well as to infer the semantic rules of the domain in a logical language based on environment feedback after execution. Our analysis on 7 environments shows that with just one expert-curated example plans, using LLMs as heuristic planners and rule predictors achieves lower environment execution steps and environment resets than random exploration while simultaneously recovering the underlying ground truth action semantics of the domain.

Current foundation models exhibit impressive capabilities when prompted either with text only or with both image and text inputs. But do their capabilities change depending on the input modality? In this work, we propose $\textbf{IsoBench}$, a benchmark dataset containing problems from four major areas: math, science, algorithms, and games. Each example is presented with multiple $\textbf{isomorphic representations}$ of inputs, such as visual, textual, and mathematical presentations. IsoBench provides fine-grained feedback to diagnose performance gaps caused by the form of the representation. Across various foundation models, we observe that on the same problem, models have a consistent preference towards textual representations. Most prominently, when evaluated on all IsoBench problems, Claude-3 Opus performs 28.7 points worse when provided with images instead of text; similarly, GPT-4 Turbo is 18.7 points worse and Gemini Pro is 14.9 points worse. Finally, we present two prompting techniques, $\textit{IsoCombination}$ and $\textit{IsoScratchPad}$, which improve model performance by considering combinations of, and translations between, different input representations.

Detecting negatives (such as non-entailment relationships, unanswerable questions, and false claims) is an important and challenging aspect of many natural language understanding tasks. Though manually collecting challenging negative examples can help models detect them, it is both costly and domain-specific. In this work, we propose Self-labeled Counterfactuals for Extrapolating to Negative Examples (SCENE), an automatic method for synthesizing training data that greatly improves models' ability to detect challenging negative examples. In contrast with standard data augmentation, which synthesizes new examples for existing labels, SCENE can synthesize negative examples zero-shot from only positive ones. Given a positive example, SCENE perturbs it with a mask infilling model, then determines whether the resulting example is negative based on a self-training heuristic. With access to only answerable training examples, SCENE can close 69.6% of the performance gap on SQuAD 2.0, a dataset where half of the evaluation examples are unanswerable, compared to a model trained on SQuAD 2.0. Our method also extends to boolean question answering and recognizing textual entailment, and improves generalization from SQuAD to ACE-whQA, an out-of-domain extractive QA benchmark.

We train a language model (LM) to robustly answer multistep questions by generating and answering sub-questions. We propose Chain-of-Questions, a framework that trains a model to generate sub-questions and sub-answers one at a time by leveraging human annotated question decomposition meaning representation (QDMR). The key technical challenge is that QDMR only contains sub-questions but not answers to those sub-questions, so we treat sub-answers as latent variables and optimize them using a novel dynamic mixture of Hard-EM and MAPO. Chain-of-Questions greatly outperforms strong neuro-symbolic methods by 9.0 F1 on DROP contrast set, and outperforms GPT-3.5 by 24.3 F1 on HOTPOTQA adversarial set, thus demonstrating the effectiveness and robustness of our framework.

Data augmentation via back-translation is common when pretraining Vision-and-Language Navigation (VLN) models, even though the generated instructions are noisy. But: does that noise matter? We find that nonsensical or irrelevant language instructions during pretraining can have little effect on downstream performance for both HAMT and VLN-BERT on R2R, and is still better than only using clean, human data. To underscore these results, we concoct an efficient augmentation method, Unigram + Object, which generates nonsensical instructions that nonetheless improve downstream performance. Our findings suggest that what matters for VLN R2R pretraining is the quantity of visual trajectories, not the quality of instructions.

Understanding visually situated language requires recognizing text and visual elements, and interpreting complex layouts. State-of-the-art methods commonly use specialized pre-processing tools, such as optical character recognition (OCR) systems, that map document image inputs to extracted information in the space of textual tokens, and sometimes also employ large language models (LLMs) to reason in text token space. However, the gains from external tools and LLMs come at the cost of increased computational and engineering complexity. In this paper, we ask whether small pretrained image-to-text models can learn selective text or layout recognition and reasoning as an intermediate inference step in an end-to-end model for pixel-level visual language understanding. We incorporate the outputs of such OCR tools, LLMs, and larger multimodal models as intermediate ``rationales'' on training data, and train a small student model to predict both rationales and answers for input questions based on those training examples. A student model based on Pix2Struct (282M parameters) achieves consistent improvements on three visual document understanding benchmarks representing infographics, scanned documents, and figures, with improvements of more than 4\% absolute over a comparable Pix2Struct model that predicts answers directly.

Large language models (LLMs) can memorize many pretrained sequences verbatim. This paper studies if we can locate a small set of neurons in LLMs responsible for memorizing a given sequence. While the concept of localization is often mentioned in prior work, methods for localization have never been systematically and directly evaluated; we address this with two benchmarking approaches. In our INJ Benchmark, we actively inject a piece of new information into a small subset of LLM weights and measure whether localization methods can identify these "ground truth" weights. In the DEL Benchmark, we study localization of pretrained data that LLMs have already memorized; while this setting lacks ground truth, we can still evaluate localization by measuring whether dropping out located neurons erases a memorized sequence from the model. We evaluate five localization methods on our two benchmarks, and both show similar rankings. All methods exhibit promising localization ability, especially for pruning-based methods, though the neurons they identify are not necessarily specific to a single memorized sequence.

We investigate the predictability of large language model (LLM) capabilities: given records of past experiments using different model families, numbers of parameters, tasks, and numbers of in-context examples, can we accurately predict LLM performance on new experiment configurations? Answering this question has practical implications for LLM users (e.g., deciding which models to try), developers (e.g., prioritizing evaluation on representative tasks), and the research community (e.g., identifying hard-to-predict capabilities that warrant further investigation). We study the performance prediction problem on experiment records from BIG-bench. On a random train-test split, an MLP-based predictor achieves an $R^2$ score greater than 95%, indicating the presence of learnable patterns within the experiment records. We then formulate the problem of searching for "small-bench," an informative subset of BIG-bench tasks from which the performance on the full set can be maximally recovered. We find a subset as informative as BIG-bench Hard for evaluating new model families, while being $3\times$ smaller. Additionally, we find competitive subsets by clustering task representations learned by our MLP-based predictor and selecting tasks close to cluster centroids, highlighting the importance of task diversity in constructing "small-bench."

Large Language Models (LLMs) have the impressive ability to perform in-context learning (ICL) from only a few examples, but the success of ICL varies widely from task to task. Thus, it is important to quickly determine whether ICL is applicable to a new task, but directly evaluating ICL accuracy can be expensive in situations where test data is expensive to annotate -- the exact situations where ICL is most appealing. In this paper, we propose the task of ICL accuracy estimation, in which we predict the accuracy of an LLM when doing in-context learning on a new task given only unlabeled test data for that task. To perform ICL accuracy estimation, we propose a method that trains a meta-model using LLM confidence scores as features. We compare our method to several strong accuracy estimation baselines on a new benchmark that covers 4 LLMs and 3 task collections. The meta-model improves over all baselines across 8 out of 12 settings and achieves the same estimation performance as directly evaluating on 40 collected labeled test examples per task. At the same time, no existing approach provides an accurate and reliable ICL accuracy estimation in every setting, highlighting the need for better ways to measure the uncertainty of LLM predictions.