(How) Do Language Models Track State?

Transformer language models (LMs) exhibit behaviors -- from storytelling to code generation -- that appear to require tracking the unobserved state of an evolving world. How do they do so? We study state tracking in LMs trained or fine-tuned to compose permutations (i.e., to compute the order of a set of objects after a sequence of swaps). Despite the simple algebraic structure of this problem, many other tasks (e.g., simulation of finite automata and evaluation of boolean expressions) can be reduced to permutation composition, making it a natural model for state tracking in general. We show that LMs consistently learn one of two state tracking mechanisms for this task. The first closely resembles the "associative scan" construction used in recent theoretical work by Liu et al. (2023) and Merrill et al. (2024). The second uses an easy-to-compute feature (permutation parity) to partially prune the space of outputs, then refines this with an associative scan. The two mechanisms exhibit markedly different robustness properties, and we show how to steer LMs toward one or the other with intermediate training tasks that encourage or suppress the heuristics. Our results demonstrate that transformer LMs, whether pretrained or fine-tuned, can learn to implement efficient and interpretable state tracking mechanisms, and the emergence of these mechanisms can be predicted and controlled.

LM Agents for Coordinating Multi-User Information Gathering

This paper introduces PeopleJoin, a benchmark for evaluating LM-mediated collaborative problem solving. Given a user request, PeopleJoin agents must identify teammates who might be able to assist, converse with these teammates to gather information, and finally compile a useful answer or summary for the original user. PeopleJoin comprises two evaluation domains: PeopleJoin-QA, focused on questions about tabular data, and PeopleJoin-DocCreation, focused on document creation tasks. The two domains are adapted from existing NLP benchmarks for database question answering and multi-document summarization; here, however, the information needed to complete these tasks is distributed across synthetic ``organizations'' of 2--20 users, simulating natural multi-user collaboration scenarios. We implemented several popular LM agent architectures, evaluating their accuracy and efficiency at completing tasks, and highlight new research questions that can be studied using PeopleJoin.

The Surprising Effectiveness of Test-Time Training for Abstract Reasoning

Language models have shown impressive performance on tasks within their training distribution, but often struggle with novel problems requiring complex reasoning. We investigate the effectiveness of test-time training (TTT) -- updating model parameters temporarily during inference using a loss derived from input data -- as a mechanism for improving models' reasoning capabilities, using the Abstraction and Reasoning Corpus (ARC) as a benchmark. Through systematic experimentation, we identify three crucial components for successful TTT: (1) initial finetuning on similar tasks (2) auxiliary task format and augmentations (3) per-instance training. TTT significantly improves performance on ARC tasks, achieving up to 6x improvement in accuracy compared to base fine-tuned models; applying TTT to an 8B-parameter language model, we achieve 53% accuracy on the ARC's public validation set, improving the state-of-the-art by nearly 25% for public and purely neural approaches. By ensembling our method with recent program generation approaches, we get SoTA public validation accuracy of 61.9%, matching the average human score. Our findings suggest that explicit symbolic search is not the only path to improved abstract reasoning in neural language models; additional test-time applied to continued training on few-shot examples can also be extremely effective.

LoRA vs Full Fine-tuning: An Illusion of Equivalence

Fine-tuning is a crucial paradigm for adapting pre-trained large language models to downstream tasks. Recently, methods like Low-Rank Adaptation (LoRA) have been shown to match the performance of fully fine-tuned models on various tasks with an extreme reduction in the number of trainable parameters. Even in settings where both methods learn similarly accurate models, \emph{are their learned solutions really equivalent?} We study how different fine-tuning methods change pre-trained models by analyzing the model's weight matrices through the lens of their spectral properties. We find that full fine-tuning and LoRA yield weight matrices whose singular value decompositions exhibit very different structure; moreover, the fine-tuned models themselves show distinct generalization behaviors when tested outside the adaptation task's distribution. More specifically, we first show that the weight matrices trained with LoRA have new, high-ranking singular vectors, which we call \emph{intruder dimensions}. Intruder dimensions do not appear during full fine-tuning. Second, we show that LoRA models with intruder dimensions, despite achieving similar performance to full fine-tuning on the target task, become worse models of the pre-training distribution and adapt less robustly to multiple tasks sequentially. Higher-rank, rank-stabilized LoRA models closely mirror full fine-tuning, even when performing on par with lower-rank LoRA models on the same tasks. These results suggest that models updated with LoRA and full fine-tuning access different parts of parameter space, even when they perform equally on the fine-tuned distribution. We conclude by examining why intruder dimensions appear in LoRA fine-tuned models, why they are undesirable, and how their effects can be minimized.

A Hitchhiker's Guide to Scaling Law Estimation

Scaling laws predict the loss of a target machine learning model by extrapolating from easier-to-train models with fewer parameters or smaller training sets. This provides an efficient way for practitioners and researchers alike to compare pretraining decisions involving optimizers, datasets, and model architectures. Despite the widespread use of scaling laws to model the dynamics of language model training, there has been little work on understanding how to best estimate and interpret them. We collect (and release) a large-scale dataset containing losses and downstream evaluations for 485 previously published pretrained models. We use these to estimate more than 1000 scaling laws, then derive a set of best practices for estimating scaling laws in new model families. We find that fitting scaling laws to intermediate checkpoints of training runs (and not just their final losses) substantially improves accuracy, and that -- all else equal -- estimates of performance are generally most accurate when derived from other models of similar sizes. However, because there is a significant degree of variability across model seeds, training multiple small models is sometimes more useful than training a single large one. Moreover, while different model families differ scaling behavior, they are often similar enough that a target model's behavior can be predicted from a single model with the same architecture, along with scaling parameter estimates derived from other model families.

MisinfoEval: Generative AI in the Era of "Alternative Facts"

The spread of misinformation on social media platforms threatens democratic processes, contributes to massive economic losses, and endangers public health. Many efforts to address misinformation focus on a knowledge deficit model and propose interventions for improving users' critical thinking through access to facts. Such efforts are often hampered by challenges with scalability, and by platform users' personal biases. The emergence of generative AI presents promising opportunities for countering misinformation at scale across ideological barriers. In this paper, we introduce a framework (MisinfoEval) for generating and comprehensively evaluating large language model (LLM) based misinformation interventions. We present (1) an experiment with a simulated social media environment to measure effectiveness of misinformation interventions, and (2) a second experiment with personalized explanations tailored to the demographics and beliefs of users with the goal of countering misinformation by appealing to their pre-existing values. Our findings confirm that LLM-based interventions are highly effective at correcting user behavior (improving overall user accuracy at reliability labeling by up to 41.72%). Furthermore, we find that users favor more personalized interventions when making decisions about news reliability and users shown personalized interventions have significantly higher accuracy at identifying misinformation.

Learning Linear Attention in Polynomial Time

Previous research has explored the computational expressivity of Transformer models in simulating Boolean circuits or Turing machines. However, the learnability of these simulators from observational data has remained an open question. Our study addresses this gap by providing the first polynomial-time learnability results (specifically strong, agnostic PAC learning) for single-layer Transformers with linear attention. We show that linear attention may be viewed as a linear predictor in a suitably defined RKHS. As a consequence, the problem of learning any linear transformer may be converted into the problem of learning an ordinary linear predictor in an expanded feature space, and any such predictor may be converted back into a multiheaded linear transformer. Moving to generalization, we show how to efficiently identify training datasets for which every empirical risk minimizer is equivalent (up to trivial symmetries) to the linear Transformer that generated the data, thereby guaranteeing the learned model will correctly generalize across all inputs. Finally, we provide examples of computations expressible via linear attention and therefore polynomial-time learnable, including associative memories, finite automata, and a class of Universal Turing Machine (UTMs) with polynomially bounded computation histories. We empirically validate our theoretical findings on three tasks: learning random linear attention networks, key--value associations, and learning to execute finite automata. Our findings bridge a critical gap between theoretical expressivity and learnability of Transformers, and show that flexible and general models of computation are efficiently learnable.

Learning How Hard to Think: Input-Adaptive Allocation of LM Computation

Computationally intensive decoding procedures--including search, reranking, and self-critique--can improve the quality of language model (LM) outputs in problems spanning code generation, numerical reasoning, and dialog. Existing work typically applies the same decoding procedure for every input to an LM. But not all inputs require the same amount of computation to process. Can we allocate decoding computation adaptively, using more resources to answer questions whose answers will be harder to compute? We present an approach that predicts the distribution of rewards given an input and computation budget, then allocates additional computation to inputs for which it is predicted to be most useful. We apply this approach in two decoding procedures: first, an adaptive best-of-k procedure that dynamically selects the number of samples to generate as input to a reranker; second, a routing procedure that dynamically responds to a query using a decoding procedure that is expensive but accurate, or one that is cheaper but less capable. Across a suite of programming, mathematics, and dialog tasks, we show that accurate computation-allocation procedures can be learned, and reduce computation by up to 50% at no cost to response quality, or improve quality by up to 10% at a fixed computational budget.

Algorithmic Capabilities of Random Transformers

Trained transformer models have been found to implement interpretable procedures for tasks like arithmetic and associative recall, but little is understood about how the circuits that implement these procedures originate during training. To what extent do they depend on the supervisory signal provided to models, and to what extent are they attributable to behavior already present in models at the beginning of training? To investigate these questions, we investigate what functions can be learned by randomly initialized transformers in which only the embedding layers are optimized, so that the only input--output mappings learnable from data are those already implemented (up to a choice of encoding scheme) by the randomly initialized model. We find that these random transformers can perform a wide range of meaningful algorithmic tasks, including modular arithmetic, in-weights and in-context associative recall, decimal addition, parenthesis balancing, and even some aspects of natural language text generation. Our results indicate that some algorithmic capabilities are present in transformers (and accessible via appropriately structured inputs) even before these models are trained. Code is available at https://github.com/fjzzq2002/random_transformers.

Adaptive Language-Guided Abstraction from Contrastive Explanations

Many approaches to robot learning begin by inferring a reward function from a set of human demonstrations. To learn a good reward, it is necessary to determine which features of the environment are relevant before determining how these features should be used to compute reward. End-to-end methods for joint feature and reward learning (e.g., using deep networks or program synthesis techniques) often yield brittle reward functions that are sensitive to spurious state features. By contrast, humans can often generalizably learn from a small number of demonstrations by incorporating strong priors about what features of a demonstration are likely meaningful for a task of interest. How do we build robots that leverage this kind of background knowledge when learning from new demonstrations? This paper describes a method named ALGAE (Adaptive Language-Guided Abstraction from [Contrastive] Explanations) which alternates between using language models to iteratively identify human-meaningful features needed to explain demonstrated behavior, then standard inverse reinforcement learning techniques to assign weights to these features. Experiments across a variety of both simulated and real-world robot environments show that ALGAE learns generalizable reward functions defined on interpretable features using only small numbers of demonstrations. Importantly, ALGAE can recognize when features are missing, then extract and define those features without any human input -- making it possible to quickly and efficiently acquire rich representations of user behavior.