Generalization or Hallucination? Understanding Out-of-Context Reasoning in Transformers

Large language models (LLMs) can acquire new knowledge through fine-tuning, but this process exhibits a puzzling duality: models can generalize remarkably from new facts, yet are also prone to hallucinating incorrect information. However, the reasons for this phenomenon remain poorly understood. In this work, we argue that both behaviors stem from a single mechanism known as out-of-context reasoning (OCR): the ability to deduce implications by associating concepts, even those without a causal link. Our experiments across five prominent LLMs confirm that OCR indeed drives both generalization and hallucination, depending on whether the associated concepts are causally related. To build a rigorous theoretical understanding of this phenomenon, we then formalize OCR as a synthetic factual recall task. We empirically show that a one-layer single-head attention-only transformer with factorized output and value matrices can learn to solve this task, while a model with combined weights cannot, highlighting the crucial role of matrix factorization. Our theoretical analysis shows that the OCR capability can be attributed to the implicit bias of gradient descent, which favors solutions that minimize the nuclear norm of the combined output-value matrix. This mathematical structure explains why the model learns to associate facts and implications with high sample efficiency, regardless of whether the correlation is causal or merely spurious. Ultimately, our work provides a theoretical foundation for understanding the OCR phenomenon, offering a new lens for analyzing and mitigating undesirable behaviors from knowledge injection.

Provable Sim-to-Real Transfer via Offline Domain Randomization

Reinforcement-learning agents often struggle when deployed from simulation to the real-world. A dominant strategy for reducing the sim-to-real gap is domain randomization (DR) which trains the policy across many simulators produced by sampling dynamics parameters, but standard DR ignores offline data already available from the real system. We study offline domain randomization (ODR), which first fits a distribution over simulator parameters to an offline dataset. While a growing body of empirical work reports substantial gains with algorithms such as DROPO, the theoretical foundations of ODR remain largely unexplored. In this work, we (i) formalize ODR as a maximum-likelihood estimation over a parametric simulator family, (ii) prove consistency of this estimator under mild regularity and identifiability conditions, showing it converges to the true dynamics as the dataset grows, (iii) derive gap bounds demonstrating ODRs sim-to-real error is up to an O(M) factor tighter than uniform DR in the finite-simulator case (and analogous gains in the continuous setting), and (iv) introduce E-DROPO, a new version of DROPO which adds an entropy bonus to prevent variance collapse, yielding broader randomization and more robust zero-shot transfer in practice.

Reasoning by Superposition: A Theoretical Perspective on Chain of Continuous Thought

Large Language Models (LLMs) have demonstrated remarkable performance in many applications, including challenging reasoning problems via chain-of-thoughts (CoTs) techniques that generate ``thinking tokens'' before answering the questions. While existing theoretical works demonstrate that CoTs with discrete tokens boost the capability of LLMs, recent work on continuous CoTs lacks a theoretical understanding of why it outperforms discrete counterparts in various reasoning tasks such as directed graph reachability, a fundamental graph reasoning problem that includes many practical domain applications as special cases. In this paper, we prove that a two-layer transformer with $D$ steps of continuous CoTs can solve the directed graph reachability problem, where $D$ is the diameter of the graph, while the best known result of constant-depth transformers with discrete CoTs requires $O(n^2)$ decoding steps where $n$ is the number of vertices ($D<n$). In our construction, each continuous thought vector is a superposition state that encodes multiple search frontiers simultaneously (i.e., parallel breadth-first search (BFS)), while discrete CoTs must choose a single path sampled from the superposition state, which leads to sequential search that requires many more steps and may be trapped into local solutions. We also performed extensive experiments to verify that our theoretical construction aligns well with the empirical solution obtained via training dynamics. Notably, encoding of multiple search frontiers as a superposition state automatically emerges in training continuous CoTs, without explicit supervision to guide the model to explore multiple paths simultaneously.

AssistanceZero: Scalably Solving Assistance Games

Assistance games are a promising alternative to reinforcement learning from human feedback (RLHF) for training AI assistants. Assistance games resolve key drawbacks of RLHF, such as incentives for deceptive behavior, by explicitly modeling the interaction between assistant and user as a two-player game where the assistant cannot observe their shared goal. Despite their potential, assistance games have only been explored in simple settings. Scaling them to more complex environments is difficult because it requires both solving intractable decision-making problems under uncertainty and accurately modeling human users' behavior. We present the first scalable approach to solving assistance games and apply it to a new, challenging Minecraft-based assistance game with over $10^{400}$ possible goals. Our approach, AssistanceZero, extends AlphaZero with a neural network that predicts human actions and rewards, enabling it to plan under uncertainty. We show that AssistanceZero outperforms model-free RL algorithms and imitation learning in the Minecraft-based assistance game. In a human study, our AssistanceZero-trained assistant significantly reduces the number of actions participants take to complete building tasks in Minecraft. Our results suggest that assistance games are a tractable framework for training effective AI assistants in complex environments. Our code and models are available at https://github.com/cassidylaidlaw/minecraft-building-assistance-game.

How Do LLMs Perform Two-Hop Reasoning in Context?

"Socrates is human. All humans are mortal. Therefore, Socrates is mortal." This classical example demonstrates two-hop reasoning, where a conclusion logically follows from two connected premises. While transformer-based Large Language Models (LLMs) can make two-hop reasoning, they tend to collapse to random guessing when faced with distracting premises. To understand the underlying mechanism, we train a three-layer transformer on synthetic two-hop reasoning tasks. The training dynamics show two stages: a slow learning phase, where the 3-layer transformer performs random guessing like LLMs, followed by an abrupt phase transitions, where the 3-layer transformer suddenly reaches $100%$ accuracy. Through reverse engineering, we explain the inner mechanisms for how models learn to randomly guess between distractions initially, and how they learn to ignore distractions eventually. We further propose a three-parameter model that supports the causal claims for the mechanisms to the training dynamics of the transformer. Finally, experiments on LLMs suggest that the discovered mechanisms generalize across scales. Our methodologies provide new perspectives for scientific understandings of LLMs and our findings provide new insights into how reasoning emerges during training.

Asking for Help Enables Safety Guarantees Without Sacrificing Effectiveness

Most reinforcement learning algorithms with regret guarantees rely on a critical assumption: that all errors are recoverable. Recent work by Plaut et al. discarded this assumption and presented algorithms that avoid "catastrophe" (i.e., irreparable errors) by asking for help. However, they provided only safety guarantees and did not consider reward maximization. We prove that any algorithm that avoids catastrophe in their setting also guarantees high reward (i.e., sublinear regret) in any Markov Decision Process (MDP), including MDPs with irreversible costs. This constitutes the first no-regret guarantee for general MDPs. More broadly, our result may be the first formal proof that it is possible for an agent to obtain high reward while becoming self-sufficient in an unknown, unbounded, and high-stakes environment without causing catastrophe or requiring resets.

International AI Safety Report

The first International AI Safety Report comprehensively synthesizes the current evidence on the capabilities, risks, and safety of advanced AI systems. The report was mandated by the nations attending the AI Safety Summit in Bletchley, UK. Thirty nations, the UN, the OECD, and the EU each nominated a representative to the report's Expert Advisory Panel. A total of 100 AI experts contributed, representing diverse perspectives and disciplines. Led by the report's Chair, these independent experts collectively had full discretion over the report's content.

Observation Interference in Partially Observable Assistance Games

We study partially observable assistance games (POAGs), a model of the human-AI value alignment problem which allows the human and the AI assistant to have partial observations. Motivated by concerns of AI deception, we study a qualitatively new phenomenon made possible by partial observability: would an AI assistant ever have an incentive to interfere with the human's observations? First, we prove that sometimes an optimal assistant must take observation-interfering actions, even when the human is playing optimally, and even when there are otherwise-equivalent actions available that do not interfere with observations. Though this result seems to contradict the classic theorem from single-agent decision making that the value of perfect information is nonnegative, we resolve this seeming contradiction by developing a notion of interference defined on entire policies. This can be viewed as an extension of the classic result that the value of perfect information is nonnegative into the cooperative multiagent setting. Second, we prove that if the human is simply making decisions based on their immediate outcomes, the assistant might need to interfere with observations as a way to query the human's preferences. We show that this incentive for interference goes away if the human is playing optimally, or if we introduce a communication channel for the human to communicate their preferences to the assistant. Third, we show that if the human acts according to the Boltzmann model of irrationality, this can create an incentive for the assistant to interfere with observations. Finally, we use an experimental model to analyze tradeoffs faced by the AI assistant in practice when considering whether or not to take observation-interfering actions.

Extractive Structures Learned in Pretraining Enable Generalization on Finetuned Facts

Pretrained language models (LMs) can generalize to implications of facts that they are finetuned on. For example, if finetuned on ``John Doe lives in Tokyo," LMs can correctly answer ``What language do the people in John Doe's city speak?'' with ``Japanese''. However, little is known about the mechanisms that enable this generalization or how they are learned during pretraining. We introduce extractive structures as a framework for describing how components in LMs (e.g., MLPs or attention heads) coordinate to enable this generalization. The structures consist of informative components that store training facts as weight changes, and upstream and downstream extractive components that query and process the stored information to produce the correct implication. We hypothesize that extractive structures are learned during pretraining when encountering implications of previously known facts. This yields two predictions: a data ordering effect where extractive structures can be learned only if facts precede their implications, and a weight grafting effect where extractive structures can be transferred to predict counterfactual implications. We empirically demonstrate these phenomena in the OLMo-7b, Llama 3-8b, Gemma 2-9b, and Qwen 2-7b models. Of independent interest, our results also indicate that fact learning can occur at both early and late layers, which lead to different forms of generalization.

Will an AI with Private Information Allow Itself to Be Switched Off?

A wide variety of goals could cause an AI to disable its off switch because "you can't fetch the coffee if you're dead" (Russell 2019). Prior theoretical work on this shutdown problem assumes that humans know everything that AIs do. In practice, however, humans have only limited information. Moreover, in many of the settings where the shutdown problem is most concerning, AIs might have vast amounts of private information. To capture these differences in knowledge, we introduce the Partially Observable Off-Switch Game (POSG), a game-theoretic model of the shutdown problem with asymmetric information. Unlike when the human has full observability, we find that in optimal play, even AI agents assisting perfectly rational humans sometimes avoid shutdown. As expected, increasing the amount of communication or information available always increases (or leaves unchanged) the agents' expected common payoff. But counterintuitively, introducing bounded communication can make the AI defer to the human less in optimal play even though communication mitigates information asymmetry. In particular, communication sometimes enables new optimal behavior requiring strategic AI deference to achieve outcomes that were previously inaccessible. Thus, designing safe artificial agents in the presence of asymmetric information requires careful consideration of the tradeoffs between maximizing payoffs (potentially myopically) and maintaining AIs' incentives to defer to humans.