When Does In-Context Search Help? A Sampling-Complexity Theory of Reflection-Driven Reasoning

Training large language models (LLMs) with extended reasoning has enabled in-context search, in which models iteratively generate, critique, and revise solution attempts. We provide a theoretical analysis of in-context search by modeling it as approximate inference over reasoning traces, where the base model defines a prior and self-reflection provides feedback for posterior updates, and study the resulting inference-time sampling complexity - the number of sequential attempts needed to achieve high success probability. We show that when reflections reliably localize early mistakes, in-context search can yield exponential improvements over the base model, solving problems with exponentially small zero-shot pass rates using only a polynomial number of sequential attempts, whereas when this property fails, conditioning on past attempts offers no asymptotic benefit over parallel sampling. We further show that these gains are robust and learnable: approximate posterior updates suffice, and cross-entropy training on search rollouts recovers the required behavior with polynomial sample complexity. Finally, we show that under a stagewise abstraction of reinforcement learning with verifiable rewards, the optimal policy extension implements the same posterior reweighting rule. We validate key qualitative predictions of the theory on real large reasoning models.

When Is Compositional Reasoning Learnable from Verifiable Rewards?

The emergence of compositional reasoning in large language models through reinforcement learning with verifiable rewards (RLVR) has been a key driver of recent empirical successes. Despite this progress, it remains unclear which compositional problems are learnable in this setting using outcome-level feedback alone. In this work, we theoretically study the learnability of compositional problems in autoregressive models under RLVR training. We identify a quantity that we call the task-advantage ratio, a joint property of the compositional problem and the base model, that characterizes which tasks and compositions are learnable from outcome-level feedback. On the positive side, using this characterization, we show that compositional problems where correct intermediate steps provide a clear advantage are efficiently learnable with RLVR. We also analyze how such an advantage naturally arises in different problems. On the negative side, when the structural advantage is not present, RLVR may converge to suboptimal compositions. We prove that, in some cases, the quality of the base model determines if such an advantage exists and whether RLVR will converge to a suboptimal solution. We hope our analysis can provide a principled theoretical understanding of when and why RLVR succeeds and when it does not.

Compositional Hardness of Code in Large Language Models -- A Probabilistic Perspective

A common practice in large language model (LLM) usage for complex analytical tasks such as code generation, is to sample a solution for the entire task within the model's context window. Previous works have shown that subtask decomposition within the model's context (chain of thought), is beneficial for solving such tasks. In this work, we point a limitation of LLMs' ability to perform several sub-tasks within the same context window - an in-context hardness of composition, pointing to an advantage for distributing a decomposed problem in a multi-agent system of LLMs. The hardness of composition is quantified by a generation complexity metric, i.e., the number of LLM generations required to sample at least one correct solution. We find a gap between the generation complexity of solving a compositional problem within the same context relative to distributing it among multiple agents, that increases exponentially with the solution's length. We prove our results theoretically and demonstrate them empirically.

Tradeoffs Between Alignment and Helpfulness in Language Models

Language model alignment has become an important component of AI safety, allowing safe interactions between humans and language models, by enhancing desired behaviors and inhibiting undesired ones. It is often done by tuning the model or inserting preset aligning prompts. Recently, representation engineering, a method which alters the model's behavior via changing its representations post-training, was shown to be effective in aligning LLMs (Zou et al., 2023a). Representation engineering yields gains in alignment oriented tasks such as resistance to adversarial attacks and reduction of social biases, but was also shown to cause a decrease in the ability of the model to perform basic tasks. In this paper we study the tradeoff between the increase in alignment and decrease in helpfulness of the model. We propose a theoretical framework which provides bounds for these two quantities, and demonstrate their relevance empirically. Interestingly, we find that while the helpfulness generally decreases, it does so quadratically with the norm of the representation engineering vector, while the alignment increases linearly with it, indicating a regime in which it is efficient to use representation engineering. We validate our findings empirically, and chart the boundaries to the usefulness of representation engineering for alignment.

Fundamental Limitations of Alignment in Large Language Models

An important aspect in developing language models that interact with humans is aligning their behavior to be useful and unharmful for their human users. This is usually achieved by tuning the model in a way that enhances desired behaviors and inhibits undesired ones, a process referred to as alignment. In this paper, we propose a theoretical approach called Behavior Expectation Bounds (BEB) which allows us to formally investigate several inherent characteristics and limitations of alignment in large language models. Importantly, we prove that for any behavior that has a finite probability of being exhibited by the model, there exist prompts that can trigger the model into outputting this behavior, with probability that increases with the length of the prompt. This implies that any alignment process that attenuates undesired behavior but does not remove it altogether, is not safe against adversarial prompting attacks. Furthermore, our framework hints at the mechanism by which leading alignment approaches such as reinforcement learning from human feedback increase the LLM's proneness to being prompted into the undesired behaviors. Moreover, we include the notion of personas in our BEB framework, and find that behaviors which are generally very unlikely to be exhibited by the model can be brought to the front by prompting the model to behave as specific persona. This theoretical result is being experimentally demonstrated in large scale by the so called contemporary "chatGPT jailbreaks", where adversarial users trick the LLM into breaking its alignment guardrails by triggering it into acting as a malicious persona. Our results expose fundamental limitations in alignment of LLMs and bring to the forefront the need to devise reliable mechanisms for ensuring AI safety.