Do Neurons Dream of Primitive Operators? Wake-Sleep Compression Rediscovers Schank's Event Semantics

Chain-of-thought traces from large reasoning models can span tens of thousands of tokens, yet we lack a vocabulary for describing their internal structure. Previous methods developed to analyze chain-of-thought traces are either too rigid or not expressive enough, failing to capture features across domains and models. To remedy this, we develop ReasonOps, an unsupervised, expressive method for annotating chain-of-thought traces, providing succinct universal operators. Using ReasonOps, we analyze 44,662 traces from 12 thinking LLMs spanning 6 families across 8 reasoning benchmarks and discover that they share a common compositional structure: 7 recurring reasoning operators -- discourse-level moves such as backtracking, inferring, and hypothesizing -- that emerge from unsupervised clustering of sentence-initial 3-token pivots. These operators appear across every model family and benchmark domain, confirmed by three independent LLM judges who classify held-out samples at 70 -76% accuracy. We analyze the structure of operators on easy vs. hard problems, revealing that reflective operators are more helpful on hard problems and harm performance on easy problems. Operator sequences are highly model-identifying: a classifier trained on operator distributions alone recovers the source model with macro-AUC, revealing that each model family has a distinctive reasoning fingerprint. Structural operator features predict within-problem answer correctness well above baselines. Classifiers built on these operators reach WP-AUC and on AIME specifically. ReasonOps further enables early quality estimation well before the trace completes: we predict at WP-AUC for only 50% of the trace. The ReasonOps pipeline is unsupervised and annotation-free, enabling deep insights into LLM reasoning traces as well as strong downstream results on model identification and correctness prediction.

What is the relation between understanding and compression, and why does human understanding take such a heavily compressed form? Across information theory, machine learning, and AI research, a substantial tradition identifies understanding with compression-a thought captured in Gregory Chaitin's dictum that "comprehension is compression." Philosophers, by contrast, have characterized understanding in terms of grasping connections, giving explanations, and handling novelty. This paper bridges the two pictures through three interlocking theses. The first concerns the concept of understanding: it serves as an efficient proxy for a distinctive form of robust competence, enabling us to identify whom to trust and whom to learn from. The second concerns the state of understanding: to understand a domain is to possess a mental model of its relational structure that enables prediction, and what enables prediction enables compression, because what becomes predictable need not be stored separately. Compression is therefore not identical with comprehension, but its representational shadow. The third concerns the characteristically human form of understanding: the fiduciary and transmission functions highlighted by the first thesis impose pressures of demonstrability and transmissibility that drive human understanding toward principled simplicity. The resulting framework explains both the appeal and the limits of compressionist accounts of understanding while shedding light on the inscrutability of AI systems.

Entity tracking (ET), the ability to keep track of states, is a fundamental skill that underlies complex reasoning. An increasing amount of work investigates how transformer language models (LMs) solve entity binding $\textit{without}$ state changes. However, there is limited understanding of how non-toy LMs address ET problems of realistic difficulties expressed in natural language. To this end, we investigate the mechanisms underlying ET in more complex scenarios featuring multiple state-changing operations. We find that LMs do not incrementally track world states across tokens or query-relevant states across layers, but simply aggregate relevant information in parallel at the last token when the query becomes evident. We further investigate mechanisms of individual operations ($\texttt{PUT}$, $\texttt{REMOVE}$, $\texttt{MOVE}$) to characterize this non-incremental ET mechanism. Surprisingly, LMs implement the $\texttt{REMOVE}$ operation with a fragile global suppression tag; this global removal mechanism predicts various failure modes that we confirm behaviorally. We provide a mechanistic solution of nullifying this tag to partially address this issue. Overall, our findings reveal that LMs solve a fundamentally sequential task using a non-sequential strategy. More broadly, our work illustrates how behavioral and mechanistic analyses can fruitfully interact. Behavioral results inform mechanistic hypotheses, and insights from mechanistic analyses help build stronger behavioral evaluations by predicting failure modes missing from existing evaluations.