These are the 10 reasoning categories discovered in QwQ-32B (Layer 27, Dictionary Size 10) using our unsupervised clustering methodology with Top-K Sparse Autoencoders. Each category represents a distinct cognitive function that the model employs during its chain-of-thought reasoning process.
From: Base Models Know How to Reason, Thinking Models Learn When
| Category | Representative Example |
|---|---|
| Adjusting problem framing | "Alternatively, maybe the question is structured so that the options include both, but since the user hasn't given options, I have to go with the standard answer." |
| Brainstorming Additional Aspects | "Also, maybe mention psychological theories explicitly, like Skinner's operant conditioning, Pavlov's classical conditioning, and maybe Maslow's hierarchy where esteem and social belonging are needs that verbal stimuli can address." |
| Numeric computations | "Let me do 60 * 0.03 = 1.8, and 60 * 0.0006 = 0.036, so total is 1.8 + 0.036 = 1.836 cal/°C. Then multiply by 307°C. Hmm, 1.836 * 300 = 550.8, and 1.836 *7 = 12.852, so total is 550.8 +12.852 = 563.652 cal." |
| Proposing Causal Hypotheses | "Also, maybe the government wants to ensure that the market remains dynamic and innovative, which collusion might hinder because if companies aren't competing, they might not feel the need to improve their products or services." |
| Recalling Domain Knowledge | "Since they are parallel, maybe I can use some proportionality theorem, like Thales' theorem or the basic proportionality theorem (Thales' theorem), which states that if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides them proportionally." |
| Drawing Deductive Inferences | "Also, the confrontation clause: since the victim is deceased, the defendant can't cross-examine them, but the dying declaration exception is an established exception to the confrontation clause as well, based on precedent like Tennessee v. Street. So, if the court determines that the victim's statement was made in reasonable belief of impending death, then it's admissible as a dying declaration." |
| Stating Known Equations | "So, the Clausius-Clapeyron equation in the form ln(P) = -ΔH_vap/(R) * (1/T) + C. The slope is -ΔH_vap/R, so if I can find the slope, I can solve for ΔH_vap." |
| Articulating the Next Subgoal | "Okay, so I need to figure out which of the given options definitely increases the equilibrium price of corn in a competitive market." |
| Planning Next Steps | "Let me think again." |
| Presenting Conclusions | "Therefore, both methods give the same answer, so I think that's correct." |
These categories were discovered through an unsupervised clustering process that analyzed 430,122 sentences from reasoning traces. The taxonomy demonstrates that thinking models employ a diverse set of cognitive operations during problem-solving, from low-level numeric computations to high-level strategic planning and hypothesis generation.