Hard reasoning forces an AI's internal signal through far more twists and turns than simple word substitution does.

This reads the question as being about the geometry of what happens *inside* the model — the path a prompt's representation traces as it moves layer to layer — and how that path differs between hard reasoning and shallow lexical variation. The sharpest anchor here is the finding that the forward pass is a geometric trajectory whose curvature encodes task difficulty: reasoning and analogy tasks bend that path 2-3x more sharply (mean curvature 0.71–0.83 rad) than lexical tasks (0.27–0.31 rad) Does transformer reasoning leave a geometric signature in representation space?. Lexical variation is nearly a straight shot — the model barely has to change direction — while reasoning forces the representation to keep turning. So the two don't 'converge' the same way at all: one settles quickly, the other carves.

What makes this interesting is that the corpus keeps finding the same split from completely different angles. If reasoning genuinely required a longer, more curved internal path, you'd expect that path to be fragile — and it is. Chain-of-thought reasoning degrades predictably the moment you push it outside its training distribution, producing fluent-but-invalid steps Does chain-of-thought reasoning actually generalize beyond training data?, and several notes argue this is because CoT is really constrained imitation of a reasoning *form*, replaying familiar schemata rather than doing novel inference Does chain-of-thought reasoning reveal genuine inference or pattern matching?. Lexical substitution has no such cliff because there's no multi-step structure to break. The high curvature of reasoning isn't a sign of robustness — it's the model working hard to stay on a memorized track.

That framing also explains where reasoning breaks. Failures cluster not at some complexity threshold but at instance-level *unfamiliarity* — the model fits instance-specific patterns and any chain succeeds if it has seen similar instances Do language models fail at reasoning due to complexity or novelty?. And when you look at token-level errors, most come from *local* memorization keyed to the immediately preceding tokens, which dominates as complexity rises Where do memorization errors arise in chain-of-thought reasoning?. A lexical task barely leans on this machinery; a reasoning task leans on it constantly, which is why its trajectory bends and why it's so distribution-sensitive.

The twist worth carrying away: the curved, effortful path of reasoning is partly optional. Optimal CoT length follows an inverted-U, and more capable models actually prefer *shorter* chains — simplicity emerges from reward, not from dumbing down Why does chain of thought accuracy eventually decline with length?. Minimal 'draft' chains match verbose ones at 7.6% of the tokens because the removed 92% was style and documentation, not computation Can minimal reasoning chains match full explanations?, and verbosity turns out to be a single steerable direction in activation space Can we steer reasoning toward brevity without retraining?. So part of what looks like reasoning's heavier convergence pattern is padding — and when models collapse, it's often an *execution* bottleneck (they know the algorithm but can't run it step-by-step in text) rather than a failure of the reasoning path itself Are reasoning model collapses really failures of reasoning?. The lexical-vs-reasoning geometry gap is real, but a chunk of the gap is the model spending motion on things that don't move the answer.