Under Review

• Shorter Chains via Macro Transitions: Constant-Factor Compression for Chain-of-Thought Counter Simulation

  HGmCGa0Q3O

  Chain-of-thought (CoT) constructions that make transformers Turing complete, typically simulate a counter machine, one transition per generated token, making autoregressive length proportional to the simulated runtime. Since serial generation is a key computational cost, we ask whether this length can be reduced while preserving the recognized language and the generalization properties of the simulation. We introduce two machine rewrites with exact recognition guarantees. First, order k macro transitions combine k reachable base transitions into one token. We prove that the resulting guards retain the per-counter threshold structure, determinism is preserved, and a run of length T is compressed to about T divided by k steps for fixed k, a constant factor reduction that leaves the asymptotic serial complexity unchanged, with a vocabulary bounded by the base vocabulary raised to k. Second, base b counting compresses monotone decrement bursts by processing b counter units per token. Both rewrites remain within the same CoT counter programming class, allowing the base construction's length generalization result to transfer under its assumptions. Experiments on synthetic counter machine tasks, including multi-counter multiplication with nested loops, show that transformers trained on compressed traces retain length generalization under moderate compression while achieving the predicted reductions in trace length, and that this retention degrades once compression becomes large relative to the counting range. We observe corresponding reductions in generation latency, attention operations, and key value cache size. Accuracy degrades as compression becomes aggressive relative to the counting range, consistent with our analysis. We further characterize reachable vocabulary growth and quantify the associated data scaling cost.
  Submitted: Aug 13, 2026

• Imagined Rollouts Are Not Dynamic: A Kinematic Diagnosis of Long-Horizon Failure in a DreamerV3-Class Locomotion World Model

  D5gNaP6QHN

  Using a per-step Kinematic-Consistency Error, we find a DreamerV3-class world model whose imagined rollouts stay invariant to a friction change that collapses the real gait, which we read as kinematic rather than dynamic imagination.
  Submitted: Jul 30, 2026

• Diagnosing the Sparse Mechanism Shift Hypothesis: A Graph-Free Invariance Test

  6AGOgvdze1

  Many methods for distribution shift under causal structure assume the sparse mechanism shift (SMS) hypothesis: that across environments only a few causal conditionals change. This assumption drives mechanism-shift scoring, causal discovery in heterogeneous data, and transportable prediction, yet it is almost never tested on the data at hand. This paper makes SMS diagnosable. We first ask why it is hard to tell which mechanisms changed once the causal graph must be estimated rather than assumed known. A controlled ablation locates the cause: the false positives that limit precision arise at the truly invariant nodes, because their parent sets are mis-estimated; a better global skeleton, repairing the changed nodes, and conditioning-set voting do not remove them. We then give a graph-free, label-free invariance test that flags a node only when no conditioning subset makes its conditional invariant across environments (an inverse use of invariant causal prediction); this is robust to the same failure mode and matches an oracle that knows the true graph. Building on it, we define a data-referenced SMS diagnostic: a discovery statistic (the fraction of mechanisms flagged as changed) with a data-driven null floor obtained by splitting one environment in half, and a bootstrap verdict (no shift / sparse / dense / inconclusive). On controlled synthetic data the verdict is broadly consistent with the true sparsity; on real protein-signalling interventions it returns a dense verdict that clears the data-referenced no-shift floor, which we read as evidence against SMS rather than as within-environment detector noise, and a paired atomic-versus-fat-hand study offers a mechanistic reading and predicts when SMS should hold. We discuss the conditions under which the invariance test localises causal mechanism changes and the statistical interpretation of the verdict. We treat the verdict as a data-calibrated diagnostic rather than a hypothesis test with formal error control, and state the assumptions this requires.
  Submitted: Jul 6, 2026

• The Feynman Trap: When Chain-of-Thought Reasoning Undermines Correct Intuitions in Language Models

  JNhGH8NVUL

  We systematically quantify a phenomenon where LLMs flip correct zero-shot answers to incorrect ones when prompted to reason step-by-step, and characterize when this cost outweighs the benefit across models and task domains.
  Submitted: May 16, 2026

• TMLR Beyond PDF Example Submission

  submission

  This is an example submission for TMLR Beyond PDF.
  Submitted: