Study demonstrates LLMs can learn multi-step reasoning on filler tokens

Details

Contradicts Pfau et al. (2024) by demonstrating that multi-step reasoning with serial dependencies can be learned using filler tokens (e.g., dots), not just fully parallelizable TC⁰ tasks.
Modified training method treats dots as input and open reasoning as output, allowing models to move information via attention between token positions without encoding reasoning in visible words.
Experiments on Qwen3.6-35B-A3B and gpt-oss-20b show the new method clearly outperforms answer-only baselines, while the original Pfau et al. method shows no advantage over baselines.
Theoretical analysis using Opus 5.5 agent swarms confirms that algorithm depth increases with task length but much slower than step count, explaining how models handle reasoning steps exceeding their layer depth.
Empirical limits reveal that tasks requiring large information packets (e.g., modular arithmetic, function composition) are harder to learn via filler tokens, while modular sum is easy; HornQA fails at very few steps.
Findings suggest that if models increasingly answer reasoning questions without explicit verbalization, chain-of-thought monitorability may be threatened even without looped architectures.

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