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Let's Think Dot by Dot: Hidden Computation in Transformer Language Models
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Chain-of-thought responses from language models improve performance across most benchmarks. However, it remains unclear to what extent these performance gains can be attributed to human-like task decomposition or simply the greater computation that additional tokens allow. We show that transformers can use meaningless filler tokens (e.g., '......') in place of a chain of thought to solve two hard algorithmic tasks they could not solve when responding without intermediate tokens. However, we find empirically that learning to use filler tokens is difficult and requires specific, dense supervision to converge. We also provide a theoretical characterization of the class of problems where filler tokens are useful in terms of the quantifier depth of a first-order formula. For problems satisfying this characterization, chain-of-thought tokens need not provide information about the intermediate computational steps involved in multi-token computations. In summary, our results show that additional tokens can provide computational benefits independent of token choice. The fact that intermediate tokens can act as filler tokens raises concerns about large language models engaging in unauditable, hidden computations that are increasingly detached from the observed chain-of-thought tokens.
Forward citations
Cited by 15 Pith papers
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Training Continuous Chain of Thought Models: A Tale of Two Regimes
C-MTP, a multi-token-prediction direct supervision method, matches slower latent-reasoning methods on short math traces, but all continuous CoT variants lose ~65% accuracy on long realistic traces.
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LLMs interleave true causal reasoning steps with decorative ones in CoT, with only ~2.3% of steps having high causal impact on AIME for Qwen-2.5, and a steering direction can force internal use of specific steps.
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Performative Thinking? The Brittle Correlation Between CoT Length and Problem Complexity
A transformer trained to imitate A* produces traces whose length reflects similarity to training data, not true problem complexity, so long chain-of-thought should not be read as more 'thinking'.
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System-1.5 Reasoning: Traversal in Language and Latent Spaces with Dynamic Shortcuts
System-1.5 Reasoning lets LLMs reason in latent space with early exits and step-skipping, matching chain-of-thought accuracy at over 20x speedup on GSM8K and StrategyQA.
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Not All LLM Reasoning is Visible in the Chain-of-Thought
Semantically empty filler tokens improve accuracy across several frontier LLMs on synthetic math tasks and let Claude Opus 4.5 satisfy a hidden modular constraint, evidence of computation invisible in output tokens.
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The Latent Space: Foundation, Evolution, Mechanism, Ability, and Outlook
A large survey organizes latent-space work in language-based models by foundation, evolution, four mechanisms, seven abilities, and open challenges.
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NEST: Nascent Encoded Steganographic Thoughts
Frontier LLMs can embed short digit sequences in sentence acrostics (Claude Opus 4.5: 92% per-digit at D=4) but fail to jointly solve hidden reasoning tasks and encode the solution.
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LLM hidden states encode enough information to predict chain-of-thought success before any reasoning tokens are generated, outperforming a text-only classifier.
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Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey
A comprehensive review that categorizes methods for shortening and adaptively triggering chain-of-thought reasoning in large language models.
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