Don't Repeat Yourself: Stopping Verbatim Loops at Sampling Time

Language models sometimes repeat verbatim until the generation limit. We study the exit rather than the entrance: given that a span has already been repeated $n$ times, when is escape still possible? Along the loop the context is deterministic, so loop survival under any sampler can be computed exactly from one forward pass. Pure sampling leaves a positive escape probability at every step; top-$p$ with threshold $π>1/2$ locks a position exactly when the continuation probability reaches $π$. A bounded penalty can leave a position locked; a penalty that outgrows the model's preference for the loop over unseen tokens guarantees escape under top-$p$. The same analysis predicts a blind spot in the widely deployed DRY sampler: its sequence breakers cap the penalty at $λb^{g-1-a}$ for loops whose longest breaker-free run has $g$ tokens. On eleven open models, 66% of locked units with $g=6$ stay locked under DRY and 1% with $g=8$. In free generation with llama.cpp, all 109 loops that survive DRY have $g\le 7$. We propose DRY-C, which adds a term that grows exponentially with the number of verbatim recurrences, up to its look-back window. With it, none of 720 structured-output generations looped to the length limit, and task completion stayed close to DRY's.

LLM reasoning is stochastic, and so understanding a model requires grappling with the distribution of reasoning chains that it might produce for a given question, i.e., its uncertainty. Resampling-based analyses characterize this distribution, revealing which steps of a rollout determine how the model arrives at its answer. However, a major limitation of these approaches is that resampling text sequences at every token or sentence in a reasoning chain is very costly. Our work strives to make resampling analysis more computationally efficient, while also shedding light on an important scientific question: what is the right statistical model for explaining uncertainty dynamics in text generation? We show that when resampling many reasoning chains, uncertainty dynamics converge to stable patterns, and noise is largely an artifact of sampling rather than an LLM's sensitivity to each individual token or reasoning step. We develop a statistical model for smoothing noisy low-sample rollout data to better approximate high-sample data, allowing us to significantly cut sampling costs.

Large language models produce repetitive output when prompted independently across many batches, a phenomenon we term cross-batch mode collapse: the progressive loss of output diversity when a language model is prompted repeatedly without access to its prior generations. Practitioners have long mitigated this with ad hoc deduplication and seed rotation, but no principled framework exists. We introduce Dynamic Context Evolution (DCE), comprising three mechanisms: (1) verbalized tail sampling (the model labels each idea with a guess about how obvious it is, and obvious ideas are discarded), which filters high-probability candidates via model self-assessment; (2) semantic memory, which maintains a persistent embedding index to reject near-duplicates across batches; and (3) adaptive prompt evolution, which reconstructs the generation prompt each batch using memory state and rotating diversity strategies. In experiments across three domains (sustainable packaging concepts, educational exam questions, and creative writing prompts) and two model families (gpt-5-mini and claude-haiku-4-5), a component ablation across 2-3 random seeds per method shows that DCE achieves 0.0 +/- 0.0% collapse versus 5.6 +/- 2.0% for naive prompting, while producing 17-18 HDBSCAN clusters per seed versus naive's volatile 2-17, indicating reliably richer conceptual structure. These results are validated with an independent embedding model (all-MiniLM-L6-v2) and hold across sensitivity sweeps of the VTS threshold tau and dedup threshold delta. Deduplication and prompt evolution are individually insufficient but jointly effective, at approximately $0.50 per 1,000 candidates using only standard API calls, with no fine-tuning or custom architectures required.