When Do Repetition Loops Lock? Truncation Sampling, Bounded Penalties, and a Blind Spot in DRY

Yichuan Chen; Xin Wang

cs.CLOct 17, 2026

When Do Repetition Loops Lock? Truncation Sampling, Bounded Penalties, and a Blind Spot in DRY

Authors: Yichuan Chen, Xin Wang

Organizations: School of Art and Design, Zhejiang Sci-Tech University, Hangzhou, China

Abstract

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.

Figures & tables

Penalty	$d$ on loop token	Class
Presence $\beta_{p}$	$\beta_{p}$	bounded
Frequency $\alpha$ , full context	$\geq\alpha n$	linear
Frequency $\alpha$ , window $W$	$\leq\alpha W$	bounded
Multiplicative $\varrho$	$z(1-\tfrac{1}{\varrho})^{\ddagger}$	bounded †
DRY, no breaker in unit	$\geq\lambda b^{(n-1)L-a}$	exponential
DRY, breaker-free run $g$	$\leq\lambda b^{g-1-a}$	bounded

Table 1: Penalties along a loop. Exponential rows assume

W=\infty

; finite windows cap their growth.

z

: loop-token logit. ‡ For

z>0

; for

z<0

it is

|z|(\varrho-1)

. The DRY lower bound needs

(n-1)L\geq a

; the DRY-C lower bound needs

n-\lceil a^{\prime}/L\rceil\geq c_{0}

. † Bounded when

z

is; multiplicative penalties depend on the logit origin.

Figure 1: (a) Log-odds after

n

repetitions: median over positions within each inline corpus sentence, then median over sentences. Dotted lines mark the lock thresholds of top-

p

0.9 and 0.95. (b) Fraction of sentences in which every position satisfies

q\geq 0.9

at repetition

n

		Truncation only			top- $p$ 0.9 + bounded penalty				top- $p$ 0.9 + other penalties
Model	pure	top- $p$	min- $p$	$\tau$ =0.7	pres.	freq. 64	rep. 64	rep. 64	freq.	DRY	DRY-C
		0.9	0.1	+top- $p$	1.0	0.5	1.1	1.3	0.1
Qwen2.5-1.5B	0	1.00	1.00	1.00	1.00	.96	.80	0	0	.02	0
Qwen2.5-7B	0	.99	.99	.99	.98	.95	.83	0	0	.02	0
Qwen3-1.7B	0	.99	.99	.99	.99	.99	.98	.21	0	.02	0
Qwen3-4B	0	1.00	1.00	1.00	.99	.99	.98	.01	0	.02	0

Table 2: Fraction of units locked through the last ten measured repetitions (150 sampled units: corpus and hand-written spans). Top-

p

, DRY and DRY-C come from a second run in which DRY and DRY-C use a 4,096-token look-back (Appendix E ); the other columns come from the first run. Subscript 64: penalty window. Temperature precedes top-

p

in the

\tau

=0.7 column. Phi-4 is limited to 4,000 tokens throughout.

Figure 2: Fraction of units that remain locked under DRY + top-

p

0.9, among units locked under top-

p

alone. Thin lines: individual models; thick line: pooled over eleven models. Top axis:

D_{g}

evaluated at the nominal gap; actual-gap regrouping is in Appendix E .

Figure 3: Loops found in free generation (four runs pooled), by the longest breaker-free run

g

of the loop unit. The dotted line separates

D_{7}=7.5

from

D_{8}=13.1

Figure 4: Structured-output prompts (360 generations per bar). Light: a loop appears; dark: the loop continues to the length limit. Numbers are counts.

	Sampler	Ans.	$\geq$ 90%	Cov.	Dup.	JSON
Qwen3	default	62.2	15.0	34.0	28.1	26.7
4B	+ DRY	68.3	20.0	40.5	18.5	31.1
	+ DRY-C	65.6	20.3	38.2	15.0	31.1
	pure	69.2	21.4	40.1	18.5	24.4
Llama	default	100	52.8	66.1	23.0	13.3
3.1-8B	+ DRY	100	58.9	71.5	12.9	26.7

Table 3: Task completion on structured prompts (%, 360 generations per row). Ans.: an answer is produced within the limit (for Qwen3-4B, the reasoning block ends);

\geq

90%: at least 90% of the requested number of distinct items; Cov.: mean fraction of requested items produced; Dup.: duplicated items among those produced; JSON: outputs that parse, on the three JSON prompts (45 generations per cell).

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

	default	+ DRY	+ pres. 1	+ rep. 1.1	pure
Qwen3-4B	78	28	44	24	37
of which $g\leq 7$	30	28	29	19	26
Qwen3.6-35B	9	4	1	0	1
of which $g\leq 7$	3	4	0	0	0

Appendix

Table 4: Loops on prompt set 1 under every sampler setting (500 generations per cell for Qwen3-4B, 200 for the 35B model).

Run	Sampler	loops	$g\leq 7$	$g\geq 8$
Qwen3-4B, set 1	default	78	30	48
	+ DRY	28	28	0
Qwen3-4B, set 2	default	75	45	30
	+ DRY	44	44	0
Qwen3.6-35B, set 1	default	9	3	6
	+ DRY	4	4	0

Appendix

Table 5: Loops per free-generation run. The last column includes units without any breaker. Prompt set 2 includes both structured and prose prompts; on Llama, 58 of the 71 default loops and all 33 DRY loops occur on the structured subset used in Table 8 .

	default			default + DRY
Criterion	all	$g\leq 7$	$g\geq 8$	all	$g\leq 7$	$g\geq 8$
$\geq$ 3 reps, $\geq$ 30 tok.	309	124	185	129	129	0
$\geq$ 4 reps, $\geq$ 40 tok.	262	120	142	116	116	0
$\geq$ 5 reps, $\geq$ 60 tok.	233	110	123	109	109	0
$\geq$ 8 reps, $\geq$ 100 tok.	184	95	89	99	99	0
$\geq$ 10 reps, $\geq$ 150 tok.	169	91	78	90	90	0

Appendix

Table 6: Loops in the four pooled free-generation runs under different detection criteria (minimum consecutive repetitions and minimum total length). The third row is the criterion used in the paper.

Model	Sampler	sent.	para.	chorus	templ.	all
Llama-3.1-8B	default	100	100	70	100	95
	+ DRY	22	0	0	8	10
	+ DRY-C	22	0	0	8	10
	+ DRY-C, $c_{0}$ =6	23	0	0	7	10
Qwen3-4B	default	100	100	80	82	91
	+ DRY	0	0	75	0	12

Appendix

Table 7: Tasks that request verbatim repetition: generations (%) containing the required number of exact copies.

Figure 5: Penalty trajectories (analytic, unit length 24, unlimited look-back for growing curves; “count term” is the DRY-C count component) against the lock margin

\operatorname{logit}(q)-\operatorname{logit}(0.9)

of Qwen3-4B (band: weakest to typical token of the median sentence). A penalty that stays below the band cannot unlock.

Model	Sampler	Loops	To limit	Loop tokens (%)	Coverage (%)	JSON (%)
Qwen3-4B	default	75	59	12.2	34.0	26.7
	DRY	44	30	6.7	40.5	31.1
	DRY-C	8	0	0.1	38.2	31.1
	frequency 0.1, $W=4096$	19	4	0.7	39.6	15.6
	rep. 1.1, $W=4096$	31	22	4.1	52.9	51.1
	DRY + rep. 1.05	20	11	2.7	47.4	42.2

Appendix

Table 8: Additional baselines, 360 structured generations per row. Loop tokens: fraction of all generated tokens covered by the detected loop; coverage and JSON use the definitions of Table 3 (45 JSON generations per row). All penalty variants are added to the model’s default sampler.

Model	$N$	ever/final	mean $k_{3}$	ever/final	mean $k_{3}$	ever/final	mean $k_{3}$
		top- $p$		DRY		DRY-C
Gemma-2-2B	150	144/120	0.0221	3/2	3.23e-10	0/0	0
Gemma-2-9B	150	150/137	0.0696	3/3	0.000738	0/0	0
Llama-3.1-8B	150	150/150	0.113	1/1	9.57e-06	0/0	0
Llama-3.2-3B	150	143/142	0.147	1/1	1.38e-06	0/0	0
Phi-4-mini	150	150/149	0.472	0/0	6.83e-35	0/0	0

Appendix

Table 9: Window

W=4096

: ever-locked/finally-locked counts and mean finite-horizon

k_{3}

. Final: last ten repetitions all locked. DRY-C uses

b_{c}=3

$g$	Nominal interval	Actual gap
2	400/400	392/392
3	404/409	410/415
4	393/419	393/418
5	–	1/2
6	276/416	277/417
8	5/422	5/418

Appendix

Table 10: DRY-locked / top-

p

-locked colon units, pooled over eleven models, under nominal and actual gap grouping.

	Llama		Qwen
Sampler	norm.	strict	norm.	strict
default	127	120	127	126
DRY	27	17	31	29
DRY + rep. 1.05	28	12	35	31
DRY, newline only	32	18	26	24
DRY-C, $c_{0}=2$	26	10	18	18

Appendix

Table 11: Requested repetition, 16-task experiment: successful generations out of 160 in every cell. Norm.: whitespace-normalized; strict: only trailing line whitespace normalized.

		Structured		Prose
$a^{\prime}$	$c_{0}$	Qwen	Llama	Qwen / Llama
12	2	68.1	53.0	14.4 / 49.7
12	4	42.8	42.7	2.8 / 19.8
24	2	37.9	18.9	5.0 / 29.9
24	4	14.4	13.2	0.0 / 15.0
48	2	27.0	10.3	1.7 / 18.0

Appendix

Table 12: Potential count activations in generations without detected loops (% with at least one activation). Structured

N=285/302

, prose

N=180/167

for Qwen/Llama; denominators are fixed across the grid.

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Large Language Models generate text autoregressively, but open-ended generation is prone to verbatim looping, in which models repeat spans already present in context. Standard defenses such as repetition, presence, and frequency penalties and n-gram blocking act on token recurrence rather than the sequential structure of a loop, and often suppress looping only at strengths that also degrade formatting or fluency. We propose Don't Repeat Yourself (DRY), a sampling-time logit adjustment that penalizes a candidate token only when generating it would extend the current suffix into an exact continuation of a span seen earlier in the context. Sequence breakers protect chat templates and formatting tokens. Across models from 1.5B to 120B parameters, nine prompt families, and a 600-pair human study, DRY reduces suffix-extension rate by 47% while improving lexical diversity. An intervention-matched placebo produces no comparable reduction, identifying suffix matching as the operative mechanism. On AWQ-quantized 70B and 120B models, DRY reduces loop rate by roughly half while preserving MT-Bench, MMLU, and GSM8K performance, whereas standard alternatives lose measurable ground. DRY has been adopted by popular open-source LLM inference frameworks including llama.cpp, ExLlamaV2, and text-generation-webui, highlighting its practical impact on text generation.

Abstract

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