Unveiling Spectral Mechanisms in Training-Free LLM Text Detection

Haitong Luo; Xuying Meng; Weiyao Zhang; Wenji Zou; Shengfeng Lou; Xuefeng Jiang; Chungang Lin; Yujun Zhang

cs.CLAug 26, 2026

Unveiling Spectral Mechanisms in Training-Free LLM Text Detection

Authors: Haitong Luo, Xuying Meng, Weiyao Zhang, Wenji Zou, Shengfeng Lou, Xuefeng Jiang, Chungang Lin, Yujun Zhang

Organizations: Institute of Computing Technology, Chinese Academy of Sciences

Abstract

The rapid advancement of Large Language Models (LLMs) makes it increasingly difficult to distinguish human writing from machine-generated text. Training-free detection offers a scalable solution, yet common confidence-based metrics mainly measure average token probabilities and often miss the signal fluctuations that characterize human writing, which we call "generative vitality". Spectral analysis offers a way to capture this vitality, but its mechanism and practical boundaries remain underexplored. In this paper, we analyze spectral detection from both theoretical and empirical perspectives. We connect spectral energy to variance in proxy log-probability trajectories and explain how broader human token choices create the fluctuations used by frequency-domain indicators. We further show that the strength of this signal depends on text length and sampling range: spectral evidence is clearest for long, continuous, constrained generation, while short, fragmented, mixed, and edited settings require complementary confidence and fluctuation views. These findings clarify when frequency-domain detection works and provide guidance for future multi-dimensional detector design.

Figures & tables

Figure 1: Illustration of Generative Vitality. The plot shows token log-likelihood trajectories computed by a proxy LLM. Human writing (red) contains vitality spikes caused by unpredictable low-probability tokens, marked in red in the text below. AI outputs (blue) are typically smoother because decoding favors high-probability tokens. Yellow-highlighted regions mark segments with large generation-probability divergence.

Figure 2: Overview of the Training-Free Detection Pipeline.

Metric	Statistical Interpretation	Conf.	Fluct.
LogLikelihood (LL)	Measures average token log-probability.	$\checkmark$	$\times$
LogRank (LR)	Average of log-rank scores for token positions.	$\checkmark$	$\times$
LRR	Ratio of log-likelihood to log-rank (relative confidence).	$\checkmark$	$\times$
Entropy	Average predictive uncertainty of the distribution.	$\checkmark$	$\times$
SpecDetect	Frequency-domain modeling of fluctuations.	$\times$	$\checkmark$
Lastde	Ratio of log-likelihood to multi-scale entropy.	$\checkmark$	$\checkmark$

Table 1: Taxonomy of training-free metrics. We classify metrics by their statistical focus using checkmarks (

\checkmark

) and cross marks (

\times

). Conf. indicates confidence-based metrics, while Fluct. indicates fluctuation-based metrics.

Figure 3: Preliminary head/tail check. Bars show the [email protected] rate under GPT-J-6B proxy scoring. Human continuations generally use more tokens outside the Top-

p=0.90

head window than paired LLM continuations, especially on WritingPrompts and Reddit. The gap is smaller on XSum.

Figure 4: Metric Relations on Writing Dataset. (Left) Correlation Heatmap : Metrics cluster into Confidence and Fluctuation families. (Right) PCA Loading Plot : PC1 (84.2%) and PC2 (8.8%) capture the dominant variance directions.

Figure 5: Performance vs. Sequence Length on Three Datasets. Fluctuation-based metrics achieve more significant gains as sequence length increases.

Figure 6: Detection Robustness vs. Sampling Parameters on XSum. Performance decays across all methods as Top-

k

, Top-

p

, and Temperature increase, yet fluctuation-based indicators demonstrate superior resilience compared to confidence-based metrics.

Metric	Pure Generation		Collaborative Mixed
Metric	SemEval	CoAuthor (H vs. L)	CoAuthor (H vs. C)	CoAuthor (L vs. C)
Confidence-based
LogLikelihood	0.9085	0.8044	0.6459	0.6951
LogRank	0.9038	0.8138	0.6514	0.7010
LRR	0.2544	0.3698	0.4425	0.4081
Entropy	0.8655	0.4322	0.4701	0.4759

Table 2: Sentence-level Detection across Pure and Collaborative Text. Average within-document AUC for binary classification among Human (H), LLM (L), and Collaborative (C) sentences. Best results are bolded ; second-best are underlined .

Confidence-based Metrics
Metric	AI-Polishing (GPT-4)				AI-Polishing (Llama-2)				Humanizing
	Polish	Polish	Complete	Rewrite	Polish	Polish	Complete	Rewrite	Adapt	Adapt	Llama-2	GPT-4
	Token	Sentence	(1/3+2/3)	(Re-gen)	Token	Sentence	(1/3+2/3)	(Re-gen)	Token	Sentence	Humanize	Humanize
LogLikelihood	0.6500	0.6167	0.6500	0.4067	0.7433	0.8233	0.8100	0.9533	0.7267	0.8300	0.7333	0.9667
LogRank	0.6033	0.5800	0.6667	0.4233	0.6967	0.8300	0.7967	0.9600	0.7133	0.8300	0.7333	0.9600
LRR	0.3067	0.3133	0.5300	0.4933	0.3067	0.2700	0.1733	0.2767	0.2100	0.2167	0.2900	0.0800

Table 3: Pairwise Accuracy on MixText Scenarios. Values are the percentage of pairs where the Modified version is ranked more machine-like than the Original. Columns are ordered by machine involvement. Best results are bolded ; second-best are underlined .

Figure 7: Case Visualization of Signal Profiles across AI-Polishing Modes. Original and polished signals under each mode. Left: time-domain log-likelihood; right: frequency-domain spectrum.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Sub-task	LLM Engine	Samples	Avg. Len.	Level	Mixed	Collab
SemEval	Prefix-Comp.	GPT-3	4,154	19.76	Sent.	✓	$\times$
CoAuthor	Interleaved	GPT-3.5	1,445	14.71	Sent.	✓	✓
MixText	AI-Polishing	GPT-4, Llama-2	3,000	130.18	Doc.	$\times$	✓
MixText	Humanizing	GPT-4, Llama-2	1,500	128.66	Doc.	$\times$	✓

Appendix

Table 4: Dataset Statistics.

Avg.\ Len.

is the word count per detection unit.

Mixed

denotes mixed-source text within a document;

Collab

indicates collaborative content.

Panel of Figure 8 — Figure 8: Analysis of Metric Relation on Additional Datasets. (Left) Correlation Heatmap : Metrics cluster into Confidence and Fluctuation families based on Spearman correlation. (Right) PCA Loading Plot : Illustrates the geometric relationship where PC1 captures the dominant variance, while PC2 captures the secondary direction of variation.

Figure 9: Input Proxy Ablation across All Metrics. While confidence metrics benefit from discretized LogRank, fluctuation-based metrics require continuous LogLikelihood to resolve high-frequency spectral signatures. Comparative analysis of input signal preference. While confidence metrics improve with discretized LogRank inputs, fluctuation-based metrics (i.e., SpecDetect) suffer a severe performance collapse, confirming the necessity of continuous LogLikelihood for resolving micro-fluctuations.

Figure 10: Performance of All Metrics vs. Sequence Length (Llama-2 Source). Fluctuation-based metrics achieve more significant gains as sequence length increases.

Panel of Figure 11 — Figure 11: Impact of Decoding Strategies across All Datasets (Llama-2 Source). Results across three evaluation scenarios demonstrate that tighter sampling constraints consistently enhance detection performance for all metrics, reinforcing the physical consistency of the variance collapse phenomenon.

Figure 12: Performance of All Metrics vs. Sequence Length (GPT-4 Source). While SpecDetect initially trails on Writing and Reddit, it achieves the steepest growth among all metrics as length increases, confirming that spectral methods require sufficient observation windows to resolve stable variance.

Panel of Figure 13 — Figure 13: Impact of Decoding Strategies across All Datasets (Qwen-3-8B Source). Tighter sampling improves separability across the three evaluation scenarios, while the exact gradients vary with the source model.

Figure 14: GPT-J-6B Rank

>

50 head/tail check. Bars show the percentage of tokens whose proxy-model rank is greater than 50.

Figure 15: Llama3-8B [email protected] head/tail check. Bars show the percentage of tokens outside the Top-

p=0.90

head set under Llama3-8B proxy scoring.

Figure 16: Llama3-8B Rank

>

50 head/tail check. Bars show the percentage of tokens whose proxy-model rank is greater than 50.

Figure 17: Llama3-8B proxy length sensitivity. This figure mirrors Figure 5 with Llama3-8B as the scoring proxy. The qualitative pattern is consistent with the main text: longer spans tend to strengthen fluctuation-based evidence, while exact values vary with the proxy model.

Panel of Figure 18 — Figure 18: Impact of Decoding Strategies across All Datasets (Llama3-8B Proxy). This figure mirrors the sampling-scope analysis with Llama3-8B as the scoring proxy. Broader sampling generally weakens separability, while exact curves vary with the proxy model and dataset.

Metric	Pure Generation		Collaborative Mixed
Metric	SemEval	CoAuthor (H vs. L)	CoAuthor (H vs. C)	CoAuthor (L vs. C)
Confidence-based
LogLikelihood	0.8698	0.6415	0.7083	0.5839
LogRank	0.8449	0.6483	0.7221	0.5982
LRR	0.2190	0.5152	0.5152	0.5276
Entropy	0.2981	0.5306	0.5306	0.4751

Appendix

Table 5: Llama3-8B Proxy Sentence-level Detection across Pure and Collaborative Text. Average within-document AUC for binary classification among Human (H), LLM (L), and Collaborative (C) sentences, following the same format as Table 2 . Best results are bolded ; second-best are underlined .

Confidence-based Metrics
Metric	AI-Polishing (GPT-4)				AI-Polishing (Llama-2)				Humanizing
	Polish	Polish	Complete	Rewrite	Polish	Polish	Complete	Rewrite	Adapt	Adapt	Llama-2	GPT-4
	Token	Sentence	(1/3+2/3)	(Re-gen)	Token	Sentence	(1/3+2/3)	(Re-gen)	Token	Sentence	Humanize	Humanize
LogLikelihood	0.3733	0.6267	0.5667	0.5300	0.6933	0.8133	0.9633	0.7733	0.7600	0.8833	0.7267	0.9900
LogRank	0.5033	0.5167	0.6467	0.3767	0.6833	0.7867	0.9767	0.7567	0.7200	0.8600	0.7100	0.9733
LRR	0.3200	0.3367	0.5100	0.5333	0.3133	0.2100	0.1067	0.2600	0.1467	0.1267	0.2967	0.0433

Appendix

Table 6: Llama3-8B Proxy Pairwise Accuracy on MixText Scenarios. Values are the percentage of pairs where the Modified version is ranked more machine-like than the Original, following the same column order and formatting as Table 3 . Best results are bolded ; second-best are underlined .

Figure 19: WMT16 cross-language test (length sensitivity). Following Figure 5 .

Figure 20: WMT16 cross-language test (decoding-scope sensitivity). Following Figure 6 .

Setting	Direction	Operation	Mean density	Best metric	Pair acc.
GPT-4	H $\to$ AI	Polish-token	0.336	Entropy	0.7867
GPT-4	H $\to$ AI	Polish-sentence	0.800	Entropy	0.7067
GPT-4	H $\to$ AI	Complete	1.089	SpecDetect	0.8100
GPT-4	H $\to$ AI	Rewrite	1.051	LRR	0.4933
Llama-2	H $\to$ AI	Polish-token	0.635	Entropy	0.8233
Llama-2	H $\to$ AI	Polish-sentence	0.810	LogRank / Lastde	0.8300

Appendix

Table 7: Edit density and compact detection summary for all MixText operations. Mean density is the average token-level edit density over 300 paired samples. The best metric and pairwise accuracy are from Table 3 .

Figure 21: Case Visualization of Signal Profiles across Humanizing Modes. Original and humanized signals under each mode. Left: time-domain log-likelihood; right: frequency-domain spectrum.

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