Hallucination Accumulation in Generative Systems

• Hallucination accumulation is the process by which generative systems progressively compound unsupported or incorrect outputs as earlier responses are reused.
• Empirical studies in multi-agent cascades and chain-of-thought reasoning indicate that sequential refinement can attenuate hallucinations while sometimes causing factual decay.
• A variety of detection and mitigation strategies, from claim-level tracking to frequency-domain analysis, are employed to monitor and control the accumulation process.

to=arxiv_search.search 天天中彩票的 天天爱彩票中奖ative 天天爱彩票 北京赛车冠军json {"query":"(Jamshidi et al., 6 Jun 2026) Hallucination Cascade Analyzing Error Propagation in Multi-Agent LLM Systems", "max_results": 5} to=arxiv_search.search 福利彩票天天彩json {"query":"(Barański et al., 22 Jun 2026) HALAS hallucinations ASR", "max_results": 5} to=arxiv_search.search qq天天中彩票 彩神争霸是不是json {"query":"(Lu et al., 5 Jan 2026) Streaming Hallucination Detection in Long Chain-of-Thought Reasoning", "max_results": 5} to=arxiv_search.search 彩神争霸大发快三 to=arxiv_search.search 娱乐赚钱 เงินฟรีjson {"query":"(Itkin, 10 Jun 2026) Quickest Detection of Hallucination Onset Delay Bounds and Learned CUSUM Statistics", "max_results": 5} Hallucination accumulation denotes the progressive compounding of unsupported, inconsistent, or factually incorrect content as a generative system reuses its own outputs, intermediate states, or latent commitments. In multi-agent LLM cascades, “hallucination accumulation” refers to net growth of hallucination as responses pass through successive agents, whereas “hallucination attenuation” refers to net reduction across agents (Jamshidi et al., 6 Jun 2026). Across adjacent literatures, the same phenomenon is treated as a dynamic process rather than a static property of single outputs: long chain-of-thought reasoning is modeled as an evolving latent state, long-form generation is described as suffering from hallucination snowballing, ASR transcripts exhibit repeated span-level insertions that recur across segments, LVLMs show accumulation when grounding signals decay or confounders propagate through layers, and theoretical work formalizes cumulative hallucination rates under repeated generation (Lu et al., 5 Jan 2026, Li et al., 2 Jun 2026, Barański et al., 22 Jun 2026, Zhang et al., 28 Jan 2026, Shoby et al., 8 Mar 2026, Das et al., 26 May 2026).

1. Formal scope and representational units

The most explicit operationalization is claim-based. In multi-agent cascades, agents generate sequentially; at step $i$, agent $A_i$ receives the prompt $p$ concatenated with earlier outputs $o_1,\ldots,o_{i-1}$ and produces $o_i$, namely

$$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$

This makes hallucination a time-dependent signal that can either accumulate or attenuate depending on interaction history, cascade depth, and model choices. Each response $t$ is decomposed into atomic claims $C(t)=\{c_1,\ldots,c_n\}$, and a normalized response-level hallucination score $H(t,k)$ is defined over matched reference facts in domain $k$. Cascade dynamics are then tracked by the trajectory $A_i$0 together with local and global propagation metrics $A_i$1, $A_i$2, $A_i$3, and $A_i$4, where $A_i$5 indicates attenuation and $A_i$6 indicates accumulation (Jamshidi et al., 6 Jun 2026).

Long chain-of-thought reasoning uses a different primitive: the reasoning step and the reasoning prefix. The generated trajectory is $A_i$7, step-level hallucination is a local observation $A_i$8, and the cumulative signal is a prefix-level confidence $A_i$9. The key distinction is that the prefix-level state summarizes contamination of the entire reasoning history rather than only whether the current step introduces unsupported content (Lu et al., 5 Jan 2026).

In long-form generation, the operative unit is the sentence or semantic segment. SHARS partitions a response into sentences $p$0 and applies a generate–detect–reject–resample loop at the sentence level. A sentence is either accepted, rewritten to retain verified facts, or discarded and resampled, so that only verified segments become future conditioning context (Li et al., 2 Jun 2026).

ASR work grounds the concept at the span level. HALAS defines hallucinations as “Specific errors in ASR predictions that have no phonetic correspondence with the content of the audio signal.” The annotation schema marks text spans and character spans with tags “Hallucination,” “Looping,” and “Looping Hallucination,” together with an utterance-level hallucination label. HALAS does not explicitly define accumulation, but the span-level labels permit within-utterance accumulation through successive hallucination spans and across-utterance accumulation through repeated phrase recurrence across segments and models (Barański et al., 22 Jun 2026).

Diffusion models localize accumulation along the reverse denoising trajectory. “Counting hallucination” is defined on counting-ready outputs whose object counts violate dataset-level counting facts, and the relevant rate is the counting hallucination rate $p$1. In this setting, accumulation concerns propagated initial error, model score error, and local truncation error across reverse-time steps (Fu et al., 15 Oct 2025).

Setting	Unit of accumulation	Representative formalization
Multi-agent LLM cascades	claim / response	$p$2, $p$3
Long CoT reasoning	step / prefix	$p$4
Long-form generation	sentence / segment	segment-wise rejection and resampling
ASR	span / utterance	“Hallucination,” “Looping,” “Looping Hallucination”
Diffusion models	denoising step / sample	$p$5 on counting-ready samples

This variety of units matters because accumulation is not tied to a single modality or metric. A plausible implication is that the central object is not the surface error token itself, but a reuse mechanism: self-conditioning on prior outputs, hidden states, attention patterns, or trajectory states.

2. Sequential propagation in language generation

The most direct empirical study of accumulation versus attenuation in sequential text generation is the multi-agent cascade setting. Across 500 cascade experiments over 10 knowledge domains using GPT-5.3, DeepSeek-V3, and LLaMA-3-70B-Instruct, 3-agent chains reduced normalized hallucination from $p$6 at the first agent to $p$7 at the final agent, with amplification factor $p$8, while 2-agent chains reduced hallucination from $p$9 to $o_1,\ldots,o_{i-1}$0 with $o_1,\ldots,o_{i-1}$1. Transition-level analysis across 750 transitions gave average per-step reduction $o_1,\ldots,o_{i-1}$2. The same experiments showed that attenuation coexists with factual decay: in 3-agent chains, factual accuracy fell from $o_1,\ldots,o_{i-1}$3 to $o_1,\ldots,o_{i-1}$4, and in 2-agent chains from $o_1,\ldots,o_{i-1}$5 to $o_1,\ldots,o_{i-1}$6 (Jamshidi et al., 6 Jun 2026).

The same paper shows that attenuation is not merely a mean-only artifact. Statistical tests reported mean $o_1,\ldots,o_{i-1}$7 per transition $o_1,\ldots,o_{i-1}$8 with $o_1,\ldots,o_{i-1}$9 and effect size $o_i$0; deeper chains reduced final hallucination and amplification with differences $o_i$1 and $o_i$2, both with $o_i$3, but increased factual decay by $o_i$4 with $o_i$5. Conditions for accumulation remained localized: “amplified hallucination” accounted for $o_i$6 of matched transitions overall, while “preserved hallucination” was $o_i$7 overall (Jamshidi et al., 6 Jun 2026).

Long chain-of-thought work reaches a compatible but structurally different conclusion. In a dataset of 10k+ CoTs and 200k+ steps, step-level hallucination rates were $o_i$8 for LLaMA, $o_i$9 for Qwen, and $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$0 for DeepSeek, whereas prefix-level hallucination rates were $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$1, $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$2, and $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$3, respectively. The gap between step-level and prefix-level rates is central: the prefix can remain contaminated after local corrections, and recovery is characteristically slower than onset (Lu et al., 5 Jan 2026).

Long-form generation emphasizes the same issue at sentence scale. SHARS begins from the observation that long-form generation is exacerbated by hallucination snowballing, because an early unsupported segment becomes part of the conditioning context for later segments. On FactScore, Qwen3-32B improved from Greedy factual precision $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$4 to SHARS Ours-Prec $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$5, while Ours-Info reached $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$6 and Ours-Resp $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$7. Under a $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$8-word constraint, the same model improved from $$o_i = M_i(p \oplus o_1 \oplus \cdots \oplus o_{i-1}).$$9 to $t$0 factual precision (Li et al., 2 Jun 2026).

These results do not imply that accumulation is the dominant empirical regime in every sequential system. Rather, they separate two regimes. In some cascades, sequential refinement suppresses hallucination but trims factual detail; in unconstrained long-form generation, unsupported content can snowball unless rejected before it becomes context. This suggests that accumulation is best understood as a conditional property of the update rule, not as a fixed trait of a model family.

3. Mechanisms of build-up, persistence, and correction

Several works identify semantic drift, information loss, and internal hypothesis instability as the main mechanisms behind hallucination accumulation. In multi-agent cascades, higher semantic drift correlates positively with hallucination and cascade risk, while stronger information retention correlates with smaller $t$1. Claim-level transition analysis attributes attenuation primarily to “corrected” and “weakened” trajectories, which together represent $t$2 of transitions, but also shows that “deleted” claims at $t$3 and “overcorrected” claims at $t$4 contribute to factual decay and slight quality loss (Jamshidi et al., 6 Jun 2026).

In VLMs, overthinking and confounder propagation provide a layer-wise account of accumulation. Decoder-layer probing shows that models repeatedly revise object hypotheses across layers, and once a confounded hypothesis is activated it propagates through subsequent layers and can terminate in a confident but incorrect final token. On MS-COCO, the share of hallucinations displaying confounder propagation was reported as $t$5 for LLaVA-1.5, $t$6 for Gemma-3, and $t$7 for Qwen3-VL. The proposed Overthinking Score,

$t$8

combines hypothesis diversity and mean layer-wise entropy, making accumulation measurable before the final-layer commitment (Shoby et al., 8 Mar 2026).

A complementary LVLM account ties accumulation to local coherence failure. LVLMs-Saliency reports that hallucinations frequently arise when preceding output tokens exhibit low saliency toward the prediction of the next token. Mean saliency for correct versus hallucinated tokens was $t$9 versus $C(t)=\{c_1,\ldots,c_n\}$0 for LLaVA-v1.5-7B, $C(t)=\{c_1,\ldots,c_n\}$1 versus $C(t)=\{c_1,\ldots,c_n\}$2 for Qwen2-VL-7B, and $C(t)=\{c_1,\ldots,c_n\}$3 versus $C(t)=\{c_1,\ldots,c_n\}$4 for InternVL-7B. Across saliency bins, hallucination rates were $C(t)=\{c_1,\ldots,c_n\}$5–$C(t)=\{c_1,\ldots,c_n\}$6 in the lowest bin $C(t)=\{c_1,\ldots,c_n\}$7 and $C(t)=\{c_1,\ldots,c_n\}$8–$C(t)=\{c_1,\ldots,c_n\}$9 in the highest bin $H(t,k)$0 (Zhang et al., 28 Jan 2026).

TARAC reaches a related conclusion using attention to image tokens rather than gradient-aware saliency. On 500 COCO images with LLaVA-1.5-7B, Gaussian KDE over 945 first-occurrence correct words and 194 first-occurrence hallucinated words showed that hallucinated tokens have lower attention to image tokens and are more likely to appear later in the caption, when visual attention has decayed more. The method interprets accumulation as a snowball effect: as attention to image tokens fades over time, the decoder relies increasingly on language co-occurrence and prior knowledge (Xie et al., 5 Apr 2025).

These mechanisms are not identical, but they converge on a common picture. This suggests that accumulation often emerges when a system loses access to the evidence that originally grounded the output and substitutes self-consistent but weakly grounded internal structure—semantic drift in cascades, contaminated prefixes in CoT, confounder propagation in VLMs, or decayed image attention in LVLM decoding.

4. Measurement, monitoring, and detection

Measurement methodologies differ sharply according to whether accumulation is treated as claim propagation, onset detection, spectral anomaly, or span recurrence. In multi-agent cascades, a hybrid estimator fuses a rule-based grounding score with an LLM judge:

$H(t,k)$1

with adaptive weight $H(t,k)$2. Statistical evaluation used Wilcoxon signed-rank tests for paired transitions and Kruskal–Wallis tests for multi-model comparisons; over 1,250 rows, the mean hallucination was $H(t,k)$3 with standard deviation $H(t,k)$4, yielding an approximate $H(t,k)$5 confidence interval $H(t,k)$6 (Jamshidi et al., 6 Jun 2026).

For streaming onset detection, the relevant metric is delay rather than AUC. “Quickest Detection of Hallucination Onset” models the latent faithful/hallucinated state as a first-order Markov chain with $H(t,k)$7 and $H(t,k)$8, so hallucination onsets are rare but spans persist for about $H(t,k)$9 tokens on average. On RAGTruth, diagonal-Gaussian feature modeling gave $k$0 nats per token, implying Lorden’s lower bound of about $k$1 tokens at false-alarm rate $k$2. At matched $k$3, a learned CUSUM detected onset in $k$4 tokens, against $k$5 tokens for a linear per-token baseline and $k$6 tokens for a nonlinear per-token classifier without explicit accumulation (Itkin, 10 Jun 2026).

Long CoT detection uses a streaming prefix statistic rather than a stopping-time formulation. The decision rule is

$k$7

Step-level probe performance reached AUC $k$8, $k$9, and $A_i$00 on LLaMA-3.1-8B, Qwen2.5-7B, and DeepSeek-R1-Distill-8B, while final prefix-level detection reached AUC $A_i$01, $A_i$02, and $A_i$03 for the same models. The methodological point is that accumulation is not inferred from isolated steps, but from the evolution of a prefix-conditioned latent score (Lu et al., 5 Jan 2026).

HALAS shows why span-level accumulation remains difficult to detect in ASR. Combined character and semantic proxy metrics reached approximately $A_i$04 ROC-AUC, XGBoost over all 7 metrics reached $A_i$05 ROC-AUC in the ALL setting, and decoder-embedding detection reached F1 $A_i$06, but state-of-the-art detection remains weak because accumulation often consists of short, plausible fillers embedded in otherwise correct text. Top-10 phrases cover about $A_i$07 of hallucinations on average, top-30 about $A_i$08, and 13 phrases appear in all models’ lists, so corpus-level accumulation can remain semantically fluent and difficult to isolate (Barański et al., 22 Jun 2026).

HSAD approaches accumulation as a frequency-domain property of hidden-layer temporal signals. Using the final generation step $A_i$09 as the observation point, it constructs a depthwise temporal signal across four key nodes per layer, applies FFT, and feeds per-dimension max non-DC magnitudes into an Enhanced MLP. On Qwen-2.5-7B-instruct, HSAD achieved AUROC $A_i$10 on TruthfulQA, $A_i$11 on TriviaQA, $A_i$12 on SciQ, and $A_i$13 on NQ Open; replacing FFT-based features with time-domain maxima caused large drops, such as $A_i$14 to $A_i$15 on TriviaQA (Li et al., 28 Sep 2025).

Taken together, these methods show that accumulation is measurable, but only when the metric matches the temporal structure of the error process. AUC over final outputs, per-token classifiers, utterance-level labels, and static hidden features often miss the onset, persistence, or compounding behavior that defines accumulation itself.

5. Mitigation and control strategies

Mitigation strategies are most effective when they intervene before hallucinated content becomes future context. In multi-agent cascades, proposed strategies include explicit verification or adjudication stages, retrieval augmentation at critical steps, consensus or ensemble selection, confidence calibration and reliability weighting, agent diversity and model order, and limiting cascade depth or filtering reused context. The paper reports that retrieval augmentation achieved accuracy $A_i$16 with hallucination $A_i$17, and that the ordering GPT-5.3 $A_i$18 DeepSeek-V3 $A_i$19 LLaMA-3-70B-Instruct yielded final hallucination $A_i$20 with low risk (Jamshidi et al., 6 Jun 2026).

SHARS is an explicit anti-accumulation design for long-form text. It accepts a sentence only when the detector verifies it, rewrites mixed sentences to retain only verified claims, and discards fully hallucinated sentences for resampling. Because only verified segments are committed, later generation is conditioned on a verified foundation rather than a contaminated prefix. On FactScore, Qwen3-32B improved from Greedy $A_i$21 factual precision to $A_i$22 under Ours-Prec; Llama3.1-8B improved from $A_i$23 to $A_i$24; and Qwen3-4B improved from $A_i$25 to $A_i$26 (Li et al., 2 Jun 2026).

LVLM mitigation work similarly targets the moment when grounding weakens. LVLMs-Saliency introduces Saliency-Guided Rejection Sampling, which rejects candidate tokens whose saliency falls below a context-adaptive threshold, and Local Coherence Reinforcement, which strengthens attention from the current token to recent predecessors. For LLaVA-1.5-7B, baseline versus +LocoRE versus +SGRS+LocoRE changed CHAIR_S from $A_i$27 to $A_i$28 to $A_i$29, POPE-F1 from $A_i$30 to $A_i$31 to $A_i$32, and POPE-Acc from $A_i$33 to $A_i$34 to $A_i$35 (Zhang et al., 28 Jan 2026).

TARAC addresses a different but related failure mode: decay of attention to image tokens over time. It accumulates and reinjects image attention during generation by updating

$A_i$36

and adding $A_i$37 back into current image attention before row-wise renormalization. On CHAIR for LLaVA-1.5-7B, greedy versus TARAC changed $A_i$38 from $A_i$39 to $A_i$40 and $A_i$41 from $A_i$42 to $A_i$43, though Recall fell from $A_i$44 to $A_i$45; compared with VCD, TARAC reduced $A_i$46 by $A_i$47 and $A_i$48 by $A_i$49 (Xie et al., 5 Apr 2025).

Diffusion-model mitigation highlights the same trade-off between perceptual quality and factual correctness. On RealHand, “Diffused” initial noise consistently lowered CHR, NCFR, and TFR relative to “Normal,” ancestral DDPM achieved the lowest CHR/NCFR/TFR, and a joint-diffusion model with structural constraints substantially reduced both CHR and NCFR. For example, under DPM-Solver-2 at 50 steps, JDM reduced CHR from $A_i$50 to $A_i$51 and NCFR from $A_i$52 to $A_i$53 (Fu et al., 15 Oct 2025).

ASR mitigation is less developed but follows the same pattern of accumulation-aware control. HALAS points to Voice Activity Detection, fine-tuning on non-speech audio, decoding constraints such as insertion penalties and length normalization, confidence-aware decoding, domain conditioning for meetings, multi-model disagreement triage, and phrase-level post-hoc filtering for frequent hallucinations such as “thank you,” “okay,” “ahead,” “question,” and “you know” (Barański et al., 22 Jun 2026).

The recurring design principle is simple: accumulation is hardest to reverse after an error has already been admitted into the context. Methods that reject, filter, re-ground, or structurally constrain outputs before commitment tend to outperform methods that diagnose only the final artifact.

6. Theoretical interpretations, limits, and open problems

Several recent theories imply that accumulation is not merely an implementation bug, but partly a consequence of how generative systems store, compress, and commit to information. In the Kalai–Vempala line of work, once a trained model’s predictive distribution $A_i$54 is fixed, repeated generations are i.i.d. draws from $A_i$55, so a per-output hallucination rate produces cumulative hallucinations that grow linearly in the number of generations. Under $A_i$56-sparsity and Regular Facts, if the innovation rate $A_i$57, then hallucination occurs with high probability; conditional on $A_i$58, the number of hallucinations in $A_i$59 generations satisfies $A_i$60 with exponential concentration around $A_i$61 (Das et al., 26 May 2026).

A separate information-theoretic account frames hallucination as a consequence of space-optimality in membership testing. In the sparse-fact regime, the optimal per-key memory equals the minimum KL divergence between score distributions on facts and non-facts. Under log-loss, the memory-optimal solution maps all facts to a single high-confidence score $A_i$62 and maps a nonzero fraction $A_i$63 of non-facts to that same score. The practical implication is direct: any threshold that preserves recall must also accept those non-facts, so expected hallucinations over $A_i$64 independent queries accumulate as $A_i$65 and the probability of at least one hallucination is $A_i$66 (Guo et al., 31 Jan 2026).

“Are Hallucinations Bad Estimations?” reaches a related conclusion from a different angle. It defines hallucination as a failure to link an estimate to any plausible latent cause and proves a lower bound on the probability that even a Bayes-optimal estimator lies outside every high conditional density region $A_i$67. The paper is explicit that its analysis is single-step, not sequential, but it argues that nonzero lower bounds naturally imply persistence and compounding in multi-step settings once later inference conditions on off-manifold intermediate states (Liu et al., 25 Sep 2025).

A more generation-specific explanation is commitment failure. “Hallucination as Commitment Failure” defines a semantic notion of answer availability at the moment of commitment and reports that $A_i$68–$A_i$69 of Instruct hallucinations occur even though the correct concept already has substantial probability mass, with the rate rising monotonically with scale. The distinctive factor is not the absence of the correct concept, but the dispersion of its probability mass across alternatives, whereas correct generations concentrate mass on a single surface form. This supports a view in which larger instruction-tuned models can misfire more decisively because instruction tuning sharpens answer commitment with scale (Yeom et al., 21 May 2026).

These theories do not collapse empirical accumulation into a single cause. Rather, they provide different lower-level explanations for why accumulation is hard to eliminate entirely: positive innovation, limited memory budgets, mode-averaging estimators, and over-sharpened commitment all create nonzero base rates of unsupported output. Empirical work then determines whether those base errors attenuate under refinement, persist through self-conditioning, or snowball into later outputs.

The literature also places clear limits on current conclusions. Multi-agent cascade results were obtained on three models and ten domains, without human annotators, and adversarial prompts or prompt injection were not modeled (Jamshidi et al., 6 Jun 2026). White-box detectors such as streaming CoT probing, Overthinking Score, HSAD, and LVLMs-Saliency require access to hidden states or gradients (Lu et al., 5 Jan 2026, Shoby et al., 8 Mar 2026, Li et al., 28 Sep 2025, Zhang et al., 28 Jan 2026). HALAS is enriched for hallucinations through disagreement-based sampling and therefore does not estimate real-world prevalence (Barański et al., 22 Jun 2026). Diffusion findings are specific to counting hallucinations and dedicated counters (Fu et al., 15 Oct 2025).

Future work therefore centers on predictive control rather than isolated detection. The most explicit agenda is to learn propagation parameters, expand domains and model sets, integrate adversarial robustness, and optimize multi-objective trade-offs among hallucination, accuracy, quality, drift, and cost under Green AI constraints (Jamshidi et al., 6 Jun 2026). A plausible implication is that the mature study of hallucination accumulation will treat factuality as a dynamical systems problem: not whether an output is wrong in isolation, but how unsupported content enters, persists, spreads, and is either damped or amplified by the system’s own update rule.