Hallucination-Associated Neurons in LLMs

• H-Neurons are defined as a sparse subset of feed-forward units whose activations statistically predict hallucination events using an ℓ1-regularized logistic regression probe.
• They are identified by constructing balanced datasets and engineering CETT metrics, achieving up to 83% accuracy in detecting hallucinations across domains.
• Experimental activation scaling demonstrates that H-Neurons causally influence model compliance, informing strategies for precise hallucination mitigation.

Hallucination-Associated Neurons (H-Neurons) are a sparse subset of feed-forward network (FFN) units in LLMs whose activity is tightly predictive of hallucination events—outputs that are plausible but factually incorrect. Recent work has provided a formal and empirical foundation for identifying, quantifying, and causally intervening upon these neurons. The existence of H-Neurons offers a bridge between macroscopic hallucination phenomena and the microscopic mechanisms encoded in neural architectures, furnishing tools for more reliable detection and mitigation of factual errors in LLM outputs (Gao et al., 1 Dec 2025).

1. Formal Definition and Mathematical Properties

An H-Neuron is defined with reference to the activations of all neurons in the FFN layers of an LLM. For $D$ total neurons, each neuron $j$ receives a weight $\theta_j$ from a sparse $\ell_1$-regularized logistic regression probe. Given per-neuron features $x\in\mathbb{R}^D$ for a single response, the probability $P(y=1|x)=\sigma(\theta^\top x)$ models hallucination presence ($y=1$).

To quantify individual contribution, the CETT (Causal Effect on Token Trajectory) metric is used: $$\mathrm{CETT}_{j,t}=\frac{\|h_t^{(j)}\|_2}{\|h_t\|_2}$$ where $h_t\in\mathbb{R}^d$ is the total token-wise hidden update and $h_t^{(j)}$ is the component due to neuron $j$0. Aggregation over answer tokens $j$1 or non-answer tokens yields: $j$2 The probe’s $j$3 penalty ensures only a minuscule fraction (typically $j$4) receive nonzero weights $j$5, forming the set of H-Neurons $j$6.

2. Identification Protocols and Predictive Generalization

The canonical methodology for identifying H-Neurons consists of:

• Dataset Construction: Balanced faithfully factual and fully hallucinatory responses, as in 1,000-trial splits from TriviaQA, are collected with randomized sampling (temperature=1.0, top_k=50, top_p=0.9) and filtered for consistency.
• Feature Engineering: Per-example vectors $j$7 concatenate the $j$8 metrics across all FFN neurons for both answer and non-answer spans.
• Label Assignment and Probe Training: Answer-span features from hallucinated outputs are labeled $j$9, and all others $\theta_j$0. The sparse logistic objective is solved for weights $\theta_j$1.
• H-Neuron Selection: Neurons with $\theta_j$2 are designated H-Neurons.
• Evaluation Metrics: Precision, recall, F1, and cross-domain generalization (on NQ-Open, BioASQ, NonExist) are reported.

A critical empirical finding is that using fewer than $\theta_j$3 of all FFN units, the probe achieves accuracy gains from $\theta_j$4–$\theta_j$5 (baseline) to $\theta_j$6–$\theta_j$7 on held-out and out-of-domain hallucination detection tasks.

3. Behavioral Causality and Intervention Studies

Direct manipulation of H-Neuron activations establishes their causal influence on model behavior:

• Activation Scaling: Pre-nonlinearity activation of H-Neuron $\theta_j$8 at token $\theta_j$9 is re-scaled: $\ell_1$0, $\ell_1$1. The corresponding causal contribution scales linearly: $\ell_1$2.
• Compliance Benchmarks: Behavioral impact is measured across benchmarks targeting over-compliance, including FalseQA, FaithEval, Sycophancy, and Jailbreak.
• Quantitative Effects: Compliance rate increases monotonically with $\ell_1$3 and decreases for $\ell_1$4; average compliance slope $\ell_1$5 (small models) and $\ell_1$6 (large models). One-sided $\ell_1$7-tests confirm the statistical significance ($\ell_1$8 for most $\ell_1$9).

This establishes H-Neurons as a direct cause of hallucinatory and over-compliant behaviors.

4. Tracing Neural Origins: Pre-training versus Instruction Tuning

A core finding is that H-Neurons originate primarily during pre-training and are largely unaffected by downstream instruction tuning:

• Backward Transferability: A probe trained on instruction-tuned activations ($x\in\mathbb{R}^D$0) is directly applied to base (pre-SFT) model activations, achieving AUROC $x\in\mathbb{R}^D$1 (up to $x\in\mathbb{R}^D$2 on TriviaQA), confirming predictive value absent alignment data.
• Drift Quantification: For each neuron $x\in\mathbb{R}^D$3, projection weight drift is measured: $x\in\mathbb{R}^D$4

$x\in\mathbb{R}^D$5

Aggregate drift $x\in\mathbb{R}^D$6 is z-normalized and rank-normalized; H-Neurons cluster at high $x\in\mathbb{R}^D$7 (mean $x\in\mathbb{R}^D$8, $x\in\mathbb{R}^D$9), indicating minimal alteration post-alignment. This suggests the emergence of “compliance” circuits is largely a consequence of the foundational training, not alignment stages.

5. Applied Implications and Mitigation Approaches

Key findings on H-Neurons directly inform strategies for detection and mitigation of hallucinations:

• Neuronal Probes: Lightweight, model-agnostic probes leveraging only the sparse H-Neuron set can serve as efficient hallucination detectors for LLM outputs.
• Activation Suppression: Real-time suppression ($P(y=1|x)=\sigma(\theta^\top x)$0) of these units reduces both hallucination and over-compliance across evaluation sets. However, uniform scaling impairs model helpfulness, indicating a need for selective or task-sensitive modulation strategies.
• Architectural Interventions: Recommendations include:
  • Dynamic gating or mask layers to down-weight H-Neurons when accuracy is required,
  • Regularization during pre-training to discourage over-dependence on compliance-encoding neurons,
  • Modification of pre-training objectives through calibration losses or uncertainty penalties to disfavor formation of these “compliance” circuits.

A summary of H-Neuron research axes and major results is presented below:

Dimension	Finding	Quantitative Summary
Sparsity	$P(y=1|x)=\sigma(\theta^\top x)$1	Probe using $P(y=1|x)=\sigma(\theta^\top x)$20.1% neurons
Generalization	AUROC $P(y=1|x)=\sigma(\theta^\top x)$3 across domains	Up to $P(y=1|x)=\sigma(\theta^\top x)$4 (TriviaQA)
Causal Impact	Monotonic compliance increase with $P(y=1|x)=\sigma(\theta^\top x)$5	$P(y=1|x)=\sigma(\theta^\top x)$6Compliance$P(y=1|x)=\sigma(\theta^\top x)$72.4–3.0
Origin	Pre-training phase	High $P(y=1|x)=\sigma(\theta^\top x)$8 with minimal drift

6. Theoretical and Practical Significance

H-Neurons provide a mechanistic linkage between single-unit FFN dynamics and global LLM failure modes, reconciling macroscopic over-compliance behaviors with microscopic neural substrates. This substantiates a neuron-level “compliance bias” that is upstream of supervised alignment, challenging the assumption that hallucinations are solely byproducts of post-pretraining tuning or data quality.

*A plausible implication is that robust factuality will not be achieved solely by alignment or prompting, but may require architectural and pre-training design changes to disrupt compliance-related neural circuits before their consolidation.

7. Open Directions and Future Work

Current suppression methods for H-Neuron activity, while effective at reducing hallucination and over-compliance, are blunt, sometimes degrading answer helpfulness. Future research directions include the development of finer-grained neuron editing or gating systems, neuron-level regularization during training, and a deeper exploration of the interaction between H-Neuron dynamics and model scaling laws. The potential for targeted architectural interventions, such as adaptive mask layers or uncertainty-guided gating, is currently under investigation (Gao et al., 1 Dec 2025).