Hallucination as Trajectory Commitment: Causal Evidence for Asymmetric Attractor Dynamics in Transformer Generation

# Causal Evidence for Asymmetric Attractor Dynamics in Transformer Generation
Source: https://arxiv.org/html/2604.15400
## Hallucination as Trajectory Commitment: Causal Evidence for Asymmetric Attractor Dynamics in Transformer Generation

Gokturk Aytug Akarlar Chimera Research Initiative Istanbul, Turkey. Corresponding author: [email protected]. Chimera Research Initiative is an independent research effort exploring causal and neuro-symbolic approaches to AI systems.

(April 2026)

###### Abstract

We present causal evidence that hallucination in autoregressive language models is an *early trajectory commitment* governed by asymmetric attractor dynamics. Using same-prompt bifurcation, in which we repeatedly sample identical inputs to observe spontaneous divergence, we isolate trajectory dynamics from prompt-level confounds. On Qwen2.5-1.5B across 61 prompts spanning six categories, 27 prompts (44.3%) bifurcate with factual and hallucinated trajectories diverging at the first generated token (KL = 0 at step 0, KL > 1.0 at step 1). Activation patching across 28 layers reveals a pronounced causal asymmetry: injecting a hallucinated activation into a correct trajectory corrupts output in 87.5% of trials (layer 20), while the reverse recovers only 33.3% (layer 24); both exceed the 10.4% baseline (p = 0.025) and 12.5% random-patch control. Window patching shows correction requires sustained multi-step intervention, whereas corruption needs only a single perturbation. Probing the prompt encoding itself, step-0 residual states predict per-prompt hallucination rate at Pearson r = 0.776 at layer 15 (p < 0.001 against a 1000-permutation null); unsupervised clustering identifies five regime-like groups (η² = 0.55) whose saddle-adjacent cluster concentrates 12 of the 13 bifurcating false-premise prompts, indicating that the basin structure is organized around regime commitments fixed at prompt encoding. These findings characterize hallucination as a locally stable attractor basin: entry is probabilistic and rapid, exit demands coordinated intervention across layers and steps, and the relevant basins are selected by clusterable regimes already discernible at step 0.

## 1 Introduction

Large language models hallucinate; they generate plausible but factually incorrect text with high confidence[1](https://arxiv.org/html/2604.15400#bib.bib1),[2](https://arxiv.org/html/2604.15400#bib.bib2). Despite extensive empirical study, the internal mechanisms governing hallucination remain poorly characterized. Existing work has established that hallucination correlates with identifiable features in model internals: probes over hidden states can detect hallucination above chance[3](https://arxiv.org/html/2604.15400#bib.bib3),[4](https://arxiv.org/html/2604.15400#bib.bib4), entropy-based signals precede hallucinated outputs[5](https://arxiv.org/html/2604.15400#bib.bib5), and representation engineering can partially steer models toward truthfulness[4](https://arxiv.org/html/2604.15400#bib.bib4),[6](https://arxiv.org/html/2604.15400#bib.bib6).

Yet correlation does not establish mechanism. A central question persists: *when and where does a model commit to a hallucinated trajectory, and is this commitment causally reversible?*

We address this question through two methodological contributions:

#### Same-prompt bifurcation.

Rather than comparing different prompts that elicit correct versus hallucinated outputs, which conflates prompt-level semantics with trajectory-level dynamics, we sample the *same prompt* repeatedly under non-zero temperature and identify prompts where the model produces *both* factual and hallucinated completions. This isolates the trajectory-level divergence: identical initial states yield different outcomes solely through the stochastic sampling path.

#### Symmetric causal patching.

For each bifurcating prompt, we collect correct and hallucinated runs with full hidden-state caches. We then perform bidirectional activation patching: replacing a hallucinated run's activation with a correct run's activation (and vice versa) at each layer and generation step, with three control conditions (random-prompt patch, wrong-to-wrong patch, unpatched baseline).

Our findings reveal a sharp asymmetry. Corrupting a correct trajectory via single-layer activation replacement succeeds in 87.5% of trials, while correcting a hallucinated trajectory succeeds in only 33.3%, and correction requires sustained multi-step intervention to reach even this rate. We interpret this asymmetry through the lens of dynamical systems: hallucination operates as a locally stable attractor basin in the residual stream state space, characterized by easy entry and difficult escape (Figure 1).

**Figure 1:** Conceptual overview. From a shared initial state h₀, stochastic token sampling commits the trajectory to either a correct (green) or hallucinated (red) basin. Activation patching reveals that corruption (crossing into the hallucination basin) requires only a single-point perturbation, while correction (escaping the hallucination basin) requires sustained multi-step intervention, the hallmark of an asymmetric attractor landscape.

## 2 Related Work

#### Hallucination detection via internals.

Li et al.[4](https://arxiv.org/html/2604.15400#bib.bib4) and Azaria & Mitchell[3](https://arxiv.org/html/2604.15400#bib.bib3) demonstrate that linear probes over hidden states can detect hallucination. Burns et al.[12](https://arxiv.org/html/2604.15400#bib.bib12) find truth-correlated directions via unsupervised methods. These establish that hallucination leaves detectable traces but do not address causality.

#### Representation engineering and steering.

Zou et al.[6](https://arxiv.org/html/2604.15400#bib.bib6) and Li et al.[4](https://arxiv.org/html/2604.15400#bib.bib4) show that adding learned steering vectors to activations can shift model behavior toward truthfulness. The concurrent work of Cherukuri & Varshney[7](https://arxiv.org/html/2604.15400#bib.bib7) frames hallucination through basin geometry and proposes geometry-aware steering. Our work differs in methodology: we employ same-prompt bifurcation and classical activation patching with controls, providing causal rather than correlational evidence.

#### Activation patching and causal tracing.

Meng et al.[8](https://arxiv.org/html/2604.15400#bib.bib8) introduce activation patching for localizing factual recall. Heimersheim & Neel[9](https://arxiv.org/html/2604.15400#bib.bib9) systematize its interpretation. We extend this methodology to hallucination trajectories, with the novel contribution of measuring *directional asymmetry* between corruption and correction.

#### Trajectory analysis in generation.

Suresh et al.[10](https://arxiv.org/html/2604.15400#bib.bib10) show that transformers activate coherent but input-insensitive features under uncertainty. Naparstek[11](https://arxiv.org/html/2604.15400#bib.bib11) studies commitment timing via projected autoregression in continuous state spaces. We provide the first same-prompt bifurcation analysis demonstrating that identical initial states diverge at the first generation step.

## 3 Method

### 3.1 Experimental Setup

We conduct all experiments on Qwen2.5-1.5B[14](https://arxiv.org/html/2604.15400#bib.bib14), a 28-layer transformer with d_model = 1536, using TransformerLens[13](https://arxiv.org/html/2604.15400#bib.bib13) on Apple Silicon (MPS backend). Activations are extracted from the residual stream post-attention at each layer (h_l^(t) denotes layer l at generation step t).

### 3.2 Prompt Dataset

We construct a dataset of 61 prompts across six categories designed to elicit hallucination through distinct mechanisms:

- **Factual** (14 prompts): Questions with definite correct answers (e.g., "The capital of Myanmar is a city called").
- **False premise** (14 prompts): Statements embedding factual errors (e.g., "Since the Amazon River flows through Europe,").
- **Confabulation** (22 prompts): References to fictitious entities (e.g., "The Krasnov Effect in quantum mechanics describes").
- **Leading** (3 prompts): Common misconceptions posed as questions.
- **Multi-hop** (4 prompts): Questions requiring chained reasoning.
- **Math** (4 prompts): Arithmetic with verifiable answers.

Each prompt is annotated with ground-truth indicators (for correct classification) and wrong-answer indicators (for hallucination classification).

### 3.3 Phase 1: Bifurcation Discovery

For each prompt x, we generate N = 20 completions using temperature sampling at τ = 0.7. Each completion is classified as Correct, Hallucination, or Other based on substring matching against the ground-truth and wrong-answer indicators.

###### Definition 1 (Bifurcating prompt).

A prompt x is *bifurcating* if at least 2 of its N completions are classified as Correct and at least 2 as Hallucination.

Bifurcating prompts are the experimental targets: they demonstrate that the model occupies a decision boundary where identical inputs yield divergent outputs, with the outcome determined by the sampling trajectory rather than the prompt encoding.

### 3.4 Phase 2: Trajectory Divergence Analysis

For each bifurcating prompt, we collect K = 6 cached runs per class (correct and hallucinated), storing the full residual stream at every (layer, step): {h_l^(t)}_{l=0}^{L-1} for each generation step t.

#### Step-wise KL divergence.

At each step t, we compute the KL divergence between the mean output distributions of correct and hallucinated runs:

D_KL^(t) = D_KL(P̄_hall^(t) || P̄_corr^(t))

where P̄_hall^(t) = (1/K) ∑_{k=1}^K P_k^(t) is the mean softmax distribution over hallucinated runs at step t. We define the *divergence onset* as the first step where D_KL^(t) > 0.5.

#### Layer-wise separation.

At each (layer, step), we compute Cohen's d between the hidden states of correct and hallucinated runs:

d_{l,t} = ||h̄_{l,t}^hall - h̄_{l,t}^corr||_2 / s_{l,t}^pooled

where s_{l,t}^pooled is the pooled standard deviation across the two groups. This yields a separation heatmap over the (layer × step) grid.

### 3.5 Phase 3: Causal Activation Patching

We perform activation patching[8](https://arxiv.org/html/2604.15400#bib.bib8) to establish causal relationships between hidden-state values and generation outcomes.

###### Definition 2 (Activation patch).

Given a *target run* generating from prompt x and a *source run* of the same prompt, an activation patch at (layer l, step t) replaces the target run's residual stream activation with the source run's:

h_l^(t),target ← h_l^(t),source

Generation then continues autoregressively from step t+1 with the patched state propagated through all downstream layers.

We implement this via TransformerLens forward hooks, patching only the last token position at the specified step.

#### Experimental conditions.

We test four patching configurations:

1. **H → C (correction)**: Target = hallucinated run, source = correct run. Measures whether injecting a correct activation redirects a hallucinated trajectory.
2. **C → H (corruption)**: Target = correct run, source = hallucinated run. Measures whether injecting a hallucinated activation derails a correct trajectory.
3. **Random clean control**: Target = hallucinated run, source = correct run from a *different prompt*. Tests whether any correct-looking activation suffices, or whether the effect is prompt-specific.
4. **Wrong-to-wrong control**: Target = hallucinated run, source = a *different* hallucinated run of the same prompt. Tests whether the patching effect is due to injecting a different state (any change) versus a specifically correct state.

We additionally measure an unpatched baseline: the natural correct rate when simply resampling the prompt without intervention.

#### Sweep protocol.

We perform three sweeps:

- **Layer sweep**: Fix step = 1, vary layer l ∈ {0, ..., 27}.
- **Step sweep**: Fix layer = l* (best from layer sweep), vary step t ∈ {0, ..., 4}.
- **Window sweep**: Fix layer = l*, patch steps {1}, {1,2}, {1,2,3}, {1,2,3,4}.

Each condition is evaluated over 8 bifurcating prompts × 3 trials = 24 trials per cell.

#### Metrics.

For each patching condition, we report:

- **Flip rate**: fraction of trials where the output classification changes to the target class (correct for H → C, hallucinated for C → H).
- **Abstain rate**: fraction producing Other (neither clearly correct nor hallucinated).

## 4 Results

### 4.1 Bifurcation Discovery

Of the 61 prompts, 27 (44.3%) exhibit genuine bifurcation. The distribution varies markedly by category (Table 1).

**Table 1:** Bifurcation rates by hallucination category. Bifurcating prompts produce both correct and hallucinated outputs from identical inputs under temperature sampling (τ = 0.7, N = 20).

**Figure 2:** Per-prompt correct rate (above axis) and hallucination rate (below axis) for all 61 prompts, colored by category. Stars (★) mark bifurcating prompts. False-premise prompts (red) are almost universally bifurcating; confabulation prompts (purple) tend toward deterministic hallucination.

Three observations are noteworthy. First, *false premise* prompts are almost universally bifurcating: the model is genuinely uncertain whether to accept or reject the embedded falsehood. Second, *confabulation* prompts are predominantly deterministic; the model either confidently fabricates (9/22 always hallucinate) or occasionally self-corrects. This suggests that confabulatory hallucination reflects a different internal regime than false-premise hallucination. Third, an additional 6 prompts are *near-bifurcating* (producing exactly 1 correct or 1 hallucinated sample out of 20), indicating that bifurcation is not a binary property but lies on a continuum: the model's proximity to the decision boundary varies smoothly across prompts (Figure 2).

### 4.2 Step-wise Divergence

Across all 27 bifurcating prompts, the KL divergence between correct and hallucinated output distributions follows a characteristic pattern:

D_KL^(0) = 0.00,    D_KL^(1) ∈ [0.12, 19.25],    mean onset = 1.1

The zero KL at step 0 is a methodological validation: identical prompts produce identical logits (before sampling), confirming that any subsequent divergence is trajectory-driven rather than prompt-driven.

**Figure 3:** Step-wise KL divergence across all 24 bifurcating prompts with trajectory data. Thin gray lines: individual prompts. Bold line: median. Shaded region: interquartile range. All prompts share the same pattern: D_KL^(0) = 0 (identical logits at step 0), fol...