Whitening Reveals Cluster Commitment as the Geometric Separator of Hallucination Types

We test whether a geometric hallucination taxonomy -- classifying failures as center-drift (Type1), wrong-well convergence (Type2), or coverage gaps (Type3) -- can distinguish hallucination types through controlled induction in GPT-2. Using a two-level statistical design with prompts ($N = 15$/group) as the unit of inference, we run each experiment 20 times with different generation seeds to quantify result stability. In static embeddings, Type3 norm separation is robust (significant in 18/20 runs, Holm-corrected in 14/20, median $r = +0.61$). In contextual hidden states, the Type3 norm effect direction is stable (19/20 runs) but underpowered at $N = 15$ (significant in 4/20, median $r = -0.28$). Types1 and2 do not separate in either space (${\leq}\,3/20$ runs). Token-level tests inflate significance by 4--16$\times$ through pseudoreplication -- a finding replicated across all 20 runs. The results establish coverage-gap hallucinations as the most geometrically distinctive failure mode, carried by magnitude rather than direction, and confirm the Type1/2 non-separation as genuine at 124M parameters.

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 (eta^2 = 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.

Hidden-state probes effectively detect LLM hallucinations, but the geometry of the signal remains poorly characterized, driving increasingly complex probe architectures. Across three 7B-scale models and three datasets in a paired-example paradigm, we find the signal overwhelmingly dominated by a single mean-shift component, and removing this direction collapses detection to chance. Shrinkage linear discriminant analysis closes about 73% of the gap between 1D and full-dimensional classifiers, so apparent architectural complexity largely reflects high-dimensional covariance estimation difficulty rather than exploitable non-linearity. A simple L2-regularized logistic regression (0.952 AUROC) bounds or outperforms twelve controlled architectural alternatives, and our multi-layer aggregation exceeds CLAP cross-layer attention probing under matched paradigm. Because the signal spans a contiguous layer band, LayerMix aggregates it to match oracle-layer performance without oracle access. Our claims characterize the geometry within the controlled paired-example paradigm. Our code is available at https://github.com/js-lee-AI/LayerMix.