Attractor Geometry of Transformer Memory: From Conflict Arbitration to Confident Hallucination

TL;DR

This paper presents a geometric framework for understanding transformer memory failures, showing how conflict and hallucination relate to attractor basins in hidden state space, and proposes a margin-based detection method.

Contribution

It introduces a unified geometric account of memory conflicts and hallucinations in language models, validated through synthetic and natural language experiments.

Findings

Attractor basins explain conflict and hallucination in hidden states.

Margin-based detection outperforms entropy-based methods.

Structural geometric properties persist across model scales.

Abstract

Language models draw on two knowledge sources: facts baked into weights (parametric memory, PM) and information in context (working memory, WM). We study two mechanistically distinct failure modes--conflict, when PM and WM disagree and interfere; and hallucination, when the queried fact was never learned. Both produce confident output regardless, making output-based monitoring blind by design. We show both failures share a unified geometric account. In the hidden-state space of autoregressive generation, learned facts form attractor basins. Conflict is basin competition: WM disrupts convergence to the correct basin without raising output entropy. Hallucination is basin absence: the hidden state drifts freely when no memorized basin exists. The frozen LM head, designed for next-token prediction, cannot distinguish these cases and fires confidently either way. We verify this account in a controlled synthetic task-entity identifiers mapped to unique codes with PM installed via LoRA adapters--where ground truth is exact and component roles can be causally isolated through targeted adapter placement. Geometric margin--the hidden state's distance to the nearest memorized basin--reads this geometry directly and separates correct recall from hallucination far more cleanly than output entropy, with zero false refusals where entropy-based detection cannot avoid rejecting the vast majority of correct outputs. The separation holds on natural-language factual queries from the pretrained model with no adaptation, confirming attractor geometry is structural rather than a fine-tuning artifact. The fraction of confident hallucinations follows a scaling law $C = \exp(-c/\bar\Delta)$, growing with scale even as overall error rates fall. Hidden states reliably encode epistemic state; the frozen output head systematically erases it--and this erasure worsens with scale.