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

2026-05-07

AI Summary

This work addresses two critical failure modes of large language models: interference when parametric and working memories conflict, and confident hallucinations about facts never learned during training. The authors propose an attractor geometry framework that unifies these phenomena through the geometric structure of attractor basins in the model’s hidden state space—memory interference arises from competing basins, while hallucinations stem from the absence of a basin altogether. Using LoRA adapters to construct controllable synthetic tasks, they combine causal interventions with geometric analyses of pretrained Transformer hidden states and find that geometric boundaries nearly perfectly discriminate correct recall from hallucination (achieving zero false rejection of correct outputs), outperforming conventional reliability metrics such as output entropy. Moreover, they reveal that the prevalence of confident hallucinations grows exponentially with model scale.

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 $C = \exp(-c/\barΔ)$, 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.

Problem

• conflict
• hallucination
• attractor geometry
• parametric memory
• working memory

Innovation

• attractor geometry
• parametric memory
• working memory
• geometric margin
• confident hallucination