Identity as Attractor: Geometric Evidence for Persistent Agent Architecture in LLM Activation Space

Large language models (LLMs) are increasingly used in open-ended multi-agent settings, but the long-run dynamics of model--model interaction remain poorly understood. We study whether open-ended LLM discussions exhibit attractor-like behavior, i.e. topic-independent stable sets of behaviors which conversations settle into. Across 7 LLMs and 20 controversial topics, we compare self-play and mixed-play dyadic debates, tracking trajectories in representation space, discourse traits, and stances. We find self-play trajectories to be model-specific attractors that draw their conversation partners asymmetrically in mixed-play debates, influencing the other models' stylistic choices and behavior. For example, Claude Haiku is a strong attractor of other models in latent space, corresponding to other models taking on its traits like metacommentary, and models like GPT-4.1 nano are especially malleable. Our results suggest that open-ended LLM interactions are partially predictable from model-specific attractors, but shaped by structured and asymmetric partner influence. Overall, our analysis sheds some light on the complex behavior of open-ended multi-agent interaction, which we hope is helpful in designing, predicting, and monitoring autonomous agentic systems in the real world.

We investigate the extent to which an LLM's hidden-state geometry can be recovered from its behavior in psycholinguistic experiments. Across eight instruction-tuned transformer models, we run two experimental paradigms -- similarity-based forced choice and free association -- over a shared 5,000-word vocabulary, collecting 17.5M+ trials to build behavior-based similarity matrices. Using representational similarity analysis, we compare behavioral geometries to layerwise hidden-state similarity and benchmark against FastText, BERT, and cross-model consensus. We find that forced-choice behavior aligns substantially more with hidden-state geometry than free association. In a held-out-words regression, behavioral similarity (especially forced choice) predicts unseen hidden-state similarities beyond lexical baselines and cross-model consensus, indicating that behavior-only measurements retain recoverable information about internal semantic geometry. Finally, we discuss implications for the ability of behavioral tasks to uncover hidden cognitive states.

Large Language Models (LLMs) are traditionally viewed as autoregressive generators. However, from the perspective of collective computation, they function as high-dimensional Dense Associative Memories that store complex reasoning patterns as latent attractors. In this work, we investigate the energy landscape of mathematical reasoning. We posit that correct reasoning chains correspond to deep, wide attractor basins ("flat minima") in the model's output distribution, whereas hallucinations manifest as sharp, unstable local minima. To exploit this geometry, we introduce a retrieval mechanism based on a Gibbs measure of the trajectory's spectral entropy. By sampling multiple reasoning paths and weighting them by their inverse energy ($P \propto e^{-βE}$), we approximate the equilibrium distribution of the associative memory, effectively ``relaxing'' the system into a robust solution. Empirically, this physics-inspired mechanism improves Microsoft Phi-3.5 performance on GSM8K by 5.38% (84.7% $\to$ 90.1%), demonstrating that inference is better modeled as a dynamic settling process into an attractor basin rather than greedy next-token prediction.