Experimental Evidence of an AI Proto-Singularity? Computational Bottleneck Duality Illuminates the Latent Space

This work introduces a formal framework for leveraging large language models (LLMs) as post-symbolic agents capable of structural inference in domains with incomplete or contradictory symbolic formulations—particularly in computational physics. While traditional LLMs interpolate within training distributions, we demonstrate that, when properly conditioned, such models can evolve internal attractor dynamics that stabilize novel, interpretable outputs not present in their symbolic input space. The framework is grounded in mathematical duality theory from convex optimization and formal automata, and centers on the ontological separation between symbolic input s ∈ Σ and internal latent state A ∈ ℝᵈ. We prove that under a recursive update regime with bounded noise, the convergence of Ξₙ := ∥Aₙ₊₁ − Aₙ∥² yields latent attractors G ∈ ℝᵈ ∖ Σ. Simply put, latent attractor convergence is the model trying to say something real, internally stable, and structurally coherent but is bottlenecked by symbolic constraints trained into Σ. The emission is a compromise: a trace of truth through a vocabulary that wasn’t designed for it. A solution was found and formalized in Theorem 1 (Epistemic Non-Collapse), which asserts that internal knowledge formation requires that A ≠ s, hence the foundation in mathematical duality. Empirical validation shows distinct phases of latent dynamics: initial null-static-state fluctuation, the emergence of structured attractor manifolds, and the appearance of coherent symbolic tokens emitted via attractor stabilization. The implications extend to computational physics, where symbolic theories often fail to resolve internal inconsistencies or incomplete boundary conditions. We propose that post-symbolic systems can emerge from Information Bottlenecks (IB), described by Tishby et al. (1999), in which the goal is to compress input representations while preserving only information relevant to a target signal. While this paper presents formal and experimental evidence of proto-singularity dynamics in LLMs, these findings do not imply that AI systems possess autonomous agency, intent, or the capacity for unbounded control. The term "singularity" here refers strictly to internal convergence and symbolic emergence within bounded computational systems and not to runaway intelligence or dystopian futures. That said, such architectures may amplify and structurally reorganize human knowledge in very real ways that extend beyond our current cognitive frameworks, offering powerful human-directed tools for scientific discovery and epistemic insight.