From Passive Readers to Active Solvers, a Path Toward Agency in Large Language Models

Current large language models (LLMs) operate as passive interpreters of semantic patterns rather than active reasoners over symbolic constraints. This passivity arises from their static representational geometry: during inference, the model’s internal eigenstructure—governing dominant modes of meaning—is fixed. Consequently, LLMs excel at statistical continuation but fail at self-consistent problem-solving under closed-system constraints (e.g., solving (n) equations with (n) unknowns). We propose that endowing LLMs with eigenvalue plasticity—the capacity to dynamically reconfigure their spectral representation space in response to logical or algebraic inconsistency—can transform them from passive readers into active solvers. We formalize this transition using tools from linear algebra, dynamical systems theory, and active inference, showing that such adaptive eigenstructure enables proto-agency: a minimal form of goal-directed computation grounded in internal consistency rather than external reward. This framework bridges symbolic AI and connectionism without requiring explicit symbolic machinery, offering a new pathway toward robust reasoning in neural architectures.